diff --git a/.buildinfo b/.buildinfo new file mode 100644 index 0000000..8d73133 --- /dev/null +++ b/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file records the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 030c48f1638182c071f4607d697d8ccf +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 0000000..e69de29 diff --git a/_modules/index.html b/_modules/index.html new file mode 100644 index 0000000..b116fe4 --- /dev/null +++ b/_modules/index.html @@ -0,0 +1,191 @@ + + + + + + + + Overview: module code — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Overview: module code
    • +
  • +
    • +
+
+
+
+
+ +

All modules for which code is available

+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bcs/distance_functions.html b/_modules/pancax/bcs/distance_functions.html new file mode 100644 index 0000000..abb0b1e --- /dev/null +++ b/_modules/pancax/bcs/distance_functions.html @@ -0,0 +1,179 @@ + + + + + + + + pancax.bcs.distance_functions — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.bcs.distance_functions
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.bcs.distance_functions

+from jax import numpy as jnp
+from jax import vmap
+from typing import List
+
+
+

+[docs]
+def get_edges(domain, sset_names: List[str]):
+  mesh = domain.fspace.mesh
+  ssets = [mesh.sideSets[name] for name in sset_names]
+  edges = jnp.vstack(ssets)
+  edges = jnp.sort(edges, axis=1)
+  edges = jnp.unique(edges, axis=0) # TODO not sure about this one
+  return edges

+
+
+

+[docs]
+def distance(x1, x2):
+  return jnp.sqrt(
+    jnp.power(x2[0] - x1[0], 2.) + 
+    jnp.power(x2[1] - x1[1], 2.)
+  )

+
+
+

+[docs]
+def line_segment(x, segment):
+  x1 = segment[:, 0]
+  x2 = segment[:, 1]
+  L = distance(x1, x2)
+  x_c = (x1 + x2) / 2.
+
+  f = (1. / L) * (
+    (x[0] - x1[0]) * (x2[1] - x1[1]) - 
+    (x[1] - x1[1]) * (x2[0] - x1[0])
+  )
+  t = (1. / L) * (
+    jnp.power(L / 2., 2.) -
+    jnp.power(distance(x, x_c), 2.)
+  )
+  varphi = jnp.sqrt(
+    jnp.power(t, 2.0) +
+    jnp.power(f, 4.0)
+  )
+  phi = jnp.sqrt(
+    jnp.power(f, 2.0) + 
+    (1. / 4.) * jnp.power(varphi - t, 2.)
+  )
+  return phi

+
+
+
+

+[docs]
+def distance_function(domain, ssets, m=1.0):
+  edges = get_edges(domain, ssets)
+  m = 1.0
+  segments = domain.fspace.mesh.coords[edges, :]
+  def inner_func(x):
+    Rs = vmap(line_segment, in_axes=(None, 0))(x, segments)
+    Rs = vmap(lambda x: 1. / jnp.power(x, m))(Rs)
+    return 1. / jnp.power(jnp.sum(Rs), 1. / m)
+  return vmap(inner_func)

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bcs/essential_bc.html b/_modules/pancax/bcs/essential_bc.html new file mode 100644 index 0000000..315017f --- /dev/null +++ b/_modules/pancax/bcs/essential_bc.html @@ -0,0 +1,150 @@ + + + + + + + + pancax.bcs.essential_bc — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.bcs.essential_bc

+from jaxtyping import Array, Float
+from typing import Callable, List, Optional
+import equinox as eqx
+
+
+BCFunc = Callable[[Float[Array, "nd"], float], float]
+
+

+[docs]
+class EssentialBC(eqx.Module):
+    """
+    :param nodeSet: A name for a nodeset in the mesh
+    :param component: The dof to apply the essential bc to
+    :param function: A function f(x, t) = u that gives the value
+        to enforce on the (nodeset, component) of a field.
+        This defaults to the zero function
+    """
+    nodeSet: str
+    component: int
+    function: Optional[BCFunc] = lambda x, t: 0.0
+
+

+[docs]
+    def coordinates(self, mesh):
+        nodes = mesh.nodeSets[self.nodeSet]
+        coords = mesh.coords
+        return coords[nodes, :]

+

+
+
+
+

+[docs]
+class EssentialBCSet(eqx.Module):
+    bcs: List[EssentialBC]

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bcs/natural_bc.html b/_modules/pancax/bcs/natural_bc.html new file mode 100644 index 0000000..50e38ea --- /dev/null +++ b/_modules/pancax/bcs/natural_bc.html @@ -0,0 +1,169 @@ + + + + + + + + pancax.bcs.natural_bc — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.bcs.natural_bc

+from jaxtyping import Array, Float
+from pancax import fem
+from pancax.fem import surface
+from typing import Callable, Optional
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+
+
+BCFunc = Callable[[Float[Array, "nd"], float], Float[Array, "nf"]]
+# remove component from the definition.
+# it doesn't appear to be doing anything
+# class NaturalBC(NamedTuple):
+

+[docs]
+class NaturalBC(eqx.Module):
+  sideset: str
+  function: Optional[BCFunc] = lambda x, t: 0.0
+
+

+[docs]
+  def coordinates(self, mesh, q_rule_1d):
+    xigauss, wgauss = q_rule_1d
+    edges = mesh.sideSets[self.sideset]
+
+    def vmap_inner(edge):
+      edge_coords = surface.get_coords(mesh.coords, mesh.conns, edge)
+      # edge_coords = fem.mesh.get.get_coords(mesh, side)
+      jac = jnp.linalg.norm(edge_coords[0,:] - edge_coords[1,:])
+      xgauss = edge_coords[0] + jnp.outer(xigauss, edge_coords[1] - edge_coords[0])
+      return xgauss
+
+    edge_coords = jax.vmap(vmap_inner)(edges)
+    edge_coords = jnp.vstack(edge_coords)
+    return edge_coords

+
+
+

+[docs]
+  def normals(self, mesh, q_rule_1d):
+    xigauss, wgauss = q_rule_1d
+    edges = mesh.sideSets[self.sideset]
+    n_gauss_points = xigauss.shape[0]
+
+    def vmap_inner(edge):
+      edge_coords = surface.get_coords(mesh.coords, mesh.conns, edge)
+      normal = surface.compute_normal(edge_coords)
+      normals = jnp.tile(normal, (n_gauss_points, 1))
+      return normals
+
+    edge_normals = jax.vmap(vmap_inner)(edges)
+    edge_normals = jnp.vstack(edge_normals)
+    return edge_normals

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bvps/biaxial_tension.html b/_modules/pancax/bvps/biaxial_tension.html new file mode 100644 index 0000000..b4519dd --- /dev/null +++ b/_modules/pancax/bvps/biaxial_tension.html @@ -0,0 +1,146 @@ + + + + + + + + pancax.bvps.biaxial_tension — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.bvps.biaxial_tension

+

+[docs]
+def BiaxialLinearRamp(
+  final_displacement_x: float,
+  final_displacement_y: float,
+  length_x: float,
+  length_y: float
+):
+  def bc_func(xs, t, z):
+    x, y = xs[0], xs[1]
+    u_out = z
+    # u_out = u_out.at[0].set(
+    #   x * (x - length_x) * t * z[0] / length_x**2 + \
+    #   x * t * final_displacement_x / length_x
+    # )
+    # u_out = u_out.at[1].set(
+    #   y * (y - length_y) * t * z[1] / length_y**2 + \
+    #   y * t * final_displacement_y / length_y
+    # )
+    u_out = u_out.at[0].set(
+      (x * (x - length_x) * t / length_x**2 * \
+       y * (y - length_y) * t / length_y**2) * z[0] + \
+      x * t * final_displacement_x / length_x
+    )
+    u_out = u_out.at[1].set(
+      (x * (x - length_x) * t / length_x**2 * \
+       y * (y - length_y) * t / length_y**2) * z[1]
+    )
+    return u_out
+
+  return bc_func

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bvps/simple_shear.html b/_modules/pancax/bvps/simple_shear.html new file mode 100644 index 0000000..c91003d --- /dev/null +++ b/_modules/pancax/bvps/simple_shear.html @@ -0,0 +1,140 @@ + + + + + + + + pancax.bvps.simple_shear — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.bvps.simple_shear

+from typing import Optional
+
+

+[docs]
+def SimpleShearLinearRamp(
+  final_displacement: float,
+  length: float,
+  direction: str
+):
+    
+  if direction == 'xy':
+    def bc_func(xs, t, z):
+      x, y = xs[0], xs[1]
+      u_out = z
+      u_out = u_out.at[0].set(
+        x * (x - length) * t * z[0] / length**2
+      )
+      u_out = u_out.at[1].set(
+        x * t * final_displacement / length + x * (x - length) * t * z[1] / length**2
+      )
+      return u_out
+  else:
+    raise ValueError('Direction must be x or y for this BVP.')
+
+  return bc_func

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/bvps/uniaxial_tension.html b/_modules/pancax/bvps/uniaxial_tension.html new file mode 100644 index 0000000..c0c1f32 --- /dev/null +++ b/_modules/pancax/bvps/uniaxial_tension.html @@ -0,0 +1,201 @@ + + + + + + + + pancax.bvps.uniaxial_tension — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.bvps.uniaxial_tension

+
+# TODO maybe have this read in a mesh
+# and use a bounding box to define these functions using xmin xmax etc.
+

+[docs]
+def UniaxialTensionLinearRamp(
+  final_displacement: float,
+  length: float,
+  direction: str,
+  n_dimensions: int
+):
+
+  if n_dimensions == 2:
+    if direction == 'x':
+      def bc_func(xs, t, nn):
+        x, y = xs[0], xs[1]
+        u_out = nn
+        u_out = u_out.at[0].set(
+          x * t * final_displacement / length + x * (x - length) * t * nn[0] / length**2
+        )
+        u_out = u_out.at[1].set(
+          x * (x - length) * t * nn[1] / length**2
+        )
+        return u_out
+    elif direction == 'y':
+      def bc_func(xs, t, nn):
+        x, y = xs[0], xs[1]
+        u_out = nn
+        u_out = u_out.at[0].set(
+          y * (y - length) * t * nn[0] / length**2
+        )
+        u_out = u_out.at[1].set(
+          y * t * final_displacement / length + y * (y - length) * t * nn[1] / length**2
+        )
+        return u_out
+    else:
+      raise ValueError('Direction must be x or y for this BVP.')
+  elif n_dimensions == 3:
+    if direction == 'x':
+      def bc_func(xs, t, nn):
+        x, y, z = xs[0], xs[1], xs[2]
+        u_out = nn
+        u_out = u_out.at[0].set(
+          x * t * final_displacement / length + x * (x - length) * t * nn[0] / length**2
+        )
+        u_out = u_out.at[1].set(
+          x * (x - length) * t * nn[1] / length**2
+        )
+        u_out = u_out.at[2].set(
+          x * (x - length) * t * nn[2] / length**2
+        )
+        return u_out
+    elif direction == 'y':
+      def bc_func(xs, t, nn):
+        x, y, z = xs[0], xs[1], xs[2]
+        u_out = nn
+        u_out = u_out.at[0].set(
+          y * (y - length) * t * nn[0] / length**2
+        )
+        u_out = u_out.at[1].set(
+          y * t * final_displacement / length + y * (y - length) * t * nn[1] / length**2
+        )
+        u_out = u_out.at[2].set(
+          y * (y - length) * t * nn[2] / length**2
+        )
+        return u_out
+    elif direction == 'z':
+      def bc_func(xs, t, nn):
+        x, y, z = xs[0], xs[1], xs[2]
+        u_out = nn
+        u_out = u_out.at[0].set(
+          z * (z - length) * t * nn[0] / length**2
+        )
+        u_out = u_out.at[1].set(
+          z * (z - length) * t * nn[1] / length**2
+        )
+        u_out = u_out.at[2].set(
+          z * t * final_displacement / length + z * (z - length) * t * nn[2] / length**2
+        )
+        return u_out
+    else:
+      raise ValueError('Direction must be x, y, or z for this BVP.')
+  else:
+    raise ValueError('Dimensions can be either 2 or 3.')
+
+  return bc_func

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/base.html b/_modules/pancax/constitutive_models/base.html new file mode 100644 index 0000000..8e02b81 --- /dev/null +++ b/_modules/pancax/constitutive_models/base.html @@ -0,0 +1,245 @@ + + + + + + + + pancax.constitutive_models.base — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.base
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.base

+from abc import abstractmethod
+from jaxtyping import Array, Float
+from typing import Tuple
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+
+
+Scalar = float
+Tensor = Float[Array, "3 3"]
+
+
+

+[docs]
+class BaseConstitutiveModel(eqx.Module):
+

+[docs]
+  def cauchy_stress(self, F: Tensor) -> Tensor:
+    # F = grad_u + jnp.eye(3)
+    J = self.jacobian(F)
+    P = self.pk1_stress(F)
+    return (1. / J) * P @ F.T

+
+
+

+[docs]
+  @abstractmethod
+  def energy(self, F: Tensor) -> Scalar:
+    """
+    This method returns the algorithmic strain energy density.
+    """
+    pass

+
+
+

+[docs]
+  def invariants(self, F: Tensor) -> Tuple[Scalar, Scalar, Scalar]:
+    I1 = self.I1(F)
+    I2 = self.I2(F)
+    I3 = self.jacobian(F)**2
+    return jnp.array([I1, I2, I3])

+
+
+

+[docs]
+  def I1(self, F: Tensor) -> Scalar:
+    r"""
+    Calculates the first invariant
+
+    :param F: the deformation gradient
+    
+    .. math::
+      I_1 = tr\left(\mathbf{F}^T\mathbf{F}\right)
+    """
+    I1 = jnp.trace(F @ F.T)
+    return I1

+
+
+

+[docs]
+  def I1_bar(self, F: Tensor) -> Scalar:
+    r"""
+    Calculates the first distortional invariant
+
+    :param F: the deformation gradient
+    
+    .. math::
+      \bar{I}_1 = J^{-2/3}tr\left(\mathbf{F}^T\mathbf{F}\right)
+    """
+    I1 = jnp.trace(F @ F.T)
+    J = self.jacobian(F)
+    return jnp.power(J, -2. / 3.) * I1

+
+
+

+[docs]
+  def I2(self, F: Tensor) -> Scalar:
+    C = F.T @ F
+    C2 = C @ C
+    I1 = jnp.trace(C)
+    I2 = 0.5 * (I1**2 - jnp.trace(C2))
+    return I2

+
+
+

+[docs]
+  def I2_bar(self, F: Tensor) -> Scalar:
+    C = F.T @ F
+    C2 = C @ C
+    I1 = jnp.trace(C)
+    I2 = 0.5 * (I1**2 - jnp.trace(C2))
+    J = self.jacobian(F)
+    return jnp.power(J, -4. / 3.) * I2

+
+
+

+[docs]
+  def jacobian(self, F: Tensor) -> Scalar:
+    r"""
+    This simply calculate the jacobian but with guard rails
+    to return nonsensical numbers if a non-positive jacobian
+    is encountered during training.
+
+    :param F: the deformation gradient
+
+    .. math::
+      J = det(\mathbf{F})
+    
+    """
+    J = jnp.linalg.det(F)
+    J = jax.lax.cond(
+      J <= 0.0,
+      lambda _: 1.0e3,
+      lambda x: x,
+      J
+    )
+    return J

+
+
+

+[docs]
+  def pk1_stress(self, F: Tensor) -> Tensor:
+    return jax.grad(self.energy, argnums=0)(F)

+
+
+

+[docs]
+  def properties(self):
+    return self.__dataclass_fields__

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/blatz_ko.html b/_modules/pancax/constitutive_models/blatz_ko.html new file mode 100644 index 0000000..b9649ba --- /dev/null +++ b/_modules/pancax/constitutive_models/blatz_ko.html @@ -0,0 +1,139 @@ + + + + + + + + pancax.constitutive_models.blatz_ko — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.blatz_ko
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.blatz_ko

+from .base import BaseConstitutiveModel
+from .properties import Property
+import jax.numpy as jnp
+
+
+

+[docs]
+class BlatzKo(BaseConstitutiveModel):
+  shear_modulus: Property
+
+

+[docs]
+  def energy(self, F):
+    # unpack properties
+    G = self.shear_modulus
+
+    # kinematics
+    I2 = self.I2(F)
+    I3 = jnp.linalg.det(F.T @ F)
+
+    # constitutive
+    W = (G / 2.) * (I2 / I3 + 2 * jnp.sqrt(I3) - 5.)
+    return W

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/gent.html b/_modules/pancax/constitutive_models/gent.html new file mode 100644 index 0000000..916b887 --- /dev/null +++ b/_modules/pancax/constitutive_models/gent.html @@ -0,0 +1,160 @@ + + + + + + + + pancax.constitutive_models.gent — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.gent
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.gent

+from .base import BaseConstitutiveModel
+from .properties import Property
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Gent(BaseConstitutiveModel):
+  r"""
+	Gent model with the following model form
+
+	.. math::
+		\psi(\mathbf{F}) = \frac{1}{2}K\left[\frac{1}{2}\left(J^2 - \ln J\right)\right] -
+						           \frac{1}{2}GJ_m\ln\left(1 - \frac{\bar{I}_1 - 3}{J_m}\right)
+	"""
+  bulk_modulus: Property
+  shear_modulus: Property
+  Jm_parameter: Property
+
+

+[docs]
+  def energy(self, F):
+    # unpack properties
+    K, G, Jm = self.bulk_modulus, self.shear_modulus, self.Jm_parameter
+
+    # kinematics
+    C = F.T @ F
+    J = self.jacobian(F)
+    I_1_bar = jnp.trace(jnp.power(J, -2. / 3.) * C)
+
+    # guard rail
+    check_value = I_1_bar > Jm + 3.0 - 0.001
+    I_1_bar = jax.lax.cond(
+      check_value,
+      lambda x: Jm + 3.0 - 0.001,
+      lambda x: x,
+      I_1_bar
+    )
+
+    # constitutive
+    W_vol = 0.5 * K * (0.5 * (J**2 - 1) - jnp.log(J))
+    W_dev = -0.5 * G * Jm * jnp.log(1. - ((I_1_bar - 3.0) / Jm))
+    return W_vol + W_dev

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/neohookean.html b/_modules/pancax/constitutive_models/neohookean.html new file mode 100644 index 0000000..9c92ed1 --- /dev/null +++ b/_modules/pancax/constitutive_models/neohookean.html @@ -0,0 +1,150 @@ + + + + + + + + pancax.constitutive_models.neohookean — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.neohookean
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.neohookean

+from .base import BaseConstitutiveModel, Scalar, Tensor
+from .properties import Property
+import jax.numpy as jnp
+
+
+

+[docs]
+class NeoHookean(BaseConstitutiveModel):
+  r"""
+	NeoHookean model with the following model form
+
+	.. math::
+		\psi(\mathbf{F}) = \frac{1}{2}K\left[\frac{1}{2}\left(J^2 - \ln J\right)\right] +
+						   \frac{1}{2}G\left(\bar{I}_1 - 3\right)
+	"""
+  bulk_modulus: Property
+  shear_modulus: Property
+
+

+[docs]
+  def energy(self, F: Tensor) -> Scalar:
+    K, G = self.bulk_modulus, self.shear_modulus
+
+    # kinematics
+    # F = jnp.eye(3) + grad_u
+    C = F.T @ F
+    J = self.jacobian(F)
+    I_1_bar = jnp.trace(1. / jnp.square(jnp.cbrt(J)) * C)
+
+    # constitutive
+    W_vol = 0.5 * K * (0.5 * (J**2 - 1) - jnp.log(J))
+    W_dev = 0.5 * G * (I_1_bar - 3.)
+
+    return W_vol + W_dev

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/properties.html b/_modules/pancax/constitutive_models/properties.html new file mode 100644 index 0000000..3870673 --- /dev/null +++ b/_modules/pancax/constitutive_models/properties.html @@ -0,0 +1,202 @@ + + + + + + + + pancax.constitutive_models.properties — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.properties
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.properties

+from jaxtyping import Array, Float
+from typing import List, Union
+import equinox as eqx
+import jax
+
+
+# TODO patch up error check in a good way
+# probably just make a method to check type on other
+

+[docs]
+class BoundedProperty(eqx.Module):
+  prop_min: float = eqx.field(static=True)
+  prop_max: float = eqx.field(static=True)
+  prop_val: float
+  # TODO
+  # activation: Callable
+
+

+[docs]
+  def __init__(
+    self, 
+    prop_min: float, 
+    prop_max: float,
+    key: jax.random.PRNGKey
+  ) -> None:
+    self.prop_min = prop_min
+    self.prop_max = prop_max
+    self.prop_val = jax.random.uniform(key, 1)

+
+
+  def __call__(self):
+    return self.prop_min + \
+           (self.prop_max - self.prop_min) * jax.nn.sigmoid(self.prop_val)[0]
+
+  def __add__(self, other):
+    self._check_other_type(other, '+')
+    return self.__call__() + other
+
+  def __div__(self, other):
+    self._check_other_type(other, '/')
+    return self.__call__() / other
+
+  def __mul__(self, other):
+    self._check_other_type(other, '*')
+    return self.__call__() * other
+
+  def __sub__(self, other):
+    self._check_other_type(other, '-')
+    return self.__call__() - other
+
+  def __radd__(self, other):
+    self._check_other_type(other, '+')
+    return other + self.__call__()
+
+  def __rdiv__(self, other):
+    self._check_other_type(other, '/')
+    return other / self.__call__()
+
+  def __rmul__(self, other):
+    self._check_other_type(other, '*')
+    return other * self.__call__()
+
+  def __rsub__(self, other):
+    self._check_other_type(other, '*')
+    return other - self.__call__()
+
+  def __rtruediv__(self, other):
+    self._check_other_type(other, '/')
+    return other / self.__call__()
+
+  def __truediv__(self, other):
+    self._check_other_type(other, '/')
+    return self.__call__() / other
+
+

+[docs]
+  def _check_other_type(self, other, op_str):
+    if isinstance(other, Array) or \
+       isinstance(other, float):
+      pass
+    else:
+      raise TypeError(f'Unsupported type {type(other)} when doing {op_str} with BoundingProperty')

+

+
+
+
+FixedProperty = float #= eqx.field(static=True)
+Property = Union[BoundedProperty, FixedProperty]
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/constitutive_models/swanson.html b/_modules/pancax/constitutive_models/swanson.html new file mode 100644 index 0000000..ad0588c --- /dev/null +++ b/_modules/pancax/constitutive_models/swanson.html @@ -0,0 +1,172 @@ + + + + + + + + pancax.constitutive_models.swanson — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.constitutive_models.swanson
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.constitutive_models.swanson

+from .base import BaseConstitutiveModel
+from .properties import Property
+import equinox as eqx
+import jax.numpy as jnp
+
+
+

+[docs]
+class Swanson(BaseConstitutiveModel):
+  r"""
+	Swanson model truncated to 4 parameters
+
+	.. math::
+		\psi(\mathbf{F}) = K\left(J\ln J - J + 1\right) +
+							         \frac{3}{2}A_1\left(\frac{\bar{I}_1}{3} - 1\right)^{P_1} + 
+                       \frac{3}{2}C_1\left(\frac{\bar{I}_1}{3} - 1\right)^{R_1}
+	"""
+  bulk_modulus: Property
+  A1: Property
+  P1: Property
+  B1: Property
+  Q1: Property
+  C1: Property
+  R1: Property
+  # hack because Swanson is a stupid model
+  cutoff_strain: float = eqx.field(static=True)
+
+

+[docs]
+  def energy(self, F):
+    K = self.bulk_modulus
+    A1, P1 = self.A1, self.P1
+    B1, Q1 = self.B1, self.Q1
+    C1, R1 = self.C1, self.R1
+    tau_cutoff = (1. / 3.) * (3. + self.cutoff_strain**2) - 1.
+
+    # kinematics
+    J = self.jacobian(F)
+    C = F.T @ F
+    C_bar = jnp.power(J, -2. / 3.) * C
+    I_1_bar = jnp.trace(C_bar)
+    tau_1 = (1. / 3.) * I_1_bar - 1.
+    tau_tilde_1 = tau_1 + tau_cutoff
+
+    # constitutive
+    W_vol = K * (J * jnp.log(J) - J + 1.)
+    W_dev_tau = 3. / 2. * (
+      A1 / (P1 + 1.) * (tau_tilde_1**(P1 + 1.)) +
+      C1 / (R1 + 1.) * (tau_tilde_1**(R1 + 1.))
+    )
+    W_dev_cutoff = 3. / 2. * (
+      A1 / (P1 + 1.) * (tau_cutoff**(P1 + 1.)) +
+      C1 / (R1 + 1.) * (tau_cutoff**(R1 + 1.))
+    )
+    W_dev = W_dev_tau - W_dev_cutoff
+    return W_vol + W_dev

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/data/full_field_data.html b/_modules/pancax/data/full_field_data.html new file mode 100644 index 0000000..117e2b0 --- /dev/null +++ b/_modules/pancax/data/full_field_data.html @@ -0,0 +1,203 @@ + + + + + + + + pancax.data.full_field_data — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.data.full_field_data

+from jaxtyping import Array
+from typing import List
+import equinox as eqx
+import jax.numpy as jnp
+import matplotlib.pyplot as plt
+import pandas
+
+
+

+[docs]
+class FullFieldData(eqx.Module):
+  """
+  Data structure to store full field data used as ground truth
+  for output fields of a PINN when solving inverse problems.
+
+  :param inputs: Data that serves as inputs to the PINN
+  :param outputs: Data that serves as outputs of the PINN
+  :param n_time_steps: Variable used for book keeping
+  """
+  inputs: Array
+  outputs: Array
+  n_time_steps: int
+
+

+[docs]
+  def __init__(
+    self,
+    data_file: str,
+    input_keys: List[str],
+    output_keys: List[str]
+  ):
+    df = pandas.read_csv(data_file)
+    df.columns = df.columns.str.strip()
+    self.inputs = jnp.array(df[input_keys].values)
+    self.outputs = jnp.array(df[output_keys].values)
+    self.n_time_steps = len(jnp.unique(self.inputs[:, -1]))

+
+
+  # TODO still need to test this
+

+[docs]
+  def plot_registration(self, domain):
+    n_points_per_step = int(self.inputs.shape[0] / self.n_time_steps)
+    first_step = self.inputs[:n_points_per_step, :]
+
+    plt.figure(1)
+    plt.scatter(first_step[:, 0], first_step[:, 1], color='blue', label='DIC')
+    plt.scatter(domain.coords[:, 0], domain.coords[:, 1], color='red', label='Mesh')
+    plt.xlabel('X coordinate (mm)')
+    plt.ylabel('Y coordinate (mm)')
+    plt.legend(loc='best')
+    plt.savefig('dic_data_mesh_registration.png')
+    print('here')

+
+    # plt.clf()
+
+

+[docs]
+  def plot_data(self, domain, time_step):
+    pass

+
+
+

+[docs]
+  def shift_inputs(self, x, y, z):
+    shifted_inputs = self.inputs
+    shifted_inputs = shifted_inputs.at[:, 0].set(shifted_inputs[:, 0] + x)
+    shifted_inputs = shifted_inputs.at[:, 1].set(shifted_inputs[:, 1] + y)
+    shifted_inputs = shifted_inputs.at[:, 2].set(shifted_inputs[:, 2] + z)
+    return eqx.tree_at(lambda x: x.inputs, self, shifted_inputs)

+
+
+

+[docs]
+  def set_input_component_values(self, component, val):
+    if component == 'x':
+      component = 0
+    elif component == 'y':
+      component = 1
+    elif component == 'z':
+      component = 2
+    else:
+      raise ValueError('Needs to be x, y, or z')
+
+    set_inputs = self.inputs
+    set_inputs = set_inputs.at[:, component].set(val)
+    return eqx.tree_at(lambda x: x.inputs, self, set_inputs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/data/global_data.html b/_modules/pancax/data/global_data.html new file mode 100644 index 0000000..e47b9a8 --- /dev/null +++ b/_modules/pancax/data/global_data.html @@ -0,0 +1,220 @@ + + + + + + + + pancax.data.global_data — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.data.global_data

+from jaxtyping import Array
+from typing import Optional, Union
+import equinox as eqx
+import exodus3 as exodus
+import jax.numpy as jnp
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas
+
+
+# TODO currently hardcoded to force which may be limiting
+# for others interested in doing other physics
+

+[docs]
+class GlobalData(eqx.Module):
+  """
+  Data structure that holds global data to be used as
+  ground truth for some global field calculated from
+  PINN outputs used in inverse modeling training
+
+  :param times: A set of times used to compare to physics calculations
+  :param displacements: Currently hardcoded to use a displacement-force curve TODO
+  :param outputs: Field used as ground truth, hardcoded essentially to a reaction force now
+  :param n_nodes: Book-keeping variable for number of nodes on nodeset to measure global response from
+  :param n_time_steps: Book-keeping variable
+  :param reaction_nodes: Node set nodes for where to measure reaction forces
+  :param reaction_dof: Degree of freedom to use for reaction force calculation
+  """
+  times: Array # change to inputs?
+  displacements: Array
+  outputs: Array
+  n_nodes: int
+  n_time_steps: int
+  reaction_nodes: Array
+  reaction_dof: int
+  
+

+[docs]
+  def __init__(
+    self,
+    data_file: str, times_key: str, disp_key: str, force_key: str,
+    mesh_file: str, nset_id: int, reaction_dof: Union[int, str], 
+    n_time_steps: int,
+    plotting: Optional[bool] = False
+  ):
+    # read in data
+    df = pandas.read_csv(data_file)  
+    df.columns = df.columns.str.strip()
+    times_in = df[times_key].values
+    disps_in = df[disp_key].values
+    forces_in = df[force_key].values
+    # interpolate data onto times
+    times = np.linspace(np.min(times_in), np.max(times_in), n_time_steps)
+    disp_interp = np.interp(times, times_in, disps_in)
+    force_interp = np.interp(times, times_in, forces_in)
+
+    if plotting:
+      plt.figure(1)
+      plt.plot(times_in, disps_in, label='Raw Data')
+      plt.plot(times, disp_interp, label='Interpolated', linestyle='None', marker='o')
+      plt.xlabel('Time (s)')
+      plt.ylabel('Displacement (mm)')
+      plt.savefig('mts_time_displacement.png')
+      # plt.clf()
+
+      plt.figure(2)
+      plt.plot(times_in, forces_in, label='Raw Data')
+      plt.plot(times, force_interp, label='Interpolated', linestyle='None', marker='o')
+      plt.xlabel('Time (s)')
+      plt.ylabel('Force (N)')
+      plt.savefig('mts_time_force.png')
+      # plt.clf()
+
+      plt.figure(3)
+      plt.plot(disps_in, forces_in, label='Raw Data')
+      plt.plot(disp_interp, force_interp, label='Interpolated', linestyle='None', marker='o')
+      plt.xlabel('Displacement (mm)')
+      plt.ylabel('Force (N)')
+      plt.savefig('mts_displacement_force.png')
+      # plt.clf()
+
+    # mesh related stuff
+    exo = exodus.exodus(mesh_file, 'r', array_type='numpy')
+    nodes = exo.get_node_set_nodes(nset_id) - 1
+    reaction_nodes = jnp.array(nodes)
+    n_nodes = len(reaction_nodes)
+
+    if reaction_dof == 'x':
+      reaction_dof = 0
+    elif reaction_dof == 'y':
+      reaction_dof = 1
+    elif reaction_dof == 'z':
+      reaction_dof = 2
+    else:
+      raise ValueError('reaction_dof needs to be either x or y.')
+
+    # set things
+    self.times = jnp.array(times)
+    self.displacements = jnp.array(disp_interp)
+    self.outputs = jnp.array(force_interp)
+    self.n_nodes = n_nodes
+    self.n_time_steps = len(times)
+    self.reaction_nodes = reaction_nodes
+    self.reaction_dof = reaction_dof

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/domains/base.html b/_modules/pancax/domains/base.html new file mode 100644 index 0000000..3fef270 --- /dev/null +++ b/_modules/pancax/domains/base.html @@ -0,0 +1,154 @@ + + + + + + + + pancax.domains.base — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.domains.base

+from jaxtyping import Array, Float
+from pancax.fem import Mesh, SimplexTriElement
+from pancax.fem import create_higher_order_mesh_from_simplex_mesh
+from pancax.fem import read_exodus_mesh
+from pancax.timer import Timer
+from typing import Optional, Union
+import equinox as eqx
+import jax.numpy as jnp
+
+
+

+[docs]
+class BaseDomain(eqx.Module):
+  mesh_file: str
+  mesh: Mesh
+  coords: Float[Array, "nn nd"]
+  times: Union[Float[Array, "nt"], Float[Array, "nn 1"]]
+
+

+[docs]
+  def __init__(
+    self, 
+    mesh_file: str, 
+    times: Float[Array, "nt"],
+    p_order: Optional[int] = 1
+  ) -> None:
+    with Timer('Reading Mesh...'):
+      mesh = read_exodus_mesh(mesh_file)
+      # if tri mesh, we can make it higher order from lower order
+      if type(mesh.parentElement) == SimplexTriElement:
+        mesh = create_higher_order_mesh_from_simplex_mesh(mesh, p_order, copyNodeSets=True)
+      else:
+        print('WARNING: Ignoring polynomial order flag for non tri mesh')
+
+      self.mesh_file = mesh_file
+      self.mesh = mesh
+      self.coords = jnp.array(mesh.coords)
+      self.times = times

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/domains/collocation_domain.html b/_modules/pancax/domains/collocation_domain.html new file mode 100644 index 0000000..8c9dd5d --- /dev/null +++ b/_modules/pancax/domains/collocation_domain.html @@ -0,0 +1,139 @@ + + + + + + + + pancax.domains.collocation_domain — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.domains.collocation_domain
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.domains.collocation_domain

+from .base import BaseDomain
+from jaxtyping import Array, Float
+from pancax.fem import Mesh
+from typing import Optional, Union
+
+
+

+[docs]
+class CollocationDomain(BaseDomain):
+  mesh_file: str
+  mesh: Mesh
+  coords: Float[Array, "nn nd"]
+  times: Union[Float[Array, "nt"], Float[Array, "nn 1"]]
+
+

+[docs]
+  def __init__(
+      self, 
+      mesh_file: str, 
+      times: Float[Array, "nt"],
+      p_order: Optional[int] = 1
+  ) -> None:
+    super().__init__(mesh_file, times, p_order=p_order)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/domains/delta_pinn_domain.html b/_modules/pancax/domains/delta_pinn_domain.html new file mode 100644 index 0000000..00d5e01 --- /dev/null +++ b/_modules/pancax/domains/delta_pinn_domain.html @@ -0,0 +1,199 @@ + + + + + + + + pancax.domains.delta_pinn_domain — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.domains.delta_pinn_domain
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.domains.delta_pinn_domain

+from jaxtyping import Array, Float
+from pancax.fem import DofManager
+from pancax.physics_kernels import LaplaceBeltrami
+from pancax.post_processor import PostProcessor
+from pancax.timer import Timer
+from scipy.sparse import linalg
+from typing import Optional
+from .variational_domain import VariationalDomain
+import jax.numpy as jnp
+import numpy as onp
+
+
+

+[docs]
+class DeltaPINNDomain(VariationalDomain):
+  n_eigen_values: int
+  physics: LaplaceBeltrami
+  eigen_modes: Float[Array, "nn nev"]
+
+

+[docs]
+  def __init__(
+    self,
+    mesh_file: str,
+    times: Float[Array, "nt"],
+    n_eigen_values: int,
+    p_order: Optional[int] = 1,
+    q_order: Optional[int] = 2
+  ):
+    super().__init__(mesh_file, times, p_order=p_order, q_order=q_order)
+    self.n_eigen_values = n_eigen_values
+    physics = LaplaceBeltrami()
+    physics = physics.update_normalization(self)
+    self.physics = physics.update_var_name_to_method()
+    self.eigen_modes = self.solve_eigen_problem()

+
+
+  # def __pos
+
+

+[docs]
+  def solve_eigen_problem(self):
+    # physics = LaplaceBeltrami()
+    dof_manager = DofManager(self.mesh, 1, [])
+    Uu = jnp.zeros(dof_manager.get_unknown_size())
+    U = dof_manager.create_field(Uu)
+    # TODO need to define these methods
+    K = self.physics.stiffness_matrix((), self, 0., U, dof_manager)
+    M = self.physics.mass_matrix((), self, 0., U, dof_manager)
+
+    with Timer('eigen solve'):
+      nModes = self.n_eigen_values
+      mu, modes = linalg.eigsh(
+        A=K, k=nModes, M=M, which='SM'
+      )
+
+      lambdas = 1. / mu
+      for n in range(len(lambdas)):
+        print(f'  Eigen mode {n} = {1. / lambdas[n]}')
+
+    with Timer('post-processing'):
+      pp = PostProcessor(self.mesh_file)
+      pp.init(self, 'output-eigen.e',
+        node_variables=[
+          'field_values'
+        ]        
+      )
+      for n in range(len(lambdas)):
+        print(f'  Post-processing eigenvector {n}')
+        field = dof_manager.create_field(modes[:, n])
+        field = onp.asarray(field)
+        # TODO will fail on no exodus post-processor
+        pp.pp.exo.put_time(n + 1, 1. / lambdas[n])
+        pp.pp.exo.put_node_variable_values('u', n + 1, field[:, 0])
+      pp.close()
+
+    # normalizing modes by default
+    modes = jnp.array(modes[:, 0:len(lambdas) - 1])
+    print(modes.shape)
+    modes = (modes - jnp.min(modes, axis=0)) / \
+            (jnp.max(modes, axis=0) - jnp.min(modes, axis=0))
+
+    return modes

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/domains/variational_domain.html b/_modules/pancax/domains/variational_domain.html new file mode 100644 index 0000000..ee1d894 --- /dev/null +++ b/_modules/pancax/domains/variational_domain.html @@ -0,0 +1,165 @@ + + + + + + + + pancax.domains.variational_domain — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.domains.variational_domain
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.domains.variational_domain

+from .base import BaseDomain
+from jaxtyping import Array, Float, Int
+from pancax.fem import DofManager, FunctionSpace, Mesh
+from pancax.fem import NonAllocatedFunctionSpace, QuadratureRule
+from typing import Optional, Union
+import equinox as eqx
+import jax.numpy as jnp
+
+
+

+[docs]
+class VariationalDomain(BaseDomain):
+  mesh_file: str
+  mesh: Mesh
+  coords: Float[Array, "nn nd"]
+  times: Union[Float[Array, "nt"], Float[Array, "nn 1"]]
+  conns: Int[Array, "ne nnpe"]
+  dof_manager: DofManager
+  fspace: FunctionSpace
+  fspace_centroid: FunctionSpace
+
+

+[docs]
+  def __init__(
+    self,
+    mesh_file: str,
+    times: Float[Array, "nt"],
+    p_order: Optional[int] = 1,
+    q_order: Optional[int] = 2
+  ):
+    super().__init__(mesh_file, times, p_order=p_order)
+    self.conns = jnp.array(self.mesh.conns)
+    self.dof_manager = None
+    self.fspace = NonAllocatedFunctionSpace(
+      self.mesh, QuadratureRule(self.mesh.parentElement, q_order)
+    )
+    self.fspace_centroid = NonAllocatedFunctionSpace(
+      self.mesh, QuadratureRule(self.mesh.parentElement, 1)
+    )

+
+
+

+[docs]
+  def update_dof_manager(self, dirichlet_bcs, n_dofs):
+    dof_manager = DofManager(self.mesh, n_dofs, dirichlet_bcs)
+    dof_manager.isUnknown = jnp.array(dof_manager.isUnknown, dtype=jnp.bool)
+    dof_manager.unknownIndices = jnp.array(dof_manager.unknownIndices)
+    new_pytree = eqx.tree_at(lambda x: x.dof_manager, self, dof_manager)
+    return new_pytree

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/dof_manager.html b/_modules/pancax/fem/dof_manager.html new file mode 100644 index 0000000..a9bda44 --- /dev/null +++ b/_modules/pancax/fem/dof_manager.html @@ -0,0 +1,268 @@ + + + + + + + + pancax.fem.dof_manager — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.dof_manager

+from .function_space import FunctionSpace
+from jaxtyping import Array, Bool, Float, Int
+from pancax.bcs import EssentialBC
+from pancax.timer import Timer
+from typing import List, Tuple
+import jax.numpy as np
+import numpy as onp
+
+# TODO
+# getting some error when making this a child of eqx.Module
+

+[docs]
+class DofManager:
+    """
+    Collection of arrays needed to differentiate between
+    fixed and free dofs for fem like calculations.
+
+    TODO better document the parameters in this guy
+    """
+

+[docs]
+    def __init__(self, mesh, dim: int, EssentialBCs: List[EssentialBC]) -> None:
+        """
+        :param functionSpace: ``FunctionSpace`` object
+        :param dim: The number of dims (really the number of active dofs for the physics)
+        :param EssentialBCs: A list of of ``EssentialBC`` objects
+        """
+        with Timer('DofManager.__init__'):
+            self.fieldShape = mesh.num_nodes, dim
+            self.isBc = onp.full(self.fieldShape, False, dtype=bool)
+            for ebc in EssentialBCs:
+                self.isBc[mesh.nodeSets[ebc.nodeSet], ebc.component] = True
+
+            self.isUnknown = ~self.isBc
+
+            self.ids = onp.arange(self.isBc.size).reshape(self.fieldShape)
+
+            self.unknownIndices = self.ids[self.isUnknown]
+            self.bcIndices = self.ids[self.isBc]
+
+            ones = onp.ones(self.isBc.size, dtype=int) * -1
+            # self.dofToUnknown = ones.at[self.unknownIndices].set(np.arange(self.unknownIndices.size)) 
+            self.dofToUnknown = ones
+            self.dofToUnknown[self.unknownIndices] = onp.arange(self.unknownIndices.size)
+
+            self.HessRowCoords, self.HessColCoords = self._make_hessian_coordinates(onp.array(mesh.conns))
+
+            self.hessian_bc_mask = self._make_hessian_bc_mask(onp.array(mesh.conns))

+
+
+

+[docs]
+    def get_bc_size(self) -> int:
+        """
+        :return: the number of fixed dofs
+        """
+        return np.sum(self.isBc).item() # item() method casts to Python int

+
+
+

+[docs]
+    def get_unknown_size(self) -> int:
+        """
+        :return: the size of the unkowns vector
+        """
+        return np.sum(self.isUnknown).item() # item() method casts to Python int

+
+
+

+[docs]
+    def create_field(self, Uu, Ubc=0.0) -> Float[Array, "nn nd"]:
+        """
+        :param Uu: Vector of unknown values
+        :param Ubc: Values for bc to apply
+        :return: U, a field of unknowns and bcs combined.
+        """
+        U = np.zeros(self.isBc.shape).at[self.isBc].set(Ubc)
+        return U.at[self.isUnknown].set(Uu)

+
+
+

+[docs]
+    def get_bc_values(self, U) -> Float[Array, "nb"]:
+        """
+        :param U: a nodal field
+        :return: the bc values in the field U
+        """
+        return U[self.isBc]

+
+
+

+[docs]
+    def get_unknown_values(self, U) -> Float[Array, "nu"]:
+        """
+        :param U: a nodal field
+        :return: the unknown values in the field U
+        """
+        return U[self.isUnknown]

+
+
+

+[docs]
+    def slice_unknowns_with_dof_indices(
+        self, Uu: Float[Array, "nu"], dofIndexSlice: Int[Array, "nn"]
+    ) -> Float[Array, "nu_new"]:
+        i = self.isUnknown[dofIndexSlice]
+        j = self.dofToUnknown.reshape(self.fieldShape)[dofIndexSlice]
+        return Uu[j[i]]

+
+
+

+[docs]
+    def _make_hessian_coordinates(self, conns: Int[Array, "ne nnpe"]) -> Tuple[Int[Array, "nn"], Int[Array, "nn"]]:
+        nElUnknowns = onp.zeros(conns.shape[0], dtype=int)
+        nHessianEntries = 0
+        for e, eNodes in enumerate(conns):
+            elUnknownFlags = self.isUnknown[eNodes,:].ravel()
+            nElUnknowns[e] = onp.sum(elUnknownFlags)
+            nHessianEntries += onp.square(nElUnknowns[e])
+
+        rowCoords = onp.zeros(nHessianEntries, dtype=int)
+        colCoords = rowCoords.copy()
+        rangeBegin = 0
+        for e,eNodes in enumerate(conns):
+            elDofs = self.ids[eNodes,:]
+            elUnknownFlags = self.isUnknown[eNodes,:]
+            elUnknowns = self.dofToUnknown[elDofs[elUnknownFlags]]
+            elHessCoords = onp.tile(elUnknowns, (nElUnknowns[e],1))
+
+            rangeEnd = rangeBegin + onp.square(nElUnknowns[e])
+
+            rowCoords[rangeBegin:rangeEnd] = elHessCoords.ravel()
+            colCoords[rangeBegin:rangeEnd] = elHessCoords.T.ravel()
+
+            rangeBegin += onp.square(nElUnknowns[e])
+        return rowCoords, colCoords

+
+
+

+[docs]
+    def _make_hessian_bc_mask(self, conns: Int[Array, "ne nnpe"]) -> Bool[Array, "ne ndpe ndpe"]:
+        nElements, nNodesPerElement = conns.shape
+        nFields = self.ids.shape[1]
+        nDofPerElement = nNodesPerElement*nFields
+
+        hessian_bc_mask = onp.full((nElements,nDofPerElement,nDofPerElement),
+                                   True, dtype=bool)
+        for e, eNodes in enumerate(conns):
+            eFlag = self.isBc[eNodes,:].ravel()
+            hessian_bc_mask[e,eFlag,:] = False
+            hessian_bc_mask[e,:,eFlag] = False
+        return hessian_bc_mask

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/base_element.html b/_modules/pancax/fem/elements/base_element.html new file mode 100644 index 0000000..ecce4a4 --- /dev/null +++ b/_modules/pancax/fem/elements/base_element.html @@ -0,0 +1,302 @@ + + + + + + + + pancax.fem.elements.base_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.base_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.base_element

+from abc import abstractmethod
+from jaxtyping import Array, Float, Int
+from scipy import special
+from typing import NamedTuple
+import jax.numpy as jnp
+import numpy as np
+import equinox as eqx
+
+
+

+[docs]
+def get_lobatto_nodes_1d(degree):
+    p = np.polynomial.Legendre.basis(degree, domain=[0.0, 1.0])
+    dp = p.deriv()
+    xInterior = dp.roots()
+    xn = jnp.hstack((jnp.array([0.0]), xInterior, jnp.array([1.0])))
+    return xn

+
+
+
+

+[docs]
+def pascal_triangle_monomials(degree):
+    p = []
+    q = []
+    for i in range(1, degree + 2):
+        monomialIndices = list(range(i))
+        p += monomialIndices
+        monomialIndices.reverse()
+        q += monomialIndices
+    return np.column_stack((q,p))

+
+
+
+

+[docs]
+def vander1d(x, degree):
+    x = np.asarray(x)
+    A = np.zeros((x.shape[0], degree + 1))
+    dA = np.zeros((x.shape[0], degree + 1))
+    domain = [0.0, 1.0]
+    for i in range(degree + 1):
+        p = np.polynomial.Legendre.basis(i, domain=domain) 
+        p *= np.sqrt(2.0*i + 1.0) # keep polynomial orthonormal
+        A[:, i] = p(x)
+        dp = p.deriv()
+        dA[:, i] = dp(x)
+    return A, dA

+
+
+
+

+[docs]
+def vander2d(x, degree):
+    x = np.asarray(x)
+    nNodes = (degree+1)*(degree+2)//2
+    pq = pascal_triangle_monomials(degree)
+
+    # It's easier to process if the input arrays
+    # always have the same shape
+    # If a 1D array is given (a single point),
+    # convert to the equivalent 2D array
+    x = x.reshape(-1,2)
+    
+    # switch to bi-unit triangle (-1,-1)--(1,-1)--(-1,1)
+    z = 2.0*x - 1.0
+    
+    def map_from_tri_to_square(xi):
+        small = 1e-12
+        # The mapping has a singularity at the vertex (-1, 1).
+        # Handle that point specially.
+        indexSingular = xi[:, 1] > 1.0 - small
+        xiShifted = xi.copy()
+        xiShifted[indexSingular, 1] = 1.0 - small
+        eta = np.zeros_like(xi)
+        eta[:, 0] = 2.0*(1.0 + xiShifted[:, 0])/(1.0 - xiShifted[:, 1]) - 1.0
+        eta[:, 1] = xiShifted[:, 1]
+        eta[indexSingular, 0] = -1.0
+        eta[indexSingular, 1] = 1.0
+        
+        # Jacobian of map. 
+        # Actually, deta is just the first row of the Jacobian.
+        # The second row is trivially [0, 1], so we don't compute it.
+        # We just use that fact directly in the derivative Vandermonde
+        # expressions.
+        deta = np.zeros_like(xi)
+        deta[:, 0] = 2/(1 - xiShifted[:, 1])
+        deta[:, 1] = 2*(1 + xiShifted[:, 0])/(1 - xiShifted[:, 1])**2
+        return eta, deta
+    
+    E, dE = map_from_tri_to_square(np.asarray(z))
+    
+    A = np.zeros((x.shape[0], nNodes))
+    Ax = A.copy()
+    Ay = A.copy()
+    N1D = np.polynomial.Polynomial([0.5, -0.5])
+    for i in range(nNodes):
+        p = np.polynomial.Legendre.basis(pq[i, 0])
+        
+        # SciPy's polynomials use the deprecated poly1d type
+        # of NumPy. To convert to the modern Polynomial type,
+        # we need to reverse the order of the coefficients.
+        qPoly1d = special.jacobi(pq[i, 1], 2*pq[i, 0] + 1, 0)
+        q = np.polynomial.Polynomial(qPoly1d.coef[::-1])
+        
+        for j in range(pq[i, 0]):
+            q *= N1D
+        
+        # orthonormality weight
+        weight = np.sqrt((2*pq[i,0] + 1) * 2*(pq[i, 0] + pq[i, 1] + 1))
+        
+        A[:, i] = weight*p(E[:, 0])*q(E[:, 1])
+        
+        # derivatives
+        dp = p.deriv()
+        dq = q.deriv()
+        Ax[:, i] = 2*weight*dp(E[:, 0])*q(E[:, 1])*dE[:, 0]
+        Ay[:, i] = 2*weight*(dp(E[:, 0])*q(E[:, 1])*dE[:, 1]
+                             + p(E[:, 0])*dq(E[:, 1]))
+        
+    return A, Ax, Ay

+
+
+
+# TODO add hessians maybe?
+

+[docs]
+class ShapeFunctions(NamedTuple):
+    """
+    Shape functions and shape function gradients (in the parametric space).
+
+    :param values: Values of the shape functions at a discrete set of points.
+        Shape is ``(nPts, nNodes)``, where ``nPts`` is the number of
+        points at which the shame functinos are evaluated, and ``nNodes``
+        is the number of nodes in the element (which is equal to the
+        number of shape functions).
+    :param gradients: Values of the parametric gradients of the shape functions.
+        Shape is ``(nPts, nDim, nNodes)``, where ``nDim`` is the number
+        of spatial dimensions. Line elements are an exception, which
+        have shape ``(nPts, nNdodes)``.
+    """
+    values: Float[Array, "np nn"]
+    gradients: Float[Array, "np nd nn"]

+
+
+
+

+[docs]
+class BaseElement(eqx.Module):
+    """
+    Base class for different element technologies
+
+    :param elementType: Element type name
+    :param degree: Polynomial degree
+    :param coordinates: Nodal coordinates in the reference configuration
+    :param vertexNodes: Vertex node number, 0-based
+    :param faceNodes: Nodes associated with each face, 0-based
+    :param interiorNodes: Nodes in the interior, 0-based or empty
+    """
+    elementType: str
+    degree: int
+    coordinates: Float[Array, "nn nd"]
+    vertexNodes: Int[Array, "nn"]
+    faceNodes: Int[Array, "nf nnpf"]
+    interiorNodes: Int[Array, "nni"]
+
+    # def __init__(self, elementType, degree, coordinates, vertexNodes, faceNodes, interiorNodes):
+    #     self.elementType = elementType
+    #     self.degree = degree
+    #     self.coordinates = coordinates
+    #     self.vertexNodes = vertexNodes
+    #     self.faceNodes = faceNodes
+    #     self.interiorNodes = interiorNodes
+
+

+[docs]
+    @abstractmethod
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        """
+        Method to be defined to calculate shape function values
+        and gradients given a list of nodal points (usually the vertexNodes)
+        and a list of evaluation points (usually the quadrature points).
+        """
+        pass

+

+
+
+    # TODO figure out how to rope in quadrature rules into this class
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/hex8_element.html b/_modules/pancax/fem/elements/hex8_element.html new file mode 100644 index 0000000..34c1348 --- /dev/null +++ b/_modules/pancax/fem/elements/hex8_element.html @@ -0,0 +1,222 @@ + + + + + + + + pancax.fem.elements.hex8_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.hex8_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.hex8_element

+from .base_element import BaseElement, ShapeFunctions
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Hex8Element(BaseElement):
+    elementType = "hex8"
+    degree = 1
+    coordinates = jnp.array(
+        [[-1.0, -1.0, -1.0],
+         [ 1.0, -1.0, -1.0],
+         [ 1.0,  1.0, -1.0],
+         [-1.0,  1.0, -1.0],
+         [-1.0, -1.0, 1.0],
+         [ 1.0, -1.0, 1.0],
+         [ 1.0,  1.0, 1.0],
+         [-1.0,  1.0, 1.0]]
+    )
+    vertexNodes = jnp.arange(8)
+    faceNodes = jnp.array(
+        [[0, 1, 5, 6],
+         [1, 2, 6, 5],
+         [2, 3, 7, 6],
+         [0, 4, 7, 3],
+         [0, 3, 2, 1],
+         [4, 5, 6, 7]],
+        dtype=jnp.int32
+    )
+    interiorNodes = None
+
+

+[docs]
+    def __init__(self):
+        pass

+
+
+    # TODO what to do about NodalPoints?
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        def shape_function_values(xi):
+            N = (1. / 8.) * jnp.array([
+                (1. - xi[0]) * (1. - xi[1]) * (1. - xi[2]),
+                (1. + xi[0]) * (1. - xi[1]) * (1. - xi[2]),
+                (1. + xi[0]) * (1. + xi[1]) * (1. - xi[2]),
+                (1. - xi[0]) * (1. + xi[1]) * (1. - xi[2]),
+                (1. - xi[0]) * (1. - xi[1]) * (1. + xi[2]),
+                (1. + xi[0]) * (1. - xi[1]) * (1. + xi[2]),
+                (1. + xi[0]) * (1. + xi[1]) * (1. + xi[2]),
+                (1. - xi[0]) * (1. + xi[1]) * (1. + xi[2])]
+            )
+            return N
+        
+        def shape_function_gradients(xi):
+            grad_N_xi = (1. / 8.) * jnp.array(
+                [
+                    [
+                        -(1. - xi[1]) * (1. - xi[2]), 
+                        -(1. - xi[0]) * (1. - xi[2]), 
+                        -(1. - xi[0]) * (1. - xi[1])
+                    ],
+                    [
+                         (1. - xi[1]) * (1. - xi[2]), 
+                        -(1. + xi[0]) * (1. - xi[2]),
+                        -(1. + xi[0]) * (1. - xi[1])
+                    ],
+                    [
+                         (1. + xi[1]) * (1. - xi[2]), 
+                         (1. + xi[0]) * (1. - xi[2]),
+                        -(1. + xi[0]) * (1. + xi[1]) 
+                    ],
+                    [
+                        -(1. + xi[1]) * (1. - xi[2]), 
+                         (1. - xi[0]) * (1. - xi[2]),
+                        -(1. - xi[0]) * (1. + xi[1])
+                    ],
+                    # positive z now
+                    [
+                        -(1. - xi[1]) * (1. + xi[2]), 
+                        -(1. - xi[0]) * (1. + xi[2]), 
+                         (1. - xi[0]) * (1. - xi[1])
+                    ],
+                    [
+                         (1. - xi[1]) * (1. + xi[2]), 
+                        -(1. + xi[0]) * (1. + xi[2]),
+                         (1. + xi[0]) * (1. - xi[1])
+                    ],
+                    [
+                         (1. + xi[1]) * (1. + xi[2]), 
+                         (1. + xi[0]) * (1. + xi[2]),
+                         (1. + xi[0]) * (1. + xi[1]) 
+                    ],
+                    [
+                        -(1. + xi[1]) * (1. + xi[2]), 
+                         (1. - xi[0]) * (1. + xi[2]),
+                         (1. - xi[0]) * (1. + xi[1])
+                    ]
+                 ]
+            )
+            return grad_N_xi
+
+        Ns = jax.vmap(shape_function_values, in_axes=(0,))(evaluationPoints)
+        dNs = jax.vmap(shape_function_gradients, in_axes=(0,))(evaluationPoints)
+        return ShapeFunctions(Ns, dNs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/line_element.html b/_modules/pancax/fem/elements/line_element.html new file mode 100644 index 0000000..a4f5ca3 --- /dev/null +++ b/_modules/pancax/fem/elements/line_element.html @@ -0,0 +1,150 @@ + + + + + + + + pancax.fem.elements.line_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.line_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.line_element

+from .base_element import BaseElement, ShapeFunctions
+from .base_element import get_lobatto_nodes_1d, vander1d
+from jaxtyping import Array, Float
+import jax.numpy as jnp
+import numpy as np
+
+
+

+[docs]
+class LineElement(BaseElement):
+    elementType = "line"
+    degree: int
+    coordinates: Float[Array, "nn nd"]
+    vertexNodes: any
+    faceNodes = None
+    interiorNodes: any
+
+

+[docs]
+    def __init__(self, degree):
+        self.degree = degree
+        self.coordinates = get_lobatto_nodes_1d(degree)
+        self.vertexNodes = jnp.array([0, degree], dtype=jnp.int32)
+        self.interiorNodes = jnp.arange(1, degree, dtype=jnp.int32)

+
+
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        A,_ = vander1d(nodalPoints, self.degree)
+        nf, nfx = vander1d(evaluationPoints, self.degree)
+        shape = np.linalg.solve(A.T, nf.T)
+        dshape = np.linalg.solve(A.T, nfx.T)
+        return ShapeFunctions(jnp.array(shape), jnp.array(dshape))

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/quad4_element.html b/_modules/pancax/fem/elements/quad4_element.html new file mode 100644 index 0000000..8521d5c --- /dev/null +++ b/_modules/pancax/fem/elements/quad4_element.html @@ -0,0 +1,173 @@ + + + + + + + + pancax.fem.elements.quad4_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.quad4_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.quad4_element

+from .base_element import BaseElement, ShapeFunctions
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Quad4Element(BaseElement):
+    elementType = "quad4"
+    degree = 1
+    coordinates = jnp.array(
+        [[-1.0, -1.0],
+         [ 1.0, -1.0],
+         [ 1.0,  1.0],
+         [-1.0,  1.0]]
+    )
+    vertexNodes = jnp.arange(3)
+    faceNodes = jnp.array(
+        [[0, 1],
+         [1, 2],
+         [2, 3],
+         [3, 0]],
+        dtype=jnp.int32
+    )
+    interiorNodes = None
+
+

+[docs]
+    def __init__(self):
+        pass

+
+
+    # TODO what to do about NodalPoints?
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        def shape_function_values(xi):
+            N = (1. / 4.) * jnp.array([
+                (1. - xi[0]) * (1. - xi[1]),
+                (1. + xi[0]) * (1. - xi[1]),
+                (1. + xi[0]) * (1. + xi[1]),
+                (1. - xi[0]) * (1. + xi[1])]
+            )
+            return N
+        
+        def shape_function_gradients(xi):
+            grad_N_xi = (1. / 4.) * jnp.array(
+                [[-(1. - xi[1]), -(1. - xi[0])],
+                 [(1. - xi[1]), -(1. + xi[0])],
+                 [(1. + xi[1]), (1. + xi[0])],
+                 [-(1. + xi[1]), (1. - xi[0])]]
+            )
+            return grad_N_xi
+
+        Ns = jax.vmap(shape_function_values, in_axes=(0,))(evaluationPoints)
+        dNs = jax.vmap(shape_function_gradients, in_axes=(0,))(evaluationPoints)
+        return ShapeFunctions(Ns, dNs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/quad9_element.html b/_modules/pancax/fem/elements/quad9_element.html new file mode 100644 index 0000000..ce22bd9 --- /dev/null +++ b/_modules/pancax/fem/elements/quad9_element.html @@ -0,0 +1,194 @@ + + + + + + + + pancax.fem.elements.quad9_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.quad9_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.quad9_element

+from .base_element import BaseElement, ShapeFunctions
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Quad9Element(BaseElement):
+    elementType = "quad9"
+    degree = 2
+    coordinates = jnp.array(
+        [[-1.0, -1.0],
+         [ 1.0, -1.0],
+         [ 1.0,  1.0],
+         [-1.0,  1.0],
+         [ 0.0, -1.0],
+         [ 1.0,  0.0],
+         [ 0.0,  1.0],
+         [-1.0,  0.0],
+         [ 0.0,  0.0]]
+
+    )
+    vertexNodes = jnp.arange(8)
+    faceNodes = jnp.array(
+        [[0, 4, 1],
+         [1, 5, 2],
+         [2, 6, 3],
+         [3, 7, 0]],
+        dtype=jnp.int32
+    )
+    interiorNodes = jnp.array([8], dtype=jnp.int32)
+
+

+[docs]
+    def __init__(self):
+        pass

+
+
+    # TODO what to do about NodalPoints?
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        def shape_function_values(xi_points):
+            xi, eta = xi_points[0], xi_points[1]
+            xi_sq, eta_sq = jnp.power(xi_points[0], 2), jnp.power(xi_points[1], 2)
+
+            N = jnp.array([
+                0.25 * (xi_sq - xi) * (eta_sq - eta),
+                0.25 * (xi_sq + xi) * (eta_sq - eta),
+                0.25 * (xi_sq + xi) * (eta_sq + eta),
+                0.25 * (xi_sq - xi) * (eta_sq + eta),
+                0.5 * (eta_sq - eta) * (1. - xi_sq),
+                0.5 * (xi_sq + xi) * (1. - eta_sq),
+                0.5 * (eta_sq + eta) * (1. - xi_sq),
+                0.5 * (xi_sq - xi) * (1. - eta_sq),
+                (1. - xi_sq) * (1. - eta_sq)
+            ])
+            return N
+
+        
+        def shape_function_gradients(xi_points):
+            xi, eta = xi_points[0], xi_points[1]
+            xi_sq, eta_sq = jnp.power(xi_points[0], 2), jnp.power(xi_points[1], 2)
+            grad_N_xi = jnp.array([[0.25 * (2. * xi - 1.) * (eta_sq - eta), 0.25 * (xi_sq - xi) * (2. * eta - 1.)],
+                                [0.25 * (2. * xi + 1.) * (eta_sq - eta), 0.25 * (xi_sq + xi) * (2. * eta - 1.)],
+                                [0.25 * (2. * xi + 1.) * (eta_sq + eta), 0.25 * (xi_sq + xi) * (2. * eta + 1.)],
+                                [0.25 * (2. * xi - 1.) * (eta_sq + eta), 0.25 * (xi_sq - xi) * (2. * eta + 1.)],
+                                [0.5 * (eta_sq - eta) * (-2. * xi), 0.5 * (2. * eta - 1.) * (1. - xi_sq)],
+                                [0.5 * (2. * xi + 1.) * (1. - eta_sq), 0.5 * (xi_sq + xi) * (-2. * eta)],
+                                [0.5 * (eta_sq + eta) * (-2. * xi), 0.5 * (2. * eta + 1.) * (1. - xi_sq)],
+                                [0.5 * (2. * xi - 1.) * (1. - eta_sq), 0.5 * (xi_sq - xi) * (-2. * eta)],
+                                [-2. * xi * (1. - eta_sq), -2. * eta * (1. - xi_sq)]])
+            return grad_N_xi
+
+
+        Ns = jax.vmap(shape_function_values, in_axes=(0,))(evaluationPoints)
+        dNs = jax.vmap(shape_function_gradients, in_axes=(0,))(evaluationPoints)
+        return ShapeFunctions(Ns, dNs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/simplex_tri_element.html b/_modules/pancax/fem/elements/simplex_tri_element.html new file mode 100644 index 0000000..b5c8f4a --- /dev/null +++ b/_modules/pancax/fem/elements/simplex_tri_element.html @@ -0,0 +1,171 @@ + + + + + + + + pancax.fem.elements.simplex_tri_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.simplex_tri_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.simplex_tri_element

+from .base_element import BaseElement, ShapeFunctions
+from .base_element import get_lobatto_nodes_1d, vander2d
+from jaxtyping import Array, Float
+import jax.numpy as jnp
+import numpy as np
+
+
+

+[docs]
+class SimplexTriElement(BaseElement):
+    elementType = "simplex tri"
+    degree: int
+    coordinates: Float[Array, "nn nd"]
+    vertexNodes: any
+    faceNodes: any
+    interiorNodes: any
+
+

+[docs]
+    def __init__(self, degree):
+        self.degree = degree
+
+        lobattoPoints = get_lobatto_nodes_1d(degree)
+        nPoints = int((degree + 1)*(degree + 2)/2)
+        points = np.zeros((nPoints, 2))
+        point = 0
+        for i in range(degree):
+            for j in range(degree + 1 - i):
+                k = degree - i - j
+                points[point, 0] = (1.0 + 2.0*lobattoPoints[k] - lobattoPoints[j] - lobattoPoints[i])/3.0
+                points[point, 1] = (1.0 + 2.0*lobattoPoints[j] - lobattoPoints[i] - lobattoPoints[k])/3.0
+                point += 1
+        self.coordinates = jnp.asarray(points)
+
+        self.vertexNodes = jnp.array([0, degree, nPoints - 1], dtype=jnp.int32)
+
+        ii = np.arange(degree + 1)
+        jj = np.cumsum(np.flip(ii)) + ii
+        kk = np.flip(jj) - ii
+        self.faceNodes = jnp.array((ii,jj,kk), dtype=jnp.int32)
+
+        interiorNodes = [i for i in range(nPoints) if i not in self.faceNodes.ravel()]
+        self.interiorNodes = np.array(interiorNodes, dtype=np.int32)

+
+
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        A, _, _ = vander2d(nodalPoints, self.degree)
+        nf, nfx, nfy = vander2d(evaluationPoints, self.degree)
+        shapes = np.linalg.solve(A.T, nf.T).T
+        dshapes = np.zeros(shapes.shape + (2,)) # shape is (nQuadPoints, nNodes, 2)
+        dshapes[:, :, 0] = np.linalg.solve(A.T, nfx.T).T
+        dshapes[:, :, 1] = np.linalg.solve(A.T, nfy.T).T
+        return ShapeFunctions(jnp.asarray(shapes), jnp.asarray(dshapes))

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/tet10_element.html b/_modules/pancax/fem/elements/tet10_element.html new file mode 100644 index 0000000..d0b4418 --- /dev/null +++ b/_modules/pancax/fem/elements/tet10_element.html @@ -0,0 +1,197 @@ + + + + + + + + pancax.fem.elements.tet10_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.tet10_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.tet10_element

+from .base_element import BaseElement, ShapeFunctions
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Tet10Element(BaseElement):
+    elementType = "tet10"
+    degree = 2
+    coordinates = jnp.array([
+        [0., 0., 0.],
+        [1., 0., 0.],
+        [0., 1., 0.],
+        [0., 0., 1.],
+        [0.5, 0., 0.],
+        [0.5, 0.5, 0.],
+        [0., 0.5, 0.],
+        [0., 0., 0.5],
+        [0.5, 0., 0.5],
+        [0., 0.5, 0.5]
+    ])
+    vertexNodes = jnp.arange(10)
+    faceNodes = jnp.array([
+        [0, 4, 1, 8, 3, 7],
+        [1, 5, 2, 9, 3, 7],
+        [0, 7, 3, 9, 2, 6],
+        [0, 6, 2, 5, 1, 4]
+    ])
+    interiorNodes = None
+
+

+[docs]
+    def __init__(self):
+        pass

+
+
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        def shape_function_values(xi):
+            t0 = 1 - xi[0] - xi[1] - xi[2]
+            t1 = xi[0]
+            t2 = xi[1]
+            t3 = xi[2]
+            N = jnp.array([
+                t0 * (2 * t0 - 1),
+                t1 * (2 * t1 - 1),
+                t2 * (2 * t2 - 1),
+                t3 * (2 * t3 - 1),
+                4 * t0 * t1,
+                4 * t1 * t2,
+                4 * t2 * t0,
+                4 * t0 * t3,
+                4 * t1 * t3,
+                4 * t2 * t3
+            ])
+            return N
+        
+        def shape_function_gradients(xi):
+            t0 = 1 - xi[0] - xi[1] - xi[2]
+            t1 = xi[0]
+            t2 = xi[1]
+            t3 = xi[2]
+            grad_N_xi = jnp.array([
+                [1 - 4 * t0, 1 - 4 * t0, 1 - 4 * t0],
+                [4 * t1 - 1, 0, 0],
+                [0, 4 * t2 - 1, 0],
+                [0, 0, 4 * t3 - 1],
+                [4 * (t0-t1), -4 * t1, -4 * t1],
+                [4 * t2, 4 * t1, 0],
+                [-4 * t2, 4 * (t0 - t2), -4 * t2],
+                [-4 * t3, -4 * t3, 4 * (t0 - t3)],
+                [4 * t3, 0, 4 * t1],
+                [0, 4 * t3, 4 * t2]
+            ])
+            return grad_N_xi
+
+        Ns = jax.vmap(shape_function_values, in_axes=(0,))(evaluationPoints)
+        dNs = jax.vmap(shape_function_gradients, in_axes=(0,))(evaluationPoints)
+        return ShapeFunctions(Ns, dNs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/elements/tet4_element.html b/_modules/pancax/fem/elements/tet4_element.html new file mode 100644 index 0000000..8e48ec5 --- /dev/null +++ b/_modules/pancax/fem/elements/tet4_element.html @@ -0,0 +1,171 @@ + + + + + + + + pancax.fem.elements.tet4_element — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.elements.tet4_element
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.elements.tet4_element

+from .base_element import BaseElement, ShapeFunctions
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class Tet4Element(BaseElement):
+    elementType = "tet4"
+    degree = 1
+    coordinates = jnp.array([
+        [0., 0., 0.],
+        [1., 0., 0.],
+        [0., 1., 0.],
+        [0., 0., 1.]
+    ])
+    vertexNodes = jnp.arange(4)
+    faceNodes = jnp.array([
+        [0, 1, 3],
+        [1, 2, 3],
+        [0, 3, 2],
+        [0, 2, 1]
+    ])
+    interiorNodes = None
+
+

+[docs]
+    def __init__(self):
+        pass

+
+
+

+[docs]
+    def compute_shapes(self, nodalPoints, evaluationPoints):
+        def shape_function_values(xi):
+            N = jnp.array([
+                1. - xi[0] - xi[1] - xi[2],
+                xi[0],
+                xi[1],
+                xi[2]
+            ])
+            return N
+        
+        def shape_function_gradients(xi):
+            grad_N_xi = jnp.array([
+                [-1., -1., -1.],
+                [1., 0., 0.],
+                [0., 1., 0.],
+                [0., 0., 1.]
+            ])
+            return grad_N_xi
+
+        Ns = jax.vmap(shape_function_values, in_axes=(0,))(evaluationPoints)
+        dNs = jax.vmap(shape_function_gradients, in_axes=(0,))(evaluationPoints)
+        return ShapeFunctions(Ns, dNs)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/function_space.html b/_modules/pancax/fem/function_space.html new file mode 100644 index 0000000..588beee --- /dev/null +++ b/_modules/pancax/fem/function_space.html @@ -0,0 +1,611 @@ + + + + + + + + pancax.fem.function_space — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.function_space

+from jaxtyping import Array, Float, Int
+from .mesh import Mesh
+from pancax.fem.quadrature_rules import QuadratureRule
+from pancax.fem.elements.base_element import ShapeFunctions
+from pancax.timer import Timer
+import equinox as eqx
+import jax
+import jax.numpy as np
+
+
+# TODO need to do checks on inputs to make sure they're compatable
+

+[docs]
+class NonAllocatedFunctionSpace(eqx.Module):
+    quadrature_rule: QuadratureRule
+    shape_functions: ShapeFunctions
+
+

+[docs]
+    def __init__(self, mesh: Mesh, q_rule: QuadratureRule) -> None:
+        with Timer("NonAllocatedFunctionSpace.__init__"):
+            self.quadrature_rule = q_rule
+            self.shape_functions = mesh.parentElement.compute_shapes(
+                mesh.parentElement.coordinates, q_rule.xigauss
+            )

+
+
+

+[docs]
+    def compute_field_gradient(self, u, X):
+        """
+        Takes in element level coordinates X and field u
+        """
+        grad_Ns = self.shape_function_gradients(X)
+        return jax.vmap(lambda u, grad_N: u.T @ grad_N, in_axes=(None, 0))(u, grad_Ns)

+
+
+

+[docs]
+    def evaluate_on_element(self, U, X, state, dt, props, func):
+        """
+        Takes in element level field, coordinates, states, etc.
+        and evaluates the function func
+        """
+        Ns = self.shape_function_values(X)
+        grad_Ns = self.shape_function_gradients(X)
+
+        u_qs = jax.vmap(lambda u, N: u.T @ N, in_axes=(None, 0))(U, Ns)
+        grad_u_qs = jax.vmap(lambda u, grad_N: u.T @ grad_N, in_axes=(None, 0))(U, grad_Ns)
+        X_qs = jax.vmap(lambda X, N: X.T @ N, in_axes=(None, 0))(X, Ns)
+        func_vals = jax.vmap(func, in_axes=(0, 0, 0, None, 0, None))(
+            u_qs, grad_u_qs, state, props, X_qs, dt
+        )
+        return func_vals

+
+
+

+[docs]
+    def integrate_on_element(self, U, X, state, dt, props, func):
+        func_vals = self.evaluate_on_element(U, X, state, dt, props, func)
+        JxWs = self.JxWs(X)
+        return np.dot(JxWs, func_vals)

+
+
+

+[docs]
+    def integrate_on_elements(self, U, X, state, dt, props, func):
+        el_vals = jax.vmap(self.integrate_on_element, in_axes=(0, 0, 0, None, None, None))(
+            U, X, state, dt, props, func
+        )
+        return np.sum(el_vals)

+
+
+

+[docs]
+    def JxWs(self, X: Float[Array, "nn nd"]) -> Float[Array, "nq"]:
+        Js = jax.vmap(lambda x, dN: (x.T @ dN).T, in_axes=(None, 0))(X, self.shape_functions.gradients)
+        return jax.vmap(lambda J, w: np.linalg.det(J) * w, in_axes=(0, 0))(Js, self.quadrature_rule.wgauss)

+
+
+

+[docs]
+    def shape_function_values(self, X: Float[Array, "nn nd"]) -> Float[Array, "nq nnpe"]:
+        return self.shape_functions.values

+
+    
+

+[docs]
+    def shape_function_gradients(self, X: Float[Array, "nn nd"]) -> Float[Array, "nq nnpe nd"]:
+        Js = jax.vmap(lambda x, dN: (x.T @ dN).T, in_axes=(None, 0))(X, self.shape_functions.gradients)
+        Jinvs = jax.vmap(lambda J: np.linalg.inv(J), in_axes=(0,))(Js)
+        return jax.vmap(lambda Jinv, dN: (Jinv @ dN.T).T, in_axes=(0, 0))(Jinvs, self.shape_functions.gradients)

+

+
+
+
+

+[docs]
+class FunctionSpace(eqx.Module):
+    """
+    Data needed for calculus on functions in the discrete function space.
+
+    In describing the shape of the attributes, ``ne`` is the number of
+    elements in the mesh, ``nqpe`` is the number of quadrature points per
+    element, ``npe`` is the number of nodes per element, and ``nd`` is the
+    spatial dimension of the domain.
+
+    :param shapes: Shape function values on each element, shape (ne, nqpe, npe)
+    :param vols: Volume attributed to each quadrature point. That is, the 
+        quadrature weight (on the parameteric element domain) multiplied by
+        the Jacobian determinant of the map from the parent element to the
+        element in the domain. Shape (ne, nqpe).
+    :param shapeGrads: Derivatives of the shape functions with respect to the
+        spatial coordinates of the domain. Shape (ne, nqpe, npe, nd).
+    :param mesh: The ``Mesh`` object of the domain.
+    :param quadratureRule: The ``QuadratureRule`` on which to sample the shape 
+        functions.
+    :param isAxisymmetric: boolean indicating if the function space data are 
+        axisymmetric.
+    """
+    shapes: Float[Array, "ne nqpe npe"]
+    vols: Float[Array, "ne nqpe"]
+    shapeGrads: Float[Array, "ne nqpe npe nd"]
+    # mesh: any
+    conns: Int[Array, "ne nnpe"]
+    quadratureRule: QuadratureRule
+    isAxisymmetric: bool

+
+
+
+

+[docs]
+def construct_function_space(mesh, quadratureRule, mode2D='cartesian'):
+    """Construct a discrete function space.
+
+    Parameters
+    ----------
+    :param mesh: The mesh of the domain.
+    :param quadratureRule: The quadrature rule to be used for integrating on the
+    domain.
+    :param mode2D: A string indicating how the 2D domain is interpreted for
+    integration. Valid values are ``cartesian`` and ``axisymmetric``.
+    Axisymetric mode will include the factor of 2*pi*r in the ``vols``
+    attribute.
+
+    Returns
+    -------
+    The ``FunctionSpace`` object.
+    """
+    with Timer('construct_function_space'):
+        # shapeOnRef = interpolants.compute_shapes(mesh.parentElement, quadratureRule.xigauss)
+        shapeOnRef = mesh.parentElement.compute_shapes(mesh.parentElement.coordinates, quadratureRule.xigauss)
+        return construct_function_space_from_parent_element(mesh, shapeOnRef, quadratureRule, mode2D)

+
+
+
+

+[docs]
+def construct_function_space_from_parent_element(mesh, shapeOnRef, quadratureRule, mode2D='cartesian'):
+    """
+    Construct a function space with precomputed shape function data on the parent element.
+
+    This version of the function space constructor is Jax-transformable,
+    and in particular can be jitted. The computation of the shape function
+    values and derivatives on the parent element is not transformable in
+    general. However, the mapping of the shape function data to the elements in
+    the mesh is transformable. One can precompute the parent element shape
+    functions once and for all, and then use this special factory function to
+    construct the function space and avoid the non-transformable part of the
+    operation. The primary use case is for shape sensitivities: the coordinates
+    of the mesh change, and we want Jax to pick up the sensitivities of the
+    shape function derivatives in space to the coordinate changes
+    (which occurs through the mapping from the parent element to the spatial
+    domain).
+
+    Parameters
+    ----------
+    :param mesh: The mesh of the domain.
+    :param shapeOnRef: A tuple of the shape function values and gradients on the
+    parent element, evaluated at the quadrature points. The caller must
+    take care to ensure the shape functions are evaluated at the same
+    points as contained in the ``quadratureRule`` parameter.
+    :param quadratureRule: The quadrature rule to be used for integrating on the
+        domain.
+    :param mode2D: A string indicating how the 2D domain is interpreted for
+    integration. See the default factory function for details.
+
+    Returns
+    -------
+    The ``FunctionSpace`` object.
+    """
+
+    shapes = jax.vmap(lambda elConns, elShape: elShape, (0, None))(mesh.conns, shapeOnRef.values)
+
+    shapeGrads = jax.vmap(map_element_shape_grads, (None, 0, None, None))(
+        mesh.coords, mesh.conns, mesh.parentElement, shapeOnRef.gradients
+    )
+
+    if mode2D == 'cartesian':
+        el_vols = compute_element_volumes
+        isAxisymmetric = False
+    elif mode2D == 'axisymmetric':
+        el_vols = compute_element_volumes_axisymmetric
+        isAxisymmetric = True
+    vols = jax.vmap(el_vols, (None, 0, None, None, None, None))(
+        mesh.coords, mesh.conns, mesh.parentElement, shapeOnRef.values, shapeOnRef.gradients, quadratureRule.wgauss
+    )
+
+    # return FunctionSpace(shapes, vols, shapeGrads, mesh, quadratureRule, isAxisymmetric)
+    return FunctionSpace(shapes, vols, shapeGrads, mesh.conns, quadratureRule, isAxisymmetric)

+
+
+
+

+[docs]
+def map_element_shape_grads(coordField, nodeOrdinals, parentElement, shapeGradients):
+    # coords here should be 3 x 2
+    # shapegrads shoudl be 3 x 2
+    # need J to be 2 x 2 but be careful about transpose
+    # below from Cthonios
+    # J    = (X_el * ∇N_ξ)'
+    # J_inv = inv(J)
+    # ∇N_X = (J_inv * ∇N_ξ')'
+    Xn = coordField.take(nodeOrdinals,0)
+    Js = jax.vmap(lambda x, dN: (x.T @ dN).T, in_axes=(None, 0))(Xn, shapeGradients)
+    Jinvs = jax.vmap(lambda J: np.linalg.inv(J), in_axes=(0,))(Js)
+    return jax.vmap(lambda Jinv, dN: (Jinv @ dN.T).T, in_axes=(0, 0))(Jinvs, shapeGradients)

+
+
+
+

+[docs]
+def compute_element_volumes(coordField, nodeOrdinals, parentElement, shapes, shapeGradients, weights):
+    Xn = coordField.take(nodeOrdinals,0)
+    Js = jax.vmap(lambda x, dN: (x.T @ dN).T, in_axes=(None, 0))(Xn, shapeGradients)
+    return jax.vmap(lambda J, w: np.linalg.det(J) * w, in_axes=(0, 0))(Js, weights)

+
+
+
+# TODO make this work for arbitrary elements
+# currently not used for any PINN stuff
+

+[docs]
+def compute_element_volumes_axisymmetric(coordField, nodeOrdinals, parentElement, shapes, shapeGradients, weights):
+    vols = compute_element_volumes(coordField, nodeOrdinals, parentElement, shapes, weights)
+    Xn = coordField.take(nodeOrdinals,0)
+    Rs = shapes@Xn[:,0]
+    return 2*np.pi*Rs*vols

+
+
+
+

+[docs]
+def default_modify_element_gradient(elemGrads, elemShapes, elemVols, elemNodalDisps, elemNodalCoords):
+    return elemGrads

+
+
+
+

+[docs]
+def compute_field_gradient(functionSpace, nodalField, nodalCoords, modify_element_gradient=default_modify_element_gradient):
+    return jax.vmap(compute_element_field_gradient, (None,None,0,0,0,0,None))(nodalField, nodalCoords, functionSpace.shapes, functionSpace.shapeGrads, functionSpace.vols, functionSpace.conns, modify_element_gradient)

+
+
+
+

+[docs]
+def interpolate_to_points(functionSpace, nodalField):
+    # return jax.vmap(interpolate_to_element_points, (None, 0, 0))(nodalField, functionSpace.shapes, functionSpace.mesh.conns)
+    return jax.vmap(interpolate_to_element_points, (None, 0, 0))(nodalField, functionSpace.shapes, functionSpace.conns)

+
+
+
+
+

+[docs]
+def integrate_over_block(functionSpace, U, X, stateVars, props, dt, func, block,
+                         *params, modify_element_gradient=default_modify_element_gradient):
+    """
+    Integrates a density function over a block of the mesh.
+
+    :param functionSpace: Function space object to do the integration with.
+    :param U: The vector of dofs for the primal field in the functional.
+    :param X: Nodal coordinates
+    :param stateVars: Internal state variable array.
+    :param dt: Current time increment
+    :param func: Lagrangian density function to integrate, Must have the signature
+        ``func(u, dudx, q, x, *params) -> scalar``, where ``u`` is the primal field, ``q`` is the
+        value of the internal variables, ``x`` is the current point coordinates, and ``*params`` is
+        a variadic set of additional parameters, which correspond to the ``*params`` argument.
+        block: Group of elements to integrate over. This is an array of element indices. For
+        performance, the elements within the block should be numbered consecutively.
+    :param modify_element_gradient: Optional function that modifies the gradient at the element level.
+        This can be to set the particular 2D mode, and additionally to enforce volume averaging
+        on the gradient operator. This is a keyword-only argument.
+
+    Returns
+    A scalar value for the integral of the density functional ``func`` integrated over the
+    block of elements.
+    """
+    # below breaks the sphinx doc stuff
+    # :param *params: Optional parameter fields to pass into Lagrangian density function. These are 
+    
+    
+    vals = evaluate_on_block(functionSpace, U, X, stateVars, props, dt, func, block, *params, modify_element_gradient=modify_element_gradient)
+    return np.dot(vals.ravel(), functionSpace.vols[block].ravel())

+
+
+
+# def evaluate_on_block(functionSpace, U, stateVars, dt, props, func, block,
+#                       *params, modify_element_gradient=default_modify_element_gradient):
+

+[docs]
+def evaluate_on_block(functionSpace, U, X, stateVars, dt, props, func, block,
+                      *params, modify_element_gradient=default_modify_element_gradient):
+    """Evaluates a density function at every quadrature point in a block of the mesh.
+
+    :param functionSpace: Function space object to do the evaluation with.
+    :param U: The vector of dofs for the primal field in the functional.
+    :param X: Nodal coordinates
+    :param stateVars: Internal state variable array.
+    :param dt: Current time increment
+    :param func: Lagrangian density function to evaluate, Must have the signature
+        ```func(u, dudx, q, x, *params) -> scalar```, where ```u``` is the primal field, ```q``` is the 
+        value of the internal variables, ```x``` is the current point coordinates, and ```*params``` is 
+        a variadic set of additional parameters, which correspond to the ```*params``` argument.
+    :param block: Group of elements to evaluate over. This is an array of element indices. For 
+        performance, the elements within the block should be numbered consecutively.
+    
+    :param modify_element_gradient: Optional function that modifies the gradient at the element level. 
+        This can be to set the particular 2D mode, and additionally to enforce volume averaging 
+        on the gradient operator. This is a keyword-only argument.
+
+    Returns 
+    An array of shape (numElements, numQuadPtsPerElement) that contains the scalar values of the 
+    density functional ```func``` at every quadrature point in the block.
+    """
+    # below breaks sphinx doc stuff
+    # :param *params: Optional parameter fields to pass into Lagrangian density function. These are 
+    #     represented as a single value per element. 
+    fs = functionSpace
+    compute_elem_values = jax.vmap(evaluate_on_element, (None, None, 0, None, None, 0, 0, 0, 0, None, None, *tuple(0 for p in params)))
+    
+    blockValues = compute_elem_values(U, X, stateVars[block], props, dt, fs.shapes[block],
+                                      fs.shapeGrads[block], fs.vols[block],
+                                      fs.conns[block], func, modify_element_gradient, *params)
+    return blockValues

+
+
+
+

+[docs]
+def integrate_element_from_local_field(elemNodalField, elemNodalCoords, elemStates, dt, elemShapes, elemShapeGrads, elemVols, func, modify_element_gradient=default_modify_element_gradient):
+    """
+    Integrate over element with element nodal field as input.
+    This allows element residuals and element stiffness matrices to computed.
+    """
+    elemVals = jax.vmap(interpolate_to_point, (None,0))(elemNodalField, elemShapes)
+    elemGrads = jax.vmap(compute_quadrature_point_field_gradient, (None,0))(elemNodalField, elemShapeGrads)
+    elemGrads = modify_element_gradient(elemGrads, elemShapes, elemVols, elemNodalField, elemNodalCoords)
+    elemPoints = jax.vmap(interpolate_to_point, (None,0))(elemNodalCoords, elemShapes)
+    fVals = jax.vmap(func, (0, 0, 0, 0, None))(elemVals, elemGrads, elemStates, elemPoints, dt)
+    return np.dot(fVals, elemVols)

+
+
+
+

+[docs]
+def compute_element_field_gradient(U, coords, elemShapes, elemShapeGrads, elemVols, elemConnectivity, modify_element_gradient):
+    elemNodalDisps = U[elemConnectivity]
+    elemGrads = jax.vmap(compute_quadrature_point_field_gradient, (None, 0))(elemNodalDisps, elemShapeGrads)
+    elemNodalCoords = coords[elemConnectivity]
+    elemGrads = modify_element_gradient(elemGrads, elemShapes, elemVols, elemNodalDisps, elemNodalCoords)
+    return elemGrads

+
+
+
+

+[docs]
+def compute_quadrature_point_field_gradient(u, shapeGrad):
+    dg = np.tensordot(u, shapeGrad, axes=[0,0])
+    return dg

+
+
+
+

+[docs]
+def interpolate_to_point(elementNodalValues, shape):
+    return np.dot(shape, elementNodalValues)

+
+
+
+

+[docs]
+def interpolate_to_element_points(U, elemShapes, elemConnectivity):
+    elemU = U[elemConnectivity]
+    return jax.vmap(interpolate_to_point, (None, 0))(elemU, elemShapes)

+
+
+
+

+[docs]
+def integrate_element(U, coords, elemStates, elemShapes, elemShapeGrads, elemVols, elemConn, func, modify_element_gradient):
+    elemVals = interpolate_to_element_points(U, elemShapes, elemConn)
+    elemGrads = compute_element_field_gradient(U, coords, elemShapes, elemShapeGrads, elemVols, elemConn, modify_element_gradient)
+    elemXs = interpolate_to_element_points(coords, elemShapes, elemConn)
+    fVals = jax.vmap(func)(elemVals, elemGrads, elemStates, elemXs)
+    return np.dot(fVals, elemVols)

+
+
+
+

+[docs]
+def evaluate_on_element(U, coords, elemStates, props, dt, elemShapes, elemShapeGrads, elemVols, elemConn, kernelFunc, modify_element_gradient, *params):
+    elemVals = interpolate_to_element_points(U, elemShapes, elemConn)
+    elemGrads = compute_element_field_gradient(U, coords, elemShapes, elemShapeGrads, elemVols, elemConn, modify_element_gradient)
+    elemXs = interpolate_to_element_points(coords, elemShapes, elemConn)
+    vmapArgs = 0, 0, 0, None, 0, None, *tuple(None for p in params)
+    fVals = jax.vmap(kernelFunc, vmapArgs)(elemVals, elemGrads, elemStates, props, elemXs, dt, *params)
+    return fVals

+
+
+
+

+[docs]
+def project_quadrature_field_to_element_field(functionSpace, quadField):
+    return jax.vmap(average_quadrature_field_over_element)(quadField, functionSpace.vols)

+
+
+
+

+[docs]
+def average_quadrature_field_over_element(elemQPData, vols):
+    S = np.tensordot(vols, elemQPData, axes=[0,0])
+    elVol = np.sum(vols)
+    return S/elVol

+
+
+
+

+[docs]
+def get_nodal_values_on_edge(functionSpace, nodalField, edge):
+    """
+    Get nodal values of a field on an element edge.
+
+    :param functionSpace: a FunctionSpace object
+    :param nodalField: The nodal vector defined over the mesh (shape is number of
+        nodes by number of field components)
+    :param edge: tuple containing the element number containing the edge and the
+        permutation (0, 1, or 2) of the edge within the triangle
+    """
+    edgeNodes = functionSpace.mesh.parentElement.faceNodes[edge[1], :]
+    nodes = functionSpace.mesh.conns[edge[0], edgeNodes]
+    return nodalField[nodes]

+
+
+
+

+[docs]
+def interpolate_nodal_field_on_edge(functionSpace, U, interpolationPoints, edge):
+    """
+    Interpolate a nodal field to specified points on an element edge.
+
+    :param functionSpace: a FunctionSpace object
+    :param U: the nodal values array
+    :param interpolationPoints: coordinates of points (in the 1D parametric space) to
+        interpolate to
+    :param edge: tuple containing the element number containing the edge and the
+        permutation (0, 1, or 2) of the edge within the triangle
+    """
+    # edgeShapes = interpolants.compute_shapes(functionSpace.mesh.parentElement1d, interpolationPoints)
+    edgeShapes = functionSpace.mesh.parentElement1d.compute_shapes(
+        functionSpace.mesh.parentElement1d.coordinates, interpolationPoints
+    )
+    edgeU = get_nodal_values_on_edge(functionSpace, U, edge)
+    return edgeShapes.values.T@edgeU

+
+
+
+

+[docs]
+def integrate_function_on_edge(functionSpace, func, U, quadRule, edge):
+    uq = interpolate_nodal_field_on_edge(functionSpace, U, quadRule.xigauss, edge)
+    Xq = interpolate_nodal_field_on_edge(functionSpace, functionSpace.mesh.coords, quadRule.xigauss, edge)
+    edgeCoords = Mesh.get_edge_coords(functionSpace.mesh, edge)
+    _, normal, jac = Mesh.compute_edge_vectors(functionSpace.mesh, edgeCoords)
+    integrand = jax.vmap(func, (0, 0, None))(uq, Xq, normal)
+    return np.dot(integrand, jac*quadRule.wgauss)

+
+
+
+

+[docs]
+def integrate_function_on_edges(functionSpace, func, U, quadRule, edges):
+    integrate_on_edges = jax.vmap(integrate_function_on_edge, (None, None, None, None, 0))
+    return np.sum(integrate_on_edges(functionSpace, func, U, quadRule, edges))

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/mesh.html b/_modules/pancax/fem/mesh.html new file mode 100644 index 0000000..7f440c8 --- /dev/null +++ b/_modules/pancax/fem/mesh.html @@ -0,0 +1,567 @@ + + + + + + + + pancax.fem.mesh — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.mesh

+from jax import vmap
+from jaxtyping import Array, Float
+from pancax.fem.elements import LineElement, SimplexTriElement
+from typing import Dict, List, Optional
+import equinox as eqx
+import jax.numpy as np
+import numpy as onp
+
+
+

+[docs]
+class Mesh(eqx.Module):
+    """
+    Triangle mesh representing a domain.
+
+    :param coords: Coordinates of the nodes, shape ``(nNodes, nDim)``.
+    :param conns: Nodal connectivity table of the elements.
+    :param simplexNodesOrdinals: Indices of the nodes that are vertices.
+    :param parentElement: A ``ParentElement`` that is the element type in
+        parametric space. A mesh can contain only 1 element type.
+    :param parentElement1d:
+    :param blocks: A dictionary mapping element block names to the indices of the
+        elements in the block.
+    :param nodeSets: A dictionary mapping node set names to the indices of the
+        nodes.
+    :param sideSets: A dictionary mapping side set names to the edges. The
+        edge data structure is a tuple of the element index and the local
+        number of the edge within that element. For example, triangle
+        elements will have edge 0, 1, or 2 for this entry.
+    """
+    coords: Float[Array, "nn nd"]
+    conns: Float[Array, "ne nnpe"]
+    simplexNodesOrdinals: Float[Array, "ne 3"]
+    # TODO finish out the typing below
+    parentElement: any
+    parentElement1d: any
+    blocks: Optional[Dict[str, Float]] = None
+    nodeSets: Optional[Dict[str, Float]] = None
+    sideSets: Optional[Dict[str, Float]] = None
+
+

+[docs]
+    def get_blocks(self, blockNames: List[str]):
+        return tuple(self.blocks[name] for name in blockNames)

+
+
+    @property
+    def num_dimensions(self) -> int:
+        """
+        :return: dimension number of mesh
+        """
+        return self.coords.shape[1]
+
+    @property
+    def num_elements(self) -> int:
+        """
+        :return: number of elements in mesh
+        """
+        return self.conns.shape[0]
+
+    @property 
+    def num_nodes(self) -> int:
+        """
+        number of nodes in mesh
+        """
+        return self.coords.shape[0]

+
+
+
+

+[docs]
+def create_structured_mesh_data(Nx, Ny, xExtent, yExtent):
+    xs = np.linspace(xExtent[0], xExtent[1], Nx)
+    ys = np.linspace(yExtent[0], yExtent[1], Ny)
+
+    Ex = Nx-1
+    Ey = Ny-1
+
+    coords = [ [xs[nx], ys[ny]] for ny in range(Ny) for nx in range(Nx) ]
+
+    conns = []
+    for ex in range(Ex):
+        for ey in range(Ey):
+            conns.append([ex + Nx*ey, ex+1 + Nx*ey,     ex+1 + Nx*(ey+1)])
+            conns.append([ex + Nx*ey, ex+1 + Nx*(ey+1), ex   + Nx*(ey+1)])
+
+    coords = np.array(coords)
+    conns = np.array(conns)
+    return (coords, conns)

+
+
+
+

+[docs]
+def construct_mesh_from_basic_data(coords, conns, blocks, nodeSets=None, sideSets=None):
+    # element, element1d = interpolants.make_parent_elements(degree=1)
+    print('Warning: This only works for tri meshes currently')
+    element = SimplexTriElement(degree=1)
+    element1d = LineElement(degree=1)
+    vertexNodes = np.arange(coords.shape[0])
+    return Mesh(coords, conns, vertexNodes,
+                element, element1d, blocks, nodeSets, sideSets)

+
+
+
+

+[docs]
+def construct_structured_mesh(Nx, Ny, xExtent, yExtent, elementOrder=1, useBubbleElement=False):
+    coords, conns = create_structured_mesh_data(Nx, Ny, xExtent, yExtent)
+    blocks = {'block_0': np.arange(conns.shape[0])}
+    mesh = construct_mesh_from_basic_data(coords, conns, blocks)
+    if elementOrder > 1:
+        mesh = create_higher_order_mesh_from_simplex_mesh(mesh, elementOrder, useBubbleElement)
+    return mesh

+
+
+
+# def get_blocks(mesh, blockNames):
+#     return tuple(mesh.blocks[name] for name in blockNames)
+
+    
+

+[docs]
+def combine_nodesets(set1, set2, nodeOffset):
+    newSet = {}
+    if set1!=None:
+        for key in set1:
+            newSet[key] = set1[key]
+    if set2!=None:
+        for key in set2:
+            newSet[key] = set2[key] + nodeOffset
+    return newSet

+
+
+
+

+[docs]
+def combine_sidesets(set1, set2, elemOffset):
+    newSet = {}
+    if set1!=None:
+        for key in set1:
+            val = set1[key]
+            newSet[key] = val
+    if set2!=None:
+        for key in set2:
+            val = set2[key]
+            newSet[key] = val.at[:,0].add(elemOffset) if len(val)>0 else np.array([])
+    return newSet

+
+
+
+

+[docs]
+def combine_blocks(set1, set2, elemOffset):
+    # meshes are required to have at least one block
+    newSet = {}
+
+    for key in set1:
+        val = set1[key]
+        newSet[key] = val
+
+    for key in set2:
+        val = set2[key]
+        newSet[key] = val + elemOffset
+    return newSet

+
+
+
+

+[docs]
+def combine_mesh(m1, m2):
+    # need to implement block combining
+    
+    mesh1, disp1 = m1
+    mesh2, disp2 = m2
+
+    # Only handle 2 linear element meshes
+    assert mesh1.parentElement.degree == 1
+    assert mesh2.parentElement.degree == 1
+
+    numNodes1 = mesh1.coords.shape[0]
+    # numElems1 = num_elements(mesh1)
+    numElems1 = mesh1.num_elements
+
+    coords = np.concatenate((mesh1.coords, mesh2.coords), axis=0)
+    conns = np.concatenate((mesh1.conns, mesh2.conns+numNodes1), axis=0)
+    disp = np.concatenate((disp1, disp2), axis=0)
+
+    nodeSets = None
+    if mesh1.nodeSets!=None or mesh2.nodeSets!=None:
+        nodeSets = combine_nodesets(mesh1.nodeSets, mesh2.nodeSets, numNodes1)
+
+    sideSets = None
+    if mesh1.sideSets!=None or mesh2.sideSets!=None:
+        sideSets = combine_sidesets(mesh1.sideSets, mesh2.sideSets, numElems1)
+
+    simplexNodeOrdinals = np.arange(coords.shape[0])
+
+    blocks = combine_blocks(mesh1.blocks, mesh2.blocks, numElems1)
+        
+    return Mesh(coords, conns, simplexNodeOrdinals,
+                mesh1.parentElement, mesh1.parentElement1d, blocks,
+                nodeSets, sideSets), disp

+
+
+
+

+[docs]
+def mesh_with_coords(mesh, coords):
+    return Mesh(coords, mesh.conns,mesh.simplexNodesOrdinals,
+                mesh.parentElement, mesh.parentElement1d, mesh.blocks, mesh.nodeSets, mesh.sideSets)

+
+
+
+

+[docs]
+def mesh_with_nodesets(mesh, nodeSets):
+    return Mesh(mesh.coords, mesh.conns,
+                mesh.simplexNodesOrdinals,
+                mesh.parentElement, mesh.parentElement1d,
+                mesh.blocks, nodeSets, mesh.sideSets)

+
+
+
+

+[docs]
+def mesh_with_blocks(mesh, blocks):
+    return Mesh(mesh.coords, mesh.conns,
+                mesh.simplexNodesOrdinals,
+                mesh.parentElement, mesh.parentElement1d,
+                blocks, mesh.nodeSets, mesh.sideSets)

+
+
+
+

+[docs]
+def create_edges(conns):
+    """Generate topological information about edges in a triangulation.
+
+    Parameters
+    ----------
+    conns : (nTriangles, 3) array
+        Connectivity table of the triangulation.
+
+    Returns
+    -------
+    edgeConns : (nEdges, 2) array
+        Vertices of each edge. Boundary edges are always in the
+        counter-clockwise sense, so that the interior of the body is on the left
+        side when walking from the first vertex to the second.
+    edges : (nEdges, 4) array
+        Edge-to-triangle topological information. Each row provides the
+        follwing information for each edge: [leftT, leftP, rightT, rightP],
+        where leftT is the ID of the triangle to the left, leftP is the
+        permutation of the edge in the left triangle (edge 0, 1, or 2), rightT
+        is the ID of the triangle to the right, and rightP is the permutation
+        of the edge in the right triangle. If the edge is a boundary edge, the
+        values of rightT and rightP are -1.
+    """
+    nTris = conns.shape[0]
+    allTriFaces = onp.vstack((conns[:, (0,1)], conns[:, (1,2)], conns[:, (2,0)]))
+    foo = onp.sort(allTriFaces, axis=1)
+    bar, i = onp.unique(foo, return_index=True, axis=0)
+    edgeConns = (allTriFaces[i,:])
+
+    nEdges = edgeConns.shape[0]
+    edges = -onp.ones((nEdges, 4), dtype=onp.int_)
+    edgeElementIds = onp.tile(np.arange(nTris), 3)
+    edges[:,0] = edgeElementIds[i]
+    edges[:,1] = i // nTris
+
+    for i, ec in enumerate(edgeConns):
+        rowsMatch = onp.all(onp.flip(ec) == allTriFaces, axis=1)
+        if onp.any(rowsMatch):
+            j = onp.where(rowsMatch)[0][0]
+            # there should only be one matching row, but take element 0
+            # because j will have the same number of axes (2) as
+            # rowsMatch.
+            edges[i, 2] = edgeElementIds[j]
+            edges[i, 3] = j // nTris
+
+    return edgeConns, edges

+
+
+
+

+[docs]
+def create_higher_order_mesh_from_simplex_mesh(mesh, order, useBubbleElement=False, copyNodeSets=False, createNodeSetsFromSideSets=False):
+    if order==1: return mesh
+
+    # parentElement1d = interpolants.make_parent_element_1d(order)
+    parentElement1d = LineElement(order)
+    
+    if useBubbleElement:
+        raise ValueError('Bubble elements arent supported right now')
+        # basis = interpolants.make_parent_element_2d_with_bubble(order)
+    else:
+        # basis = interpolants.make_parent_element_2d(order)
+        basis = SimplexTriElement(order)
+
+    # conns = np.zeros((num_elements(mesh), basis.coordinates.shape[0]), dtype=np.int_)
+    conns = np.zeros((mesh.num_elements, basis.coordinates.shape[0]), dtype=np.int_)
+
+    # step 1/3: vertex nodes
+    conns = conns.at[:,basis.vertexNodes].set(mesh.conns)
+    simplexNodesOrdinals = np.arange(mesh.coords.shape[0])
+
+    nodeOrdinalOffset = mesh.coords.shape[0] # offset for later node numbering
+
+    # step 2/3: mid-edge nodes (excluding vertices)
+    edgeConns, edges = create_edges(mesh.conns)
+    A = np.column_stack((1.0-parentElement1d.coordinates[parentElement1d.interiorNodes],
+                         parentElement1d.coordinates[parentElement1d.interiorNodes]))
+    edgeCoords = vmap(lambda edgeConn: np.dot(A, mesh.coords[edgeConn,:]))(edgeConns)
+
+    nNodesPerEdge = parentElement1d.interiorNodes.size
+    for e, edge in enumerate(edges):
+        edgeNodeOrdinals = nodeOrdinalOffset + np.arange(e*nNodesPerEdge,(e+1)*nNodesPerEdge)
+        
+        elemLeft = edge[0]
+        sideLeft = edge[1]
+        edgeMasterNodes = basis.faceNodes[sideLeft][parentElement1d.interiorNodes]
+        conns = conns.at[elemLeft, edgeMasterNodes].set(edgeNodeOrdinals)
+
+        elemRight = edge[2]
+        if elemRight >= 0:
+            sideRight = edge[3]
+            edgeMasterNodes = basis.faceNodes[sideRight][parentElement1d.interiorNodes]
+            conns = conns.at[elemRight, edgeMasterNodes].set(np.flip(edgeNodeOrdinals))
+
+    nEdges = edges.shape[0]
+    nodeOrdinalOffset += nEdges*nNodesPerEdge # for offset of interior node numbering
+
+    # step 3/3: interior nodes
+    nInNodesPerTri = basis.interiorNodes.shape[0]
+    if nInNodesPerTri > 0:
+        N0 = basis.coordinates[basis.interiorNodes,0]
+        N1 = basis.coordinates[basis.interiorNodes,1]
+        N2 = 1.0 - N0 - N1
+        A = np.column_stack((N0,N1,N2))
+        interiorCoords = vmap(lambda triConn: np.dot(A, mesh.coords[triConn]))(mesh.conns)
+
+        def add_element_interior_nodes(conn, newNodeOrdinals):
+            return conn.at[basis.interiorNodes].set(newNodeOrdinals)
+
+        nTri = conns.shape[0]
+        newNodeOrdinals = np.arange(nTri*nInNodesPerTri).reshape(nTri,nInNodesPerTri) \
+            + nodeOrdinalOffset
+        
+        conns = vmap(add_element_interior_nodes)(conns, newNodeOrdinals)
+    else:
+        interiorCoords = np.zeros((0,2))
+
+
+    coords = np.vstack((mesh.coords,edgeCoords.reshape(-1,2),interiorCoords.reshape(-1,2)))
+    nodeSets = mesh.nodeSets if copyNodeSets else None
+
+    newMesh = Mesh(coords, conns, simplexNodesOrdinals, basis,
+                   parentElement1d, mesh.blocks, nodeSets, mesh.sideSets)
+    
+    if createNodeSetsFromSideSets:
+        nodeSets = create_nodesets_from_sidesets(newMesh)
+        newMesh = mesh_with_nodesets(newMesh, nodeSets)
+
+    return newMesh

+
+
+
+

+[docs]
+def create_nodesets_from_sidesets(mesh):
+    nodeSets = {}
+    print(mesh)
+    def get_nodes_from_edge(edge):
+        elemOrdinal = edge[0]
+        sideOrdinal = edge[1]
+        return mesh.conns[elemOrdinal, mesh.parentElement.faceNodes[sideOrdinal,:]]
+    
+    for setName, sideSet in mesh.sideSets.items():
+        nodes = vmap(get_nodes_from_edge)(sideSet)
+        nodeSets[setName] = np.unique(nodes.ravel())
+
+    return nodeSets

+
+
+
+# def num_elements(mesh):
+#     return mesh.conns.shape[0]
+
+
+

+[docs]
+def num_nodes(mesh):
+    return mesh.coords.shape[0]

+
+
+
+

+[docs]
+def get_edge_node_indices(mesh : Mesh, edge):
+    edgeNodes = mesh.parentElement.faceNodes[edge[1], :]
+    return mesh.conns[edge[0], edgeNodes]

+
+
+
+

+[docs]
+def get_edge_field(mesh : Mesh, edge, field):
+    """
+    Evaluate field on nodes of an element edge.
+    Arguments:
+
+    :param mesh: a Mesh object
+    :param edge: tuple containing the element number containing the edge and the 
+        permutation (0, 1, or 2) of the edge within the triangle
+    """
+    return field[get_edge_node_indices(mesh, edge)]

+
+
+
+

+[docs]
+def get_edge_coords(mesh : Mesh, edge):
+    return get_edge_field(mesh, edge, mesh.coords)

+
+
+
+

+[docs]
+def compute_edge_vectors(mesh : Mesh, edgeCoords):
+    """
+    Get geometric vectors for an element edge.
+    
+    Assumes that the edgs has a constant shape jacobian, that is, the
+    transformation from the parent element is affine.
+    
+    Arguments
+    :param mesh: a Mesh object
+    :param edgeCoords: coordinates of all nodes on the edge, in the order 
+    defined by the 1D parent element convention
+
+    Returns
+    tuple (t, n, j) with
+    :return t: the unit tangent vector
+    :return n: the outward unit normal vector
+    :return j: jacobian of the transformation from parent to physical space
+    """
+    Xv = edgeCoords[mesh.parentElement1d.vertexNodes, :]
+    tangent = Xv[1] - Xv[0]
+    normal = np.array([tangent[1], -tangent[0]])
+    jac = np.linalg.norm(tangent)
+    return tangent/jac, normal/jac, jac

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/quadrature_rules.html b/_modules/pancax/fem/quadrature_rules.html new file mode 100644 index 0000000..93a3f47 --- /dev/null +++ b/_modules/pancax/fem/quadrature_rules.html @@ -0,0 +1,539 @@ + + + + + + + + pancax.fem.quadrature_rules — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.quadrature_rules

+from .elements import *
+from .elements.base_element import BaseElement
+from jax.lax import switch
+from jaxtyping import Array, Float
+from pancax.timer import Timer
+import equinox as eqx
+import jax.numpy as jnp
+import math
+import numpy as ojnp
+import scipy.special
+
+
+# TODO 
+# think about moving this stuff into elements
+
+

+[docs]
+class QuadratureRule(eqx.Module):
+    """
+    Quadrature rule points and weights.
+    A ``namedtuple`` containing ``xigauss``, a numpy array of the
+    coordinates of the sample points in the reference domain, and
+    ``wgauss``, a numpy array with the weights.
+
+    :param xigauss: coordinates of gauss points in reference element
+    :param wgauss: weights of gauss points in reference element
+    """
+    xigauss: Float[Array, "nq nd"]
+    wgauss: Float[Array, "nq"]
+
+

+[docs]
+    def __init__(self, parentElement: BaseElement, degree: int) -> None:
+        with Timer('QuadratureRule.__init__'):
+            if type(parentElement) == Hex8Element:
+                xi, w = create_quadrature_rule_on_hex(degree)
+            elif type(parentElement) == LineElement:
+                xi, w = create_quadrature_rule_1D(degree)
+            elif type(parentElement) == Quad4Element or \
+                 type(parentElement) == Quad9Element:
+                xi, w = create_quadrature_rule_on_quad(degree)
+            elif type(parentElement) == SimplexTriElement:
+                xi, w = create_quadrature_rule_on_triangle(degree)
+            elif type(parentElement) == Tet4Element or \
+                 type(parentElement) == Tet10Element:
+                xi, w = create_quadrature_rule_on_tet(degree)
+            else:
+                raise TypeError(f'Element type {type(parentElement)} does not '
+                                'have a supported quadrature rule.')
+            self.xigauss = xi
+            self.wgauss = w

+
+
+    # TODO maybe there's a better way?
+    # TODO below is just so we don't have to change any tests for now
+    def __iter__(self):
+        yield self.xigauss
+        yield self.wgauss
+
+    def __len__(self):
+        return self.xigauss.shape[0]
+
+

+[docs]
+    def eval_at_iso_points(self, field):
+        xigauss = self.xigauss
+        fields = jnp.array([field[0,:] + (field[1,:]-field[0,:]) * xi for xi in xigauss])
+        return fields

+

+
+
+

+[docs]
+def create_quadrature_rule_1D(degree: int) -> QuadratureRule:
+    """Creates a Gauss-Legendre quadrature on the unit interval.
+
+    The rule can exactly integrate polynomials of degree up to 
+    ``degree``.
+
+    Parameters
+    ----------
+    degree: Highest degree polynomial to be exactly integrated by the quadrature rule
+
+    Returns
+    -------
+    A ``QuadratureRule`` named tuple containing the quadrature point coordinates
+    and the weights.
+    """
+
+    n = math.ceil((degree + 1)/2)
+    xi, w = scipy.special.roots_sh_legendre(n)
+    return xi, w

+
+
+
+# TODO is this being used at all
+

+[docs]
+def eval_at_iso_points(xigauss, field):
+    fields = jnp.array([field[0,:] + (field[1,:]-field[0,:]) * xi for xi in xigauss])
+    return fields

+
+
+
+

+[docs]
+def create_quadrature_rule_on_hex(quad_degree: int) -> QuadratureRule:
+    if quad_degree == 1:
+        xi = jnp.array([[0.0, 0.0, 0.0]])
+        w = 8.0 * jnp.ones(1)
+    elif quad_degree == 2:
+        xi = jnp.sqrt(1. / 3.) * jnp.array(
+            [[-1., -1., -1.],
+             [1., -1., -1.],
+             [1., 1., -1.],
+             [-1., 1., -1.],
+             [-1., -1., 1.],
+             [1., -1., 1.],
+             [1., 1., 1.],
+             [-1., 1., 1.]],
+        )
+        w = jnp.ones(8)
+    else:
+        raise ValueError(f'Unsupported quadrature degree {quad_degree} on hex element.')
+
+    return xi, w

+
+
+
+

+[docs]
+def create_quadrature_rule_on_quad(quad_degree: int) -> QuadratureRule:
+    """
+    :param quad_degree: degree of quadrature rule to create
+    """
+    if quad_degree == 1:
+        xi = jnp.array([[0.0, 0.0]])
+        w = 4.0 * jnp.ones(1)
+    elif quad_degree == 2:
+        xi = jnp.sqrt(1. / 3.) * jnp.array([
+            [-1., -1.],
+            [1., -1.],
+            [1., 1.],
+            [-1., 1.]
+        ])
+        w = jnp.ones(4)
+    elif quad_degree == 3:
+        # TODO not quite accurate currently for some reason?
+        # TODO
+        # TODO
+        xi = jnp.array([
+            [-jnp.sqrt(3. / 5.), -jnp.sqrt(3. / 5.)],
+            [0., -jnp.sqrt(3. / 5.)],
+            [jnp.sqrt(3. / 5.), -jnp.sqrt(3. / 5.)],
+            [-jnp.sqrt(3. / 5.), 0.],
+            [0., 0.],
+            [jnp.sqrt(3. / 5.), 0.],
+            [-jnp.sqrt(3. / 5.), jnp.sqrt(3. / 5.)],
+            [0., jnp.sqrt(3. / 5.)],
+            [jnp.sqrt(3. / 5.), jnp.sqrt(3. / 5.)]
+        ])
+        w = jnp.array([
+            25. / 81.,
+            40. / 81.,
+            25. / 81.,
+            40. / 81.,
+            64. / 81.,
+            40. / 81.,
+            25. / 81.,
+            40. / 81.,
+            25. / 80.
+        ])
+    else:
+        raise ValueError('Invalid quadrature degree: %s' % quad_degree)
+
+    return xi, w

+
+
+
+

+[docs]
+def create_quadrature_rule_on_tet(degree: int) -> QuadratureRule:
+    if degree == 1:
+        xi = jnp.array([
+            [1. / 4., 1. / 4., 1. / 4.]
+        ])
+        w = jnp.array([1. / 6.])
+    elif degree == 2:
+        xi = jnp.array([
+            [1. / 4., 1. / 4., 1. / 4.],
+            [1. / 6., 1. / 6., 1. / 6.],
+            [1. / 6., 1. / 6., 1. / 2.],
+            [1. / 6., 1. / 2., 1. / 6.],
+            [1. / 2., 1. / 6., 1. / 6.]
+        ])
+        w = jnp.array([-2. / 15., 3. / 40., 3. / 40., 3. / 40., 3. / 40.])
+    else:
+        raise ValueError('Invalid quadrature degree: %s' % degree)
+    
+    return xi, w

+
+
+
+

+[docs]
+def create_quadrature_rule_on_triangle(degree: int) -> QuadratureRule:
+    """Creates a Gauss-Legendre quadrature on the unit triangle.
+
+    The rule can exactly integrate 2D polynomials up to the value of 
+    ``degree``. The domain is the triangle between the vertices
+    (0, 0)-(1, 0)-(0, 1). The rules here are guaranteed to be 
+    cyclically symmetric in triangular coordinates and to have strictly
+    positive weights.
+
+    Parameters
+    ----------
+    degree: Highest degree polynomial to be exactly integrated by the quadrature rule
+
+    Returns
+    -------
+    A ``QuadratureRule`` named tuple containing the quadrature point coordinates
+    and the weights.
+    """
+    if degree == 1:
+        xi = ojnp.array([[3.33333333333333333E-01,  3.33333333333333333E-01]])
+
+        w  = ojnp.array([ 5.00000000000000000E-01 ])
+    elif degree == 2:
+        xi = ojnp.array([[6.66666666666666667E-01,  1.66666666666666667E-01],
+                        [1.66666666666666667E-01,  6.66666666666666667E-01],
+                        [1.66666666666666667E-01,  1.66666666666666667E-01]])
+
+        w  = ojnp.array([1.66666666666666666E-01,
+                        1.66666666666666667E-01,
+                        1.66666666666666667E-01])
+    elif degree <= 4:
+        xi = ojnp.array([[1.081030181680700E-01,  4.459484909159650E-01],
+                        [4.459484909159650E-01,  1.081030181680700E-01],
+                        [4.459484909159650E-01,  4.459484909159650E-01],
+                        [8.168475729804590E-01,  9.157621350977100E-02],
+                        [9.157621350977100E-02,  8.168475729804590E-01],
+                        [9.157621350977100E-02,  9.157621350977100E-02]])
+
+        w  = ojnp.array([1.116907948390055E-01,
+                        1.116907948390055E-01,
+                        1.116907948390055E-01,
+                        5.497587182766100E-02,
+                        5.497587182766100E-02,
+                        5.497587182766100E-02])
+    elif degree <= 5:
+        xi = ojnp.array([[3.33333333333333E-01,  3.33333333333333E-01],
+                        [5.97158717897700E-02,  4.70142064105115E-01],
+                        [4.70142064105115E-01,  5.97158717897700E-02],
+                        [4.70142064105115E-01,  4.70142064105115E-01],
+                        [7.97426985353087E-01,  1.01286507323456E-01],
+                        [1.01286507323456E-01,  7.97426985353087E-01],
+                        [1.01286507323456E-01,  1.01286507323456E-01]])
+
+        w = ojnp.array([1.12500000000000E-01,
+                       6.61970763942530E-02,
+                       6.61970763942530E-02,
+                       6.61970763942530E-02,
+                       6.29695902724135E-02,
+                       6.29695902724135E-02,
+                       6.29695902724135E-02])
+    elif degree <= 6:
+        xi = ojnp.array([[5.01426509658179E-01,  2.49286745170910E-01],
+                        [2.49286745170910E-01,  5.01426509658179E-01],
+                        [2.49286745170910E-01,  2.49286745170910E-01],
+                        [8.73821971016996E-01,  6.30890144915020E-02],
+                        [6.30890144915020E-02,  8.73821971016996E-01],
+                        [6.30890144915020E-02,  6.30890144915020E-02],
+                        [5.31450498448170E-02,  3.10352451033784E-01],
+                        [6.36502499121399E-01,  5.31450498448170E-02],
+                        [3.10352451033784E-01,  6.36502499121399E-01],
+                        [5.31450498448170E-02,  6.36502499121399E-01],
+                        [6.36502499121399E-01,  3.10352451033784E-01],
+                        [3.10352451033784E-01,  5.31450498448170E-02]])
+
+        w = ojnp.array([5.83931378631895E-02,
+                       5.83931378631895E-02,
+                       5.83931378631895E-02,
+                       2.54224531851035E-02,
+                       2.54224531851035E-02,
+                       2.54224531851035E-02,
+                       4.14255378091870E-02,
+                       4.14255378091870E-02,
+                       4.14255378091870E-02,
+                       4.14255378091870E-02,
+                       4.14255378091870E-02,
+                       4.14255378091870E-02])
+    elif degree <= 10:
+        xi = ojnp.array([[0.33333333333333333E+00, 0.33333333333333333E+00],
+                        [0.4269134091050342E-02,  0.49786543295447483E+00],
+                        [0.49786543295447483E+00, 0.4269134091050342E-02],
+                        [0.49786543295447483E+00, 0.49786543295447483E+00],
+                        [0.14397510054188759E+00, 0.42801244972905617E+00],
+                        [0.42801244972905617E+00, 0.14397510054188759E+00],
+                        [0.42801244972905617E+00, 0.42801244972905617E+00],
+                        [0.6304871745135507E+00,  0.18475641274322457E+00],
+                        [0.18475641274322457E+00, 0.6304871745135507E+00],
+                        [0.18475641274322457E+00, 0.18475641274322457E+00],
+                        [0.9590375628566448E+00,  0.20481218571677562E-01],
+                        [0.20481218571677562E-01, 0.9590375628566448E+00],
+                        [0.20481218571677562E-01, 0.20481218571677562E-01],
+                        [0.3500298989727196E-01,  0.1365735762560334E+00],
+                        [0.1365735762560334E+00,  0.8284234338466947E+00],
+                        [0.8284234338466947E+00,  0.3500298989727196E-01],
+                        [0.1365735762560334E+00,  0.3500298989727196E-01],
+                        [0.8284234338466947E+00,  0.1365735762560334E+00],
+                        [0.3500298989727196E-01,  0.8284234338466947E+00],
+                        [0.37549070258442674E-01, 0.3327436005886386E+00],
+                        [0.3327436005886386E+00,  0.6297073291529187E+00],
+                        [0.6297073291529187E+00,  0.37549070258442674E-01],
+                        [0.3327436005886386E+00,  0.37549070258442674E-01],
+                        [0.6297073291529187E+00,  0.3327436005886386E+00],
+                        [0.37549070258442674E-01, 0.6297073291529187E+00]])
+
+        w = ojnp.array([0.4176169990259819E-01,
+                       0.36149252960283717E-02,
+                       0.36149252960283717E-02,
+                       0.36149252960283717E-02,
+                       0.3724608896049025E-01,
+                       0.3724608896049025E-01,
+                       0.3724608896049025E-01,
+                       0.39323236701554264E-01,
+                       0.39323236701554264E-01,
+                       0.39323236701554264E-01,
+                       0.3464161543553752E-02,
+                       0.3464161543553752E-02,
+                       0.3464161543553752E-02,
+                       0.147591601673897E-01,
+                       0.147591601673897E-01,
+                       0.147591601673897E-01,
+                       0.147591601673897E-01,
+                       0.147591601673897E-01,
+                       0.147591601673897E-01,
+                       0.1978968359803062E-01,
+                       0.1978968359803062E-01,
+                       0.1978968359803062E-01,
+                       0.1978968359803062E-01,
+                       0.1978968359803062E-01,
+                       0.1978968359803062E-01])
+    else:
+        raise ValueError("Quadrature of precision this high is not implemented.")
+
+    return xi, w

+
+
+
+# TODO remove this stuff
+

+[docs]
+def create_padded_quadrature_rule_1D(degree):
+    """Creates 1D Gauss quadrature rule data that are padded to maintain a 
+    uniform size, which makes this function jit-able. 
+
+    This function is inteded to be used only when jit compilation of calls to the
+    quadrature rules are needed. Otherwise, prefer to use the standard quadrature 
+    rules. The standard rules do not contain extra 0s for padding, which makes 
+    them more efficient when  used repeatedly (such as in the global energy).
+
+    Args:
+      degree: degree of highest polynomial to be integrated exactly
+    """
+
+    jnpts = jnp.ceil((degree + 1)/2).astype(int)
+    xi,w = switch(jnpts,
+                  [_gauss_quad_1D_1pt, _gauss_quad_1D_2pt, _gauss_quad_1D_3pt,
+                   _gauss_quad_1D_4pt, _gauss_quad_1D_5pt],
+                  None)
+    return 0.5 * (xi + 1.0), 0.5 * w

+
+
+
+

+[docs]
+def _gauss_quad_1D_1pt(_):
+    xi = jnp.array([0., 0., 0., 0., 0.])
+    w  = jnp.array([2., 0., 0., 0., 0.])
+    return xi,w

+
+
+
+

+[docs]
+def _gauss_quad_1D_2pt(_):
+    xi = jnp.array([-0.5773502691896257,  0.5773502691896257,   0.,
+                    0.,                  0.])
+    w  = jnp.array([ 1.,                  1.                ,   0.,
+                    0.,                 0.])
+    return xi,w

+
+
+
+

+[docs]
+def _gauss_quad_1D_3pt(_):
+    xi = jnp.array([-0.7745966692414834,  0.                ,  0.7745966692414834,
+                    0.,                  0.])
+    w  = jnp.array([ 0.5555555555555557,  0.8888888888888888,  0.5555555555555557,
+                    0.,                  0.])
+    return xi,w

+
+
+
+

+[docs]
+def _gauss_quad_1D_4pt(_):
+    xi = jnp.array([-0.8611363115940526 , -0.33998104358485626,  0.33998104358485626,
+                    0.8611363115940526 ,  0.])
+    w  = jnp.array([ 0.3478548451374537 ,  0.6521451548625462 ,  0.6521451548625462 ,
+                    0.3478548451374537,   0.])
+    return xi,w

+
+
+
+

+[docs]
+def _gauss_quad_1D_5pt(_):
+    xi = jnp.array([-0.906179845938664  ,  -0.5384693101056831,  0.                ,  0.5384693101056831,  0.906179845938664  ])
+    w  = jnp.array([ 0.23692688505618942,   0.4786286704993662,  0.568888888888889 ,  0.4786286704993662,  0.23692688505618942])
+
+    return xi,w

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/read_exodus_mesh.html b/_modules/pancax/fem/read_exodus_mesh.html new file mode 100644 index 0000000..0b1607a --- /dev/null +++ b/_modules/pancax/fem/read_exodus_mesh.html @@ -0,0 +1,324 @@ + + + + + + + + pancax.fem.read_exodus_mesh — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.read_exodus_mesh

+from .elements import *
+from .mesh import *
+from pancax.timer import Timer
+import netCDF4
+import numpy as onp
+
+exodusToNativeTri6NodeOrder = np.array([0, 3, 1, 5, 4, 2])
+
+
+

+[docs]
+def read_exodus_mesh(fileName: str):
+    """
+    :param fileName: file name of exodus mesh to read
+    :return: A mesh object
+    """
+    with Timer('read_exodus_mesh'):
+        with netCDF4.Dataset(fileName) as exData:
+            coords = _read_coordinates(exData)
+            conns, blocks = _read_blocks(exData)
+            nodeSets = _read_node_sets(exData)
+            sideSets = _read_side_sets(exData)
+
+            elementType = _read_element_type(exData).lower()
+            if elementType == "hex8" or elementType == "hex":
+                basis = Hex8Element()
+                basis1d = Quad4Element()
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "quad4":
+                basis = Quad4Element()
+                basis1d = LineElement(degree=1)
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "quad9":
+                basis = Quad9Element()
+                basis1d = LineElement(degree=2)
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "tet4":
+                basis = Tet4Element()
+                basis1d = SimplexTriElement(degree=1)
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "tet10":
+                basis = Tet10Element()
+                basis1d = SimplexTriElement(degree=1)
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "tri3" or elementType == "tri":
+                basis = SimplexTriElement(degree=1)
+                basis1d = LineElement(degree=1)
+                simplexNodesOrdinals = np.arange(coords.shape[0])
+            elif elementType == "tri6":
+                basis = SimplexTriElement(degree=2)
+                basis1d = LineElement(degree=2)
+                simplexNodesOrdinals = _get_vertex_nodes_from_exodus_tri6_mesh(conns)
+                conns = conns[:, exodusToNativeTri6NodeOrder]
+            else:
+                raise ValueError(f'Unsupported element type: {elementType}')
+
+            return Mesh(coords, conns, simplexNodesOrdinals, basis, basis1d,
+                        blocks, nodeSets, sideSets)

+
+        
+        
+# TODO add support for 3D
+

+[docs]
+def _read_coordinates(exodusDataset):
+    nNodes = len(exodusDataset.dimensions['num_nodes'])
+    nDims = len(exodusDataset.dimensions['num_dim'])
+    # assert nDims == 2
+
+    coordsX = exodusDataset.variables['coordx'][:]
+    coordsY = exodusDataset.variables['coordy'][:]
+    
+    if nDims == 2:
+        return np.array(onp.column_stack([coordsX, coordsY]))
+    elif nDims == 3:
+        coordsZ = exodusDataset.variables['coordz'][:]
+        return np.array(onp.column_stack([coordsX, coordsY, coordsZ]))

+
+
+
+
+

+[docs]
+def _read_block_conns(exodusDataset, blockOrdinal):
+    key = 'connect' + str(blockOrdinal + 1)
+    record = exodusDataset.variables[key]
+    record.set_auto_mask(False)
+
+    nElemsInBlock = len(exodusDataset.dimensions['num_el_in_blk' + str(blockOrdinal + 1)])
+    return np.array(record[:] - 1)

+
+
+
+

+[docs]
+def _read_blocks(exodusDataset):
+    nodesPerElem = len(exodusDataset.dimensions['num_nod_per_el1'])
+
+    blockNames = _read_names_list(exodusDataset, 'eb_names')
+    # give unnamed blocks an auto-generated name
+    for i, name in enumerate(blockNames):
+        if not name:
+            blockNames[i] = "block_" + str(i+1)
+            
+    nBlocks = len(exodusDataset.dimensions['num_el_blk'])
+    blockConns = []
+    blocks = {}
+    firstElemInBlock = 0
+    for i in range(nBlocks):
+        nodesPerElemInBlock = len(exodusDataset.dimensions['num_nod_per_el' + str(i+1)])
+        assert nodesPerElemInBlock == nodesPerElem
+
+        blockConns.append(_read_block_conns(exodusDataset, i))
+        
+        nElemsInBlock = len(exodusDataset.dimensions['num_el_in_blk' + str(i + 1)])
+        elemRange = np.arange(firstElemInBlock, firstElemInBlock + nElemsInBlock)
+        blocks[blockNames[i]] = elemRange
+        firstElemInBlock += nElemsInBlock
+
+    conns = np.vstack(blockConns)
+    return conns, blocks

+
+
+
+

+[docs]
+def _read_node_sets(exodusDataset):
+    if "num_node_sets" in exodusDataset.dimensions:
+        nodeSetNames = _read_names_list(exodusDataset, "ns_names")
+        for i, name in enumerate(nodeSetNames):
+            if not name:
+                nodeSetNames[i] = "nodeset_" + str(i+1)
+            
+        nodeSetNodes = []
+        nNodeSets = len(exodusDataset.dimensions["num_node_sets"])
+        for i in range(nNodeSets):
+            key = 'node_ns' + str(i + 1)
+            record = exodusDataset.variables[key]
+            record.set_auto_mask(False)
+            nodeSetNodes.append(record[:] - 1)
+        nodeSets = dict(zip(nodeSetNames, nodeSetNodes))
+    else:
+        nodeSets = {}
+
+    return nodeSets

+
+
+
+

+[docs]
+def _read_side_sets(exodusDataset):
+    if "num_side_sets" in exodusDataset.dimensions:
+        sideSetNames = _read_names_list(exodusDataset, 'ss_names')
+        for i, name in enumerate(sideSetNames):
+            if not name:
+                sideSetNames[i] = "sideset_" + str(i+1)
+
+        nSideSets = len(exodusDataset.dimensions['num_side_sets'])
+        sideSetEntries = []
+        for i in range(nSideSets):
+            key = 'elem_ss' + str(i + 1)
+            record = exodusDataset.variables[key]
+            record.set_auto_mask(False)
+            sideSetElems = np.array(record[:] - 1)
+
+            key = 'side_ss' + str(i + 1)
+            record = exodusDataset.variables[key]
+            record.set_auto_mask(False)
+            sideSetSides = np.array(record[:] - 1)
+
+            sideSetEntries.append(np.column_stack((sideSetElems, sideSetSides)))
+        sideSets = dict(zip(sideSetNames, sideSetEntries))
+    else:
+        sideSets = {}
+
+    return sideSets

+
+
+
+

+[docs]
+def _read_element_type(exodusDataset):
+    elemType = exodusDataset.variables['connect1'].elem_type
+
+    nBlocks = len(exodusDataset.dimensions['num_el_blk'])
+    for i in range(nBlocks):
+        key = 'connect' + str(i + 1)
+        blockElemType = exodusDataset[key].elem_type
+        assert (blockElemType == elemType), 'Different element types present in exodus file'
+    return elemType

+
+
+
+

+[docs]
+def _read_names_list(exodusDataset, recordName):
+    record = exodusDataset.variables[recordName]
+    record.set_auto_mask(False)
+    namesList = [b"".join(c).decode("UTF-8") for c in record[:]]
+    return namesList

+
+
+
+

+[docs]
+def _get_vertex_nodes_from_exodus_tri6_mesh(conns):
+    vertexSet = set(conns[:,:3].ravel().tolist())
+    vertices = [v for v in vertexSet]
+    return np.array(vertices, dtype = np.int_)

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/sparse_matrix_assembler.html b/_modules/pancax/fem/sparse_matrix_assembler.html new file mode 100644 index 0000000..a62a1fa --- /dev/null +++ b/_modules/pancax/fem/sparse_matrix_assembler.html @@ -0,0 +1,131 @@ + + + + + + + + pancax.fem.sparse_matrix_assembler — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.fem.sparse_matrix_assembler
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.fem.sparse_matrix_assembler

+from scipy.sparse import coo_matrix
+
+
+

+[docs]
+def assemble_sparse_stiffness_matrix(kValues, conns, dofManager):
+     nElements, nNodesPerElement = conns.shape
+     nFields = kValues.shape[2]
+     nDofPerElement = nNodesPerElement * nFields
+     
+     kValues = kValues.reshape((nElements, nDofPerElement, nDofPerElement))
+
+     nUnknowns = dofManager.unknownIndices.size
+     
+     K = coo_matrix((kValues[dofManager.hessian_bc_mask], (dofManager.HessRowCoords, dofManager.HessColCoords)), shape = (nUnknowns, nUnknowns))
+     return K.tocsc()

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/surface.html b/_modules/pancax/fem/surface.html new file mode 100644 index 0000000..f11bc41 --- /dev/null +++ b/_modules/pancax/fem/surface.html @@ -0,0 +1,222 @@ + + + + + + + + pancax.fem.surface — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.surface

+# from optimism.JaxConfig import *
+from jax import vmap
+import jax.numpy as jnp
+
+# this is hard coded for tri elements
+
+

+[docs]
+def create_edges(coords, conns, edge_is_potentially_in_contact):
+    edges = []
+    for e,elem in enumerate(conns):
+        edgeCoords = coords.take(elem,0)
+        for n in range(3):
+            nn = (n+1)%3
+            edgeConn = jnp.array([n,nn])
+            if (edge_is_potentially_in_contact(edgeCoords[edgeConn])):
+                edges.append([e,n])
+    return jnp.array(edges)

+
+
+
+

+[docs]
+def get_coords(mesh, side):
+    elem = mesh.conns[side[0],:]
+    lSide = side[1]
+    elemCoords = mesh.coords.take(elem,0)
+    return elemCoords[ jnp.array([lSide, (lSide+1)%3]), : ]

+
+
+
+

+[docs]
+def integrate_values(quadratureRule, coords, gaussField):
+    _, wgauss = quadratureRule
+    jac = jnp.linalg.norm(coords[0,:] - coords[1,:])
+    dx = jac*wgauss
+    return dx.dot(gaussField)

+
+
+
+

+[docs]
+def integrate_function(quadratureRule, coords, field_func):
+    xigauss, wgauss = quadratureRule
+    jac = jnp.linalg.norm(coords[0,:] - coords[1,:])
+    xgauss = jnp.array([coords[0] + (coords[1] - coords[0])*xi for xi in xigauss])
+    dx = jac*wgauss
+    return jnp.dot(vmap(field_func)(xgauss), dx)

+
+
+
+

+[docs]
+def integrate_function_on_surface(quadratureRule, edges, mesh, func):
+    F = vmap(integrate_function_on_edge, (None,0,None,None))
+    return jnp.sum(F(quadratureRule, edges, mesh, func))

+
+
+
+

+[docs]
+def integrate_function_on_edge(quadratureRule, edge, mesh, func):
+    edgeCoords = get_coords(mesh, edge)
+    xigauss, wgauss = quadratureRule
+    jac = jnp.linalg.norm(edgeCoords[0,:] - edgeCoords[1,:])
+    xgauss = edgeCoords[0] + jnp.outer(xigauss, edgeCoords[1] - edgeCoords[0])
+    dx = jac*wgauss
+    normal = compute_normal(edgeCoords)
+    return jnp.dot(vmap(func, (0,None))(xgauss, normal), dx)

+
+
+
+

+[docs]
+def compute_normal(edgeCoords):
+    tangent = edgeCoords[1]-edgeCoords[0]
+    normal = jnp.array([tangent[1], -tangent[0]])
+    return normal / jnp.linalg.norm(normal)

+
+
+
+

+[docs]
+def get_field_index(edge, conns):
+    elemIndex = edge[0]
+    elemConns = conns[elemIndex]
+    n1 = edge[1]
+    n2 = (n1+1)%3
+    return elemConns, jnp.array([n1,n2])

+
+
+
+

+[docs]
+def eval_field(field, fieldIndex):
+    return field[fieldIndex[0]][fieldIndex[1]]

+
+
+
+

+[docs]
+def compute_edge_vectors(edgeCoords):
+    tangent = edgeCoords[1]-edgeCoords[0]
+    normal = jnp.array([tangent[1], -tangent[0]])
+    jac = jnp.linalg.norm(tangent)
+    return tangent/jac, normal/jac, jac

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/fem/traction_bc.html b/_modules/pancax/fem/traction_bc.html new file mode 100644 index 0000000..776efea --- /dev/null +++ b/_modules/pancax/fem/traction_bc.html @@ -0,0 +1,162 @@ + + + + + + + + pancax.fem.traction_bc — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.fem.traction_bc

+import jax
+import jax.numpy as np
+
+import pancax.fem.quadrature_rules as quadrature_rules
+import pancax.fem.surface as surface
+
+# def interpolate_nodal_field_on_edge(mesh, U, quadRule, edge):
+#     fieldIndex = Surface.get_field_index(edge, mesh.conns)  
+

+[docs]
+def interpolate_nodal_field_on_edge(conns, U, quadRule, edge):
+    fieldIndex = surface.get_field_index(edge, conns)  
+    nodalValues = surface.eval_field(U, fieldIndex)    
+    return quadrature_rules.eval_at_iso_points(quadRule.xigauss, nodalValues)

+
+
+
+# def compute_traction_potential_energy_on_edge(mesh, U, quadRule, edge, load, time):
+#     uq = interpolate_nodal_field_on_edge(mesh, U, quadRule, edge)
+#     Xq = interpolate_nodal_field_on_edge(mesh, mesh.coords, quadRule, edge)
+#     edgeCoords = Surface.get_coords(mesh, edge)
+

+[docs]
+def compute_traction_potential_energy_on_edge(coords, conns, U, quadRule, edge, load, time):
+    uq = interpolate_nodal_field_on_edge(conns, U, quadRule, edge)
+    Xq = interpolate_nodal_field_on_edge(conns, coords, quadRule, edge)
+    edgeCoords = surface.get_coords(coords, conns, edge)
+    edgeNormal = surface.compute_normal(edgeCoords)
+    tq = jax.vmap(load, (0, None, None))(Xq, edgeNormal, time)
+    integrand = jax.vmap(lambda u,t: u@t)(uq, tq)
+    return -surface.integrate_values(quadRule, edgeCoords, integrand)

+
+
+
+# def compute_traction_potential_energy(mesh, U, quadRule, edges, load, time=0.0):
+#     return np.sum(jax.vmap(
+#         compute_traction_potential_energy_on_edge, 
+#         (None,None,None,0,None,None)
+#     )(mesh, U, quadRule, edges, load, time) )
+
+

+[docs]
+def compute_traction_potential_energy(coords, conns, U, quadRule, edges, load, time=0.0):
+    return np.sum(jax.vmap(
+        compute_traction_potential_energy_on_edge, 
+        (None, None, None, None, 0, None, None)
+    )(coords, conns, U, quadRule, edges, load, time))

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/history_writer.html b/_modules/pancax/history_writer.html new file mode 100644 index 0000000..4cc08c1 --- /dev/null +++ b/_modules/pancax/history_writer.html @@ -0,0 +1,304 @@ + + + + + + + + pancax.history_writer — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.history_writer

+from abc import abstractmethod
+from pathlib import Path
+from typing import List
+import equinox as eqx
+import pandas
+
+
+

+[docs]
+class BaseHistoryWriter(eqx.Module):
+  log_every: int
+  write_every: int
+
+

+[docs]
+  @abstractmethod
+  def to_csv(self):
+    pass

+
+
+

+[docs]
+  def write_data(self, key: str, val: float) -> None:
+    if key in self.data_dict.keys():
+      self.data_dict[key].append(val)
+    else:
+      self.data_dict[key] = [val]

+
+
+

+[docs]
+  @abstractmethod
+  def write_aux_values(self, loss):
+    pass

+
+
+

+[docs]
+  @abstractmethod
+  def write_epoch(self, epoch):
+    pass

+
+
+

+[docs]
+  def write_history(self, loss, epoch: int):
+    if epoch % self.log_every == 0:
+      self.write_aux_values(loss)
+      self.write_epoch(epoch)
+      self.write_loss(loss)
+
+    if epoch % self.write_every == 0:
+      self.to_csv()

+
+
+

+[docs]
+  @abstractmethod
+  def write_loss(self, loss):
+    pass

+

+
+
+
+

+[docs]
+class HistoryWriter(BaseHistoryWriter):
+  log_every: int
+  write_every: int
+  data_dict: dict
+  history_file: Path
+
+

+[docs]
+  def __init__(self, history_file: str, log_every: int, write_every: int) -> None:
+    super().__init__(log_every, write_every)
+    self.history_file = Path(history_file)
+    self.data_dict = dict()

+
+
+

+[docs]
+  def to_csv(self) -> None:
+    df = pandas.DataFrame(self.data_dict)
+    df.to_csv(self.history_file, index=False)

+
+
+

+[docs]
+  def write_aux_values(self, loss):
+    for key, val in loss[1].items():
+      if key == 'props':
+        for prop_num, prop_val in enumerate(val):
+          self.write_data(f'property_{prop_num}', prop_val.item())
+      elif key == 'dprops':
+        for prop_num, prop_val in enumerate(val):
+          self.write_data(f'dproperty_{prop_num}', prop_val.item())
+      else:
+        self.write_data(key, val.item())

+
+
+

+[docs]
+  def write_epoch(self, epoch):
+    self.write_data('epoch', epoch)

+
+
+

+[docs]
+  def write_loss(self, loss):
+    self.write_data('loss', loss[0].item())

+
+
+
+

+[docs]
+  def _write_loss(self, loss, epoch: int, log_every=1, save_every=1000):
+    if epoch % log_every == 0:
+      self.write_data('epoch', epoch)
+      self.write_data('loss', loss[0].item())
+      for key, val in loss[1].items():
+        if key == 'props':
+          for prop_num, prop_val in enumerate(val):
+            self.write_data(f'property_{prop_num}', prop_val.item())
+        elif key == 'dprops':
+          for prop_num, prop_val in enumerate(val):
+            self.write_data(f'dproperty_{prop_num}', prop_val.item())
+        else:
+          self.write_data(key, val.item())
+
+    if epoch % save_every == 0:
+      print(f'Saving history buffer to {self.history_file}')
+      self.to_csv(self.history_file)

+

+
+
+
+

+[docs]
+class EnsembleHistoryWriter(BaseHistoryWriter):
+  log_every: int
+  write_every: int
+  history_writers: List[HistoryWriter]
+
+

+[docs]
+  def __init__(self, base_name: str, n_pinns: int, log_every: int, write_every: int) -> None:
+    super().__init__(log_every, write_every)
+    self.history_writers = [
+      HistoryWriter(f'{base_name}_{n}.csv', log_every, write_every) for n in range(n_pinns)
+    ]

+
+    
+

+[docs]
+  def to_csv(self):
+    for writer in self.history_writers:
+      writer.to_csv()

+
+
+

+[docs]
+  def write_aux_values(self, loss):
+    for key, val in loss[1].items():
+      for n, writer in enumerate(self.history_writers):
+        if key == 'props':
+          # for prop_num, prop_val in enumerate(val):
+          #   writer.write_data(f'property_{prop_num}', prop_val[n].item())
+          # writer.write_data(f'property_{prop_num}')
+          for prop_num, prop_val in enumerate(val[n]):
+            writer.write_data(f'property_{prop_num}', prop_val.item())
+          # writer.write_data(f'property_')
+        else:
+          writer.write_data(key, val[n].item())

+
+
+

+[docs]
+  def write_epoch(self, epoch):
+    for writer in self.history_writers:
+      writer.write_epoch(epoch)

+
+
+

+[docs]
+  def write_loss(self, loss):
+    for n, writer in enumerate(self.history_writers):
+      writer.write_data('loss', loss[0][n].item())

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/kernels/base_kernel.html b/_modules/pancax/kernels/base_kernel.html new file mode 100644 index 0000000..bdee416 --- /dev/null +++ b/_modules/pancax/kernels/base_kernel.html @@ -0,0 +1,393 @@ + + + + + + + + pancax.kernels.base_kernel — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.kernels.base_kernel

+from abc import ABC
+from abc import abstractmethod
+from jax import hessian, jacfwd, vmap
+from jax import numpy as jnp
+from pancax.fem import read_exodus_mesh
+from pancax.fem.function_space import compute_field_gradient
+from typing import Callable, Dict, List, Union
+import equinox as eqx
+
+
+

+[docs]
+def vector_names(base_name: str, dim: int):
+	pass

+
+
+
+

+[docs]
+def full_tensor_names(base_name: str):
+	"""
+	Provides a full list of tensorial variable component names
+	:param base_name: base name for a tensor variable e.g. base_name_xx
+	"""
+	return [
+		f'{base_name}_xx', f'{base_name}_xy', f'{base_name}_xz', 
+		f'{base_name}_yx', f'{base_name}_yy', f'{base_name}_yz', 
+		f'{base_name}_zx', f'{base_name}_zy', f'{base_name}_zz'
+	]

+
+
+
+

+[docs]
+def full_tensor_names_2D(base_name: str):
+	"""
+	Provides a full list of tensorial variable component names
+	:param base_name: base name for a tensor variable e.g. base_name_xx
+	"""
+	return [
+		f'{base_name}_xx', f'{base_name}_xy', 
+		f'{base_name}_yx', f'{base_name}_yy'
+	]

+
+
+# TODO improve this
+

+[docs]
+def element_pp(func, has_props=False, jit=True):
+	"""
+	:param func: Function to use for an element property output variable
+	:param has_props: Whether or not this function need properties
+	:param jit: Whether or not to jit this function
+	"""
+	if jit:
+		return eqx.filter_jit(func)
+	else:
+		return func

+
+
+
+

+[docs]
+def nodal_pp(func, has_props=False, jit=True):
+	"""
+	:param func: Function to use for a nodal property output variable
+	:param has_props: Whether or not this function need properties
+	:param jit: Whether or not to jit this function
+	"""
+	if has_props:
+		# new_func = lambda p, d, t: vmap(
+		# 	func, in_axes=(None, 0, None, None)
+		# )(p.fields, d.coords, t, p.properties)
+		new_func = lambda p, d, t: vmap(
+			func, in_axes=(None, 0, None)
+		)(p, d.coords, t)
+	else:
+		new_func = lambda p, d, t: vmap(
+			func, in_axes=(None, 0, None)
+		)(p.fields, d.coords, t)
+	
+	if jit:
+		return eqx.filter_jit(new_func)
+	else:
+		return new_func

+
+
+
+# make a standard pp method that just has nodal fields, element grads, etc.
+

+[docs]
+def standard_pp(physics):
+	d = {
+		'field_values': {
+			'method': nodal_pp(physics.field_values),
+			'names' : physics.field_value_names
+		}
+	}
+	return d

+
+
+
+

+[docs]
+class PhysicsKernel(ABC):
+	n_dofs: int
+	field_value_names: List[str]
+	bc_func: Callable # further type this guy
+	var_name_to_method: Dict[str, Dict[str, Union[Callable, List[str]]]] = {}
+	use_delta_pinn: bool
+
+

+[docs]
+	def __init__(
+		self, 
+		mesh_file, 
+		bc_func, 
+		use_delta_pinn
+	) -> None:
+		self.bc_func = bc_func
+		self.use_delta_pinn = use_delta_pinn
+
+		# currently a dumb setup
+		mesh = read_exodus_mesh(mesh_file)
+
+		self.x_mins = jnp.min(mesh.coords, axis=0)
+		self.x_maxs = jnp.max(mesh.coords, axis=0)
+
+		print('Bounding box for mesh:')
+		print(f'  x_mins = {self.x_mins}')
+		print(f'  x_maxs = {self.x_maxs}')
+
+		if self.use_delta_pinn:
+			def field_basis(self, basis_network, x, t, v):
+				inputs = jnp.hstack((v, t))
+				z = basis_network(inputs)
+				return z
+
+			def field_values(field_network, x, t, v):
+				# TODO assume here for now that modes are normalized
+				# v_temp = (v - jnp.min(v, axis=0)) / (jnp.max(v, axis=0) - jnp.min(v, axis=0))
+				# inputs = jnp.hstack((v_temp, t))
+				inputs = jnp.hstack((v, t))
+				z = field_network(inputs)
+				u = self.bc_func(x, t, z)
+				return u
+		else:
+			def field_basis(self, basis_network, x, t):
+				x = (x - self.x_mins) / (self.x_maxs - self.x_mins)
+				inputs = jnp.hstack((x, t))
+				z = basis_network(inputs)
+				return z
+
+			def field_values(field_network, x, t):
+				x_temp = (x - self.x_mins) / (self.x_maxs - self.x_mins)
+				inputs = jnp.hstack((x_temp, t))
+				z = field_network(inputs)
+				u = self.bc_func(x, t, z)
+				return u
+	
+		self.field_basis = field_basis
+		self.field_values = field_values

+

+
+
+
+

+[docs]
+class StrongFormPhysicsKernel(PhysicsKernel):
+	n_dofs: int
+	field_value_names: List[str]
+	bc_func: Callable # further type this guy
+	use_delta_pinn: bool
+	
+

+[docs]
+	def __init__(self, mesh_file, bc_func, use_delta_pinn) -> None:
+		# if use_delta_pinn:
+		# 	raise ValueError('DeltaPINNs are currently not supported with collocation PINNs.')
+		super().__init__(mesh_file, bc_func, use_delta_pinn)

+
+
+

+[docs]
+	def field_gradients(self, field_network, x, t):
+		return jacfwd(self.field_values, argnums=1)(field_network, x, t)

+
+
+

+[docs]
+	def field_hessians(self, field_network, x, t):
+		return hessian(self.field_values, argnums=1)(field_network, x, t)

+
+
+

+[docs]
+	def field_laplacians(self, field_network, x, t):
+		return jnp.trace(self.field_hessians(field_network, x, t), axis1=1, axis2=2)

+
+
+

+[docs]
+	def field_time_derivatives(self, field_network, x, t):
+		return jacfwd(self.field_values, argnums=2)(field_network, x, t)

+
+
+

+[docs]
+	def field_second_time_derivatives(self, field_network, x, t):
+		return jacfwd(self.field_time_derivatives, argnums=2)(field_network, x, t)

+
+
+

+[docs]
+	@abstractmethod
+	def strong_form_neumann_bc(self, params, x, t, n):
+		pass

+
+
+

+[docs]
+	@abstractmethod
+	def strong_form_residual(self, params, x, t):
+		pass

+

+
+
+
+

+[docs]
+class WeakFormPhysicsKernel(PhysicsKernel):
+	n_dofs: int
+	field_value_names: List[str]
+	bc_func: Callable # further type this guy
+	use_delta_pinn: bool
+	
+

+[docs]
+	def __init__(self, mesh_file, bc_func, use_delta_pinn) -> None:
+		super().__init__(mesh_file, bc_func, use_delta_pinn)

+
+
+

+[docs]
+	def element_field_gradient(self, params, domain, t):
+		us = self.field_values(params, domain.coords, t)
+		grads = compute_field_gradient(domain.fspace, us, domain.coords)
+		return grads

+
+
+	# newer methods
+

+[docs]
+	def element_quantity(self, f, fspace, x_el, u_el, props):
+		Ns = fspace.shape_function_values(x_el)
+		grad_Ns = fspace.shape_function_gradients(x_el)
+		JxWs = fspace.JxWs(x_el)
+		return jnp.sum(vmap(f, in_axes=(None, None, 0, 0, 0, None))(x_el, u_el, Ns, grad_Ns, JxWs, props))

+
+
+

+[docs]
+	def element_quantity_grad(self, f, fspace, x_el, u_el, props):
+		return jacfwd(self.element_quantity, argnums=3)(f, fspace, x_el, u_el, props)

+
+
+

+[docs]
+	def element_quantity_hessian(self, f, fspace, x_el, u_el, props):
+		return hessian(self.element_quantity, argnums=3)(f, fspace, x_el, u_el, props)

+
+
+

+[docs]
+	@abstractmethod
+	def energy(self, x_el, u_el, N, grad_N, JxW, props):
+		pass

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/kernels/laplace_beltrami.html b/_modules/pancax/kernels/laplace_beltrami.html new file mode 100644 index 0000000..ccdfe94 --- /dev/null +++ b/_modules/pancax/kernels/laplace_beltrami.html @@ -0,0 +1,158 @@ + + + + + + + + pancax.kernels.laplace_beltrami — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.kernels.laplace_beltrami
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.kernels.laplace_beltrami

+from .base_kernel import WeakFormPhysicsKernel
+from .base_kernel import nodal_pp
+from typing import Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+class LaplaceBeltrami(WeakFormPhysicsKernel):
+  n_dofs = 1
+  field_names = ['eigenvector']
+  use_delta_pinn: bool
+
+

+[docs]
+  def __init__(self, mesh_file, bc_func, n_eigs: int, use_delta_pinn: Optional[bool] = False):
+    super().__init__(mesh_file, bc_func, use_delta_pinn)
+    self.n_eigs = n_eigs
+    self.var_name_to_method = {
+      'eigenvector': {
+        'method': nodal_pp(self.field_values),
+        'names' : self.field_names
+      }
+    }

+
+
+

+[docs]
+  def energy(self, x_el, u_el, N, grad_N, JxW, props):
+    # caclulate quadrature level fields
+    grad_u_q = (grad_N.T @ u_el).T
+
+    # kernel specific stuff here
+    pi_q = 0.5 * jnp.dot(grad_u_q, grad_u_q.T)
+
+    return JxW * pi_q

+
+
+

+[docs]
+  def kinetic_energy(self, x_el, u_el, N, grad_N, JxW, props):
+    return JxW * 0.5 * jnp.dot(u_el.T, u_el)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/kernels/linear_elasticity.html b/_modules/pancax/kernels/linear_elasticity.html new file mode 100644 index 0000000..9c7314a --- /dev/null +++ b/_modules/pancax/kernels/linear_elasticity.html @@ -0,0 +1,199 @@ + + + + + + + + pancax.kernels.linear_elasticity — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.kernels.linear_elasticity
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.kernels.linear_elasticity

+from .base_kernel import StrongFormPhysicsKernel, WeakFormPhysicsKernel
+from .base_kernel import nodal_pp, standard_pp, full_tensor_names_2D
+from jax import jacfwd
+from typing import Callable, Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+class LinearElasticity2D(StrongFormPhysicsKernel, WeakFormPhysicsKernel):
+  n_dofs = 2
+  field_value_names = ['displ_x', 'displ_y']
+  use_delta_pinn: bool
+
+

+[docs]
+  def __init__(
+    self, 
+    mesh_file: str,
+    bc_func: Callable,
+    body_force: Callable = lambda x, t: jnp.zeros(2),
+    use_delta_pinn: Optional[bool] = False
+  ) -> None:
+    super().__init__(mesh_file, bc_func, use_delta_pinn)
+    self.body_force = body_force
+    self.var_name_to_method = standard_pp(self)
+    self.var_name_to_method['field_gradients'] = {
+      'names': full_tensor_names_2D('grad_displ'),
+      'method': nodal_pp(self.field_gradients)
+    }
+    self.var_name_to_method['linear_strain'] = {
+      'names': full_tensor_names_2D('linear_strain'),
+      'method': nodal_pp(self.linear_strain)
+    }
+    self.var_name_to_method['cauchy_stress'] = {
+      'names': full_tensor_names_2D('cauchy_stress'),
+      'method': nodal_pp(self.cauchy_stress, has_props=True)
+    }

+
+
+

+[docs]
+  def energy(self, x_el, u_el, N, grad_N, JxW, props):
+    lambda_, mu = props()
+    grad_u_q = (grad_N.T @ u_el).T
+    strain = 0.5 * (grad_u_q + grad_u_q.T)
+    return 0.5 * lambda_ * jnp.trace(strain)**2 + \
+           mu * jnp.trace(strain @ strain)

+
+
+

+[docs]
+  def strong_form_residual(self, params, x, t):
+    div_stress = jacfwd(self.cauchy_stress, argnums=1)(params, x, t)
+    div_stress = jnp.trace(div_stress, axis1=1, axis2=2)
+    f = self.body_force(x, t)
+    return div_stress + f

+
+
+

+[docs]
+  def strong_form_neumann_bc(self, params, x, t, n):
+    sigma = self.cauchy_stress(params, x, t)
+    traction = sigma @ n
+    return traction

+
+
+

+[docs]
+  def linear_strain(self, field_network, x, t):
+    grad_u = self.field_gradients(field_network, x, t)
+    return 0.5 * (grad_u + grad_u.T)

+
+
+

+[docs]
+  def cauchy_stress(self, params, x, t):
+    field_network, props = params
+    lambda_, mu = props()
+    strain = self.linear_strain(field_network, x, t)
+    stress = lambda_ * jnp.trace(strain) * jnp.eye(2) + \
+             2. * mu * strain
+    return stress

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/kernels/poisson.html b/_modules/pancax/kernels/poisson.html new file mode 100644 index 0000000..b93e640 --- /dev/null +++ b/_modules/pancax/kernels/poisson.html @@ -0,0 +1,172 @@ + + + + + + + + pancax.kernels.poisson — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.kernels.poisson

+from .base_kernel import StrongFormPhysicsKernel, WeakFormPhysicsKernel
+from .base_kernel import standard_pp
+from typing import Callable, Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+class Poisson(StrongFormPhysicsKernel, WeakFormPhysicsKernel):
+	n_dofs = 1
+	field_value_names = ['u']
+	use_delta_pinn: bool
+
+

+[docs]
+	def __init__(
+		self, 
+		mesh_file, 
+		bc_func: Callable, 
+		f: Callable,
+		use_delta_pinn: Optional[bool] = False
+	):
+		super().__init__(mesh_file, bc_func, use_delta_pinn)
+		self.f = f
+		self.var_name_to_method = standard_pp(self)

+
+
+

+[docs]
+	def energy(self, x_el, u_el, N, grad_N, JxW, props):
+		# caclulate quadrature level fields
+		x_q = jnp.dot(N, x_el)
+		u_q = jnp.dot(N, u_el)
+		grad_u_q = (grad_N.T @ u_el).T
+
+		# kernel specific stuff here
+		f_q = self.f(x_q)
+		pi_q = 0.5 * jnp.dot(grad_u_q, grad_u_q.T) - f_q * u_q
+		return JxW * pi_q

+
+
+

+[docs]
+	def strong_form_residual(self, params, x, t):
+		field_network, props = params
+		delta_u = self.field_laplacians(field_network, x, t)[0]
+		f = self.f(x)
+		return -delta_u - f

+
+
+

+[docs]
+	def strong_form_neumann_bc(self, params, x, t, n):
+		field_network, props = params
+		grad_u = self.field_gradients(field_network, x, t)
+		return -jnp.dot(grad_u, n)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/kinematics.html b/_modules/pancax/kinematics.html new file mode 100644 index 0000000..68b9654 --- /dev/null +++ b/_modules/pancax/kinematics.html @@ -0,0 +1,222 @@ + + + + + + + + pancax.kinematics — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.kinematics

+from jax import hessian
+from jax import jacfwd
+from jax import vmap
+from .math.tensor_math import tensor_2D_to_3D
+import jax.numpy as jnp
+
+
+# single point methods
+# def field_value(network, x, t):e
+
+

+[docs]
+def create_field_methods(domain, bc_func):
+  # normalization up front
+  # TODO currently hard-coded to min-max normalization
+  # TODO make this selectable
+  x_mins = jnp.min(domain.coords, axis=0)
+  x_maxs = jnp.max(domain.coords, axis=0)
+
+  # single point methods
+  def field_value(network, x, t):
+    x_normalized = (x - x_mins) / (x_maxs - x_mins)
+    z = network(jnp.hstack((x_normalized, t)))
+    u = bc_func(x, t, z)
+    return u
+
+  def field_gradient(network, x, t):
+    return jacfwd(field_value, argnums=1)(network, x, t)
+
+  def field_hessian(network, x, t):
+    return hessian(field_value, argnums=1)(network, x, t)
+
+  def field_time_derivative(network, x, t):
+    return jacfwd(field_value, argnums=2)(network, x, t)
+
+  return field_value, field_gradient, field_hessian, field_time_derivative

+
+  # all point methods at single time step
+  # def field_values(network, xs, t):
+  #   return vmap(field_value, in_axes=(None, 0, None))(network, xs, t)
+  
+  # def field_gradients(network, xs, t):
+  #   return vmap(field_gradient, in_axes=(None, 0, None))(network, xs, t)
+
+  # def field_hessians(network, xs, t):
+  #   return vmap(field_hessian, in_axes=(None, 0, None))(network, xs, t)
+
+  # def field_time_derivatives(network, xs, t):
+  #   return vmap(field_time_derivative, in_axes=(None, 0, None))(network, xs, t)
+
+  # return field_values, field_gradients, field_hessians, field_time_derivatives
+
+
+

+[docs]
+def deformation_gradients(grad_us, formulation):
+  temp = vmap(lambda x: tensor_2D_to_3D(x) + jnp.eye(3))(grad_us)
+  # temp = tensor_2D_to_3D(grad_us) + jnp.eye(3)
+  Fs = vmap(lambda x: formulation(x), in_axes=(0,))(temp)
+  return Fs

+
+
+
+

+[docs]
+def invariants_old(grad_us, formulation):
+  Fs         = deformation_gradients(grad_us, formulation)
+  Cs         = vmap(lambda F: F.T @ F, in_axes=(0,))(Fs)
+  Cs_squared = vmap(lambda C: C @ C, in_axes=(0,))(Cs)
+  I1s        = vmap(lambda C: jnp.trace(C), in_axes=(0,))(Cs)
+  I2s        = vmap(lambda I1, C_squared: 0.5 * (I1**2 - jnp.trace(C_squared)), in_axes=(0, 0))(I1s, Cs_squared)
+  I3s        = vmap(lambda C: jnp.linalg.det(C), in_axes=(0,))(Cs)
+  return I1s, I2s, I3s

+
+
+
+

+[docs]
+def invariants(grad_u):
+  F         = grad_u + jnp.eye(3)
+  C         = F.T @ F
+  C_squared = C @ C
+  I1        = jnp.trace(C)
+  I2        = 0.5 * (I1**2 - jnp.trace(C_squared))
+  I3        = jnp.linalg.det(C)
+  return I1, I2, I3

+
+
+
+

+[docs]
+def plane_strain(F):
+  return F

+
+
+
+

+[docs]
+def incompressible_plane_stress(F):
+  F_33 = 1.0 / (F[0, 0] * F[1, 1] - F[0, 1] * F[1, 0])
+  return jnp.array(
+    [
+      [F[0, 0], F[0, 1], 0.0],
+      [F[1, 0], F[1, 1], 0.0],
+      [0.0    , 0.0    , F_33]
+    ]
+  )

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/logging.html b/_modules/pancax/logging.html new file mode 100644 index 0000000..a26f0e5 --- /dev/null +++ b/_modules/pancax/logging.html @@ -0,0 +1,270 @@ + + + + + + + + pancax.logging — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.logging

+from abc import abstractmethod
+from pathlib import Path
+from typing import List
+import equinox as eqx
+
+
+

+[docs]
+def log_loss(loss, n, log_every):
+  if n % log_every == 0:
+    print(f'Epoch {n}:')
+    print(f'\tLoss = {loss[0].item()}')
+    for key, val in loss[1].items():
+      if key == 'props' or key == 'dprops':
+        print(f'\t{key} = {val}')
+      else:
+        print(f'\t{key} = {val.item()}')

+
+
+
+

+[docs]
+class BaseLogger(eqx.Module):
+  log_every: int
+
+

+[docs]
+  @abstractmethod
+  def flush(self):
+    pass

+
+
+

+[docs]
+  def log_loss(self, loss, epoch):
+    if epoch % self.log_every == 0:
+      self.write_epoch_value(epoch)
+      self.write_loss_value(loss)
+      self.write_aux_values(loss)
+      self.flush()

+
+
+

+[docs]
+  @abstractmethod
+  def write_aux_values(self, loss):
+    pass

+
+
+

+[docs]
+  @abstractmethod
+  def write_epoch_value(self, epoch):
+    pass

+
+
+

+[docs]
+  @abstractmethod
+  def write_loss_value(self, loss):
+    pass

+

+
+
+
+

+[docs]
+class Logger(BaseLogger):
+  log_file: any
+
+

+[docs]
+  def __init__(self, log_file_in: str, log_every: int) -> None:
+    super().__init__(log_every)
+    log_file_in = Path(log_file_in)
+    self.log_file = open(log_file_in, 'w')

+
+
+  def __exit__(self, exc_type, exc_value, exc_traceback):
+    print(f'Closing log file.')
+    self.log_file.close()
+
+

+[docs]
+  def flush(self):
+    self.log_file.flush()

+
+
+

+[docs]
+  def write_aux_values(self, loss):
+    for key, val in loss[1].items():
+      if key == 'props' or key == 'dprops':
+        self.log_file.write(f'  {key} = {val}\n')
+      else:
+        self.log_file.write(f'  {key} = {val.item()}\n')

+
+
+

+[docs]
+  def write_epoch_value(self, epoch):
+    self.log_file.write(f'Epoch {epoch}:\n')

+
+
+

+[docs]
+  def write_loss_value(self, loss):
+    self.log_file.write(f'  Loss = {loss[0].item()}\n')

+

+
+
+
+

+[docs]
+class EnsembleLogger(BaseLogger):
+  loggers: List[Logger]
+
+

+[docs]
+  def __init__(self, base_name: str, n_pinns: int, log_every: int) -> None:
+    super().__init__(log_every)
+    self.loggers = [Logger(f'{base_name}_{n}.log', log_every) for n in range(n_pinns)]

+
+
+

+[docs]
+  def flush(self):
+    for logger in self.loggers:
+      logger.flush()

+
+
+

+[docs]
+  def write_aux_values(self, loss):
+    for key, val in loss[1].items():
+      for n, logger in enumerate(self.loggers):
+        if key == 'props' or key == 'dprops':
+          logger.log_file.write(f'  {key} = {val[n]}\n')
+        else:
+          logger.log_file.write(f'  {key} = {val[n].item()}\n')

+
+
+

+[docs]
+  def write_epoch_value(self, epoch):
+    for logger in self.loggers:
+      logger.write_epoch_value(epoch)

+
+
+

+[docs]
+  def write_loss_value(self, loss):
+    for n, val in enumerate(loss[0]):
+      self.loggers[n].log_file.write(f'  Loss = {val.item()}\n')

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/base_loss_function.html b/_modules/pancax/loss_functions/base_loss_function.html new file mode 100644 index 0000000..32171f4 --- /dev/null +++ b/_modules/pancax/loss_functions/base_loss_function.html @@ -0,0 +1,172 @@ + + + + + + + + pancax.loss_functions.base_loss_function — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.base_loss_function
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.base_loss_function

+from abc import abstractmethod
+import equinox as eqx
+
+
+

+[docs]
+class BaseLossFunction(eqx.Module):
+  """
+  Base class for loss functions. 
+  Currently does nothing but helps build a 
+  type hierarchy.
+  """
+  
+

+[docs]
+  def filtered_loss(self, diff_params, static_params, domain):
+    params = eqx.combine(diff_params, static_params)
+    return self.__call__(params, domain) 

+

+
+
+
+

+[docs]
+class BCLossFunction(BaseLossFunction):
+  """
+  Base class for boundary condition loss functions.
+
+  A ``load_step`` method is expect with the following
+  type signature
+  ``load_step(self, params, domain, t)``
+  """
+

+[docs]
+  @abstractmethod
+  def load_step(self, params, domain, t):
+    pass

+

+
+
+
+

+[docs]
+class PhysicsLossFunction(BaseLossFunction):
+  """
+  Base class for physics loss functions.
+
+  A ``load_step`` method is expect with the following
+  type signature
+  ``load_step(self, params, domain, t)``
+  """
+

+[docs]
+  @abstractmethod
+  def load_step(self, params, domain, t):
+    pass

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/bc_loss_functions.html b/_modules/pancax/loss_functions/bc_loss_functions.html new file mode 100644 index 0000000..9f6115c --- /dev/null +++ b/_modules/pancax/loss_functions/bc_loss_functions.html @@ -0,0 +1,201 @@ + + + + + + + + pancax.loss_functions.bc_loss_functions — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.bc_loss_functions
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.bc_loss_functions

+from .base_loss_function import BCLossFunction
+from jax import vmap
+from typing import Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+class DirichletBCLoss(BCLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    error = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    ).mean()
+    return self.weight * error, dict(dirichlet_bc=error)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    # TODO switch to using a jax.lax.scan below
+    # error = 0.0
+    # for bc in domain.essential_bcs:
+    #   coords = domain.coords[domain.mesh.nodeSets[bc.nodeSet]]
+    #   us_predicted = vmap(domain.physics.field_values, in_axes=(None, 0, None))(
+    #     field_network, coords, t
+    #   )[:, bc.component]
+    #   us_expected = vmap(bc.function, in_axes=(0, None))(coords, t)
+    #   error += jnp.square(us_predicted - us_expected).mean()
+    
+    # print(type(domain.essential_bcs))
+    def vmap_func(bc):
+      coords = domain.coords[domain.mesh.nodeSets[bc.nodeSet]]
+      us_predicted = vmap(domain.physics.field_values, in_axes=(None, 0, None))(
+        field_network, coords, t
+      )[:, bc.component]
+      us_expected = vmap(bc.function, in_axes=(0, None))(coords, t)
+      return jnp.square(us_predicted - us_expected).mean()
+
+    # errors = vmap(vmap_func)(domain.essential_bcs)
+    # error = jnp.sum(errors)
+    error = 0.0
+    for bc in domain.essential_bcs:
+      error = error + vmap_func(bc)
+    return error

+

+
+
+
+# NOTE below only supports zero neumann conditions currently
+# NOTE this will break on delta PINNs maybe?
+

+[docs]
+class NeumannBCLoss(BCLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    error = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    ).mean()
+    return self.weight * error, dict(neumann_bc=error)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    func = domain.physics.strong_form_neumann_bc
+    xs = domain.neumann_xs
+    ns = domain.neumann_ns
+    error = jnp.square(vmap(func, in_axes=(None, 0, None, 0))(
+      params, xs, t, ns
+    )).mean()
+    return error

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/data_loss_functions.html b/_modules/pancax/loss_functions/data_loss_functions.html new file mode 100644 index 0000000..4b50af8 --- /dev/null +++ b/_modules/pancax/loss_functions/data_loss_functions.html @@ -0,0 +1,150 @@ + + + + + + + + pancax.loss_functions.data_loss_functions — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.data_loss_functions
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.data_loss_functions

+from .base_loss_function import BaseLossFunction
+from jax import vmap
+from typing import Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+class FullFieldDataLoss(BaseLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(
+    self, 
+    weight: Optional[float] = 1.0
+  ):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    field_network, _ = params
+    n_dims = domain.coords.shape[1]
+    xs = domain.field_data.inputs[:, 0:n_dims]
+    # TODO need time normalization
+    ts = domain.field_data.inputs[:, n_dims]
+    # TODO below is currenlty the odd ball for the field_value API
+    u_pred = vmap(domain.physics.field_values, in_axes=(None, 0, 0))(
+      field_network, xs, ts
+    )
+
+    # TODO add output normalization
+    loss = jnp.square(u_pred - domain.field_data.outputs).mean()
+    aux = {'field_data_loss': loss}
+    return self.weight * loss, aux

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/ic_loss_function.html b/_modules/pancax/loss_functions/ic_loss_function.html new file mode 100644 index 0000000..9854e90 --- /dev/null +++ b/_modules/pancax/loss_functions/ic_loss_function.html @@ -0,0 +1,137 @@ + + + + + + + + pancax.loss_functions.ic_loss_function — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.ic_loss_function
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.ic_loss_function

+from .base_loss_function import BaseLossFunction
+from jax import vmap
+import jax.numpy as jnp
+
+

+[docs]
+class ICLossFunction(BaseLossFunction):
+  weight: float = 1.0
+
+  def __call__(self, params, problem):
+    def vmap_func(ic):
+      field, _ = params
+      coords = problem.domain.coords
+      physics = problem.physics
+      us_predicted = physics.vmap_field_values(field, coords, 0.)
+      us_expected = vmap(ic)(coords)
+      return jnp.square(us_predicted - us_expected).mean()
+    
+    error = 0.0
+    for ic in problem.ics:
+      error = error + vmap_func(ic)
+    return self.weight * error, dict(ic=error)

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/physics_loss_functions_strong_form.html b/_modules/pancax/loss_functions/physics_loss_functions_strong_form.html new file mode 100644 index 0000000..36ac388 --- /dev/null +++ b/_modules/pancax/loss_functions/physics_loss_functions_strong_form.html @@ -0,0 +1,175 @@ + + + + + + + + pancax.loss_functions.physics_loss_functions_strong_form — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.physics_loss_functions_strong_form
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.physics_loss_functions_strong_form

+from jax import vmap
+from pancax.physics import nodal_incompressibility_constraint
+from typing import Optional
+import jax.numpy as jnp
+
+
+

+[docs]
+def StrongFormResidualLoss(weight: Optional[float] = 1.0):
+  def loss_func(params, domain):
+    times = domain.times
+    func = domain.physics.strong_form_residual
+    xs = domain.coords
+    def vmap_func(params, xs, t):
+      residuals = vmap(func, in_axes=(None, 0, None))(params, xs, t)
+      residuals = residuals[domain.dof_manager.unknownIndices].flatten()
+      residual = jnp.square(residuals).mean()
+      return residual
+    residual = vmap(vmap_func, in_axes=(None, None, 0))(params, xs, times)
+    residual = residual.mean()
+    return weight * residual, dict(residual=residual)
+  return loss_func

+
+
+
+# def StrongFormDirichletBCLoss(weight: Optional[float] = 1.0):
+#   def loss_func(params, domain):
+#     times = domain.times
+#     func = domain.physics.field_values
+
+
+# TODO need to add support for inhomogeneous neumann conditions
+

+[docs]
+def StrongFormNeumannBCLoss(weight: Optional[float] = 1.0):
+  def loss_func(params, domain):
+    times = domain.times
+    func = domain.physics.strong_form_neumann_bc
+    xs = domain.neumann_inputs
+    ns = domain.neumann_normals
+    def vmap_func(params, xs, t, ns):
+      residuals = vmap(func, in_axes=(None, 0, None, 0))(params, xs, t, ns)
+      residual = jnp.square(residuals - domain.neumann_outputs).mean()
+      return residual
+    residual = vmap(vmap_func, in_axes=(None, None, 0, None))(params, xs, times, ns)
+    residual = residual.mean()
+    return weight * residual, dict(neumann=residual)
+  return loss_func

+
+
+
+

+[docs]
+def StrongFormIncompressibilityConstraint(weight: Optional[bool] = 1.0):
+  def loss_func(params, domain):
+    def vmap_func(params, domain, time):
+      return nodal_incompressibility_constraint(params, domain, time)
+    loss = jnp.mean(vmap(vmap_func, in_axes=(None, None, 0))(params, domain, domain.times))
+    return weight * loss, dict(incompressibility_error=loss)
+  return loss_func

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/strong_form_loss_functions.html b/_modules/pancax/loss_functions/strong_form_loss_functions.html new file mode 100644 index 0000000..ea22095 --- /dev/null +++ b/_modules/pancax/loss_functions/strong_form_loss_functions.html @@ -0,0 +1,147 @@ + + + + + + + + pancax.loss_functions.strong_form_loss_functions — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.strong_form_loss_functions
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.strong_form_loss_functions

+from .base_loss_function import PhysicsLossFunction
+from jax import vmap
+from typing import Optional
+import jax.numpy as jnp
+
+
+# NOTE this probably does not currently dsupport deltaPINNs
+

+[docs]
+class StrongFormResidualLoss(PhysicsLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    residual = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    ).mean()
+    return self.weight * residual, dict(residual=residual)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    func = domain.physics.strong_form_residual
+    # TODO this will fail on delta PINNs currently
+    residuals = vmap(func, in_axes=(None, 0, None))(params, domain.coords, t)
+    return jnp.square(residuals).mean()

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/utils.html b/_modules/pancax/loss_functions/utils.html new file mode 100644 index 0000000..917c6e5 --- /dev/null +++ b/_modules/pancax/loss_functions/utils.html @@ -0,0 +1,147 @@ + + + + + + + + pancax.loss_functions.utils — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.loss_functions.utils

+from .base_loss_function import BaseLossFunction
+
+
+

+[docs]
+class CombineLossFunctions(BaseLossFunction):
+  funcs: any
+  with_props: bool
+
+

+[docs]
+  def __init__(self, *funcs, with_props=False):
+    temp_funcs = []
+    for f in funcs:
+      temp_funcs.append(f)
+    self.funcs = funcs
+    self.with_props = with_props

+
+
+  def __call__(self, params, domain):
+    loss = 0.0
+    aux = dict()
+    for f in self.funcs:
+      temp_loss, temp_aux = f(params, domain)
+      loss = loss + temp_loss
+      aux.update(temp_aux)
+
+    if self.with_props:
+      props = params.properties()
+      aux.update({'props': props})
+
+    return loss, aux

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/loss_functions/weak_form_loss_functions.html b/_modules/pancax/loss_functions/weak_form_loss_functions.html new file mode 100644 index 0000000..30a3fd8 --- /dev/null +++ b/_modules/pancax/loss_functions/weak_form_loss_functions.html @@ -0,0 +1,450 @@ + + + + + + + + pancax.loss_functions.weak_form_loss_functions — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.loss_functions.weak_form_loss_functions
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.loss_functions.weak_form_loss_functions

+from .base_loss_function import PhysicsLossFunction
+from jax import vmap
+from pancax.physics import potential_energy, potential_energy_and_residual
+from pancax.physics import incompressible_energy, incompressible_energy_and_residual
+from pancax.physics import potential_energy_residual_and_reaction_force
+from pancax.physics import quadrature_incompressibility_constraint
+from pancax.physics import residual_mse
+from typing import Optional
+import equinox as eqx
+import jax.numpy as jnp
+
+
+

+[docs]
+class EnergyLoss(PhysicsLossFunction):
+  r"""
+  Energy loss function akin to the deep energy method.
+
+  Calculates the following quantity
+
+  .. math::
+    \mathcal{L} = w\Pi\left[u\right] = w\int_\Omega\psi\left(\mathbf{F}\right)
+
+  :param weight: weight for this loss function
+  """
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    energies = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    )
+    energy = jnp.sum(energies)
+    loss = energy
+    return self.weight * loss, dict(energy=energy)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    # field_network, props = params
+    # us = domain.physics.field_values(field_network, t)
+    # us = domain.physics.vmap_field_values(field_network, domain.coords, t)
+    # props = props()
+    # pi = potential_energy(domain, us, props)
+    field, physics = params
+    us = physics.vmap_field_values(field, domain.coords, t)
+    pi = physics.potential_energy(params, domain.domain, t, us)
+    return pi

+

+
+
+
+

+[docs]
+class EnergyAndResidualLoss(PhysicsLossFunction):
+  r"""
+  Energy and residual loss function used in Hamel et. al
+
+  Calculates the following quantity
+
+  .. math::
+    \mathcal{L} = w_1\Pi\left[u\right] + w_2\delta\Pi\left[u\right]_{free}
+
+  :param energy_weight: Weight for the energy w_1
+  :param residual_weight: Weight for the residual w_2
+  """
+  energy_weight: float
+  residual_weight: float
+
+

+[docs]
+  def __init__(
+    self, 
+    energy_weight: Optional[float] = 1.0,
+    residual_weight: Optional[float] = 1.0
+  ):
+    self.energy_weight = energy_weight
+    self.residual_weight = residual_weight

+
+
+  def __call__(self, params, domain):
+    pis, Rs = vmap(self.load_step, in_axes=(None, None, 0))(params, domain, domain.times)
+    pi, R = jnp.sum(pis), jnp.sum(Rs)
+    loss = self.energy_weight * pi + self.residual_weight * R
+    return loss, dict(energy=pi, residual=R)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    us = domain.field_values(field_network, t)
+    props = props()
+    pi, R = potential_energy_and_residual(domain, us, props)
+    return pi, R

+

+
+  
+
+

+[docs]
+class EnergyResidualAndReactionLoss(PhysicsLossFunction):
+  energy_weight: float
+  residual_weight: float
+  reaction_weight: float
+  
+

+[docs]
+  def __init__(
+    self, 
+    energy_weight: Optional[float] = 1.0,
+    residual_weight: Optional[float] = 1.0,
+    reaction_weight: Optional[float] = 1.0
+  ):
+    self.energy_weight = energy_weight
+    self.residual_weight = residual_weight
+    self.reaction_weight = reaction_weight

+
+
+  def __call__(self, params, domain):
+    pis, Rs, reactions = vmap(self.load_step, in_axes=(None, None, 0))(params, domain, domain.times)
+    pi, R = jnp.sum(pis), jnp.sum(Rs) / len(domain.times)
+    reaction_loss = jnp.square(reactions - domain.global_data.outputs).mean()
+    loss = self.energy_weight * pi + \
+           self.residual_weight * R + \
+           self.reaction_weight * reaction_loss
+    return loss, dict(energy=pi, residual=R, global_data_loss=reaction_loss, reactions=reactions)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    # field_network, props = params
+    field, physics = params
+    # us = domain.field_values(field_network, t)
+    us = physics.vmap_field_values(field, domain.coords, t)
+    return physics.potential_energy_residual_and_reaction_force(params, domain, t, us, domain.global_data)

+

+
+    # props = props()
+    # return potential_energy_residual_and_reaction_force(domain, us, props)
+
+
+

+[docs]
+class QuadratureIncompressibilityConstraint(PhysicsLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    losses = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    )
+    loss = jnp.mean(losses)
+    return self.weight * loss, dict(incompressibility_error=loss)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    us = domain.field_values(field_network, t)
+    props = props()
+    return quadrature_incompressibility_constraint(domain, us, props)

+

+
+
+
+# class QuadratureIncompressibilityConstraintWithForce(PhysicsLossFunction):
+#   energy_weight: float
+#   residual_weight: float
+
+#   def __init__(
+#     self, 
+#     energy_weight: Optional[float] = 1.0,
+#     residual_weight: Optional[float] = 1.0
+#   ):
+#     self.energy_weight = energy_weight
+#     self.residual_weight = residual_weight
+
+#   def __call__(self, params, domain):
+#     losses, residuals = vmap(self.load_step, in_axes=(None, None, 0))(
+#       params, domain, domain.times
+#     )
+#     loss, R = jnp.sum(losses), jnp.sum(residuals)
+#     # return self.weight * loss, dict(incompressibility_error=loss)
+#     loss = self.energy_weight * loss + self.residual_weight * R
+#     return loss, dict(constraint_energy=loss, constraint_force=R)
+
+#   def load_step(self, params, domain, t):
+#     field_network, props = params
+#     us = domain.field_values(field_network, t)
+#     props = props()
+#     return quadrature_incompressibility_constraint_energy_and_residual(domain, us, props)
+
+#   def __call__(self, params, domain):
+#     pis, Rs = vmap(self.load_step, in_axes=(None, None, 0))(params, domain, domain.times)
+#     pi, R = jnp.sum(pis), jnp.sum(Rs)
+#     loss = self.energy_weight * pi + self.residual_weight * R
+#     return loss, dict(energy=pi, residual=R)
+
+#   def load_step(self, params, domain, t):
+#     field_network, props = params
+#     us = domain.field_values(field_network, t)
+#     props = props()
+#     pi, R = potential_energy_and_residual(domain, us, props)
+#     return pi, R
+
+
+

+[docs]
+class ResidualMSELoss(PhysicsLossFunction):
+  weight: float
+
+

+[docs]
+  def __init__(
+    self, 
+    weight: Optional[float] = 1.0
+  ):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    residuals = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    )
+    residual = jnp.sum(residuals)
+    loss = residual
+    return self.weight * loss, dict(residual=residual)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    us = domain.field_values(field_network, t)
+    props = props()
+    R = residual_mse(domain, us, props)
+    return R

+

+
+
+
+

+[docs]
+class IncompressibleEnergyLoss(PhysicsLossFunction):
+  r"""
+  Energy loss function akin to the deep energy method.
+
+  Calculates the following quantity
+
+  .. math::
+    \mathcal{L} = w\Pi\left[u\right] = w\int_\Omega\psi\left(\mathbf{F}\right)
+
+  :param weight: weight for this loss function
+  """
+  weight: float
+
+

+[docs]
+  def __init__(self, weight: Optional[float] = 1.0):
+    self.weight = weight

+
+
+  def __call__(self, params, domain):
+    energies = vmap(self.load_step, in_axes=(None, None, 0))(
+      params, domain, domain.times
+    )
+    energy = jnp.sum(energies)
+    loss = energy
+    return self.weight * loss, dict(energy=energy)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    us = domain.field_values(field_network, t)
+    props = props()
+    pi = incompressible_energy(domain, us, props)
+    return pi

+

+
+
+
+

+[docs]
+class IncompressibleEnergyAndResidualLoss(PhysicsLossFunction):
+  r"""
+  Energy and residual loss function used in Hamel et. al
+
+  Calculates the following quantity
+
+  .. math::
+    \mathcal{L} = w_1\Pi\left[u\right] + w_2\delta\Pi\left[u\right]_{free}
+
+  :param energy_weight: Weight for the energy w_1
+  :param residual_weight: Weight for the residual w_2
+  """
+  energy_weight: float
+  residual_weight: float
+
+

+[docs]
+  def __init__(
+    self, 
+    energy_weight: Optional[float] = 1.0,
+    residual_weight: Optional[float] = 1.0
+  ):
+    self.energy_weight = energy_weight
+    self.residual_weight = residual_weight

+
+
+  def __call__(self, params, domain):
+    pis, Rs = vmap(self.load_step, in_axes=(None, None, 0))(params, domain, domain.times)
+    pi, R = jnp.sum(pis), jnp.sum(Rs)
+    loss = self.energy_weight * pi + self.residual_weight * R
+    return loss, dict(energy=pi, residual=R)
+
+

+[docs]
+  def load_step(self, params, domain, t):
+    field_network, props = params
+    us = domain.field_values(field_network, t)
+    props = props()
+    pi, R = incompressible_energy_and_residual(domain, us, props)
+    return pi, R

+

+
+  
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/math/math.html b/_modules/pancax/math/math.html new file mode 100644 index 0000000..1eb5ae4 --- /dev/null +++ b/_modules/pancax/math/math.html @@ -0,0 +1,265 @@ + + + + + + + + pancax.math.math — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.math.math

+from jax import custom_jvp
+from jax import lax
+import jax.numpy as np
+
+# constants
+# Assumes IEEE double precision
+_DBL_PRECISION_SIGNIFICAND_BITS = 53
+
+# equivalent to ceil(_DBL_PRECISION_SIGNIFICAND_BITS / 2) as an integer
+_SPLIT_S = -(-_DBL_PRECISION_SIGNIFICAND_BITS // 2)
+_SPLIT_FACTOR = 1<<_SPLIT_S + 1
+
+@custom_jvp
+def safe_sqrt(x):
+    return np.sqrt(x)
+
+
+

+[docs]
+@safe_sqrt.defjvp
+def safe_sqrt_jvp(xt, vt):
+    x, = xt
+    v, = vt
+    f = safe_sqrt(x)
+    df = v * lax.cond( x <= 0,
+                       lambda x: 0.,
+                       lambda x: 0.5/f,
+                       x )
+    return f, df

+
+
+
+

+[docs]
+def sum2(a):
+    """
+    Sum a vector to much higher accuracy than numpy.sum.
+
+    Parameters
+    ----------
+    a : ndarray, with only one axis (shape [n,])
+
+    Returns
+    -------
+    sum : real
+        The sum of the numbers in the array
+
+
+    This special sum method computes the result as accurate as if 
+    computed in quadruple precision.
+
+    Reference:
+    T. Ogita, S. M. Rump, and S. Oishi. Accurate sum and dot product.
+    SIAM J. Sci. Comput., Vol 26, No 6, pp. 1955-1988.
+    doi: 10.1137/030601818
+    """
+    def f(carry, ai):
+        p, sigma = carry
+        p, q = _two_sum(p, ai)
+        sigma += q
+        return (p, sigma), p
+
+    total = 0.0
+    c = 0.0
+    (total, c), partialSums = lax.scan(f, (total, c), a)
+    return total + c

+
+
+
+

+[docs]
+def _two_sum(a, b):
+    x = a + b
+    z = x - a
+    y = (a - (x - z)) + (b - z)
+    return x, y

+
+
+
+

+[docs]
+def dot2(x, y):
+    """
+    Compute inner product of 2 vectors to much higher accuracy than numpy.dot.
+
+    Parameters
+    ----------
+    :param x: ndarray, with only one axis (shape [n,])
+    :param y: ndarray, with only one axis (shape [n,])
+
+    Returns
+    -------
+    :return dotprod: real
+        The inner product of the input vectors.
+
+
+    This special inner product  method computes the result as accurate
+    as if computed in quadruple precision. This algorithm is useful to
+    computing objective functions from numerical integration. It avoids
+    accumulation of floating point cancellation error that can obscure
+    whether an objective function has truly decreased.
+
+    The environment variable setting 
+    'XLA_FLAGS = "--xla_cpu_enable_fast_math=false"'
+    is critical for this function to work on the CPU. Otherwise, xla
+    apparently sets a flag for LLVM that allows unsafe floating point
+    optimizations that can change associativity.
+
+    Reference
+    T. Ogita, S. M. Rump, and S. Oishi. Accurate sum and dot product.
+    SIAM J. Sci. Comput., Vol 26, No 6, pp. 1955-1988.
+    doi 10.1137/030601818
+
+    """
+    def f(carry, xy):
+        p, s = carry
+        xi, yi = xy
+        h, r = _two_product(xi, yi)
+        p, q = _two_sum(p, h)
+        s = s + (q + r)
+        return (p, s), p
+
+    rawTotal = 0.0
+    compensation = 0.0
+    X = np.column_stack((x,y))
+    (rawTotal, compensation), partialSums = lax.scan(f,
+                                                     (rawTotal, compensation),
+                                                     X)
+    return rawTotal + compensation

+
+
+
+

+[docs]
+def _two_product(a, b):
+    x = a*b
+    a1, a2 = _float_split(a)
+    b1, b2 = _float_split(b)
+    y = a2*b2 - (((x - a1*b1) - a2*b1) - a1*b2)
+    return x, y

+
+
+
+

+[docs]
+def _float_split(a):
+    c = _SPLIT_FACTOR*a
+    x = c - (c - a)
+    y = a - x
+    return x, y

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/math/tensor_math.html b/_modules/pancax/math/tensor_math.html new file mode 100644 index 0000000..66cd6c8 --- /dev/null +++ b/_modules/pancax/math/tensor_math.html @@ -0,0 +1,886 @@ + + + + + + + + pancax.math.tensor_math — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.math.tensor_math

+from functools import partial
+from jax import custom_jvp
+from jax import jacfwd
+from jax import lax
+from jax import vmap
+from jax.lax import while_loop
+from jax.scipy import linalg
+from pancax.fem.quadrature_rules import create_padded_quadrature_rule_1D
+from pancax.math import math
+import jax.numpy as np
+
+
+

+[docs]
+def if_then_else(cond, val1, val2):
+    return lax.cond(cond,
+                    lambda x: val1,
+                    lambda x: val2,
+                    None)

+
+
+
+

+[docs]
+def compute_deviatoric_tensor(strain):
+    dil = np.trace(strain)
+    return strain - (dil/3.)*np.identity(3)

+
+
+
+

+[docs]
+def dev(strain): return compute_deviatoric_tensor(strain)

+
+
+
+

+[docs]
+def tensor_norm(tensor):
+    return np.linalg.norm(tensor, ord='fro')

+
+
+
+

+[docs]
+def norm_of_deviator_squared(tensor):
+    dev = compute_deviatoric_tensor(tensor)
+    return np.tensordot(dev,dev)

+
+
+
+

+[docs]
+def norm_of_deviator(tensor):
+    return tensor_norm( compute_deviatoric_tensor(tensor) )

+
+
+
+

+[docs]
+def mises_equivalent_stress(stress):
+    return np.sqrt(1.5)*norm_of_deviator(stress)

+
+
+
+

+[docs]
+def triaxiality(A):
+    mean_normal = np.trace(A)/3.0
+    mises_norm = mises_equivalent_stress(A)
+    # avoid division by zero in case of spherical tensor
+    mises_norm += np.finfo(np.dtype("float64")).eps
+    return mean_normal/mises_norm

+
+
+
+

+[docs]
+def sym(A):
+    return 0.5*(A + A.T)

+
+
+
+

+[docs]
+def logh(A):
+    d,V = linalg.eigh(A)
+    return logh_from_eigen(d,V)

+
+
+
+

+[docs]
+def logh_from_eigen(eVals, eVecs):
+    return eVecs@np.diag(np.log(eVals))@eVecs.T

+
+
+
+

+[docs]
+def tensor_2D_to_3D(H):
+    return np.zeros((3,3)).at[ 0:H.shape[0], 0:H.shape[1] ].set(H)

+
+
+
+#  Compute eigen values and vectors of a symmetric 3x3 tensor
+#  Note, returned eigen vectors may not be unit length
+#
+#  Note, this routine involves high powers of the input tensor (~M^8).  
+#  Thus results can start to denormalize when the infinity norm of the input
+#  tensor falls outside the range 1.0e-40 to 1.0e+40.
+#
+#  Outside this range use  eigen_sym33_unit
+

+[docs]
+def eigen_sym33_non_unit(tensor):
+    cxx = tensor[0,0]
+    cyy = tensor[1,1]
+    czz = tensor[2,2]
+    cxy = 0.5*(tensor[0,1]+tensor[1,0])
+    cyz = 0.5*(tensor[1,2]+tensor[2,1])
+    czx = 0.5*(tensor[2,0]+tensor[0,2])
+
+    c1 = (cxx + cyy + czz)/(3.0)
+    cxx -= c1
+    cyy -= c1
+    czz -= c1
+
+    cxy_cxy = cxy*cxy
+    cyz_cyz = cyz*cyz
+    czx_czx = czx*czx
+    cxx_cyy = cxx*cyy
+
+    c2 = cxx_cyy + cyy*czz + czz*cxx - cxy_cxy - cyz_cyz - czx_czx
+
+    c2Negative = c2 < 0
+    denom = np.where(c2Negative, c2, 1.0)
+    ThreeOverA = np.where(c2Negative, -3.0/denom, 1.0)
+    sqrtThreeOverA = np.where(c2Negative, np.sqrt(ThreeOverA), 1.0)
+    
+    c3 = cxx*cyz_cyz + cyy*czx_czx - 2.0*cxy*cyz*czx + czz*(cxy_cxy - cxx_cyy)
+
+    rr = -0.5*c3*ThreeOverA*sqrtThreeOverA
+    
+    arg = np.minimum(abs(rr), 1.0) # Check in the case rr = -1-eps
+    
+    cos_thd3 = cos_of_acos_divided_by_3(arg)
+
+    two_cos_thd3 = 2.0*cos_thd3*np.sign(rr)
+
+    eval2 = np.where(c2Negative, two_cos_thd3/sqrtThreeOverA, 1.0)
+    
+    crow0 = np.array([cxx - eval2, cxy,         czx        ])
+    crow1 = np.array([cxy,         cyy - eval2, cyz        ])
+    crow2 = np.array([czx,         cyz,         czz - eval2])
+
+    #
+    # do QR decomposition with column pivoting
+    #
+    k0 = crow0[0]*crow0[0] + cxy_cxy           + czx_czx
+    k1 = cxy_cxy           + crow1[1]*crow1[1] + cyz_cyz
+    k2 = czx_czx           + cyz_cyz           + crow2[2]*crow2[2]
+    
+    # returns zero or nan
+    k0gk1 = k1<=k0
+    k0gk2 = k2<=k0
+    k1gk2 = k2<=k1
+    
+    k0_largest = k0gk1 & k0gk2
+    k1_largest = k1gk2 & (~ k0gk1)
+    k2_largest = ~ (k0_largest | k1_largest)
+    k_largest = np.array([k0_largest, k1_largest, k2_largest])
+
+    k_row1_0 = if_then_else(k0_largest, crow0[0], 0.0)   \
+        +         if_then_else(k1_largest, crow1[0], 0.0) \
+        +         if_then_else(k2_largest, crow2[0], 0.0)
+
+    k_row1_1 = if_then_else(k0_largest, crow0[1], 0.0)   \
+        +         if_then_else(k1_largest, crow1[1], 0.0) \
+        +         if_then_else(k2_largest, crow2[1], 0.0)
+
+    k_row1_2 = if_then_else(k0_largest, crow0[2], 0.0)   \
+        +         if_then_else(k1_largest, crow1[2], 0.0) \
+        +         if_then_else(k2_largest, crow2[2], 0.0)
+
+    k_row1 = np.array([k_row1_0, k_row1_1, k_row1_2])
+    
+    row2_0 = if_then_else(k0_largest, crow1[0], crow0[0])
+    row2_1 = if_then_else(k0_largest, crow1[1], crow0[1])
+    row2_2 = if_then_else(k0_largest, crow1[2], crow0[2])
+    row2 = np.array([row2_0, row2_1, row2_2])
+
+    row3_0 = if_then_else(k2_largest, crow1[0], crow2[0])
+    row3_1 = if_then_else(k2_largest, crow1[1], crow2[1])
+    row3_2 = if_then_else(k2_largest, crow1[2], crow2[2])
+    row3 = np.array([row3_0, row3_1, row3_2])
+
+    ki_ki = 1.0 / ( if_then_else(k0_largest, k0, 0.0)   \
+                    + if_then_else(k1_largest, k1, 0.0) \
+                    + if_then_else(k2_largest, k2, 0.0) )
+    
+    ki_dpr1 = ki_ki*(k_row1[0]*row2[0] + k_row1[1]*row2[1] + k_row1[2]*row2[2])
+    ki_dpr2 = ki_ki*(k_row1[0]*row3[0] + k_row1[1]*row3[1] + k_row1[2]*row3[2])
+
+    row2 = row2 - ki_dpr1*k_row1
+    row3 = row3 - ki_dpr2*k_row1
+
+    a0 = row2[0]*row2[0] + row2[1]*row2[1] + row2[2]*row2[2]
+    a1 = row3[0]*row3[0] + row3[1]*row3[1] + row3[2]*row3[2]
+
+    a0lea1 = a0 <= a1
+
+    a_row2 = if_then_else(a0lea1, row3, row2)
+    ai_ai = 1.0 / if_then_else(a0lea1, a1, a0)
+    
+    evec2 = np.array([k_row1[1]*a_row2[2] - k_row1[2]*a_row2[1],
+                      k_row1[2]*a_row2[0] - k_row1[0]*a_row2[2],
+                      k_row1[0]*a_row2[1] - k_row1[1]*a_row2[0]])
+
+    k_atr11 = cxx*k_row1[0] + cxy*k_row1[1] + czx*k_row1[2]
+    k_atr21 = cxy*k_row1[0] + cyy*k_row1[1] + cyz*k_row1[2]
+    k_atr31 = czx*k_row1[0] + cyz*k_row1[1] + czz*k_row1[2]
+
+    a_atr12 = cxx*a_row2[0] + cxy*a_row2[1] + czx*a_row2[2]
+    a_atr22 = cxy*a_row2[0] + cyy*a_row2[1] + cyz*a_row2[2]
+    a_atr32 = czx*a_row2[0] + cyz*a_row2[1] + czz*a_row2[2]
+
+    rm2xx     = (k_row1[0]*k_atr11 + k_row1[1]*k_atr21 + k_row1[2]*k_atr31)*ki_ki
+    k_a_rm2xy = (k_row1[0]*a_atr12 + k_row1[1]*a_atr22 + k_row1[2]*a_atr32)
+    rm2yy     = (a_row2[0]*a_atr12 + a_row2[1]*a_atr22 + a_row2[2]*a_atr32)*ai_ai
+    rm2xy_rm2xy = k_a_rm2xy*k_a_rm2xy*ai_ai*ki_ki
+
+    #
+    # Wilkinson shift
+    #
+    b = 0.5*(rm2xx-rm2yy)
+
+    sqrtTerm = math.safe_sqrt(b*b+rm2xy_rm2xy)*np.sign(b)
+    #sqrtTerm = np.sqrt(b*b+rm2xy_rm2xy)*np.sign(b)
+    
+    eval0 = rm2yy + b - sqrtTerm
+    eval1 = rm2xx + rm2yy - eval0
+
+    rm2xx -= eval0
+    rm2yy -= eval0
+
+    rm2xx2 = rm2xx*rm2xx
+    rm2yy2 = rm2yy*rm2yy
+
+    fac1 = if_then_else(rm2xx2 < rm2yy2, k_a_rm2xy*ai_ai, rm2xx)
+    fac2 = if_then_else(rm2xx2 < rm2yy2, rm2yy, ki_ki*k_a_rm2xy)
+
+    evec0 = fac1*a_row2 - fac2*k_row1
+
+    rm2xx2iszero = rm2xx2 == (0.0)
+    rm2xy_rm2xyiszero = rm2xy_rm2xy == (0.0)
+    both_zero = rm2xx2iszero & rm2xy_rm2xyiszero
+
+    # check degeneracy
+    
+    evec0 = if_then_else(both_zero, a_row2, evec0)
+
+    evec1 = np.array([evec2[1]*evec0[2] - evec2[2]*evec0[1],
+                      evec2[2]*evec0[0] - evec2[0]*evec0[2],
+                      evec2[0]*evec0[1] - evec2[1]*evec0[0]])
+
+    eval0 = eval0 + c1
+    eval1 = eval1 + c1
+    eval2 = eval2 + c1
+    
+    c2tol = (c1*c1)*(-1.0e-30)
+
+    c2lsmall_neg = c2 < c2tol
+    
+    eval0 = if_then_else(c2lsmall_neg, eval0, c1)
+    eval1 = if_then_else(c2lsmall_neg, eval1, c1)
+    eval2 = if_then_else(c2lsmall_neg, eval2, c1)
+
+    evec0 = if_then_else(c2lsmall_neg, evec0, np.array([1.0, 0.0, 0.0]))
+    evec1 = if_then_else(c2lsmall_neg, evec1, np.array([0.0, 1.0, 0.0]))
+    evec2 = if_then_else(c2lsmall_neg, evec2, np.array([0.0, 0.0, 1.0]))
+    
+    evals = np.array([eval0, eval1, eval2])
+    evecs = np.column_stack((evec0,evec1,evec2))
+
+    #idx = np.arange(3)  # np.argsort(evals)
+    idx = np.argsort(evals)
+    
+    return evals[idx],evecs[:,idx]

+
+
+
+

+[docs]
+def eigen_sym33_unit(tensor):
+    cmax = np.linalg.norm(tensor, ord=np.inf)
+    cmaxInv = if_then_else(cmax > 0.0, 1.0/cmax, 1.0)
+    scaledTensor = cmaxInv * tensor
+   
+    evals, evecs = eigen_sym33_non_unit(scaledTensor)
+    
+    evec0 = evecs[:,0]/np.linalg.norm(evecs[:,0])
+    evec1 = evecs[:,1]/np.linalg.norm(evecs[:,1])
+    evec2 = evecs[:,2]/np.linalg.norm(evecs[:,2])
+    
+    evecs = np.column_stack((evec0,evec1,evec2))
+    evals = cmax*evals
+
+    return (evals,evecs)

+
+
+
+# Helper function for 3x3 spectral decompositions
+# Pade approximation to cos( acos(x)/3 )
+# was obtained from Mathematica with the following commands:
+#  
+# Needs["FunctionApproximations`"]
+# r1 = MiniMaxApproximation[Cos[ArcCos[x]/3], {x, {0, 1}, 6, 5}, WorkingPrecision -> 18, MaxIterations -> 500]
+#
+# 6 and 5 indicate the polynomial order in the numerator and denominator.
+

+[docs]
+def cos_of_acos_divided_by_3(x):
+    
+    x2 = x*x;
+    x4 = x2*x2;
+
+    numer = 0.866025403784438713 + 2.12714890259493060 * x + \
+        ( ( 1.89202064815951569  + 0.739603278343401613 * x ) * x2 + \
+          ( 0.121973926953064794 + x * (0.00655637626263929360 + 0.0000390884982780803443 * x) ) *x4 )
+
+    denom =     1.0 + 2.26376989330935617* x + \
+        ( ( 1.80461009751278976 + 0.603976798217196003 * x ) * x2 + \
+         ( 0.0783255761115461708 + 0.00268525944538021629 * x) * x4 )
+    
+    return numer/denom

+
+
+
+@custom_jvp
+def mtk_log_sqrt(A):
+    lam,V = eigen_sym33_unit(A)
+    return V @ np.diag(0.5*np.log(lam)) @ V.T
+
+
+

+[docs]
+@mtk_log_sqrt.defjvp
+def mtk_log_sqrt_jvp(Cpack, Hpack):
+    C, = Cpack
+    H, = Hpack
+
+    logSqrtC = mtk_log_sqrt(C)
+    lam,V = eigen_sym33_unit(C)
+    
+    lam1 = lam[0]
+    lam2 = lam[1]
+    lam3 = lam[2]
+    
+    e1 = V[:,0]
+    e2 = V[:,1]
+    e3 = V[:,2]
+    
+    hHat = 0.5 * (V.T @ H @ V)
+
+    l1111 = hHat[0,0] / lam1
+    l2222 = hHat[1,1] / lam2
+    l3333 = hHat[2,2] / lam3
+    
+    l1212 = 0.5*(hHat[0,1]+hHat[1,0]) * relative_log_difference(lam1, lam2)
+    l2323 = 0.5*(hHat[1,2]+hHat[2,1]) * relative_log_difference(lam2, lam3)
+    l3131 = 0.5*(hHat[2,0]+hHat[0,2]) * relative_log_difference(lam3, lam1)
+
+    t00 = l1111 * e1[0] * e1[0] + l2222 * e2[0] * e2[0] + l3333 * e3[0] * e3[0] + \
+        2 * l1212 * e1[0] * e2[0] + \
+        2 * l2323 * e2[0] * e3[0] + \
+        2 * l3131 * e3[0] * e1[0]
+    t11 = l1111 * e1[1] * e1[1] + l2222 * e2[1] * e2[1] + l3333 * e3[1] * e3[1] + \
+        2 * l1212 * e1[1] * e2[1] + \
+        2 * l2323 * e2[1] * e3[1] + \
+        2 * l3131 * e3[1] * e1[1]
+    t22 = l1111 * e1[2] * e1[2] + l2222 * e2[2] * e2[2] + l3333 * e3[2] * e3[2] + \
+        2 * l1212 * e1[2] * e2[2] + \
+        2 * l2323 * e2[2] * e3[2] + \
+        2 * l3131 * e3[2] * e1[2]
+
+    t01 = l1111 * e1[0] * e1[1] + l2222 * e2[0] * e2[1] + l3333 * e3[0] * e3[1] + \
+        l1212 * (e1[0] * e2[1] + e2[0] * e1[1]) + \
+        l2323 * (e2[0] * e3[1] + e3[0] * e2[1]) + \
+        l3131 * (e3[0] * e1[1] + e1[0] * e3[1])
+    t12 = l1111 * e1[1] * e1[2] + l2222 * e2[1] * e2[2] + l3333 * e3[1] * e3[2] + \
+        l1212 * (e1[1] * e2[2] + e2[1] * e1[2]) + \
+        l2323 * (e2[1] * e3[2] + e3[1] * e2[2]) + \
+        l3131 * (e3[1] * e1[2] + e1[1] * e3[2])
+    t20 = l1111 * e1[2] * e1[0] + l2222 * e2[2] * e2[0] + l3333 * e3[2] * e3[0] + \
+        l1212 * (e1[2] * e2[0] + e2[2] * e1[0]) + \
+        l2323 * (e2[2] * e3[0] + e3[2] * e2[0]) + \
+        l3131 * (e3[2] * e1[0] + e1[2] * e3[0])
+    
+    sol = np.array([ [t00, t01, t20],
+                     [t01, t11, t12],
+                     [t20, t12, t22] ])
+        
+    return logSqrtC, sol

+
+
+
+@partial(custom_jvp, nondiff_argnums=(1,))
+def mtk_pow(A,m):
+    lam,V = eigen_sym33_unit(A)
+    return V @ np.diag(np.power(lam,m)) @ V.T
+
+
+

+[docs]
+@mtk_pow.defjvp
+def mtk_pow_jvp(m, Cpack, Hpack):
+    C, = Cpack
+    H, = Hpack
+
+    powC = mtk_pow(C,m)
+    lam,V = eigen_sym33_unit(C)
+    
+    lam1 = lam[0]
+    lam2 = lam[1]
+    lam3 = lam[2]
+    
+    e1 = V[:,0]
+    e2 = V[:,1]
+    e3 = V[:,2]
+    
+    hHat = m * (V.T @ H @ V)
+
+    l1111 = hHat[0,0] * np.power(lam1, m-1)
+    l2222 = hHat[1,1] * np.power(lam2, m-1)
+    l3333 = hHat[2,2] * np.power(lam3, m-1)
+    
+    l1212 = 0.5*(hHat[0,1]+hHat[1,0]) * relative_log_difference(lam1, lam2)
+    l2323 = 0.5*(hHat[1,2]+hHat[2,1]) * relative_log_difference(lam2, lam3)
+    l3131 = 0.5*(hHat[2,0]+hHat[0,2]) * relative_log_difference(lam3, lam1)
+
+    t00 = l1111 * e1[0] * e1[0] + l2222 * e2[0] * e2[0] + l3333 * e3[0] * e3[0] + \
+        2 * l1212 * e1[0] * e2[0] + \
+        2 * l2323 * e2[0] * e3[0] + \
+        2 * l3131 * e3[0] * e1[0]
+    t11 = l1111 * e1[1] * e1[1] + l2222 * e2[1] * e2[1] + l3333 * e3[1] * e3[1] + \
+        2 * l1212 * e1[1] * e2[1] + \
+        2 * l2323 * e2[1] * e3[1] + \
+        2 * l3131 * e3[1] * e1[1]
+    t22 = l1111 * e1[2] * e1[2] + l2222 * e2[2] * e2[2] + l3333 * e3[2] * e3[2] + \
+        2 * l1212 * e1[2] * e2[2] + \
+        2 * l2323 * e2[2] * e3[2] + \
+        2 * l3131 * e3[2] * e1[2]
+
+    t01 = l1111 * e1[0] * e1[1] + l2222 * e2[0] * e2[1] + l3333 * e3[0] * e3[1] + \
+        l1212 * (e1[0] * e2[1] + e2[0] * e1[1]) + \
+        l2323 * (e2[0] * e3[1] + e3[0] * e2[1]) + \
+        l3131 * (e3[0] * e1[1] + e1[0] * e3[1])
+    t12 = l1111 * e1[1] * e1[2] + l2222 * e2[1] * e2[2] + l3333 * e3[1] * e3[2] + \
+        l1212 * (e1[1] * e2[2] + e2[1] * e1[2]) + \
+        l2323 * (e2[1] * e3[2] + e3[1] * e2[2]) + \
+        l3131 * (e3[1] * e1[2] + e1[1] * e3[2])
+    t20 = l1111 * e1[2] * e1[0] + l2222 * e2[2] * e2[0] + l3333 * e3[2] * e3[0] + \
+        l1212 * (e1[2] * e2[0] + e2[2] * e1[0]) + \
+        l2323 * (e2[2] * e3[0] + e3[2] * e2[0]) + \
+        l3131 * (e3[2] * e1[0] + e1[2] * e3[0])
+    
+    sol = np.array([ [t00, t01, t20],
+                     [t01, t11, t12],
+                     [t20, t12, t22] ])
+        
+    return powC, sol

+
+
+
+

+[docs]
+def relative_log_difference_taylor(lam1, lam2):
+    # Compute a more accurate (mtk::log(lam1) - log(lam2)) / (lam1-lam2) as lam1 -> lam2
+    third2 = 2.0 / 3.0
+    fifth2 = 2.0 / 5.0
+    seventh2 = 2.0 / 7.0
+    ninth2 = 2.0 / 9.0
+    
+    frac = (lam1 - lam2) / (lam1 + lam2)
+    frac2 = frac*frac
+    frac4 = frac2*frac2
+    
+    # relative tolerance of 0.05 for this approx (with more terms its valid over larger range)
+    return (2.0 + third2 * frac2 + fifth2 * frac4 + seventh2 * frac4 * frac2 + ninth2 * frac4 * frac4) / (lam1 + lam2)

+
+
+
+

+[docs]
+def relative_log_difference_no_tolerance_check(lam1, lam2):
+  return np.log(lam1 / lam2) / (lam1 - lam2)

+
+
+
+

+[docs]
+def relative_log_difference(lam1, lam2):
+    haveLargeDiff = np.abs(lam1 - lam2) > 0.05 * np.minimum(lam1, lam2)
+    lamFake = np.where(haveLargeDiff, lam2, 2.0*lam2)
+    return np.where(haveLargeDiff,
+                    relative_log_difference_no_tolerance_check(lam1, lamFake),
+                    relative_log_difference_taylor(lam1, lam2))

+
+
+
+# C must be symmetric!
+@custom_jvp
+def log_sqrt(C):
+    return 0.5*logh(C)
+
+
+

+[docs]
+@log_sqrt.defjvp
+def log_jvp(Cpack, Hpack):
+    C, = Cpack
+    H, = Hpack
+
+    logSqrtC = log_sqrt(C)
+    lam,V = linalg.eigh(C)
+    
+    lam1 = lam[0]
+    lam2 = lam[1]
+    lam3 = lam[2]
+    
+    e1 = V[:,0]
+    e2 = V[:,1]
+    e3 = V[:,2]
+    
+    hHat = 0.5 * (V.T @ H @ V)
+
+    l1111 = hHat[0,0] / lam1
+    l2222 = hHat[1,1] / lam2
+    l3333 = hHat[2,2] / lam3
+    
+    l1212 = 0.5*(hHat[0,1]+hHat[1,0]) * relative_log_difference(lam1, lam2)
+    l2323 = 0.5*(hHat[1,2]+hHat[2,1]) * relative_log_difference(lam2, lam3)
+    l3131 = 0.5*(hHat[2,0]+hHat[0,2]) * relative_log_difference(lam3, lam1)
+
+    t00 = l1111 * e1[0] * e1[0] + l2222 * e2[0] * e2[0] + l3333 * e3[0] * e3[0] + \
+        2 * l1212 * e1[0] * e2[0] + \
+        2 * l2323 * e2[0] * e3[0] + \
+        2 * l3131 * e3[0] * e1[0]
+    t11 = l1111 * e1[1] * e1[1] + l2222 * e2[1] * e2[1] + l3333 * e3[1] * e3[1] + \
+        2 * l1212 * e1[1] * e2[1] + \
+        2 * l2323 * e2[1] * e3[1] + \
+        2 * l3131 * e3[1] * e1[1]
+    t22 = l1111 * e1[2] * e1[2] + l2222 * e2[2] * e2[2] + l3333 * e3[2] * e3[2] + \
+        2 * l1212 * e1[2] * e2[2] + \
+        2 * l2323 * e2[2] * e3[2] + \
+        2 * l3131 * e3[2] * e1[2]
+
+    t01 = l1111 * e1[0] * e1[1] + l2222 * e2[0] * e2[1] + l3333 * e3[0] * e3[1] + \
+        l1212 * (e1[0] * e2[1] + e2[0] * e1[1]) + \
+        l2323 * (e2[0] * e3[1] + e3[0] * e2[1]) + \
+        l3131 * (e3[0] * e1[1] + e1[0] * e3[1])
+    t12 = l1111 * e1[1] * e1[2] + l2222 * e2[1] * e2[2] + l3333 * e3[1] * e3[2] + \
+        l1212 * (e1[1] * e2[2] + e2[1] * e1[2]) + \
+        l2323 * (e2[1] * e3[2] + e3[1] * e2[2]) + \
+        l3131 * (e3[1] * e1[2] + e1[1] * e3[2])
+    t20 = l1111 * e1[2] * e1[0] + l2222 * e2[2] * e2[0] + l3333 * e3[2] * e3[0] + \
+        l1212 * (e1[2] * e2[0] + e2[2] * e1[0]) + \
+        l2323 * (e2[2] * e3[0] + e3[2] * e2[0]) + \
+        l3131 * (e3[2] * e1[0] + e1[2] * e3[0])
+    
+    sol = np.array([ [t00, t01, t20],
+                     [t01, t11, t12],
+                     [t20, t12, t22] ])
+        
+    return logSqrtC, sol

+
+
+
+@custom_jvp
+def sqrtm(A):
+    sqrtA,_ = sqrtm_dbp(A)
+    return sqrtA
+
+
+

+[docs]
+@sqrtm.defjvp
+def jvp_sqrtm(primals, tangents):
+    A, = primals
+    H, = tangents
+    sqrtA = sqrtm(A)
+    dim = A.shape[0]
+    # TODO(brandon): Use a stable algorithm for solving a Sylvester equation.
+    # See https://en.wikipedia.org/wiki/Bartels%E2%80%93Stewart_algorithm
+    # The following will only reliably work for small matrices.
+    I = np.identity(dim)
+    M = np.kron(sqrtA.T, I) + np.kron(I, sqrtA)
+    Hvec = H.T.ravel()
+    return sqrtA, (linalg.solve(M, Hvec)).reshape((dim,dim)).T

+
+
+
+

+[docs]
+def sqrtm_dbp(A):
+    """ Matrix square root by product form of Denman-Beavers iteration.
+    
+    Translated from the Matrix Function Toolbox
+    http://www.ma.man.ac.uk/~higham/mftoolbox
+    Nicholas J. Higham, Functions of Matrices: Theory and Computation,
+    SIAM, Philadelphia, PA, USA, 2008. ISBN 978-0-898716-46-7,
+    """
+    dim        = A.shape[0]
+    tol        = 0.5 * np.sqrt(dim) * np.finfo(np.dtype("float64")).eps
+    maxIters   = 32
+    scaleTol   = 0.01
+
+    def scaling(M):
+        d  = np.abs(linalg.det(M))**(1.0/(2.0*dim))
+        g = 1.0 / d
+        return g
+    
+    def cond_f(loopData):
+        _,_,error,k,_ = loopData
+        p = np.array([k < maxIters, error > tol], dtype=bool)
+        return np.all(p)
+    
+    def body_f(loopData):
+        X, M, error, k, diff = loopData
+        g = np.where(diff >= scaleTol,
+                     scaling(M),
+                     1.0)
+        
+        X *= g
+        M *= g * g
+        
+        Y = X
+        N = linalg.inv(M)
+        I = np.identity(dim)
+        X = 0.5 * X @ (I + N)
+        M = 0.5 * (I + 0.5 * (M + N))
+        error = np.linalg.norm(M - I, 'fro')
+        diff  = np.linalg.norm(X - Y, 'fro') / np.linalg.norm(X, 'fro')
+        k += 1
+        return (X, M, error, k, diff)
+
+    X0        = A
+    M0        = A
+    error0    = np.finfo(np.dtype("float64")).max
+    k0        = 0
+    diff0     = 2.0*scaleTol # want to force scaling on first iteration
+    loopData0 = (X0, M0, error0, k0, diff0)
+    
+    X,_,_,k,_ = while_loop(cond_f, body_f, loopData0)
+
+    return X,k

+
+
+
+@custom_jvp
+def logm_iss(A):
+    X,k,m = _logm_iss(A)
+    return (1 << k) * log_pade_pf(X - np.identity(A.shape[0]), m)
+
+
+

+[docs]
+@logm_iss.defjvp
+def logm_jvp(primals, tangents):
+    A, = primals
+    H, = tangents
+    logA = logm_iss(A)
+    DexpLogA = jacfwd(linalg.expm)(logA)
+    dim = A.shape[0]
+    JVP = linalg.solve(DexpLogA.reshape(dim*dim,-1), H.ravel())
+    return logA, JVP.reshape(dim,dim)

+
+
+
+

+[docs]
+def _logm_iss(A):
+    """Logarithmic map by inverse scaling and squaring and Padé approximants
+    
+    Translated from the Matrix Function Toolbox
+    http://www.ma.man.ac.uk/~higham/mftoolbox
+    Nicholas J. Higham, Functions of Matrices: Theory and Computation,
+    SIAM, Philadelphia, PA, USA, 2008. ISBN 978-0-898716-46-7,
+    """
+    dim = A.shape[0]
+    c15 = log_pade_coefficients[15]
+
+    def cond_f(loopData):
+        _,_,k,_,_,converged = loopData
+        conditions = np.array([~converged, k < 16], dtype = bool)
+        return conditions.all()
+
+    def compute_pade_degree(diff, j, itk):
+        j += 1
+        # Manually force the return type of searchsorted to be 64-bit int, because it
+        # returns 32-bit ints, ignoring the global `jax_enable_x64` flag. This looks
+        # like a bug. I filed an issue (#11375) with Jax to correct this.
+        # If they fix it, the conversions on p and q can be removed.
+        p = np.searchsorted(log_pade_coefficients[2:16], diff, side='right').astype(np.int64)
+        p += 2
+        q = np.searchsorted(log_pade_coefficients[2:16], diff/2.0, side='right').astype(np.int64)
+        q += 2
+        m,j,converged = if_then_else((2 * (p - q) // 3 < itk) | (j == 2),
+                                     (p+1,j,True), (0,j,False))
+        return m,j,converged
+
+    def body_f(loopData):
+        X,j,k,m,itk,converged = loopData
+        diff = np.linalg.norm(X - np.identity(dim), ord=1)
+        m,j,converged = if_then_else(diff < c15,
+                                     compute_pade_degree(diff, j, itk),
+                                     (m, j, converged))
+        X,itk = sqrtm_dbp(X)
+        k += 1
+        return X,j,k,m,itk,converged
+
+    X   = A
+    j   = 0
+    k   = 0
+    m   = 0
+    itk = 5
+    converged = False
+    X,j,k,m,itk,converged = while_loop(cond_f, body_f, (X,j,k,m,itk,converged))
+    return X,k,m

+
+
+
+

+[docs]
+def log_pade_pf(A, n):
+    """Logarithmic map by Padé approximant and partial fractions
+    """
+    I = np.identity(A.shape[0])
+    X = np.zeros_like(A)
+    quadPrec = 2*n - 1
+    xs,ws = create_padded_quadrature_rule_1D(quadPrec)
+
+    def get_log_inc(A, x, w):
+        B = I + x*A
+        dXT = w*linalg.solve(B.T, A.T)
+        return dXT
+
+    dXsTransposed = vmap(get_log_inc, (None, 0, 0))(A, xs, ws)
+    X = np.sum(dXsTransposed, axis=0).T
+        
+    return X

+
+
+
+log_pade_coefficients = np.array([
+    1.100343044625278e-05, 1.818617533662554e-03, 1.620628479501567e-02, 5.387353263138127e-02,
+    1.135280226762866e-01, 1.866286061354130e-01, 2.642960831111435e-01, 3.402172331985299e-01,
+    4.108235000556820e-01, 4.745521256007768e-01, 5.310667521178455e-01, 5.806887133441684e-01,
+    6.240414344012918e-01, 6.618482563071411e-01, 6.948266172489354e-01, 7.236382701437292e-01,
+    7.488702930926310e-01, 7.710320825151814e-01, 7.905600074925671e-01, 8.078252198050853e-01,
+    8.231422814010787e-01, 8.367774696147783e-01, 8.489562661576765e-01, 8.598698723737197e-01,
+    8.696807597657327e-01, 8.785273397512191e-01, 8.865278635527148e-01, 8.937836659824918e-01,
+    9.003818585631236e-01, 9.063975647545747e-01, 9.118957765024351e-01, 9.169328985287867e-01,
+    9.215580354375991e-01, 9.258140669835052e-01, 9.297385486977516e-01, 9.333644683151422e-01,
+    9.367208829050256e-01, 9.398334570841484e-01, 9.427249190039424e-01, 9.454154478075423e-01,
+    9.479230038146050e-01, 9.502636107090112e-01, 9.524515973891873e-01, 9.544998058228285e-01,
+    9.564197701703862e-01, 9.582218715590143e-01, 9.599154721638511e-01, 9.615090316568806e-01,
+    9.630102085912245e-01, 9.644259488813590e-01, 9.657625632018019e-01, 9.670257948457799e-01,
+    9.682208793510226e-01, 9.693525970039069e-01, 9.704253191689650e-01, 9.714430492527785e-01,
+    9.724094589950460e-01, 9.733279206814576e-01, 9.742015357899175e-01, 9.750331605111618e-01,
+    9.758254285248543e-01, 9.765807713611383e-01, 9.773014366339591e-01, 9.779895043950849e-01 ])
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks.html b/_modules/pancax/networks.html new file mode 100644 index 0000000..84ec741 --- /dev/null +++ b/_modules/pancax/networks.html @@ -0,0 +1,130 @@ + + + + + + + + pancax.networks — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks

+from .elm import ELM, ELM2
+from .field_property_pair import FieldPropertyPair
+from .mlp import Linear
+from .mlp import MLP
+from .mlp import MLPBasis
+from .properties import *
+from .rbf import RBFBasis
+from .rbf import rbf_normalization
+from .initialization import *
+
+

+[docs]
+def Network(network_type, *args, **kwargs):
+  return network_type(*args, **kwargs)

+
+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/elm.html b/_modules/pancax/networks/elm.html new file mode 100644 index 0000000..53d83f7 --- /dev/null +++ b/_modules/pancax/networks/elm.html @@ -0,0 +1,172 @@ + + + + + + + + pancax.networks.elm — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.elm

+from typing import Callable
+import equinox as eqx
+import jax
+
+
+

+[docs]
+def activation(x):
+    alpha = 3.
+    return 1. / (1. + jax.numpy.exp(-alpha * x))

+
+
+
+

+[docs]
+class ELM(eqx.Module):
+  layer: any
+  beta: any
+  n_outputs: int
+
+

+[docs]
+  def __init__(self, n_inputs, n_outputs, n_neurons, key):
+    radius = 3.
+    # setup linear layer to have normal distribtuion
+    layer = eqx.nn.Linear(n_inputs, n_neurons, use_bias=True, key=key)
+    k1, k2 = jax.random.split(key, 2)
+    new_weight = radius * jax.random.normal(k1, (n_neurons, n_inputs))
+    new_bias = radius * jax.random.normal(k2, (n_neurons,))
+    layer = eqx.tree_at(lambda m: m.weight, layer, new_weight)
+    layer = eqx.tree_at(lambda m: m.bias, layer, new_bias)
+    self.layer = layer
+    self.beta = jax.numpy.zeros((n_outputs * n_neurons,))
+    self.n_outputs = n_outputs

+
+
+  def __call__(self, x):
+    n_neurons = self.layer.out_features
+    beta_temp = self.beta.reshape((n_neurons, self.n_outputs))
+    H = activation(self.layer(x))
+    return H @ beta_temp

+
+
+
+

+[docs]
+class ELM2(eqx.Module):
+  layer: any
+  beta: any
+  n_outputs: int
+
+  def __call__(self, x):
+    n_neurons = self.layer.out_features
+    beta_temp = self.beta.reshape((n_neurons, self.n_outputs))
+    H = activation(self.layer(x))
+    return H @ beta_temp

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/field_property_pair.html b/_modules/pancax/networks/field_property_pair.html new file mode 100644 index 0000000..53e1108 --- /dev/null +++ b/_modules/pancax/networks/field_property_pair.html @@ -0,0 +1,182 @@ + + + + + + + + pancax.networks.field_property_pair — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.field_property_pair

+import equinox as eqx
+import jax.tree_util as jtu
+
+
+

+[docs]
+class BasePancaxModel(eqx.Module):
+  """
+  Base class for pancax model parameters.
+
+  This includes a few helper methods
+  """
+

+[docs]
+  def serialise(self, base_name, epoch):
+    file_name = f'{base_name}_{str(epoch).zfill(7)}.eqx'
+    print(f'Serialising current parameters to {file_name}')
+    eqx.tree_serialise_leaves(file_name, self)

+

+
+
+
+

+[docs]
+class FieldPropertyPair(BasePancaxModel):
+  """
+  Data structure for storing a set of field network
+  parameters and a set of material properties
+
+  :param fields: field network parameters object
+  :param properties: property parameters object
+  """
+  fields: eqx.Module
+  properties: eqx.Module
+
+  def __iter__(self):
+    """
+    Iterator for user friendliness
+    """
+    return iter((self.fields, self.properties))
+
+

+[docs]
+  def freeze_fields_filter(self):
+    filter_spec = jtu.tree_map(lambda _: False, self)
+    filter_spec = eqx.tree_at(
+        # lambda tree: tree.properties.prop_params,
+        lambda tree: tree.properties,
+        filter_spec,
+        replace=True
+    )
+    return filter_spec

+
+
+

+[docs]
+  def freeze_props_filter(self):
+    filter_spec = jtu.tree_map(lambda _: False, self)
+    for n in range(len(self.fields.layers)):
+      filter_spec = eqx.tree_at(
+        lambda tree: (tree.fields.layers[n].weight, tree.fields.layers[n].bias),
+        filter_spec,
+        replace=(True, True),
+      )
+    return filter_spec

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/initialization.html b/_modules/pancax/networks/initialization.html new file mode 100644 index 0000000..34dc1dc --- /dev/null +++ b/_modules/pancax/networks/initialization.html @@ -0,0 +1,252 @@ + + + + + + + + pancax.networks.initialization — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.initialization

+from jaxtyping import Array, Float
+from typing import Callable
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+def zero_init(key: jax.random.PRNGKey, shape) -> Float[Array, "no ni"]:
+  """
+  :param weight: current weight array for sizing
+  :param key: rng key
+  :return: A new set of weights
+  """
+  out, in_ = weight.shape
+  return jnp.zeros(shape, dtype=jnp.float64)

+
+
+
+

+[docs]
+def trunc_init(key: jax.random.PRNGKey, shape) -> Float[Array, "no ni"]:
+  """
+  :param weight: current weight array for sizing
+  :param key: rng key
+  :return: A new set of weights
+  """
+  stddev = jnp.sqrt(1 / shape[0])
+  return stddev * jax.random.truncated_normal(key, shape=shape, lower=-2, upper=2)

+
+
+
+

+[docs]
+def init_linear_weight(model: eqx.Module, init_fn: Callable, key: jax.random.PRNGKey) -> eqx.Module:
+  """
+  :param model: equinox  model
+  :param init_fn: function to initialize weigth with
+  :param key: rng key
+  :return: a new equinox model
+  """
+  is_linear = lambda x: isinstance(x, eqx.nn.Linear)
+  get_weights = lambda m: [
+    x.weight
+    for x in jax.tree_util.tree_leaves(m, is_leaf=is_linear)
+    if is_linear(x)
+  ]
+  weights = get_weights(model)
+  new_weights = [
+    init_fn(subkey, weight.shape)
+    for subkey, weight in zip(jax.random.split(key, len(weights)), weights)
+  ]
+  new_model = eqx.tree_at(get_weights, model, new_weights)
+  return new_model

+
+
+
+

+[docs]
+def init_linear(model: eqx.Module, init_fn: Callable, key: jax.random.PRNGKey):
+  """
+  :param model: equinox  model
+  :param init_fn: function to initialize weigth with
+  :param key: rng key
+  :return: a new equinox model
+  """
+  is_linear = lambda x: isinstance(x, eqx.nn.Linear)
+  get_biases = lambda m: [
+    x.bias
+    for x in jax.tree_util.tree_leaves(m, is_leaf=is_linear)
+    if is_linear(x)
+  ]
+  get_weights = lambda m: [
+    x.weight
+    for x in jax.tree_util.tree_leaves(m, is_leaf=is_linear)
+    if is_linear(x)
+  ]
+  get_layers = lambda m: [
+    x
+    for x in jax.tree_util.tree_leaves(m, is_leaf=is_linear)
+    if is_linear(x)
+  ]
+  layers = get_layers(model)
+  weights = get_weights(model)
+  biases = get_biases(model)
+  new_layers = [
+    init_fn(layer, subkey)
+    for layer, subkey in zip(layers, jax.random.split(key, len(layers)))
+  ]
+  new_weights = [x[0] for x in new_layers]
+  new_biases = [x[1] for x in new_layers]
+  new_model = eqx.tree_at(get_weights, model, new_weights)
+  new_model = eqx.tree_at(get_biases, model, new_biases)
+  return new_model

+
+
+
+

+[docs]
+def box_init(layer: eqx.nn.Linear, key: jax.random.PRNGKey):
+  in_size = layer.in_features
+  out_size = layer.out_features
+  k1, k2 = jax.random.split(key, 2)
+  p = jax.random.uniform(k1, (out_size, in_size))
+  n = jax.random.normal(k2, (out_size, in_size))
+
+  # normalize normals
+  # for i in range(n.shape[0]):
+  #   n = n.at[i, :].set(n[i, :] / jnp.linalg.norm(n[i, :]))
+
+  # calculate p_max
+  # p_max = jnp.max(jnp.sign(n))
+  # p_max = jnp.max(jnp.array([0.0, p_max]))
+
+  # setup A and b one vector at a time
+  A = jnp.zeros((out_size, in_size))
+  b = jnp.zeros((out_size,))
+  for i in range(n.shape[0]):
+    p_temp = p[i, :]
+    n_temp = n[i, :] / jnp.linalg.norm(n[i, :])
+    p_max = jnp.max(jnp.array([0.0, jnp.max(jnp.sign(n_temp))]))
+    k = 1. / jnp.sum((p_max - p_temp) * n_temp)
+    A = A.at[i, :].set(k * n_temp)
+    b = b.at[i].set(k * jnp.dot(p_temp, n_temp))
+
+  # k = jnp.zeros((n.shape[0],))
+  # for i in range(n.shape[0]):
+  #   k = k.at[i].set(1. / jnp.sum((p_max - p[i, :]) * n[i, :]))
+  
+  # A = jax.vmap(lambda k, n: k * n, in_axes=(0, 0))(k, n)
+  # b = k * jax.vmap(lambda x: jnp.sum(x), in_axes=(1,))(n @ p.T)
+  # print(A)
+  # print(b)
+  # assert False
+  return A, b

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/mlp.html b/_modules/pancax/networks/mlp.html new file mode 100644 index 0000000..2cf9b4b --- /dev/null +++ b/_modules/pancax/networks/mlp.html @@ -0,0 +1,227 @@ + + + + + + + + pancax.networks.mlp — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.mlp

+from .initialization import *
+from typing import Callable
+from typing import Optional
+import equinox as eqx
+import jax
+
+
+# TODO should we convert these to actual classes?
+
+

+[docs]
+def Linear(
+  n_inputs: int,
+  n_outputs: int,
+  key: jax.random.PRNGKey
+):
+  """
+  :param n_inputs: Number of inputs to linear layer
+  :param n_outputs: Number of outputs of the linear layer
+  :param key: rng key
+  :return: Equinox Linear layer
+  """
+  model = eqx.nn.Linear(
+    n_inputs, n_outputs,
+    use_bias=False,
+    key=key
+  )
+  model = eqx.tree_at(lambda l: l.weight, model, jnp.zeros((n_outputs, n_inputs), dtype=jnp.float64))
+  return model

+
+
+
+

+[docs]
+def MLP(
+  n_inputs: int,
+  n_outputs: int,
+  n_neurons: int,
+  n_layers: int,
+  activation: Callable,
+  key: jax.random.PRNGKey,
+  use_final_bias: Optional[bool] = False,
+  init_func: Optional[Callable] = trunc_init
+):
+  """
+  :param n_inputs: Number of inputs to the MLP
+  :param n_outputs: Number of outputs of the MLP
+  :param n_neurons: Number of neurons in each hidden layer of the MLP
+  :param n_layers: Number of hidden layers in the MLP
+  :param activation: Activation function, e.g. tanh or relu
+  :param key: rng key
+  :param use_final_bias: Boolean for whether or not to use a bias
+    vector in the final layer
+  :return: Equinox MLP layer
+  """
+  model = eqx.nn.MLP(
+    n_inputs, n_outputs, n_neurons, n_layers, 
+    activation=activation, 
+    use_final_bias=use_final_bias,
+    key=key
+  )
+  # model = init_linear_weight(model, init_func, key)
+  # model = init_linear(model, init_func, key)
+  return model

+
+
+
+

+[docs]
+def MLPBasis(
+  n_inputs: int,
+  n_neurons: int,
+  n_layers: int,
+  activation: Callable,
+  key: jax.random.PRNGKey,
+  init_func: Optional[Callable] = trunc_init
+):
+  return MLP(
+    n_inputs, n_neurons, n_neurons, n_layers, 
+    activation=activation, 
+    use_final_bias=True,
+    key=key,
+    init_func=init_func
+  )

+
+
+
+# class MLP(BaseNetwork):
+#   mlp: eqx.nn.MLP
+
+#   def __init__(
+#     self,
+#     n_inputs: int,
+#     n_outputs: int,
+#     n_neurons: int,
+#     n_layers: int,
+#     activation: Callable,
+#     key: jax.random.PRNGKey,
+#     use_final_bias: Optional[bool] = False
+#   ):
+#     super().__init__(self)
+#     model = eqx.nn.MLP(
+#       n_inputs, n_outputs, n_neurons, n_layers, 
+#       activation=activation, 
+#       use_final_bias=use_final_bias,
+#       key=key
+#     )
+#     model = init_linear_weight(model, trunc_init, key)
+#     self.mlp = model
+
+#   def __call__(self, params, x):
+#     return self.mlp(params, x)
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/properties.html b/_modules/pancax/networks/properties.html new file mode 100644 index 0000000..06e3b71 --- /dev/null +++ b/_modules/pancax/networks/properties.html @@ -0,0 +1,182 @@ + + + + + + + + pancax.networks.properties — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.properties

+from jax._src.random import PRNGKey as PRNGKey
+from jax import random
+from jaxtyping import Array, Float
+from typing import Callable, Optional
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+
+
+
+

+[docs]
+class Properties(eqx.Module):
+  """
+  :param prop_mins: Minimum allowable properties
+  :param prop_maxs: Maximum allowable properties
+  :param prop_params: Actual tunable parameters
+  """
+  prop_mins: jax.Array = eqx.field(static=True)
+  prop_maxs: jax.Array = eqx.field(static=True)
+  prop_params: jax.Array
+  activation_func: Callable
+
+

+[docs]
+  def __init__(
+    self, 
+    prop_mins: jax.Array,
+    prop_maxs: jax.Array,
+    key: jax.random.PRNGKey,
+    activation_func: Optional[Callable] = jax.nn.sigmoid
+  ) -> None:
+    """
+    :param prop_mins: Minimum allowable properties
+    :param prop_maxs: Maximum allowable properties
+    :param key: rng key
+    """
+
+    self.prop_mins = jnp.array(prop_mins)
+    self.prop_maxs = jnp.array(prop_maxs)
+    self.prop_params = jax.random.uniform(key, self.prop_mins.shape)
+    self.activation_func = activation_func

+
+
+  def __call__(self) -> Float[Array, "np"]:
+    """
+    :return: Predicted properties
+    """
+    props = self.prop_mins + \
+            (self.prop_maxs - self.prop_mins) * self.activation_func(self.prop_params)
+    return props

+
+
+
+

+[docs]
+class FixedProperties(Properties):
+

+[docs]
+  def __init__(self, props: jax.Array) -> None:
+    """
+    :param props: Property values to be fixed
+    """
+    key = random.key(0)
+    super().__init__(props, props, key)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/networks/rbf.html b/_modules/pancax/networks/rbf.html new file mode 100644 index 0000000..4529d1e --- /dev/null +++ b/_modules/pancax/networks/rbf.html @@ -0,0 +1,151 @@ + + + + + + + + pancax.networks.rbf — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.networks.rbf

+import equinox as eqx
+import jax
+import jax.numpy as jnp
+
+
+

+[docs]
+class RBFBasis(eqx.Module):
+  center: jax.Array
+  sigma: jax.Array
+
+

+[docs]
+  def __init__(
+    self, 
+    n_inputs: int, 
+    n_neurons: int, 
+    key: jax.random.PRNGKey
+  ) -> None:
+    ckey, skey  = jax.random.split(key)
+    self.center = jax.random.normal(ckey, (n_neurons, n_inputs))
+    self.sigma  = 1.0 * jnp.ones((n_neurons,), dtype=jnp.float64)

+
+
+  def __call__(self, x):
+    out = self.center - x
+    out = jax.vmap(lambda a: jnp.dot(a, a))(out)
+    out = jnp.exp(-out / jnp.square(self.sigma))
+    return out

+
+
+

+[docs]
+def rbf_normalization(hidden):
+  return hidden / jnp.sum(hidden, axis=1)[:, None]

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/optimizers/adam.html b/_modules/pancax/optimizers/adam.html new file mode 100644 index 0000000..bf6798b --- /dev/null +++ b/_modules/pancax/optimizers/adam.html @@ -0,0 +1,190 @@ + + + + + + + + pancax.optimizers.adam — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.optimizers.adam

+from .base import Optimizer
+from typing import Callable
+from typing import Optional
+import equinox as eqx
+import optax
+
+
+

+[docs]
+class Adam(Optimizer):
+

+[docs]
+  def __init__(
+    self,
+    loss_function: Callable,
+    has_aux: Optional[bool] = False,
+    jit: Optional[bool] = True,
+    learning_rate: Optional[float] = 1.0e-3,
+    transition_steps: Optional[int] = 500,
+    decay_rate: Optional[float] = 0.99,
+    clip_gradients: Optional[bool] = False,
+    filter_spec: Optional[Callable] = None
+  ) -> None:
+    super().__init__(loss_function, has_aux, jit)
+    scheduler = optax.exponential_decay(
+      init_value=learning_rate,
+      transition_steps=transition_steps,
+      decay_rate=decay_rate
+    )
+    if clip_gradients:
+      self.opt = optax.chain(
+        optax.clip_by_global_norm(1.0),
+        optax.scale_by_adam(),
+        optax.scale_by_schedule(scheduler),
+        optax.scale(-1.0)
+      )
+    else:
+      self.opt = optax.chain(
+        optax.scale_by_adam(),
+        optax.scale_by_schedule(scheduler),
+        optax.scale(-1.0)
+      )
+    
+    if filter_spec is None:
+      self.loss_and_grads = eqx.filter_value_and_grad(self.loss_function, has_aux=self.has_aux)
+    else:
+      self.loss_and_grads = eqx.filter_value_and_grad(self.loss_function.filtered_loss, has_aux=self.has_aux)
+    self.filter_spec = filter_spec

+
+  
+

+[docs]
+  def make_step_method(self):
+    if self.filter_spec is None:
+      def step(params, domain, opt_st):
+        loss, grads = self.loss_and_grads(params, domain)
+        updates, opt_st = self.opt.update(grads, opt_st)
+        params = eqx.apply_updates(params, updates)
+        # add grad props to output
+        # TODO what to do about below?
+        # loss[1].update({'dprops': grads.properties.prop_params})
+        return params, opt_st, loss
+    else:
+      def step(params, domain, opt_st):
+        diff_params, static_params = eqx.partition(params, self.filter_spec)
+        loss, grads = self.loss_and_grads(diff_params, static_params, domain)
+        updates, opt_st = self.opt.update(grads, opt_st)
+        params = eqx.apply_updates(params, updates)
+
+        # add grad props to output
+        # loss[1].update({'dprops': grads.properties()})
+        return params, opt_st, loss
+
+    return step

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/optimizers/base.html b/_modules/pancax/optimizers/base.html new file mode 100644 index 0000000..d645faa --- /dev/null +++ b/_modules/pancax/optimizers/base.html @@ -0,0 +1,226 @@ + + + + + + + + pancax.optimizers.base — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.optimizers.base

+from abc import ABC
+from abc import abstractmethod
+from pancax.logging import log_loss
+from typing import Callable
+from typing import Optional
+import equinox as eqx
+
+
+

+[docs]
+class Optimizer(ABC):
+

+[docs]
+  def __init__(
+    self,
+    loss_function: Callable,
+    has_aux: Optional[bool] = False,
+    jit: Optional[bool] = True
+  ) -> None:
+    self.loss_function = loss_function
+    self.has_aux = has_aux
+    self.jit = jit
+    self.step = None
+    self.epoch = 0

+
+
+

+[docs]
+  @abstractmethod
+  def make_step_method(self, params):
+    pass

+
+
+

+[docs]
+  def ensemble_init(self, params):
+    self.step = self.make_step_method()
+    # if self.jit:
+    #   self.step = eqx.filter_jit(self.step)
+
+    # need to now make an ensemble wrapper our self.step
+    # but make sure not to jit it until after the vmap
+    def ensemble_step(params, domain, opt_st):
+      params, opt_st, loss = eqx.filter_vmap(
+        self.step, in_axes=(eqx.if_array(0), None, eqx.if_array(0))
+      )(params, domain, opt_st)
+      return params, opt_st, loss
+    
+    if self.jit:
+      self.ensemble_step = eqx.filter_jit(ensemble_step)
+
+    def vmap_func(p):
+      return self.opt.init(eqx.filter(p, eqx.is_array))
+    
+    opt_st = eqx.filter_vmap(vmap_func, in_axes=(eqx.if_array(0),))(params)
+    return opt_st

+
+
+

+[docs]
+  def ensemble_step_old(self, params, domain, opt_st):
+    params, opt_st, loss = eqx.filter_vmap(
+      self.step, in_axes=(eqx.if_array(0), None, eqx.if_array(0))
+    )(params, domain, opt_st)
+    return params, opt_st, loss

+
+
+

+[docs]
+  def init(self, params):
+    self.step = self.make_step_method()
+    if self.jit:
+      self.step = eqx.filter_jit(self.step)
+
+    opt_st = self.opt.init(eqx.filter(params, eqx.is_array))
+    # opt_st = self.opt.init(eqx.filter(params, filter_spec))
+    return opt_st

+
+
+  # def train(self, params, opt_st, domain, n_epochs, log_every):
+  #   for n in range(n_epochs):
+  #     params, opt_st, loss = self.step(params, domain, opt_st)
+  #     log_loss(loss, self.epoch, log_every)
+  #     self.epoch = self.epoch + 1
+  #   return params, opt_st
+

+[docs]
+  def train(
+    self, 
+    params, domain, times, opt, logger, history, pp,
+    n_epochs,
+    log_every: Optional[int] = 100,
+    serialise_every: Optional[int] = 10000,
+    postprocess_every: Optional[int] = 10000
+  ):
+    opt_st = opt.init(params)
+    for epoch in range(int(n_epochs)):
+      params, opt_st, loss = opt.step(params, domain, opt_st)
+      logger.log_loss(loss, epoch, log_every)
+      history.write_loss(loss, epoch)
+
+      if epoch % serialise_every == 0:
+        params.serialise('checkpoint', epoch)
+
+      if epoch % postprocess_every == 0:
+        pp.init(params, domain, f'output_{str(epoch).zfill(6)}.e')
+        pp.write_outputs(params, domain, times, [
+          'displacement',
+        ])
+        pp.close()

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/optimizers/lbfgs.html b/_modules/pancax/optimizers/lbfgs.html new file mode 100644 index 0000000..fa5965d --- /dev/null +++ b/_modules/pancax/optimizers/lbfgs.html @@ -0,0 +1,217 @@ + + + + + + + + pancax.optimizers.lbfgs — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.optimizers.lbfgs

+from .base import Optimizer
+from optax import tree_utils as otu
+# from optimistix._misc import filter_cond
+from typing import Any, Callable, Optional
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+import optax
+
+
+

+[docs]
+def value_and_grad_from_state(value_fn):
+  def _value_and_grad(
+    params, domain,
+    *fn_args: Any,
+    state,
+    **fn_kwargs: dict[str, Any],
+  ):
+    value = otu.tree_get(state, 'value')
+    grad = otu.tree_get(state, 'grad')
+    aux = dict(energy=jnp.array(0.0), residual=jnp.array(1000.0))
+    if (value is None) or (grad is None):
+      raise ValueError(
+        'Value or gradient not found in the state. '
+        'Make sure that these values are stored in the state by the '
+        'optimizer.'
+      )
+    # (value, aux), grad = filter_cond(
+    #     (~jnp.isinf(value)) & (~jnp.isnan(value)),
+    #     lambda p, a, kwa: ((value, aux), grad),
+    #     lambda p, a, kwa: eqx.filter_value_and_grad(value_fn, has_aux=True)(p, domain, *a, **kwa),
+    #     params,
+    #     fn_args,
+    #     fn_kwargs,
+    # )
+    print(value)
+    (value, aux), grad = filter_cond(
+      (~jnp.isinf(value)) & (~jnp.isnan(value)),
+      lambda p: ((value, aux), grad),
+      # lambda p: (value, grad),
+      lambda p: eqx.filter_value_and_grad(value_fn, has_aux=True)(p, domain),
+      params
+    )
+    # TODO
+    # probably really slow right now
+    # value, grad = eqx.filter_value_and_grad(value_fn, has_aux=True)(params, domain)
+    return (value, aux), grad
+
+  return _value_and_grad

+
+
+
+

+[docs]
+class LBFGS(Optimizer):
+

+[docs]
+  def __init__(
+    self, 
+    loss_function: Callable, 
+    has_aux: Optional[bool] = False, 
+    jit: Optional[bool] = False,
+    learning_rate: Optional[float] = 1.0e-1
+  ) -> None:
+    super().__init__(loss_function, has_aux, jit)
+
+    # TODO setup up optimizer stuff here
+    linesearch = optax.scale_by_backtracking_linesearch(
+      max_backtracking_steps=15, store_grad=True
+    )
+    # self.opt = optax.chain(
+
+    # )
+    self.opt = optax.lbfgs(
+      learning_rate=learning_rate,
+      linesearch=linesearch
+    )
+
+    # self.loss_and_grads = eqx.filter_value_and_grad(self.loss_function, has_aux=self.has_aux)
+    self.loss_and_grads = value_and_grad_from_state(self.loss_function)

+
+
+

+[docs]
+  def make_step_method(self):
+    def step(params, domain, opt_st):
+      loss, grads = self.loss_and_grads(params, domain, state=opt_st)
+      updates, opt_st = self.opt.update(
+        grads, opt_st, params, value=loss, grad=grads, 
+        value_fn=self.loss_function
+      )
+      print('here')
+      print(updates)
+      print('here')
+      print(opt_st)
+      print('here')
+      params = eqx.apply_updates(params, updates)
+      return params, opt_st, loss
+
+    return step

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/optimizers/utils.html b/_modules/pancax/optimizers/utils.html new file mode 100644 index 0000000..1c061f3 --- /dev/null +++ b/_modules/pancax/optimizers/utils.html @@ -0,0 +1,161 @@ + + + + + + + + pancax.optimizers.utils — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.optimizers.utils

+from typing import Optional
+import equinox as eqx
+import jax
+
+
+

+[docs]
+def trainable_filter(
+  params: any,
+  # freeze_fields: Optional[bool] = False,
+  freeze_properties: Optional[bool] = True,
+  freeze_basis: Optional[bool] = False,
+  # freeze_linear_layer: Optional[bool] = False
+):
+  # TODO there's some logic to work out here
+  filter_spec = jax.tree_util.tree_map(
+    lambda _: True, params
+  )
+
+  # filter_spec = eqx.tree_at(
+  #   lambda tree: tree.fields,
+  #   filter_spec,
+  #   replace=not freeze_fields
+  # )
+  filter_spec = eqx.tree_at(
+    lambda tree: tree.properties.prop_params,
+    filter_spec,
+    replace=not freeze_properties
+  )
+
+  if freeze_basis:
+    try:
+      filter_spec = eqx.tree_at(
+        lambda tree: (tree.fields.basis.weight, tree.fields.basis.bias),
+        filter_spec,
+        replace=(not freeze_basis, not freeze_basis)
+      )
+      filter_spec = eqx.tree_at(
+        lambda tree: (tree.fields.linear.weight, tree.fields.linear.bias),
+        filter_spec,
+        replace=(True, True)
+      )
+    except:
+      raise AttributeError('This network does not have a basis!')
+  
+  return filter_spec

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics.html b/_modules/pancax/physics.html new file mode 100644 index 0000000..3f8fac5 --- /dev/null +++ b/_modules/pancax/physics.html @@ -0,0 +1,320 @@ + + + + + + + + pancax.physics — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.physics

+from jax import grad
+from jax import hessian
+from jax import jacfwd
+from jax import value_and_grad
+from jax import vmap
+from pancax.fem import assemble_sparse_stiffness_matrix
+from pancax.timer import Timer
+import jax.numpy as jnp
+import numpy as onp
+
+
+# TODO remove above and start using this method below
+

+[docs]
+def element_quantity(f, x, u, conn, N, grad_N, JxW, props):
+	x_el = x[conn, :]
+	u_el = u[conn, :]
+	return vmap(f, in_axes=(None, None, 0, 0, 0, None))(x_el, u_el, N, grad_N, JxW, props)

+
+	
+
+

+[docs]
+def element_quantity_new(f, fspace, x_el, u_el, props):
+	Ns = fspace.shape_function_values(x_el)
+	grad_Ns = fspace.shape_function_gradients(x_el)
+	JxWs = fspace.JxWs(x_el)
+	return jnp.sum(vmap(f, in_axes=(None, None, 0, 0, 0, None))(x_el, u_el, Ns, grad_Ns, JxWs, props))

+
+
+
+element_quantity_grad = jacfwd(element_quantity_new, argnums=3)
+element_quantity_hessian = hessian(element_quantity_new, argnums=3)
+
+
+

+[docs]
+def potential_energy(domain, us, props):
+
+	# unpack some stuff
+	us = us[domain.conns, :]
+	coords = domain.coords[domain.conns, :]
+	func = domain.physics.energy
+
+	pis = vmap(element_quantity_new, in_axes=(None, None, 0, 0, None))(
+		func, domain.fspace, coords, us, props
+	)
+	return jnp.sum(pis)

+
+
+
+

+[docs]
+def residual_mse(domain, us, props):
+	# unpack some stuff
+	us = us[domain.conns, :]
+	coords = domain.coords[domain.conns, :]
+	kernel = domain.physics
+
+	func = element_quantity_grad
+	fs = vmap(func, in_axes=(None, None, 0, 0, None))(
+		kernel.energy, domain.fspace, coords, us, props
+	)
+	def vmap_func(f, unknowns):
+		return jnp.square(jnp.where(unknowns, f, 0)).mean()
+
+	return vmap(vmap_func, in_axes=(0, 0))(fs, domain.dof_manager.isUnknown[domain.conns, :]).mean()

+
+
+
+

+[docs]
+def mass_matrix(domain, us, props):
+	with Timer('mass matrix assembly'):
+		us = us[domain.conns, :]
+		coords = domain.coords[domain.conns, :]
+		kernel = domain.physics
+
+		func = element_quantity_hessian
+		fs = vmap(func, in_axes=(None, None, 0, 0, None))(
+			kernel.kinetic_energy, domain.fspace, coords, us, props
+		)
+		return assemble_sparse_stiffness_matrix(
+			onp.asarray(fs), onp.asarray(domain.conns), domain.dof_manager
+		)

+
+
+
+

+[docs]
+def stiffness_matrix(domain, us, props):
+	with Timer('stiffness matrix assembly'):
+		us = us[domain.conns, :]
+		coords = domain.coords[domain.conns, :]
+		kernel = domain.physics
+
+		func = element_quantity_hessian
+		fs = vmap(func, in_axes=(None, None, 0, 0, None))(
+			kernel.energy, domain.fspace, coords, us, props
+		)
+		return assemble_sparse_stiffness_matrix(
+			onp.asarray(fs), onp.asarray(domain.conns), domain.dof_manager
+		)

+
+
+
+# TODO
+

+[docs]
+def traction_energy():
+  pass

+
+
+
+# internal force methods
+internal_force = grad(potential_energy, argnums=1)
+
+# residual methods
+residual = lambda x, y, z: jnp.linalg.norm(internal_force(x, y, z).flatten()[x.dof_manager.unknownIndices])
+
+# combined methods
+potential_energy_and_internal_force = value_and_grad(potential_energy, argnums=1)
+
+
+

+[docs]
+def potential_energy_and_residual(domain, us, props):
+	pi, f = potential_energy_and_internal_force(domain, us, props)
+	return pi, jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])

+
+
+
+

+[docs]
+def potential_energy_residual_and_reaction_force(domain, us, props):
+	pi, f = potential_energy_and_internal_force(domain, us, props)
+	R = jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])
+	reaction = jnp.sum(f[domain.global_data.reaction_nodes, domain.global_data.reaction_dof])
+	return pi, R, reaction

+
+
+
+

+[docs]
+def strong_form_residual(params, domain, t):
+	residuals = vmap(domain.physics.strong_form, in_axes=(None, 0, None))(params, domain.coords, t)
+	residual = jnp.square(residuals.flatten()[domain.dof_manager.unknownIndices]).mean()
+	return residual

+
+
+
+# test
+

+[docs]
+def nodal_incompressibility_constraint(params, domain, t):
+	vals = vmap(domain.physics.nodal_incompressibility_constraint, in_axes=(None, 0, None))(
+		params.fields, domain.coords, t
+	)
+	return jnp.sum(vals)

+
+	# return domain.physics.nodal_incompressibility_constraint(params, domain, t)
+
+
+

+[docs]
+def quadrature_incompressibility_constraint(domain, us, props):
+	# unpack some stuff
+	us = us[domain.conns, :]
+	coords = domain.coords[domain.conns, :]
+	func = domain.physics.quadrature_incompressibility_constraint
+
+	# vmap over elements
+	vals = vmap(element_quantity_new, in_axes=(None, None, 0, 0, None))(
+		func, domain.fspace_centroid, coords, us, props
+	)
+	# return jnp.mean(vals)
+	return jnp.sum(vals)

+
+
+# quadrature_incompressibility_constraint_energy_and_residual = grad(
+# 	quadrature_incompressibility_constraint, argnums=1
+# )
+
+# def quadrature_incompressibility_constraint_energy_and_residual(domain, us, props):
+# 	loss, f = quadrature_incompressibility_constraint_energy_and_residual(domain, us, props)
+# 	return loss, jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])
+
+
+

+[docs]
+def incompressible_energy(domain, us, props):
+	K = 100.0
+	pi = potential_energy(domain, us, props)
+	constraint = quadrature_incompressibility_constraint(domain, us, props)
+	return pi + K * constraint

+
+
+incompressible_internal_force = grad(incompressible_energy, argnums=1)
+incompressible_energy_and_internal_force = value_and_grad(incompressible_energy, argnums=1)
+
+

+[docs]
+def incompressible_energy_and_residual(domain, us, props):
+	pi, f = incompressible_energy_and_internal_force(domain, us, props)
+	return pi, jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/base.html b/_modules/pancax/physics_kernels/base.html new file mode 100644 index 0000000..f4d4313 --- /dev/null +++ b/_modules/pancax/physics_kernels/base.html @@ -0,0 +1,458 @@ + + + + + + + + pancax.physics_kernels.base — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.physics_kernels.base

+from abc import abstractmethod
+from jax import hessian, jacfwd, value_and_grad, vmap
+from jax.lax import stop_gradient
+from jaxtyping import Array, Float
+from pancax.fem import assemble_sparse_stiffness_matrix
+from typing import Callable, Dict
+import equinox as eqx
+import jax
+import jax.numpy as jnp
+import numpy as onp
+
+
+# TODO clean this up
+

+[docs]
+def nodal_pp(func, has_props=False, jit=True):
+	"""
+	:param func: Function to use for a nodal property output variable
+	:param has_props: Whether or not this function need properties
+	:param jit: Whether or not to jit this function
+	"""
+	if has_props:
+		# new_func = lambda p, d, t: vmap(
+		# 	func, in_axes=(None, 0, None, None)
+		# )(p.fields, d.coords, t, p.properties)
+		new_func = lambda p, d, t: vmap(
+			func, in_axes=(None, 0, None)
+		)(p, d.coords, t)
+	else:
+		new_func = lambda p, d, t: vmap(
+			func, in_axes=(None, 0, None)
+		)(p.fields, d.coords, t)
+	
+	if jit:
+		return eqx.filter_jit(new_func)
+	else:
+		return new_func

+
+
+
+

+[docs]
+def standard_pp(physics):
+	d = {
+		'field_values': {
+			'method': nodal_pp(physics.field_values),
+			'names' : physics.field_value_names
+		}
+	}
+	return d

+
+
+
+

+[docs]
+class BasePhysics(eqx.Module):
+  field_value_names: tuple[str, ...]  
+  var_name_to_method: Dict[str, Callable] #= field(default_factory=lambda: {})
+  # needs to be set
+  # by default it just returns network output
+  dirichlet_bc_func: Callable #= lambda x, t, z: z
+  # TODO how to make this dimension dependent?
+  # finally use generics in python?
+  x_mins: Float[Array, "nd"] #= jnp.zeros(3)
+  x_maxs: Float[Array, "nd"] #= jnp.zeros(3)
+
+

+[docs]
+  def __init__(self, field_value_names: tuple[str, ...]) -> None:
+    self.field_value_names = field_value_names
+    self.var_name_to_method = {}
+    self.dirichlet_bc_func = lambda x, t, z: z
+    # TODO improve this error handling
+    self.x_mins = jnp.zeros(3)
+    self.x_maxs = jnp.zeros(3)

+
+
+  # TODO need to modify for delta pinn
+

+[docs]
+  def field_values(self, field, x, t, *args):
+    x = (x - stop_gradient(self.x_mins)) / (stop_gradient(self.x_maxs) - stop_gradient(self.x_mins))
+    inputs = jnp.hstack((x, t))
+    z = field(inputs)
+    u = self.dirichlet_bc_func(x, t, z)
+    return u

+
+  
+

+[docs]
+  def field_gradients(self, field, x, t, *args):
+    return jacfwd(self.field_values, argnums=1)(field, x, t, *args)

+
+
+

+[docs]
+  def field_hessians(self, field, x, t, *args):
+    return hessian(self.field_values, argnums=1)(field, x, t, *args)

+
+
+

+[docs]
+  def field_laplacians(self, field, x, t, *args):
+    return jnp.trace(self.field_hessians(field, x, t, *args), axis1=1, axis2=2)

+
+
+

+[docs]
+  def field_time_derivatives(self, field, x, t, *args):
+    return jacfwd(self.field_values, argnums=2)(field, x, t, *args)

+
+
+

+[docs]
+  def field_second_time_derivatives(self, field, x, t, *args):
+    return jacfwd(self.field_time_derivatives, argnums=2)(field, x, t, *args)

+
+
+

+[docs]
+  def update_dirichlet_bc_func(self, bc_func: Callable):
+    get_fn = lambda x: x.dirichlet_bc_func
+    new_pytree = eqx.tree_at(get_fn, self, bc_func)
+    return new_pytree

+
+
+

+[docs]
+  def update_normalization(self, domain):
+    x_mins = jnp.min(domain.coords, axis=0)
+    x_maxs = jnp.max(domain.coords, axis=0)
+    new_pytree = eqx.tree_at(lambda x: x.x_mins, self, x_mins)
+    new_pytree = eqx.tree_at(lambda x: x.x_maxs, new_pytree, x_maxs)
+    return new_pytree

+
+  
+

+[docs]
+  def update_var_name_to_method(self):
+    var_name_to_method = standard_pp(self)
+    new_pytree = eqx.tree_at(lambda x: x.var_name_to_method, self, var_name_to_method)
+    return new_pytree

+
+
+  # some helpful vmaps
+

+[docs]
+  def vmap_field_values(self, field, xs, t, *args):
+    in_axes = (None, 0, None) + len(args) * (None,)
+    return vmap(self.field_values, in_axes=in_axes)(field, xs, t, *args)

+
+
+

+[docs]
+  def vmap_field_gradients(self, field, xs, t, *args):
+    in_axes = (None, 0, None) + len(args) * (None,)
+    return vmap(self.field_gradients, in_axes=in_axes)(field, xs, t, *args)

+
+
+  @property
+  def n_dofs(self):
+    return len(self.field_value_names)

+
+
+
+

+[docs]
+class BaseVariationalFormPhysics(BasePhysics):
+  pass

+
+
+
+

+[docs]
+class BaseEnergyFormPhysics(BaseVariationalFormPhysics):
+  field_value_names: tuple[str, ...]
+
+

+[docs]
+  def element_energy(self, params, x, t, u, fspace, *args):
+    vs = fspace.shape_function_values(x)
+    grad_vs = fspace.shape_function_gradients(x)
+    JxWs = fspace.JxWs(x)
+    xs = vmap(lambda y: jnp.dot(y, x))(vs)
+    us = vmap(lambda y: jnp.dot(y, u))(vs)
+    grad_us = vmap(lambda y: (y.T @ u).T)(grad_vs)
+    in_axes = (None, 0, None, 0, 0) + len(args) * (None,)
+    pis = vmap(self.energy, in_axes=in_axes)(params, xs, t, us, grad_us, *args)
+    return jnp.dot(JxWs, pis)

+
+
+

+[docs]
+  def element_kinetic_energy(self, params, x, t, u, fspace, *args):
+    vs = fspace.shape_function_values(x)
+    grad_vs = fspace.shape_function_gradients(x)
+    JxWs = fspace.JxWs(x)
+    xs = vmap(lambda y: jnp.dot(y, x))(vs)
+    us = vmap(lambda y: jnp.dot(y, u))(vs)
+    grad_us = vmap(lambda y: (y.T @ u).T)(grad_vs)
+    in_axes = (None, 0, None, 0, 0) + len(args) * (None,)
+    pis = vmap(self.kinetic_energy, in_axes=in_axes)(params, xs, t, us, grad_us, *args)
+    return jnp.dot(JxWs, pis)

+
+
+

+[docs]
+  @abstractmethod
+  def energy(self, params, x, t, u, grad_u, *args):
+    pass

+
+
+  # TODO currently only valid for one block
+

+[docs]
+  def potential_energy_on_block(self, params, x, t, us, fspace, conns, *args):
+    # field, _ = params
+    # us = self.field_values(field, x, t, *args)
+    # us = self.vmap_field_values(params, x, t, *args)
+    us = us[conns, :]
+    xs = x[conns, :]
+    return self.vmap_element_energy(params, xs, t, us, fspace, conns, *args)

+
+  
+  # TODO only works on a single block
+  # def potential_energy(self, params, domain, t, *args):
+

+[docs]
+  def potential_energy(self, params, domain, t, us, *args):
+    return self.potential_energy_on_block(params, domain.coords, t, us, domain.fspace, domain.conns, *args)

+
+
+

+[docs]
+  def potential_energy_and_internal_force(self, params, domain, t, us, *args):
+    return value_and_grad(self.potential_energy, argnums=3)(params, domain, t, us, *args)

+
+
+

+[docs]
+  def potential_energy_and_residual(self, params, domain, t, us, *args):
+    pi, f = self.potential_energy_and_internal_force(params, domain, t, us, *args)
+    return pi, jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])

+
+  
+

+[docs]
+  def potential_energy_residual_and_reaction_force(self, params, domain, t, us, *args):
+    global_data = args[0]
+    pi, f = self.potential_energy_and_internal_force(params, domain, t, us, *args)
+    R = jnp.linalg.norm(f.flatten()[domain.dof_manager.unknownIndices])
+    reaction = jnp.sum(f[global_data.reaction_nodes, global_data.reaction_dof])
+    return pi, R, reaction

+
+
+

+[docs]
+  def mass_matrix(self, params, domain, t, us, *args):
+    # us = self.vmap_field_values(params, domain.coords, t, *args)
+    dof_manager = args[0]
+    us = us[domain.conns, :]
+    xs = domain.coords[domain.conns, :]
+    func = jax.hessian(self.element_kinetic_energy, argnums=3)
+    in_axes = (None, 0, None, 0, None, 0) + len(args) * (None,)
+    fs = vmap(func, in_axes=in_axes)(params, xs, t, us, domain.fspace, domain.conns, *args)
+    return assemble_sparse_stiffness_matrix(
+       onp.asarray(fs), onp.asarray(domain.conns), dof_manager
+    )

+
+
+

+[docs]
+  def stiffness_matrix(self, params, domain, t, us, *args):
+    # us = self.vmap_field_values(params, domain.coords, t, *args)
+    dof_manager = args[0]
+    us = us[domain.conns, :]
+    xs = domain.coords[domain.conns, :]
+    func = jax.hessian(self.element_energy, argnums=3)
+    in_axes = (None, 0, None, 0, None, 0) + len(args) * (None,)
+    fs = vmap(func, in_axes=in_axes)(params, xs, t, us, domain.fspace, domain.conns, *args)
+    return assemble_sparse_stiffness_matrix(
+       onp.asarray(fs), onp.asarray(domain.conns), dof_manager
+    )

+
+
+

+[docs]
+  def vmap_element_energy(self, params, x, t, u, fspace, conns, *args):
+    in_axes = (None, 0, None, 0, None, 0) + len(args) * (None,)
+    pis = vmap(self.element_energy, in_axes=in_axes)(params, x, t, u, fspace, conns, *args)
+    return jnp.sum(pis)

+

+
+
+
+

+[docs]
+class BaseStrongFormPhysics(BasePhysics):
+  field_value_names: tuple[int, ...]
+
+

+[docs]
+  def strong_form_neumann_bc(self, params, x, t, n, *args):
+    assert False, 'Can\'t call this on the base method. Need to implement for physics.'

+
+
+

+[docs]
+  @abstractmethod
+  def strong_form_residual(self, params, x, t, *args):
+    pass

+

+
+
+  # def vmap_strong_form_residual(    # us = self.field_values(params, x, t, *args)
+    # us = us[fspace.conns, :]
+    # xs = x[fspace.conns, :])
+
+# class BaseWeakFormPhysics(BasePhysics):
+#   n_dofs: int
+#   field_value_names: tuple[int, ...]
+
+#   def element_field(self, params, x, t, func, u, fspace):
+#     # x_el = x[conn, :]
+#     # u_el = u[conn, :]
+#     # return vmap(func, in_axes=(None, None, None, ))
+#     v = fspace.shape_function_values(x)
+#     grad_v = fspace.shape_function_gradients(x)
+#     JxWs = fspace.JxWs(x)
+#     return jnp
+#     pass
+
+#   def element_field_gradient(self, params, x, t, *args):
+#     pass
+
+#   def quadrature_field(self, params, x, t, *args):
+#     pass
+  
+#   # def quadrature_field_gradient(self):
+#   #   pass
+
+#   @abstractmethod
+#   def energy(self, params, x, t, u, grad_u, *args):
+#     pass
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/burgers_equation.html b/_modules/pancax/physics_kernels/burgers_equation.html new file mode 100644 index 0000000..0d2bdd1 --- /dev/null +++ b/_modules/pancax/physics_kernels/burgers_equation.html @@ -0,0 +1,143 @@ + + + + + + + + pancax.physics_kernels.burgers_equation — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.physics_kernels.burgers_equation
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.physics_kernels.burgers_equation

+from .base import BaseStrongFormPhysics
+import jax.numpy as jnp
+
+
+

+[docs]
+class BurgersEquation(BaseStrongFormPhysics):
+  field_value_names: tuple[int, ...]
+  # v: float
+
+

+[docs]
+  def __init__(self):
+    super().__init__(('u', 'v'))

+
+    # self.v = v
+
+

+[docs]
+  def strong_form_residual(self, params, x, t, *args):
+    field, _ = params
+    u = self.field_values(field, x, t, *args)
+    grad_u = self.field_gradients(field, x, t, *args)
+    # delta_u = self.field_laplacians(field, x, t, *args)
+    dudt = self.field_time_derivatives(field, x, t, *args)
+    # return dudt + 0.01 * jnp.dot(grad_u, grad_u.T)
+    return dudt + jnp.dot(u, grad_u.T)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/heat_equation.html b/_modules/pancax/physics_kernels/heat_equation.html new file mode 100644 index 0000000..017b467 --- /dev/null +++ b/_modules/pancax/physics_kernels/heat_equation.html @@ -0,0 +1,148 @@ + + + + + + + + pancax.physics_kernels.heat_equation — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.physics_kernels.heat_equation
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.physics_kernels.heat_equation

+from .base import BaseStrongFormPhysics
+import jax.numpy as jnp
+
+
+

+[docs]
+class HeatEquation(BaseStrongFormPhysics):
+  field_value_names: tuple[int]
+
+

+[docs]
+  def __init__(self):
+    super().__init__(('temperature'))

+
+
+

+[docs]
+  def strong_form_residual(self, params, x, t, *args):
+    field, props = params
+    delta_u = self.field_laplacians(field, x, t, *args)
+    dudt = self.field_time_derivatives(field, x, t, *args)
+    rho, c, k = props
+    return rho * c * dudt - k * delta_u

+
+  
+

+[docs]
+  def strong_form_neumann_bc(self, params, x, t, n, *args):
+    field, props = params
+    grad_u = self.field_gradients(field, x, t, *args)
+    _, _, k = props
+    return -k * jnp.dot(grad_u, n)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/laplace_beltrami.html b/_modules/pancax/physics_kernels/laplace_beltrami.html new file mode 100644 index 0000000..89107d1 --- /dev/null +++ b/_modules/pancax/physics_kernels/laplace_beltrami.html @@ -0,0 +1,141 @@ + + + + + + + + pancax.physics_kernels.laplace_beltrami — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.physics_kernels.laplace_beltrami
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.physics_kernels.laplace_beltrami

+from .base import BaseEnergyFormPhysics
+import jax.numpy as jnp
+
+
+

+[docs]
+class LaplaceBeltrami(BaseEnergyFormPhysics):
+  field_value_names: tuple[int, ...] = ('u')
+
+

+[docs]
+  def __init__(self):
+    super().__init__(('u'))

+
+
+

+[docs]
+  def energy(self, params, x, t, u, grad_u, *args):
+    return jnp.sum(0.5 * jnp.dot(grad_u, grad_u.T))

+
+
+

+[docs]
+  def kinetic_energy(self, params, x, t, u, grad_u, *args):
+    return 0.5 * jnp.dot(u, u)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/poisson.html b/_modules/pancax/physics_kernels/poisson.html new file mode 100644 index 0000000..4c62f42 --- /dev/null +++ b/_modules/pancax/physics_kernels/poisson.html @@ -0,0 +1,157 @@ + + + + + + + + pancax.physics_kernels.poisson — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.physics_kernels.poisson
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.physics_kernels.poisson

+from .base import BaseEnergyFormPhysics, BaseStrongFormPhysics
+from typing import Callable
+import jax.numpy as jnp
+
+
+

+[docs]
+class Poisson(BaseEnergyFormPhysics, BaseStrongFormPhysics):
+  field_value_names: tuple[str, ...] = ('u')
+  f: Callable
+
+

+[docs]
+  def __init__(self, f: Callable) -> None:
+    super().__init__(('u'))
+    self.f = f

+
+
+

+[docs]
+  def energy(self, params, x, t, u, grad_u, *args):
+    f = self.f(x)
+    pi = 0.5 * jnp.dot(grad_u, grad_u.T) - f * u
+    return jnp.sum(pi)

+
+
+

+[docs]
+  def strong_form_neumann_bc(self, params, x, t, n, *args):
+    field, _ = params
+    grad_u = self.field_gradients(field, x, t, *args)
+    return -jnp.dot(grad_u, n)

+
+
+

+[docs]
+  def strong_form_residual(self, params, x, t, *args):
+    field, _ = params
+    delta_u = self.field_laplacians(field, x, t, *args)
+    f = self.f(x)
+    return -delta_u - f

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/physics_kernels/solid_mechanics.html b/_modules/pancax/physics_kernels/solid_mechanics.html new file mode 100644 index 0000000..835512a --- /dev/null +++ b/_modules/pancax/physics_kernels/solid_mechanics.html @@ -0,0 +1,231 @@ + + + + + + + + pancax.physics_kernels.solid_mechanics — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.physics_kernels.solid_mechanics
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.physics_kernels.solid_mechanics

+from abc import abstractmethod
+from .base import BaseEnergyFormPhysics
+from pancax.math.tensor_math import tensor_2D_to_3D
+from typing import Callable
+import equinox as eqx
+import jax.numpy as jnp
+
+
+# different formulations e.g. plane strain/stress, axisymmetric etc.
+

+[docs]
+class BaseMechanicsFormulation(eqx.Module):
+  n_dimensions: int = eqx.field(static=True)
+
+

+[docs]
+  @abstractmethod
+  def modify_field_gradient(self, grad_u):
+    pass

+

+
+
+
+# note for this formulation we're getting NaNs if the 
+# reference configuration is used during calculation 
+# of the loss function
+

+[docs]
+class IncompressiblePlaneStress(BaseMechanicsFormulation):
+	n_dimensions = 2
+
+

+[docs]
+	def __init__(self) -> None:
+		print('WARNING: Do not include a time of 0.0 with this formulation. You will get NaNs.')

+
+
+

+[docs]
+	def deformation_gradient(self, grad_u):
+		F = tensor_2D_to_3D(grad_u) + jnp.eye(3)
+		F = F.at[2, 2].set(1. / jnp.linalg.det(grad_u + jnp.eye(2)))
+		return F

+
+
+

+[docs]
+	def modify_field_gradient(self, grad_u):
+		F = self.deformation_gradient(grad_u)
+		return F - jnp.eye(3)

+

+
+
+
+

+[docs]
+class PlaneStrain(BaseMechanicsFormulation):
+	n_dimensions: int = 2
+
+

+[docs]
+	def extract_stress(self, P):
+		return P[0:2, 0:2]

+
+
+

+[docs]
+	def modify_field_gradient(self, grad_u):
+		return tensor_2D_to_3D(grad_u)

+

+
+
+
+

+[docs]
+class ThreeDimensional(BaseMechanicsFormulation):
+	n_dimensions: int = 3
+
+

+[docs]
+	def modify_field_gradient(self, grad_u):
+		return grad_u

+

+
+
+
+

+[docs]
+class SolidMechanics(BaseEnergyFormPhysics):
+	field_value_names: tuple[str, ...]
+	constitutive_model: any
+	formulation: BaseMechanicsFormulation
+
+

+[docs]
+	def __init__(self, constitutive_model, formulation) -> None:
+		field_value_names = ('displ_x', 'displ_y')
+		super().__init__(field_value_names)
+		if formulation.n_dimensions > 2:
+			field_value_names = field_value_names + ('displ_z',)
+		
+		self.field_value_names = field_value_names
+		self.constitutive_model = constitutive_model
+		self.formulation = formulation

+
+		
+

+[docs]
+	def energy(self, params, x, t, u, grad_u, *args):
+		# _, model = params
+		grad_u = self.formulation.modify_field_gradient(grad_u)
+		F = grad_u + jnp.eye(3)
+		return self.constitutive_model.energy(F)

+

+
+		# return self.constitutive_model.energy(grad_u)
+		# return model.energy(grad_u)
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/post_processor.html b/_modules/pancax/post_processor.html new file mode 100644 index 0000000..1bf5c2f --- /dev/null +++ b/_modules/pancax/post_processor.html @@ -0,0 +1,540 @@ + + + + + + + + pancax.post_processor — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.post_processor

+from pancax.physics import incompressible_internal_force, internal_force
+from typing import List, Optional
+
+try:
+  import exodus3 as exodus
+except:
+  print('WARNING: Could not find exodus3 module. You\'ll need to use vtk output')
+
+try:
+  import vtk
+except:
+  print('WARNING: Could not find vtk module. You\'ll need to use another form of output')
+
+import jax
+import os
+import numpy as onp
+# import vtk
+
+
+

+[docs]
+class ExodusPostProcessor:
+

+[docs]
+  def __init__(self, mesh_file: str) -> None:
+    self.mesh_file = mesh_file
+    self.exo = None
+    self.node_variables = None
+    self.element_variables = None

+
+
+

+[docs]
+  def check_variable_names(self, domain, variables) -> None:
+    for var in variables:
+      if var == 'internal_force' or var == 'incompressible_internal_force':
+        continue
+
+      if var not in domain.physics.var_name_to_method.keys():
+        str = f'Unsupported variable requested for output {var}.\n'
+        str += f'Supported variables include:\n'
+        for v in domain.physics.var_name_to_method.keys():
+          str += f'  {v}\n'
+        raise ValueError(str)

+
+
+

+[docs]
+  def close(self) -> None:
+    self.exo.close()

+
+
+

+[docs]
+  def copy_mesh(self, output_file: str) -> None:
+    if os.path.isfile(output_file):
+      os.remove(output_file)
+
+    exo_temp = exodus.copy_mesh(self.mesh_file, output_file)
+    exo_temp.close()
+    self.exo = exodus.exodus(output_file, mode='a', array_type='numpy')

+
+
+

+[docs]
+  def get_node_variable_number(self, domain, variables) -> int:
+    n = 0
+    for var in variables:
+      if var == 'internal_force' or var == 'incompressible_internal_force':
+        n = n + len(domain.physics.field_value_names)
+      else:
+        n = n + len(domain.physics.var_name_to_method[var]['names'])
+    
+    return n

+
+
+

+[docs]
+  def get_element_variable_number(self, domain, variables) -> int:
+    n = 0
+    for var in variables:
+      n = n + len(domain.physics.var_name_to_method[var]['names'])
+    if n > 0:
+      q_points = len(domain.fspace.quadrature_rule)
+      return n * q_points
+    else:
+      return 0

+
+
+

+[docs]
+  def init(
+    self, 
+    domain, output_file: str, 
+    node_variables: List[str],
+    element_variables: List[str]
+  ) -> None:
+    self.copy_mesh(output_file)
+    self.check_variable_names(domain, node_variables)
+    self.check_variable_names(domain, element_variables)
+    self.node_variables = node_variables
+    self.element_variables = element_variables
+    self.exo.set_node_variable_number(
+      self.get_node_variable_number(domain, node_variables)
+    )
+    self.exo.set_element_variable_number(
+      self.get_element_variable_number(domain, element_variables)
+    )
+    n = 1
+    for var in self.node_variables:
+      if var == 'internal_force' or var == 'incompressible_internal_force':
+        self.exo.put_node_variable_name('internal_force_x', n)
+        self.exo.put_node_variable_name('internal_force_y', n + 1)
+        self.exo.put_node_variable_name('internal_force_z', n + 2)
+        n = n + 3
+      else:
+        for v in domain.physics.var_name_to_method[var]['names']:
+          self.exo.put_node_variable_name(v, n)
+          n = n + 1
+
+    if len(element_variables) > 0:
+      q_points = len(domain.fspace.quadrature_rule)
+      n = 1
+      for var in self.element_variables:
+        for v in domain.physics.var_name_to_method[var]['names']:
+          for q in range(q_points):
+            name = f'{v}_{q + 1}'
+            self.exo.put_element_variable_name(name, n)
+            n = n + 1

+
+
+

+[docs]
+  def index_to_component(self, index):
+    if index == 0:
+      string = 'x'
+    elif index == 1:
+      string = 'y'
+    elif index == 2:
+      string = 'z'
+    else:
+      raise ValueError('Should be 0, 1, or 2')
+    return string

+
+
+

+[docs]
+  def write_outputs(self, params, domain) -> None:
+    physics = domain.physics
+    times = domain.times
+    for n, time in enumerate(times):
+      self.exo.put_time(n + 1, time)
+
+      for var in self.node_variables:
+        if var == 'internal_force' or var == 'incompressible_internal_force':
+          us = jax.vmap(physics.field_values, in_axes=(None, 0, None))(params.fields, domain.coords, time)
+          fs = onp.array(internal_force(domain, us, params.properties()))
+          for i in range(fs.shape[1]):
+            self.exo.put_node_variable_values(f'internal_force_{self.index_to_component(i)}', n + 1, fs[:, i])
+        else:
+          output = physics.var_name_to_method[var]
+          pred = onp.array(output['method'](params, domain, time))
+          if len(pred.shape) > 2:
+            for i in range(pred.shape[1]):
+              for j in range(pred.shape[2]):
+                k = pred.shape[1] * i + j
+                self.exo.put_node_variable_values(output['names'][k], n + 1, pred[:, i, j])
+          else:
+            for i in range(pred.shape[1]):
+              self.exo.put_node_variable_values(output['names'][i], n + 1, pred[:, i])
+
+      if len(self.element_variables) > 0:
+        n_q_points = len(domain.fspace.quadrature_rule)
+        for var in self.element_variables:
+          output = physics.var_name_to_method[var]
+          pred = onp.array(output['method'](params, domain, time))
+          for q in range(n_q_points):
+            for i in range(pred.shape[2]):
+              name = f'{output["names"][i]}_{q + 1}'
+              # NOTE this will only work on a single block 
+              self.exo.put_element_variable_values(1, name, n + 1, pred[:, q, i])

+

+
+
+
+

+[docs]
+class VtkPostProcessor:
+

+[docs]
+  def __init__(self, mesh_file: str) -> None:
+    self.mesh_file = mesh_file
+    self.node_variables = None
+    self.element_variables = None
+    self.vtk_points = None
+    self.poly_data = None
+    self.writer = vtk.vtkXMLMultiBlockDataWriter()

+
+
+

+[docs]
+  def close(self):
+    pass 

+
+
+

+[docs]
+  def init(
+    self,
+    domain, output_file: str,
+    node_variables,
+    element_variables
+  ) -> None:
+    
+    self.node_variables = node_variables
+    self.element_variables = element_variables
+
+    # self.convert_exodus_to_xml(domain.mesh_file, output_file)
+    reader = vtk.vtkExodusIIReader()
+    reader.SetFileName(domain.mesh_file)
+    reader.Update()
+
+    writer = vtk.vtkXMLMultiBlockDataWriter()
+    writer.SetFileName(output_file)
+    writer.SetInputData(reader.GetOutput())
+    writer.Write()
+    assert False

+
+
+    # exodus_reader = vtk.vtkExodusIIReader()
+    # exodus_reader.SetFileName(domain.mesh_file)
+    # exodus_reader.Update()
+    # # output = exodus_reader.GetOutput()
+    # # print(exodus_reader.GetOutput())
+    # self.poly_data = exodus_reader.GetOutput()
+    # # writer = vtk.vtkXMLMultiBlockDataWriter()
+    # self.writer.SetFileName(output_file)
+    # writer.SetInputData(exodus_reader.GetOutput())
+    # writer.Write()
+
+    # delete this
+    # writer.SetInputData(poly_data)
+    # writer.Write()
+
+

+[docs]
+  def write_outputs(self, params, domain) -> None:
+    physics = domain.physics
+    times = domain.times
+
+    multi_block = vtk.vtkMultiBlockDataSet()
+    for n, time in enumerate(times):
+      # self.exo.put_time(n + 1, time)
+
+      # poly_data = vtk.vtkPolyData()
+      # poly_data.SetPoints(self.vtk_points)
+
+      for var in self.node_variables:
+        vector_array = vtk.vtkDoubleArray()
+        vector_array.SetName(var)
+
+        if var == 'internal_force' or var == 'incompressible_internal_force':
+          assert False
+          us = jax.vmap(physics.field_values, in_axes=(None, 0, None))(params.fields, domain.coords, time)
+          fs = onp.array(internal_force(domain, us, params.properties()))
+          # for i in range(fs.shape[1]):
+          #   self.exo.put_node_variable_values(f'internal_force_{self.index_to_component(i)}', n + 1, fs[:, i])
+        else:
+          output = physics.var_name_to_method[var]
+          pred = onp.array(output['method'](params, domain, time))
+          if len(pred.shape) > 2:
+            assert False, 'still need to hook this up'
+          #   for i in range(pred.shape[1]):
+          #     for j in range(pred.shape[2]):
+          #       k = pred.shape[1] * i + j
+          #       self.exo.put_node_variable_values(output['names'][k], n + 1, pred[:, i, j])
+          else:
+            # vector_array.SetNumberOfComponents(pred.shape[1])
+            vector_array.SetNumberOfComponents(3)
+
+            for i in range(pred.shape[0]):
+              if pred.shape[1] == 2:
+                vector_array.InsertNextTuple(tuple(pred[i, :]) + (0.,))
+              elif pred.shape[2] == 3:
+                vector_array.InsertNextTuple(tuple(pred[i, :]))
+              else:
+                assert False
+
+            # self.poly_data.GetBlock(n).SetVectors(vector_array)
+            self.poly_data.GetFieldData().AddArray(vector_array)
+
+            # time_array = vtk.vtkDoubleArray()
+            # time_array.SetName('Times')
+            # time_array.InsertNextValue(n)
+
+            multi_block.SetBlock(n, self.poly_data)
+
+            # time_array = vtk.vtkDoubleArray()
+            # time_array.SetName('TimeValues')
+            # time_array.InsertNextValue(n)  # Store the time step index or actual time value
+            multi_block.GetMetaData(n).Set('Time', time)
+
+            # multi_block.GetMetaData(n).Set(time_array)
+            # multi_block.GetMetaData(n).Set(vtk.vtkCompositeDataSet.NAME(), f'Time Step {n}')
+            # multi_block.GetMetaData(n).Set(vtk.vtkCompositeDataSet.TIME(), n)
+
+            #   self.exo.put_node_variable_values(output['names'][i], n + 1, pred[:, i])
+
+      # if len(self.element_variables) > 0:
+      #   n_q_points = len(domain.fspace.quadrature_rule)
+      #   for var in self.element_variables:
+      #     output = physics.var_name_to_method[var]
+      #     pred = onp.array(output['method'](params, domain, time))
+      #     for q in range(n_q_points):
+      #       for i in range(pred.shape[2]):
+      #         name = f'{output["names"][i]}_{q + 1}'
+      #         # NOTE this will only work on a single block 
+      #         self.exo.put_element_variable_values(1, name, n + 1, pred[:, q, i])
+
+    self.writer.SetInputData(multi_block)
+    self.writer.Write()

+
+
+

+[docs]
+  def convert_exodus_to_xml(self, exodus_file, xml_file):
+    """Converts an Exodus II file to a VTK XML MultiBlock dataset."""
+
+    # Read the Exodus file
+    reader = vtk.vtkExodusIIReader()
+    reader.SetFileName(exodus_file)
+    reader.Update()
+
+    # Convert to a multi-block dataset
+    multiblock = vtk.vtkMultiBlockDataSet()
+    multiblock.SetNumberOfBlocks(reader.GetNumberOfBlockArrays())
+
+    for i in range(reader.GetNumberOfBlockArrays()):
+        block_name = reader.GetBlockArrayName(i)
+        block = reader.GetBlock(i)
+        multiblock.SetBlock(i, block)
+        multiblock.GetMetaData(i).Set(vtk.vtkCompositeDataSet.NAME(), block_name)
+
+    # Write the XML file
+    writer = vtk.vtkXMLMultiBlockDataWriter()
+    writer.SetFileName(xml_file)
+    writer.SetInputData(multiblock)
+    writer.Write()

+
+
+

+[docs]
+  def get_vtk_cell_type(self, exodus_element_type):
+    """Map Exodus element types to VTK cell types."""
+    if exodus_element_type == "QUAD":
+        return vtk.VTK_QUAD
+    elif exodus_element_type == "TRI":
+        return vtk.VTK_TRIANGLE
+    elif exodus_element_type == "TET":
+        return vtk.VTK_TETRA
+    elif exodus_element_type == "HEX":
+        return vtk.VTK_HEXAHEDRON
+    # elif exodus_element_type == "PYRAMID":
+    #     return vtk.VTK_PYRAMID
+    # elif exodus_element_type == "WEDGE":
+    #     return vtk.VTK_WEDGE
+    else:
+        raise ValueError(f"Unsupported element type: {exodus_element_type}")

+
+
+

+[docs]
+  def cell_type(self, vtk_cell_type, num_nodes_in_element):
+    if vtk_cell_type == vtk.VTK_TETRA and num_nodes_in_element == 4:
+      cell = vtk.vtkTetra()
+    elif vtk_cell_type == vtk.VTK_HEXAHEDRON and num_nodes_in_element == 8:
+      cell = vtk.vtkHexahedron()
+    elif vtk_cell_type == vtk.VTK_QUAD and num_nodes_in_element == 4:
+      cell = vtk.vtkQuad()
+    elif vtk_cell_type == vtk.VTK_TRIANGLE and num_nodes_in_element == 3:
+      cell = vtk.vtkTriangle()
+    elif vtk_cell_type == vtk.VTK_PYRAMID and num_nodes_in_element == 5:
+      cell = vtk.vtkPyramid()
+    elif vtk_cell_type == vtk.VTK_WEDGE and num_nodes_in_element == 6:
+      cell = vtk.vtkWedge()
+    else:
+      print(f"Skipping unsupported element type: {vtk_cell_type} with {num_nodes_in_element} nodes.")
+      # continue
+      cell = None
+    return cell

+

+
+
+# duck typing ... sort of?
+

+[docs]
+class PostProcessor:
+

+[docs]
+  def __init__(self, mesh_file: str, mesh_type = 'exodus') -> None:
+    if mesh_type == 'exodus':
+      self.pp = ExodusPostProcessor(mesh_file)
+    elif mesh_type == 'vtk':
+      self.pp = VtkPostProcessor(mesh_type)
+    else:
+      raise ValueError(f'Unsupported mesh type = {mesh_type}')

+
+  
+

+[docs]
+  def close(self):
+    self.pp.close()

+
+
+

+[docs]
+  def init(self, domain, output_file, node_variables, element_variables = []):
+    self.pp.init(domain, output_file, node_variables, element_variables)

+
+
+

+[docs]
+  def write_outputs(self, params, domain):
+    self.pp.write_outputs(params, domain)

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/problems/forward_problem.html b/_modules/pancax/problems/forward_problem.html new file mode 100644 index 0000000..ee54055 --- /dev/null +++ b/_modules/pancax/problems/forward_problem.html @@ -0,0 +1,214 @@ + + + + + + + + pancax.problems.forward_problem — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.problems.forward_problem
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.problems.forward_problem

+from ..bcs import EssentialBC, NaturalBC
+from ..domains import BaseDomain, CollocationDomain, VariationalDomain
+from ..physics_kernels import BasePhysics, BaseStrongFormPhysics, BaseVariationalFormPhysics
+from typing import Callable, List
+import equinox as eqx
+
+
+

+[docs]
+class DomainPhysicsCompatabilityError(Exception):
+  pass

+
+
+
+# note that physics here will note hold the correct parameters
+# after initialization
+

+[docs]
+class ForwardProblem(eqx.Module):
+  domain: BaseDomain
+  physics: BasePhysics
+  ics: List[Callable]
+  essential_bcs: List[EssentialBC]
+  natural_bcs: List[NaturalBC]
+
+

+[docs]
+  def __init__(
+    self, 
+    domain: BaseDomain,
+    physics: BasePhysics,
+    ics: List[Callable],
+    essential_bcs: List[EssentialBC],
+    natural_bcs: List[NaturalBC]
+  ) -> None:
+    
+    # check compatability between domain and physics
+    if type(domain) == CollocationDomain:
+      if not issubclass(type(physics), BaseStrongFormPhysics):
+        raise DomainPhysicsCompatabilityError(
+          f'Incompatable domain and physics.\n'
+          f'Got domain of type = {type(domain)}\n'
+          f'Got physics of type = {type(physics)}'
+        )
+    elif type(domain) == VariationalDomain:
+      # TODO also need a weak form catch here
+      # TODO or just maybe make a base variational physics class
+      if not issubclass(type(physics), BaseVariationalFormPhysics):
+        print(physics.__class__.__bases__)
+        print(physics.__class__.__mro__)
+        raise DomainPhysicsCompatabilityError(
+          f'Incompatable domain and physics.\n'
+          f'Got domain of type = {type(domain)}\n'
+          f'Got physics of type = {type(physics)}'
+        )
+    else:
+      assert False, 'wtf is this domain'
+
+    if type(domain) == VariationalDomain:
+      domain = domain.update_dof_manager(essential_bcs, physics.n_dofs)
+
+    self.domain = domain
+    physics = physics.update_normalization(domain)
+    self.physics = physics.update_var_name_to_method()
+    self.ics = ics
+    self.essential_bcs = essential_bcs
+    self.natural_bcs = natural_bcs

+
+
+  # TODO a lot of these below are for some backwards
+  # compatability during a transition period to
+  # this new interface
+  @property
+  def conns(self):
+    return self.domain.conns
+
+  @property
+  def coords(self):
+    return self.domain.coords
+  
+  @property
+  def dof_manager(self):
+    return self.domain.dof_manager
+
+  @property
+  def fspace(self):
+    return self.domain.fspace
+
+  @property
+  def mesh(self):
+    return self.domain.mesh
+
+  @property
+  def mesh_file(self):
+    return self.domain.mesh_file
+
+  @property
+  def times(self):
+    return self.domain.times

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/problems/inverse_problem.html b/_modules/pancax/problems/inverse_problem.html new file mode 100644 index 0000000..469ead1 --- /dev/null +++ b/_modules/pancax/problems/inverse_problem.html @@ -0,0 +1,145 @@ + + + + + + + + pancax.problems.inverse_problem — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Module code
    • +
  • pancax.problems.inverse_problem
    • +
  • +
    • +
+
+
+
+
+ +

Source code for pancax.problems.inverse_problem

+from .forward_problem import ForwardProblem
+from pancax.bcs import EssentialBC, NaturalBC
+from pancax.data import FullFieldData, GlobalData
+from pancax.domains import BaseDomain
+from pancax.physics_kernels import BasePhysics
+from typing import Callable, List
+
+
+

+[docs]
+class InverseProblem(ForwardProblem):
+  field_data: FullFieldData
+  global_data: GlobalData
+
+

+[docs]
+  def __init__(
+    self,
+    domain: BaseDomain,
+    physics: BasePhysics,
+    ics: List[Callable],
+    essential_bcs: List[EssentialBC],
+    natural_bcs: List[NaturalBC],
+    field_data: FullFieldData,
+    global_data: GlobalData
+  ) -> None:
+    super().__init__(domain, physics, ics, essential_bcs, natural_bcs)
+    self.field_data = field_data
+    self.global_data = global_data

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/timer.html b/_modules/pancax/timer.html new file mode 100644 index 0000000..c3ae232 --- /dev/null +++ b/_modules/pancax/timer.html @@ -0,0 +1,186 @@ + + + + + + + + pancax.timer — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.timer

+from contextlib import ContextDecorator
+from dataclasses import dataclass, field
+import time
+from typing import Any, Callable, ClassVar, Dict, Optional
+
+
+

+[docs]
+class TimerError(Exception):
+    """A custom exception used to report errors in use of Timer class"""

+
+
+
+

+[docs]
+@dataclass
+class Timer(ContextDecorator):
+    """Time your code using a class, context manager, or decorator"""
+
+    timers: ClassVar[Dict[str, float]] = dict()
+    name: Optional[str] = None
+    text: str = "Time in {name}: {:0.8f} seconds"
+    logger: Optional[Callable[[str], None]] = print
+    _start_time: Optional[float] = field(default=None, init=False, repr=False)
+
+    def __post_init__(self) -> None:
+        """Initialization: add timer to dict of timers"""
+        if self.name:
+            self.timers.setdefault(self.name, 0)
+
+

+[docs]
+    def start(self) -> None:
+        """Start a new timer"""
+        if self._start_time is not None:
+            raise TimerError(f"Timer is running. Use .stop() to stop it")
+
+        self._start_time = time.perf_counter()

+
+
+

+[docs]
+    def stop(self) -> float:
+        """Stop the timer, and report the elapsed time"""
+        if self._start_time is None:
+            raise TimerError(f"Timer is not running. Use .start() to start it")
+
+        # Calculate elapsed time
+        elapsed_time = time.perf_counter() - self._start_time
+        self._start_time = None
+
+        # Report elapsed time
+        if self.logger:
+            if (self.name):
+                self.logger(self.text.format(elapsed_time, name=self.name))
+            else:
+                self.logger(self.text.format(elapsed_time, name=''))
+        if self.name:
+            self.timers[self.name] += elapsed_time
+
+        return elapsed_time

+
+
+    def __enter__(self) -> "Timer":
+        """Start a new timer as a context manager"""
+        self.start()
+        return self
+
+    def __exit__(self, *exc_info: Any) -> None:
+        """Stop the context manager timer"""
+        self.stop()

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/trainer.html b/_modules/pancax/trainer.html new file mode 100644 index 0000000..a51fb17 --- /dev/null +++ b/_modules/pancax/trainer.html @@ -0,0 +1,213 @@ + + + + + + + + pancax.trainer — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.trainer

+from pancax.history_writer import HistoryWriter
+from pancax.logging import Logger
+from pancax.post_processor import PostProcessor
+from pancax.utils import set_checkpoint_file
+from pathlib import Path
+import os
+
+# TODO make this a proper equinox module
+

+[docs]
+class Trainer:
+

+[docs]
+    def __init__(
+        self,
+        domain,
+        opt,
+        checkpoint_base = 'checkpoint',
+        history_file = 'history.csv',
+        log_file = 'pinn.log',
+        output_file_base = 'output',
+        output_node_variables = [],
+        output_element_variables = [],
+        log_every = 1000,
+        output_every = 10000,
+        serialise_every = 10000,
+        workdir = os.getcwd()
+    ) -> None:
+        try:
+            os.makedirs(Path(os.path.join(workdir, 'checkpoint')))
+            os.makedirs(Path(os.path.join(workdir, 'history')))
+            os.makedirs(Path(os.path.join(workdir, 'log')))
+            os.makedirs(Path(os.path.join(workdir, 'results')))
+        except FileExistsError:
+            pass
+
+        self.domain = domain
+        self.opt = opt
+        self.checkpoint_base = Path(os.path.join(workdir, 'checkpoint', checkpoint_base))
+        self.serialise_every = serialise_every
+        self.history = HistoryWriter(Path(os.path.join(workdir, 'history', history_file)), log_every, log_every)
+        self.logger = Logger(Path(os.path.join(workdir, 'log', log_file)), log_every)
+        self.output_every = output_every
+        self.output_file_base = Path(os.path.join(workdir, 'results', output_file_base))
+        self.output_node_variables = output_node_variables
+        self.output_element_variables = output_element_variables
+        self.pp = PostProcessor(domain.mesh_file)
+        self.epoch = 0

+
+
+

+[docs]
+    def init(self, params):
+        opt_st = self.opt.init(params)
+        return opt_st

+
+
+

+[docs]
+    def serialise(self, params):
+        if self.epoch % self.serialise_every == 0:
+            params.serialise(self.checkpoint_base, self.epoch)

+
+
+

+[docs]
+    def step(self, params, opt_st):
+        params, opt_st, loss = self.opt.step(params, self.domain, opt_st)
+        self.history.write_history(loss, self.epoch)
+        self.logger.log_loss(loss, self.epoch)
+        self.serialise(params)
+        self.write_outputs(params)
+        self.epoch = self.epoch + 1
+        return params, opt_st

+
+
+

+[docs]
+    def train(self, params, n_epochs):
+        opt_st = self.init(params)
+        for epoch in range(n_epochs):
+            params, opt_st = self.step(params, opt_st)
+        return params

+
+
+

+[docs]
+    def write_outputs(self, params):
+        if self.epoch % self.output_every == 0:
+            self.pp.init(
+                self.domain, 
+                f'{self.output_file_base}_{str(self.epoch).zfill(8)}.e',
+                node_variables=self.output_node_variables,
+                element_variables=self.output_element_variables
+            )
+            self.pp.write_outputs(params, self.domain)
+            self.pp.close()

+

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_modules/pancax/utils.html b/_modules/pancax/utils.html new file mode 100644 index 0000000..f01c09a --- /dev/null +++ b/_modules/pancax/utils.html @@ -0,0 +1,209 @@ + + + + + + + + pancax.utils — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +

Source code for pancax.utils

+from pathlib import Path
+import inspect
+import os
+
+
+

+[docs]
+class DataFileNotFoundException(Exception):
+  pass

+
+
+
+

+[docs]
+class MeshFileNotFoundException(Exception):
+  pass

+
+
+
+

+[docs]
+def find_data_file(data_file_in: str):
+  call_file = Path(inspect.stack()[1].filename)
+  call_file_dir = call_file.parent
+
+  data_file = Path(os.path.join(
+    call_file_dir, 'data', data_file_in
+  ))
+
+  if not data_file.is_file():
+    data_file = Path(os.path.join(call_file_dir, data_file))
+    if not data_file.is_file():
+      raise DataFileNotFoundException(
+        f'Could not find data file {data_file_in} in either '
+        f'{call_file_dir} or {call_file_dir}/data'
+      )
+
+  print(f'Found {data_file_in} in {data_file.parent}')
+  return data_file

+
+
+
+

+[docs]
+def find_mesh_file(mesh_file_in: str):
+  call_file = Path(inspect.stack()[1].filename)
+  call_file_dir = call_file.parent
+
+  mesh_file = Path(os.path.join(
+    call_file_dir, 'mesh', mesh_file_in
+  ))
+
+  if not mesh_file.is_file():
+    mesh_file = Path(os.path.join(call_file_dir, mesh_file))
+    if not mesh_file.is_file():
+      raise MeshFileNotFoundException(
+        f'Could not find data file {mesh_file_in} in either '
+        f'{call_file_dir} or {call_file_dir}/mesh'
+      )
+
+  print(f'Found {mesh_file_in} in {mesh_file.parent}')
+  return mesh_file

+
+
+
+

+[docs]
+def set_checkpoint_file(checkpoint_file_base: str):
+  call_file = Path(inspect.stack()[3].filename)
+  call_file_dir = call_file.parent
+
+  checkpoint_dir = Path(os.path.join(
+    call_file_dir, 'checkpoint'
+  ))
+
+  if not checkpoint_dir.is_dir():
+    os.makedirs(checkpoint_dir)
+  
+
+  checkpoint_file = Path(os.path.join(
+    checkpoint_dir, checkpoint_file_base
+  ))
+
+  # if not mesh_file.is_file():
+  #   mesh_file = Path(os.path.join(call_file_dir, mesh_file))
+  #   if not mesh_file.is_file():
+  #     raise MeshFileNotFoundException(
+  #       f'Could not find data file {mesh_file_in} in either '
+  #       f'{call_file_dir} or {call_file_dir}/mesh'
+  #     )
+
+  # print(f'Found {mesh_file_in} in {mesh_file.parent}')
+  # return mesh_file
+  return checkpoint_file

+
+
+ +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/_sources/index.rst.txt b/_sources/index.rst.txt new file mode 100644 index 0000000..b61a3e8 --- /dev/null +++ b/_sources/index.rst.txt @@ -0,0 +1,24 @@ +Pancax +======================================= +.. toctree:: + :maxdepth: 2 + + modules + pancax.bcs + pancax.bvps + pancax.constitutive_models + pancax.data + pancax.domains + pancax.fem + pancax.kernels + pancax.loss_functions + pancax.math + pancax.networks + pancax.optimizers + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/_sources/modules.rst.txt b/_sources/modules.rst.txt new file mode 100644 index 0000000..dc79a09 --- /dev/null +++ b/_sources/modules.rst.txt @@ -0,0 +1,7 @@ +pancax +====== + +.. toctree:: + :maxdepth: 4 + + pancax diff --git a/_sources/pancax.bcs.rst.txt b/_sources/pancax.bcs.rst.txt new file mode 100644 index 0000000..800d640 --- /dev/null +++ b/_sources/pancax.bcs.rst.txt @@ -0,0 +1,41 @@ +pancax.bcs package +================== + +Submodules +---------- + +pancax.bcs.distance\_functions module +------------------------------------- + +.. automodule:: pancax.bcs.distance_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.bcs.essential\_bc module +------------------------------- + +.. automodule:: pancax.bcs.essential_bc + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.bcs.natural\_bc module +----------------------------- + +.. automodule:: pancax.bcs.natural_bc + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.bcs + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.bvps.rst.txt b/_sources/pancax.bvps.rst.txt new file mode 100644 index 0000000..d07e860 --- /dev/null +++ b/_sources/pancax.bvps.rst.txt @@ -0,0 +1,41 @@ +pancax.bvps package +=================== + +Submodules +---------- + +pancax.bvps.biaxial\_tension module +----------------------------------- + +.. automodule:: pancax.bvps.biaxial_tension + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.bvps.simple\_shear module +-------------------------------- + +.. automodule:: pancax.bvps.simple_shear + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.bvps.uniaxial\_tension module +------------------------------------ + +.. automodule:: pancax.bvps.uniaxial_tension + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.bvps + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.constitutive_models.rst.txt b/_sources/pancax.constitutive_models.rst.txt new file mode 100644 index 0000000..9e5ad05 --- /dev/null +++ b/_sources/pancax.constitutive_models.rst.txt @@ -0,0 +1,68 @@ +pancax.constitutive\_models package +=================================== + +Submodules +---------- + +pancax.constitutive\_models.base module +--------------------------------------- + +.. automodule:: pancax.constitutive_models.base + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.constitutive\_models.blatz\_ko module +-------------------------------------------- + +.. automodule:: pancax.constitutive_models.blatz_ko + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.constitutive\_models.gent module +--------------------------------------- + +.. automodule:: pancax.constitutive_models.gent + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.constitutive\_models.neohookean module +--------------------------------------------- + +.. automodule:: pancax.constitutive_models.neohookean + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.constitutive\_models.properties module +--------------------------------------------- + +.. automodule:: pancax.constitutive_models.properties + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.constitutive\_models.swanson module +------------------------------------------ + +.. automodule:: pancax.constitutive_models.swanson + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.constitutive_models + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.data.rst.txt b/_sources/pancax.data.rst.txt new file mode 100644 index 0000000..3b2f0ff --- /dev/null +++ b/_sources/pancax.data.rst.txt @@ -0,0 +1,32 @@ +pancax.data package +=================== + +Submodules +---------- + +pancax.data.full\_field\_data module +------------------------------------ + +.. automodule:: pancax.data.full_field_data + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.data.global\_data module +------------------------------- + +.. automodule:: pancax.data.global_data + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.data + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.domains.rst.txt b/_sources/pancax.domains.rst.txt new file mode 100644 index 0000000..bdcc272 --- /dev/null +++ b/_sources/pancax.domains.rst.txt @@ -0,0 +1,50 @@ +pancax.domains package +====================== + +Submodules +---------- + +pancax.domains.base module +-------------------------- + +.. automodule:: pancax.domains.base + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.domains.collocation\_domain module +----------------------------------------- + +.. automodule:: pancax.domains.collocation_domain + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.domains.delta\_pinn\_domain module +----------------------------------------- + +.. automodule:: pancax.domains.delta_pinn_domain + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.domains.variational\_domain module +----------------------------------------- + +.. automodule:: pancax.domains.variational_domain + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.domains + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.fem.elements.rst.txt b/_sources/pancax.fem.elements.rst.txt new file mode 100644 index 0000000..3134a2d --- /dev/null +++ b/_sources/pancax.fem.elements.rst.txt @@ -0,0 +1,86 @@ +pancax.fem.elements package +=========================== + +Submodules +---------- + +pancax.fem.elements.base\_element module +---------------------------------------- + +.. automodule:: pancax.fem.elements.base_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.hex8\_element module +---------------------------------------- + +.. automodule:: pancax.fem.elements.hex8_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.line\_element module +---------------------------------------- + +.. automodule:: pancax.fem.elements.line_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.quad4\_element module +----------------------------------------- + +.. automodule:: pancax.fem.elements.quad4_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.quad9\_element module +----------------------------------------- + +.. automodule:: pancax.fem.elements.quad9_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.simplex\_tri\_element module +------------------------------------------------ + +.. automodule:: pancax.fem.elements.simplex_tri_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.tet10\_element module +----------------------------------------- + +.. automodule:: pancax.fem.elements.tet10_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.elements.tet4\_element module +---------------------------------------- + +.. automodule:: pancax.fem.elements.tet4_element + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.fem.elements + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.fem.rst.txt b/_sources/pancax.fem.rst.txt new file mode 100644 index 0000000..4c96e1d --- /dev/null +++ b/_sources/pancax.fem.rst.txt @@ -0,0 +1,94 @@ +pancax.fem package +================== + +Subpackages +----------- + +.. toctree:: + :maxdepth: 4 + + pancax.fem.elements + +Submodules +---------- + +pancax.fem.dof\_manager module +------------------------------ + +.. automodule:: pancax.fem.dof_manager + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.function\_space module +--------------------------------- + +.. automodule:: pancax.fem.function_space + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.mesh module +---------------------- + +.. automodule:: pancax.fem.mesh + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.quadrature\_rules module +----------------------------------- + +.. automodule:: pancax.fem.quadrature_rules + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.read\_exodus\_mesh module +------------------------------------ + +.. automodule:: pancax.fem.read_exodus_mesh + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.sparse\_matrix\_assembler module +------------------------------------------- + +.. automodule:: pancax.fem.sparse_matrix_assembler + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.surface module +------------------------- + +.. automodule:: pancax.fem.surface + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.fem.traction\_bc module +------------------------------ + +.. automodule:: pancax.fem.traction_bc + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.fem + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.kernels.rst.txt b/_sources/pancax.kernels.rst.txt new file mode 100644 index 0000000..057766b --- /dev/null +++ b/_sources/pancax.kernels.rst.txt @@ -0,0 +1,59 @@ +pancax.kernels package +====================== + +Submodules +---------- + +pancax.kernels.base\_kernel module +---------------------------------- + +.. automodule:: pancax.kernels.base_kernel + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.kernels.laplace\_beltrami module +--------------------------------------- + +.. automodule:: pancax.kernels.laplace_beltrami + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.kernels.linear\_elasticity module +---------------------------------------- + +.. automodule:: pancax.kernels.linear_elasticity + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.kernels.poisson module +----------------------------- + +.. automodule:: pancax.kernels.poisson + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.kernels.solid\_mechanics module +-------------------------------------- + +.. automodule:: pancax.kernels.solid_mechanics + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.kernels + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.loss_functions.rst.txt b/_sources/pancax.loss_functions.rst.txt new file mode 100644 index 0000000..0c3109b --- /dev/null +++ b/_sources/pancax.loss_functions.rst.txt @@ -0,0 +1,86 @@ +pancax.loss\_functions package +============================== + +Submodules +---------- + +pancax.loss\_functions.base\_loss\_function module +-------------------------------------------------- + +.. automodule:: pancax.loss_functions.base_loss_function + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.bc\_loss\_functions module +------------------------------------------------- + +.. automodule:: pancax.loss_functions.bc_loss_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.data\_loss\_functions module +--------------------------------------------------- + +.. automodule:: pancax.loss_functions.data_loss_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.ic\_loss\_function module +------------------------------------------------ + +.. automodule:: pancax.loss_functions.ic_loss_function + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.physics\_loss\_functions\_strong\_form module +-------------------------------------------------------------------- + +.. automodule:: pancax.loss_functions.physics_loss_functions_strong_form + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.strong\_form\_loss\_functions module +----------------------------------------------------------- + +.. automodule:: pancax.loss_functions.strong_form_loss_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.utils module +----------------------------------- + +.. automodule:: pancax.loss_functions.utils + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.loss\_functions.weak\_form\_loss\_functions module +--------------------------------------------------------- + +.. automodule:: pancax.loss_functions.weak_form_loss_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.loss_functions + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.math.rst.txt b/_sources/pancax.math.rst.txt new file mode 100644 index 0000000..df1e3f7 --- /dev/null +++ b/_sources/pancax.math.rst.txt @@ -0,0 +1,32 @@ +pancax.math package +=================== + +Submodules +---------- + +pancax.math.math module +----------------------- + +.. automodule:: pancax.math.math + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.math.tensor\_math module +------------------------------- + +.. automodule:: pancax.math.tensor_math + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.math + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.networks.rst.txt b/_sources/pancax.networks.rst.txt new file mode 100644 index 0000000..e6d26da --- /dev/null +++ b/_sources/pancax.networks.rst.txt @@ -0,0 +1,68 @@ +pancax.networks package +======================= + +Submodules +---------- + +pancax.networks.elm module +-------------------------- + +.. automodule:: pancax.networks.elm + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.networks.field\_property\_pair module +-------------------------------------------- + +.. automodule:: pancax.networks.field_property_pair + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.networks.initialization module +------------------------------------- + +.. automodule:: pancax.networks.initialization + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.networks.mlp module +-------------------------- + +.. automodule:: pancax.networks.mlp + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.networks.properties module +--------------------------------- + +.. automodule:: pancax.networks.properties + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.networks.rbf module +-------------------------- + +.. automodule:: pancax.networks.rbf + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.networks + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.optimizers.rst.txt b/_sources/pancax.optimizers.rst.txt new file mode 100644 index 0000000..635e252 --- /dev/null +++ b/_sources/pancax.optimizers.rst.txt @@ -0,0 +1,50 @@ +pancax.optimizers package +========================= + +Submodules +---------- + +pancax.optimizers.adam module +----------------------------- + +.. automodule:: pancax.optimizers.adam + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.optimizers.base module +----------------------------- + +.. automodule:: pancax.optimizers.base + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.optimizers.lbfgs module +------------------------------ + +.. automodule:: pancax.optimizers.lbfgs + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.optimizers.utils module +------------------------------ + +.. automodule:: pancax.optimizers.utils + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.optimizers + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.physics_kernels.rst.txt b/_sources/pancax.physics_kernels.rst.txt new file mode 100644 index 0000000..ece9d84 --- /dev/null +++ b/_sources/pancax.physics_kernels.rst.txt @@ -0,0 +1,68 @@ +pancax.physics\_kernels package +=============================== + +Submodules +---------- + +pancax.physics\_kernels.base module +----------------------------------- + +.. automodule:: pancax.physics_kernels.base + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics\_kernels.burgers\_equation module +------------------------------------------------ + +.. automodule:: pancax.physics_kernels.burgers_equation + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics\_kernels.heat\_equation module +--------------------------------------------- + +.. automodule:: pancax.physics_kernels.heat_equation + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics\_kernels.laplace\_beltrami module +------------------------------------------------ + +.. automodule:: pancax.physics_kernels.laplace_beltrami + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics\_kernels.poisson module +-------------------------------------- + +.. automodule:: pancax.physics_kernels.poisson + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics\_kernels.solid\_mechanics module +----------------------------------------------- + +.. automodule:: pancax.physics_kernels.solid_mechanics + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.physics_kernels + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.problems.rst.txt b/_sources/pancax.problems.rst.txt new file mode 100644 index 0000000..e6a202b --- /dev/null +++ b/_sources/pancax.problems.rst.txt @@ -0,0 +1,32 @@ +pancax.problems package +======================= + +Submodules +---------- + +pancax.problems.forward\_problem module +--------------------------------------- + +.. automodule:: pancax.problems.forward_problem + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.problems.inverse\_problem module +--------------------------------------- + +.. automodule:: pancax.problems.inverse_problem + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax.problems + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_sources/pancax.rst.txt b/_sources/pancax.rst.txt new file mode 100644 index 0000000..52869dc --- /dev/null +++ b/_sources/pancax.rst.txt @@ -0,0 +1,115 @@ +pancax package +============== + +Subpackages +----------- + +.. toctree:: + :maxdepth: 4 + + pancax.bcs + pancax.bvps + pancax.constitutive_models + pancax.data + pancax.domains + pancax.fem + pancax.kernels + pancax.loss_functions + pancax.math + pancax.networks + pancax.optimizers + pancax.physics_kernels + pancax.problems + +Submodules +---------- + +pancax.\_\_main\_\_ module +-------------------------- + +.. automodule:: pancax.__main__ + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.history\_writer module +----------------------------- + +.. automodule:: pancax.history_writer + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.kinematics module +------------------------ + +.. automodule:: pancax.kinematics + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.logging module +--------------------- + +.. automodule:: pancax.logging + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.physics module +--------------------- + +.. automodule:: pancax.physics + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.post\_processor module +----------------------------- + +.. automodule:: pancax.post_processor + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.timer module +------------------- + +.. automodule:: pancax.timer + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.trainer module +--------------------- + +.. automodule:: pancax.trainer + :members: + :undoc-members: + :show-inheritance: + :private-members: + +pancax.utils module +------------------- + +.. automodule:: pancax.utils + :members: + :undoc-members: + :show-inheritance: + :private-members: + +Module contents +--------------- + +.. automodule:: pancax + :members: + :undoc-members: + :show-inheritance: + :private-members: diff --git a/_static/_sphinx_javascript_frameworks_compat.js b/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery 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+ } +} \ No newline at end of file diff --git a/_static/check-solid.svg b/_static/check-solid.svg new file mode 100644 index 0000000..92fad4b --- /dev/null +++ b/_static/check-solid.svg @@ -0,0 +1,4 @@ + + + + diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js new file mode 100644 index 0000000..54b3c46 --- /dev/null +++ b/_static/clipboard.min.js @@ -0,0 +1,7 @@ +/*! + * clipboard.js v2.0.8 + * https://clipboardjs.com/ + * + * Licensed MIT © Zeno Rocha + */ +!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 + + + + diff --git a/_static/copybutton.css b/_static/copybutton.css new file mode 100644 index 0000000..f1916ec --- /dev/null +++ b/_static/copybutton.css @@ -0,0 +1,94 @@ +/* Copy buttons */ +button.copybtn { + position: absolute; + display: flex; + top: .3em; + right: .3em; + width: 1.7em; + height: 1.7em; + opacity: 0; + transition: opacity 0.3s, border .3s, background-color .3s; + user-select: none; + padding: 0; + border: none; + outline: none; + border-radius: 0.4em; + /* The colors that GitHub uses */ + border: #1b1f2426 1px solid; + background-color: #f6f8fa; + color: #57606a; +} + +button.copybtn.success { + border-color: #22863a; + color: #22863a; +} + +button.copybtn svg { + stroke: currentColor; + width: 1.5em; + height: 1.5em; + padding: 0.1em; +} + +div.highlight { + position: relative; +} + +/* Show the copybutton */ +.highlight:hover button.copybtn, button.copybtn.success { + opacity: 1; +} + +.highlight button.copybtn:hover { + background-color: rgb(235, 235, 235); +} + +.highlight button.copybtn:active { + background-color: rgb(187, 187, 187); +} + +/** + * A minimal CSS-only tooltip copied from: + * https://codepen.io/mildrenben/pen/rVBrpK + * + * To use, write HTML like the following: + * + *

Short

+ */ + .o-tooltip--left { + position: relative; + } + + .o-tooltip--left:after { + opacity: 0; + visibility: hidden; + position: absolute; + content: attr(data-tooltip); + padding: .2em; + font-size: .8em; + left: -.2em; + background: grey; + color: white; + white-space: nowrap; + z-index: 2; + border-radius: 2px; + transform: translateX(-102%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); +} + +.o-tooltip--left:hover:after { + display: block; + opacity: 1; + visibility: visible; + transform: translateX(-100%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); + transition-delay: .5s; +} + +/* By default the copy button shouldn't show up when printing a page */ +@media print { + button.copybtn { + display: none; + } +} diff --git a/_static/copybutton.js b/_static/copybutton.js new file mode 100644 index 0000000..2ea7ff3 --- /dev/null +++ b/_static/copybutton.js @@ -0,0 +1,248 @@ +// Localization support +const messages = { + 'en': { + 'copy': 'Copy', + 'copy_to_clipboard': 'Copy to clipboard', + 'copy_success': 'Copied!', + 'copy_failure': 'Failed to copy', + }, + 'es' : { + 'copy': 'Copiar', + 'copy_to_clipboard': 'Copiar al portapapeles', + 'copy_success': '¡Copiado!', + 'copy_failure': 'Error al copiar', + }, + 'de' : { + 'copy': 'Kopieren', + 'copy_to_clipboard': 'In die Zwischenablage kopieren', + 'copy_success': 'Kopiert!', + 'copy_failure': 'Fehler beim Kopieren', + }, + 'fr' : { + 'copy': 'Copier', + 'copy_to_clipboard': 'Copier dans le presse-papier', + 'copy_success': 'Copié !', + 'copy_failure': 'Échec de la copie', + }, + 'ru': { + 'copy': 'Скопировать', + 'copy_to_clipboard': 'Скопировать в буфер', + 'copy_success': 'Скопировано!', + 'copy_failure': 'Не удалось скопировать', + }, + 'zh-CN': { + 'copy': '复制', + 'copy_to_clipboard': '复制到剪贴板', + 'copy_success': '复制成功!', + 'copy_failure': '复制失败', + }, + 'it' : { + 'copy': 'Copiare', + 'copy_to_clipboard': 'Copiato negli appunti', + 'copy_success': 'Copiato!', + 'copy_failure': 'Errore durante la copia', + } +} + +let locale = 'en' +if( document.documentElement.lang !== undefined + && messages[document.documentElement.lang] !== undefined ) { + locale = document.documentElement.lang +} + +let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; +if (doc_url_root == '#') { + doc_url_root = ''; +} + +/** + * SVG files for our copy buttons + */ +let iconCheck = ` + ${messages[locale]['copy_success']} + + +` + +// If the user specified their own SVG use that, otherwise use the default +let iconCopy = ``; +if (!iconCopy) { + iconCopy = ` + ${messages[locale]['copy_to_clipboard']} + + + +` +} + +/** + * Set up copy/paste for code blocks + */ + +const runWhenDOMLoaded = cb => { + if (document.readyState != 'loading') { + cb() + } else if (document.addEventListener) { + document.addEventListener('DOMContentLoaded', cb) + } else { + document.attachEvent('onreadystatechange', function() { + if (document.readyState == 'complete') cb() + }) + } +} + +const codeCellId = index => `codecell${index}` + +// Clears selected text since ClipboardJS will select the text when copying +const clearSelection = () => { + if (window.getSelection) { + window.getSelection().removeAllRanges() + } else if (document.selection) { + document.selection.empty() + } +} + +// Changes tooltip text for a moment, then changes it back +// We want the timeout of our `success` class to be a bit shorter than the +// tooltip and icon change, so that we can hide the icon before changing back. +var timeoutIcon = 2000; +var timeoutSuccessClass = 1500; + +const temporarilyChangeTooltip = (el, oldText, newText) => { + el.setAttribute('data-tooltip', newText) + el.classList.add('success') + // Remove success a little bit sooner than we change the tooltip + // So that we can use CSS to hide the copybutton first + setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) + setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) +} + +// Changes the copy button icon for two seconds, then changes it back +const temporarilyChangeIcon = (el) => { + el.innerHTML = iconCheck; + setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) +} + +const addCopyButtonToCodeCells = () => { + // If ClipboardJS hasn't loaded, wait a bit and try again. This + // happens because we load ClipboardJS asynchronously. + if (window.ClipboardJS === undefined) { + setTimeout(addCopyButtonToCodeCells, 250) + return + } + + // Add copybuttons to all of our code cells + const COPYBUTTON_SELECTOR = 'div.highlight pre'; + const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) + codeCells.forEach((codeCell, index) => { + const id = codeCellId(index) + codeCell.setAttribute('id', id) + + const clipboardButton = id => + `` + codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) + }) + +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} + + +var copyTargetText = (trigger) => { + var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); + + // get filtered text + let exclude = '.linenos'; + + let text = filterText(target, exclude); + return formatCopyText(text, '', false, true, true, true, '', '') +} + + // Initialize with a callback so we can modify the text before copy + const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) + + // Update UI with error/success messages + clipboard.on('success', event => { + clearSelection() + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) + temporarilyChangeIcon(event.trigger) + }) + + clipboard.on('error', event => { + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) + }) +} + +runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js new file mode 100644 index 0000000..dbe1aaa --- /dev/null +++ b/_static/copybutton_funcs.js @@ -0,0 +1,73 @@ +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +export function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} diff --git a/_static/css/badge_only.css b/_static/css/badge_only.css new file mode 100644 index 0000000..88ba55b --- /dev/null +++ b/_static/css/badge_only.css @@ -0,0 +1 @@ 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+ document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/_static/language_data.js b/_static/language_data.js new file mode 100644 index 0000000..c7fe6c6 --- /dev/null +++ b/_static/language_data.js @@ -0,0 +1,192 @@ +/* + * This script contains the language-specific data used by searchtools.js, + * namely the list of stopwords, stemmer, scorer and splitter. + */ + +var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; + + +/* Non-minified version is copied as a separate JS file, if available */ + +/** + * Porter Stemmer + */ +var Stemmer = function() { + + var step2list = { + ational: 'ate', + tional: 'tion', + enci: 'ence', + anci: 'ance', + izer: 'ize', + bli: 'ble', + alli: 'al', + entli: 'ent', + eli: 'e', + ousli: 'ous', + ization: 'ize', + ation: 'ate', + ator: 'ate', + alism: 'al', + iveness: 'ive', + fulness: 'ful', + ousness: 'ous', + aliti: 'al', + iviti: 'ive', + biliti: 'ble', + logi: 'log' + }; 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+ +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename, kind] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +// Global search result kind enum, used by themes to style search results. +class SearchResultKind { + static get index() { return "index"; } + static get object() { return "object"; } + static get text() { return "text"; } + static get title() { return "title"; } +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename, kind] = item; + + let listItem = document.createElement("li"); + // Add a class representing the item's type: + // can be used by a theme's CSS selector for styling + // See SearchResultKind for the class names. + listItem.classList.add(`kind-${kind}`); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms, anchor) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = Documentation.ngettext( + "Search finished, found one page matching the search query.", + "Search finished, found ${resultCount} pages matching the search query.", + resultCount, + ).replace('${resultCount}', resultCount); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; +// Helper function used by query() to order search results. +// Each input is an array of [docname, title, anchor, descr, score, filename, kind]. +// Order the results by score (in opposite order of appearance, since the +// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically. +const _orderResultsByScoreThenName = (a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString, anchor) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + for (const removalQuery of [".headerlink", "script", "style"]) { + htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); + } + if (anchor) { + const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`); + if (anchorContent) return anchorContent.textContent; + + console.warn( + `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.` + ); + } + + // if anchor not specified or not found, fall back to main content + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent) return docContent.textContent; + + console.warn( + "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.setAttribute("role", "list"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + _parseQuery: (query) => { + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + return [query, searchTerms, excludedTerms, highlightTerms, objectTerms]; + }, + + /** + * execute search (requires search index to be loaded) + */ + _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // Collect multiple result groups to be sorted separately and then ordered. + // Each is an array of [docname, title, anchor, descr, score, filename, kind]. + const normalResults = []; + const nonMainIndexResults = []; + + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase().trim(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + const score = Math.round(Scorer.title * queryLower.length / title.length); + const boost = titles[file] === title ? 1 : 0; // add a boost for document titles + normalResults.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score + boost, + filenames[file], + SearchResultKind.title, + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id, isMain] of foundEntries) { + const score = Math.round(100 * queryLower.length / entry.length); + const result = [ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + SearchResultKind.index, + ]; + if (isMain) { + normalResults.push(result); + } else { + nonMainIndexResults.push(result); + } + } + } + } + + // lookup as object + objectTerms.forEach((term) => + normalResults.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) { + normalResults.forEach((item) => (item[4] = Scorer.score(item))); + nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item))); + } + + // Sort each group of results by score and then alphabetically by name. + normalResults.sort(_orderResultsByScoreThenName); + nonMainIndexResults.sort(_orderResultsByScoreThenName); + + // Combine the result groups in (reverse) order. + // Non-main index entries are typically arbitrary cross-references, + // so display them after other results. + let results = [...nonMainIndexResults, ...normalResults]; + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + return results.reverse(); + }, + + query: (query) => { + const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query); + const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + SearchResultKind.object, + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + if (!terms.hasOwnProperty(word)) { + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + } + if (!titleTerms.hasOwnProperty(word)) { + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: titleTerms[term], score: Scorer.partialTitle }); + }); + } + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (!fileMap.has(file)) fileMap.set(file, [word]); + else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + SearchResultKind.text, + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords, anchor) => { + const text = Search.htmlToText(htmlText, anchor); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/_static/sphinx_highlight.js b/_static/sphinx_highlight.js new file mode 100644 index 0000000..8a96c69 --- /dev/null +++ b/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/genindex.html b/genindex.html new file mode 100644 index 0000000..0d16f2e --- /dev/null +++ b/genindex.html @@ -0,0 +1,3020 @@ + + + + + + + + Index — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Index
    • +
  • +
    • +
+
+
+
+
+ + +

Index

+ +
+ _ + | A + | B + | C + | D + | E + | F + | G + | H + | I + | J + | K + | L + | M + | N + | O + | P + | Q + | R + | S + | T + | U + | V + | W + | X + | Z + +
+

_

+ + + +
+ +

A

+ + + +
+ +

B

+ + + +
+ +

C

+ + + +
+ +

D

+ + + +
+ +

E

+ + + +
+ +

F

+ + + +
+ +

G

+ + + +
+ +

H

+ + + +
+ +

I

+ + + +
+ +

J

+ + + +
+ +

K

+ + +
+ +

L

+ + + +
+ +

M

+ + + +
+ +

N

+ + + +
+ +

O

+ + + +
+ +

P

+ + + +
    +
  • P1 (pancax.constitutive_models.swanson.Swanson attribute) +
    • +
  • + pancax + +
    • +
  • + pancax.bcs + +
    • +
  • + pancax.bcs.distance_functions + +
    • +
  • + pancax.bcs.essential_bc + +
    • +
  • + pancax.bcs.natural_bc + +
    • +
  • + pancax.bvps + +
    • +
  • + pancax.bvps.biaxial_tension + +
    • +
  • + pancax.bvps.simple_shear + +
    • +
  • + pancax.bvps.uniaxial_tension + +
    • +
  • + pancax.constitutive_models + +
    • +
  • + pancax.constitutive_models.base + +
    • +
  • + pancax.constitutive_models.blatz_ko + +
    • +
  • + pancax.constitutive_models.gent + +
    • +
  • + pancax.constitutive_models.neohookean + +
    • +
  • + pancax.constitutive_models.properties + +
    • +
  • + pancax.constitutive_models.swanson + +
    • +
  • + pancax.data + +
    • +
  • + pancax.data.full_field_data + +
    • +
  • + pancax.data.global_data + +
    • +
  • + pancax.domains + +
    • +
  • + pancax.domains.base + +
    • +
  • + pancax.domains.collocation_domain + +
    • +
  • + pancax.domains.delta_pinn_domain + +
    • +
  • + pancax.domains.variational_domain + +
    • +
  • + pancax.fem + +
    • +
  • + pancax.fem.dof_manager + +
    • +
  • + pancax.fem.elements + +
    • +
  • + pancax.fem.elements.base_element + +
    • +
  • + pancax.fem.elements.hex8_element + +
    • +
  • + pancax.fem.elements.line_element + +
    • +
  • + pancax.fem.elements.quad4_element + +
    • +
  • + pancax.fem.elements.quad9_element + +
    • +
  • + pancax.fem.elements.simplex_tri_element + +
    • +
  • + pancax.fem.elements.tet10_element + +
    • +
  • + pancax.fem.elements.tet4_element + +
    • +
  • + pancax.fem.function_space + +
    • +
  • + pancax.fem.mesh + +
    • +
  • + pancax.fem.quadrature_rules + +
    • +
  • + pancax.fem.read_exodus_mesh + +
    • +
  • + pancax.fem.sparse_matrix_assembler + +
    • +
  • + pancax.fem.surface + +
    • +
  • + pancax.fem.traction_bc + +
    • +
  • + pancax.history_writer + +
    • +
  • + pancax.kernels + +
    • +
  • + pancax.kernels.base_kernel + +
    • +
  • + pancax.kernels.laplace_beltrami + +
    • +
  • + pancax.kernels.linear_elasticity + +
    • +
  • + pancax.kernels.poisson + +
    • +
  • + pancax.kinematics + +
    • +
  • + pancax.logging + +
    • +
  • + pancax.loss_functions + +
    • +
  • + pancax.loss_functions.base_loss_function + +
    • +
  • + pancax.loss_functions.bc_loss_functions + +
    • +
+ +

Q

+ + + +
+ +

R

+ + + +
+ +

S

+ + + +
+ +

T

+ + + +
+ +

U

+ + + +
+ +

V

+ + + +
+ +

W

+ + + +
+ +

X

+ + + +
+ +

Z

+ + +
+ + + +
+
+
+ +
+ +
+

© Copyright 2024, Craig M. Hamel.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + \ No newline at end of file diff --git a/index.html b/index.html new file mode 100644 index 0000000..c8826d5 --- /dev/null +++ b/index.html @@ -0,0 +1,244 @@ + + + + + + + + + Pancax — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

Pancax

+
+ +
+
+
+

Indices and tables

+ +
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/modules.html b/modules.html new file mode 100644 index 0000000..3919083 --- /dev/null +++ b/modules.html @@ -0,0 +1,441 @@ + + + + + + + + + pancax — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax

+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/objects.inv b/objects.inv new file mode 100644 index 0000000..76c71fd Binary files /dev/null and b/objects.inv differ diff --git a/pancax.bcs.html b/pancax.bcs.html new file mode 100644 index 0000000..a200a30 --- /dev/null +++ b/pancax.bcs.html @@ -0,0 +1,336 @@ + + + + + + + + + pancax.bcs package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.bcs package

+
+

Submodules

+
+
+

pancax.bcs.distance_functions module

+
+
+pancax.bcs.distance_functions.get_edges(domain, sset_names: List[str])[source]
+
+ +
+
+pancax.bcs.distance_functions.distance(x1, x2)[source]
+
+ +
+
+pancax.bcs.distance_functions.line_segment(x, segment)[source]
+
+ +
+
+pancax.bcs.distance_functions.distance_function(domain, ssets, m=1.0)[source]
+
+ +
+
+

pancax.bcs.essential_bc module

+
+
+class pancax.bcs.essential_bc.EssentialBC(nodeSet: str, component: int, function: ~typing.Callable[[~jaxtyping.Float[Array, 'nd'], float], float] | None = <function EssentialBC.<lambda>>)[source]
+

Bases: Module

+
+
Parameters:
+
    +

  • nodeSet – A name for a nodeset in the mesh

    • +

  • component – The dof to apply the essential bc to

    • +

  • function – A function f(x, t) = u that gives the value +to enforce on the (nodeset, component) of a field. +This defaults to the zero function

    • +
+
+
+
+
+nodeSet: str
+
+ +
+
+component: int
+
+ +
+
+function(t)
+
+ +
+
+coordinates(mesh)[source]
+
+ +
+
+__init__(nodeSet: str, component: int, function: ~typing.Callable[[~jaxtyping.Float[Array, 'nd'], float], float] | None = <function EssentialBC.<lambda>>) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.bcs.essential_bc.EssentialBCSet(bcs: List[pancax.bcs.essential_bc.EssentialBC])[source]
+

Bases: Module

+
+
+bcs: List[EssentialBC]
+
+ +
+
+__init__(bcs: List[EssentialBC]) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.bcs.natural_bc module

+
+
+class pancax.bcs.natural_bc.NaturalBC(sideset: str, function: Optional[Callable[[jaxtyping.Float[Array, 'nd'], float], jaxtyping.Float[Array, 'nf']]] = <function NaturalBC.<lambda> at 0x7f76545a3380>)[source]
+

Bases: Module

+
+
+sideset: str
+
+ +
+
+function(t)
+
+ +
+
+coordinates(mesh, q_rule_1d)[source]
+
+ +
+
+normals(mesh, q_rule_1d)[source]
+
+ +
+
+__init__(sideset: str, function: ~typing.Callable[[~jaxtyping.Float[Array, 'nd'], float], ~jaxtyping.Float[Array, 'nf']] | None = <function NaturalBC.<lambda>>) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.bvps.html b/pancax.bvps.html new file mode 100644 index 0000000..9656d4c --- /dev/null +++ b/pancax.bvps.html @@ -0,0 +1,202 @@ + + + + + + + + + pancax.bvps package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.bvps package

+
+

Submodules

+
+
+

pancax.bvps.biaxial_tension module

+
+
+pancax.bvps.biaxial_tension.BiaxialLinearRamp(final_displacement_x: float, final_displacement_y: float, length_x: float, length_y: float)[source]
+
+ +
+
+

pancax.bvps.simple_shear module

+
+
+pancax.bvps.simple_shear.SimpleShearLinearRamp(final_displacement: float, length: float, direction: str)[source]
+
+ +
+
+

pancax.bvps.uniaxial_tension module

+
+
+pancax.bvps.uniaxial_tension.UniaxialTensionLinearRamp(final_displacement: float, length: float, direction: str, n_dimensions: int)[source]
+
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.constitutive_models.html b/pancax.constitutive_models.html new file mode 100644 index 0000000..edd098a --- /dev/null +++ b/pancax.constitutive_models.html @@ -0,0 +1,565 @@ + + + + + + + + + pancax.constitutive_models package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.constitutive_models package

+
+

Submodules

+
+
+

pancax.constitutive_models.base module

+
+
+class pancax.constitutive_models.base.BaseConstitutiveModel[source]
+

Bases: Module

+
+
+cauchy_stress(F: Float[Array, '3 3']) → Float[Array, '3 3'][source]
+
+ +
+
+abstract energy(F: Float[Array, '3 3']) → float[source]
+

This method returns the algorithmic strain energy density.

+
+ +
+
+invariants(F: Float[Array, '3 3']) → Tuple[float, float, float][source]
+
+ +
+
+I1(F: Float[Array, '3 3']) → float[source]
+

Calculates the first invariant

+
+
Parameters:
+

F – the deformation gradient

+
+
+
+\[I_1 = tr\left(\mathbf{F}^T\mathbf{F}\right)\]
+
+ +
+
+I1_bar(F: Float[Array, '3 3']) → float[source]
+

Calculates the first distortional invariant

+
+
Parameters:
+

F – the deformation gradient

+
+
+
+\[\bar{I}_1 = J^{-2/3}tr\left(\mathbf{F}^T\mathbf{F}\right)\]
+
+ +
+
+I2(F: Float[Array, '3 3']) → float[source]
+
+ +
+
+I2_bar(F: Float[Array, '3 3']) → float[source]
+
+ +
+
+jacobian(F: Float[Array, '3 3']) → float[source]
+

This simply calculate the jacobian but with guard rails +to return nonsensical numbers if a non-positive jacobian +is encountered during training.

+
+
Parameters:
+

F – the deformation gradient

+
+
+
+\[J = det(\mathbf{F})\]
+
+ +
+
+pk1_stress(F: Float[Array, '3 3']) → Float[Array, '3 3'][source]
+
+ +
+
+properties()[source]
+
+ +
+
+__init__() → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.constitutive_models.blatz_ko module

+
+
+class pancax.constitutive_models.blatz_ko.BlatzKo(shear_modulus: pancax.constitutive_models.properties.BoundedProperty | float)[source]
+

Bases: BaseConstitutiveModel

+
+
+shear_modulus: BoundedProperty | float
+
+ +
+
+energy(F)[source]
+

This method returns the algorithmic strain energy density.

+
+ +
+
+__init__(shear_modulus: BoundedProperty | float) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.constitutive_models.gent module

+
+
+class pancax.constitutive_models.gent.Gent(bulk_modulus: BoundedProperty | float, shear_modulus: BoundedProperty | float, Jm_parameter: BoundedProperty | float)[source]
+

Bases: BaseConstitutiveModel

+

Gent model with the following model form

+
+\[\psi(\mathbf{F}) = \frac{1}{2}K\left[\frac{1}{2}\left(J^2 - \ln J\right)\right] - + \frac{1}{2}GJ_m\ln\left(1 - \frac{\bar{I}_1 - 3}{J_m}\right)\]
+
+
+bulk_modulus: BoundedProperty | float
+
+ +
+
+shear_modulus: BoundedProperty | float
+
+ +
+
+Jm_parameter: BoundedProperty | float
+
+ +
+
+energy(F)[source]
+

This method returns the algorithmic strain energy density.

+
+ +
+
+__init__(bulk_modulus: BoundedProperty | float, shear_modulus: BoundedProperty | float, Jm_parameter: BoundedProperty | float) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.constitutive_models.neohookean module

+
+
+class pancax.constitutive_models.neohookean.NeoHookean(bulk_modulus: BoundedProperty | float, shear_modulus: BoundedProperty | float)[source]
+

Bases: BaseConstitutiveModel

+

NeoHookean model with the following model form

+
+\[\psi(\mathbf{F}) = \frac{1}{2}K\left[\frac{1}{2}\left(J^2 - \ln J\right)\right] + + \frac{1}{2}G\left(\bar{I}_1 - 3\right)\]
+
+
+bulk_modulus: BoundedProperty | float
+
+ +
+
+shear_modulus: BoundedProperty | float
+
+ +
+
+energy(F: Float[Array, '3 3']) → float[source]
+

This method returns the algorithmic strain energy density.

+
+ +
+
+__init__(bulk_modulus: BoundedProperty | float, shear_modulus: BoundedProperty | float) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.constitutive_models.properties module

+
+
+class pancax.constitutive_models.properties.BoundedProperty(prop_min: float, prop_max: float, key: <function PRNGKey at 0x7f76547353a0>)[source]
+

Bases: Module

+
+
+__init__(prop_min: float, prop_max: float, key: PRNGKey) → None[source]
+
+ +
+
+prop_min: float
+
+ +
+
+prop_max: float
+
+ +
+
+prop_val: float
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+_check_other_type(other, op_str)[source]
+
+ +
+ +
+
+

pancax.constitutive_models.swanson module

+
+
+class pancax.constitutive_models.swanson.Swanson(bulk_modulus: BoundedProperty | float, A1: BoundedProperty | float, P1: BoundedProperty | float, B1: BoundedProperty | float, Q1: BoundedProperty | float, C1: BoundedProperty | float, R1: BoundedProperty | float, cutoff_strain: float)[source]
+

Bases: BaseConstitutiveModel

+

Swanson model truncated to 4 parameters

+
+\[\psi(\mathbf{F}) = K\left(J\ln J - J + 1\right) + + \frac{3}{2}A_1\left(\frac{\bar{I}_1}{3} - 1\right)^{P_1} + + \frac{3}{2}C_1\left(\frac{\bar{I}_1}{3} - 1\right)^{R_1}\]
+
+
+bulk_modulus: BoundedProperty | float
+
+ +
+
+A1: BoundedProperty | float
+
+ +
+
+P1: BoundedProperty | float
+
+ +
+
+B1: BoundedProperty | float
+
+ +
+
+Q1: BoundedProperty | float
+
+ +
+
+C1: BoundedProperty | float
+
+ +
+
+R1: BoundedProperty | float
+
+ +
+
+cutoff_strain: float
+
+ +
+
+energy(F)[source]
+

This method returns the algorithmic strain energy density.

+
+ +
+
+__init__(bulk_modulus: BoundedProperty | float, A1: BoundedProperty | float, P1: BoundedProperty | float, B1: BoundedProperty | float, Q1: BoundedProperty | float, C1: BoundedProperty | float, R1: BoundedProperty | float, cutoff_strain: float) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.data.html b/pancax.data.html new file mode 100644 index 0000000..d7d1639 --- /dev/null +++ b/pancax.data.html @@ -0,0 +1,331 @@ + + + + + + + + + pancax.data package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.data package

+
+

Submodules

+
+
+

pancax.data.full_field_data module

+
+
+class pancax.data.full_field_data.FullFieldData(data_file: str, input_keys: List[str], output_keys: List[str])[source]
+

Bases: Module

+

Data structure to store full field data used as ground truth +for output fields of a PINN when solving inverse problems.

+
+
Parameters:
+
    +

  • inputs – Data that serves as inputs to the PINN

    • +

  • outputs – Data that serves as outputs of the PINN

    • +

  • n_time_steps – Variable used for book keeping

    • +
+
+
+
+
+__init__(data_file: str, input_keys: List[str], output_keys: List[str])[source]
+
+ +
+
+inputs: Array
+
+ +
+
+outputs: Array
+
+ +
+
+n_time_steps: int
+
+ +
+
+plot_registration(domain)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+plot_data(domain, time_step)[source]
+
+ +
+
+shift_inputs(x, y, z)[source]
+
+ +
+
+set_input_component_values(component, val)[source]
+
+ +
+ +
+
+

pancax.data.global_data module

+
+
+class pancax.data.global_data.GlobalData(data_file: str, times_key: str, disp_key: str, force_key: str, mesh_file: str, nset_id: int, reaction_dof: int | str, n_time_steps: int, plotting: bool | None = False)[source]
+

Bases: Module

+

Data structure that holds global data to be used as +ground truth for some global field calculated from +PINN outputs used in inverse modeling training

+
+
Parameters:
+
    +

  • times – A set of times used to compare to physics calculations

    • +

  • displacements – Currently hardcoded to use a displacement-force curve TODO

    • +

  • outputs – Field used as ground truth, hardcoded essentially to a reaction force now

    • +

  • n_nodes – Book-keeping variable for number of nodes on nodeset to measure global response from

    • +

  • n_time_steps – Book-keeping variable

    • +

  • reaction_nodes – Node set nodes for where to measure reaction forces

    • +

  • reaction_dof – Degree of freedom to use for reaction force calculation

    • +
+
+
+
+
+__init__(data_file: str, times_key: str, disp_key: str, force_key: str, mesh_file: str, nset_id: int, reaction_dof: int | str, n_time_steps: int, plotting: bool | None = False)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+times: Array
+
+ +
+
+displacements: Array
+
+ +
+
+outputs: Array
+
+ +
+
+n_nodes: int
+
+ +
+
+n_time_steps: int
+
+ +
+
+reaction_nodes: Array
+
+ +
+
+reaction_dof: int
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.domains.html b/pancax.domains.html new file mode 100644 index 0000000..4d71ba4 --- /dev/null +++ b/pancax.domains.html @@ -0,0 +1,400 @@ + + + + + + + + + pancax.domains package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.domains package

+
+

Submodules

+
+
+

pancax.domains.base module

+
+
+class pancax.domains.base.BaseDomain(mesh_file: str, times: jaxtyping.Float[Array, 'nt'], p_order: int | None = 1)[source]
+

Bases: Module

+
+
+__init__(mesh_file: str, times: Float[Array, 'nt'], p_order: int | None = 1) → None[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+mesh_file: str
+
+ +
+
+mesh: Mesh
+
+ +
+
+coords: Float[Array, 'nn nd']
+
+ +
+
+times: Float[Array, 'nt'] | Float[Array, 'nn 1']
+
+ +
+ +
+
+

pancax.domains.collocation_domain module

+
+
+class pancax.domains.collocation_domain.CollocationDomain(mesh_file: str, times: jaxtyping.Float[Array, 'nt'], p_order: int | None = 1)[source]
+

Bases: BaseDomain

+
+
+mesh_file: str
+
+ +
+
+mesh: Mesh
+
+ +
+
+coords: Float[Array, 'nn nd']
+
+ +
+
+times: Float[Array, 'nt'] | Float[Array, 'nn 1']
+
+ +
+
+__init__(mesh_file: str, times: Float[Array, 'nt'], p_order: int | None = 1) → None[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.domains.delta_pinn_domain module

+
+
+class pancax.domains.delta_pinn_domain.DeltaPINNDomain(mesh_file: str, times: jaxtyping.Float[Array, 'nt'], n_eigen_values: int, p_order: int | None = 1, q_order: int | None = 2)[source]
+

Bases: VariationalDomain

+
+
+__init__(mesh_file: str, times: Float[Array, 'nt'], n_eigen_values: int, p_order: int | None = 1, q_order: int | None = 2)[source]
+
+ +
+
+n_eigen_values: int
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+physics: LaplaceBeltrami
+
+ +
+
+eigen_modes: Float[Array, 'nn nev']
+
+ +
+
+solve_eigen_problem()[source]
+
+ +
+ +
+
+

pancax.domains.variational_domain module

+
+
+class pancax.domains.variational_domain.VariationalDomain(mesh_file: str, times: jaxtyping.Float[Array, 'nt'], p_order: int | None = 1, q_order: int | None = 2)[source]
+

Bases: BaseDomain

+
+
+mesh_file: str
+
+ +
+
+mesh: Mesh
+
+ +
+
+coords: Float[Array, 'nn nd']
+
+ +
+
+times: Float[Array, 'nt'] | Float[Array, 'nn 1']
+
+ +
+
+__init__(mesh_file: str, times: Float[Array, 'nt'], p_order: int | None = 1, q_order: int | None = 2)[source]
+
+ +
+
+conns: Int[Array, 'ne nnpe']
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+dof_manager: DofManager
+
+ +
+
+fspace: FunctionSpace
+
+ +
+
+fspace_centroid: FunctionSpace
+
+ +
+
+update_dof_manager(dirichlet_bcs, n_dofs)[source]
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.fem.elements.html b/pancax.fem.elements.html new file mode 100644 index 0000000..5f47a62 --- /dev/null +++ b/pancax.fem.elements.html @@ -0,0 +1,742 @@ + + + + + + + + + pancax.fem.elements package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.fem.elements package

+
+

Submodules

+
+
+

pancax.fem.elements.base_element module

+
+
+pancax.fem.elements.base_element.get_lobatto_nodes_1d(degree)[source]
+
+ +
+
+pancax.fem.elements.base_element.pascal_triangle_monomials(degree)[source]
+
+ +
+
+pancax.fem.elements.base_element.vander1d(x, degree)[source]
+
+ +
+
+pancax.fem.elements.base_element.vander2d(x, degree)[source]
+
+ +
+
+class pancax.fem.elements.base_element.ShapeFunctions(values: Float[Array, 'np nn'], gradients: Float[Array, 'np nd nn'])[source]
+

Bases: NamedTuple

+

Shape functions and shape function gradients (in the parametric space).

+
+
Parameters:
+
    +

  • values – Values of the shape functions at a discrete set of points. +Shape is (nPts, nNodes), where nPts is the number of +points at which the shame functinos are evaluated, and nNodes +is the number of nodes in the element (which is equal to the +number of shape functions).

    • +

  • gradients – Values of the parametric gradients of the shape functions. +Shape is (nPts, nDim, nNodes), where nDim is the number +of spatial dimensions. Line elements are an exception, which +have shape (nPts, nNdodes).

    • +
+
+
+
+
+values: Float[Array, 'np nn']
+

Alias for field number 0

+
+ +
+
+gradients: Float[Array, 'np nd nn']
+

Alias for field number 1

+
+ +
+
+_asdict()
+

Return a new dict which maps field names to their values.

+
+ +
+
+_field_defaults = {}
+
+ +
+
+_fields = ('values', 'gradients')
+
+ +
+
+classmethod _make(iterable)
+

Make a new ShapeFunctions object from a sequence or iterable

+
+ +
+
+_replace(**kwds)
+

Return a new ShapeFunctions object replacing specified fields with new values

+
+ +
+ +
+
+class pancax.fem.elements.base_element.BaseElement(elementType: str, degree: int, coordinates: Float[Array, 'nn nd'], vertexNodes: Int[Array, 'nn'], faceNodes: Int[Array, 'nf nnpf'], interiorNodes: Int[Array, 'nni'])[source]
+

Bases: Module

+

Base class for different element technologies

+
+
Parameters:
+
    +

  • elementType – Element type name

    • +

  • degree – Polynomial degree

    • +

  • coordinates – Nodal coordinates in the reference configuration

    • +

  • vertexNodes – Vertex node number, 0-based

    • +

  • faceNodes – Nodes associated with each face, 0-based

    • +

  • interiorNodes – Nodes in the interior, 0-based or empty

    • +
+
+
+
+
+elementType: str
+
+ +
+
+degree: int
+
+ +
+
+coordinates: Float[Array, 'nn nd']
+
+ +
+
+vertexNodes: Int[Array, 'nn']
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf']
+
+ +
+
+interiorNodes: Int[Array, 'nni']
+
+ +
+
+abstract compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+__init__(elementType: str, degree: int, coordinates: Float[Array, 'nn nd'], vertexNodes: Int[Array, 'nn'], faceNodes: Int[Array, 'nf nnpf'], interiorNodes: Int[Array, 'nni']) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.fem.elements.hex8_element module

+
+
+class pancax.fem.elements.hex8_element.Hex8Element[source]
+

Bases: BaseElement

+
+
+elementType: str = 'hex8'
+
+ +
+
+degree: int = 1
+
+ +
+
+coordinates: Float[Array, 'nn nd'] = Array([[-1., -1., -1.],        [ 1., -1., -1.],        [ 1.,  1., -1.],        [-1.,  1., -1.],        [-1., -1.,  1.],        [ 1., -1.,  1.],        [ 1.,  1.,  1.],        [-1.,  1.,  1.]], dtype=float32)
+
+ +
+
+vertexNodes: Int[Array, 'nn'] = Array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int32)
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = Array([[0, 1, 5, 6],        [1, 2, 6, 5],        [2, 3, 7, 6],        [0, 4, 7, 3],        [0, 3, 2, 1],        [4, 5, 6, 7]], dtype=int32)
+
+ +
+
+interiorNodes: Int[Array, 'nni'] = None
+
+ +
+
+__init__()[source]
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.fem.elements.line_element module

+
+
+class pancax.fem.elements.line_element.LineElement(degree)[source]
+

Bases: BaseElement

+
+
+elementType: str = 'line'
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = None
+
+ +
+
+__init__(degree)[source]
+
+ +
+
+degree: int
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+coordinates: Float[Array, 'nn nd']
+
+ +
+
+vertexNodes: any
+
+ +
+
+interiorNodes: any
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+ +
+
+

pancax.fem.elements.quad4_element module

+
+
+class pancax.fem.elements.quad4_element.Quad4Element[source]
+

Bases: BaseElement

+
+
+elementType: str = 'quad4'
+
+ +
+
+degree: int = 1
+
+ +
+
+coordinates: Float[Array, 'nn nd'] = Array([[-1., -1.],        [ 1., -1.],        [ 1.,  1.],        [-1.,  1.]], dtype=float32)
+
+ +
+
+vertexNodes: Int[Array, 'nn'] = Array([0, 1, 2], dtype=int32)
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = Array([[0, 1],        [1, 2],        [2, 3],        [3, 0]], dtype=int32)
+
+ +
+
+interiorNodes: Int[Array, 'nni'] = None
+
+ +
+
+__init__()[source]
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.fem.elements.quad9_element module

+
+
+class pancax.fem.elements.quad9_element.Quad9Element[source]
+

Bases: BaseElement

+
+
+elementType: str = 'quad9'
+
+ +
+
+degree: int = 2
+
+ +
+
+coordinates: Float[Array, 'nn nd'] = Array([[-1., -1.],        [ 1., -1.],        [ 1.,  1.],        [-1.,  1.],        [ 0., -1.],        [ 1.,  0.],        [ 0.,  1.],        [-1.,  0.],        [ 0.,  0.]], dtype=float32)
+
+ +
+
+vertexNodes: Int[Array, 'nn'] = Array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int32)
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = Array([[0, 4, 1],        [1, 5, 2],        [2, 6, 3],        [3, 7, 0]], dtype=int32)
+
+ +
+
+interiorNodes: Int[Array, 'nni'] = Array([8], dtype=int32)
+
+ +
+
+__init__()[source]
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.fem.elements.simplex_tri_element module

+
+
+class pancax.fem.elements.simplex_tri_element.SimplexTriElement(degree)[source]
+

Bases: BaseElement

+
+
+elementType: str = 'simplex tri'
+
+ +
+
+__init__(degree)[source]
+
+ +
+
+degree: int
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+coordinates: Float[Array, 'nn nd']
+
+ +
+
+vertexNodes: any
+
+ +
+
+faceNodes: any
+
+ +
+
+interiorNodes: any
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+ +
+
+

pancax.fem.elements.tet10_element module

+
+
+class pancax.fem.elements.tet10_element.Tet10Element[source]
+

Bases: BaseElement

+
+
+elementType: str = 'tet10'
+
+ +
+
+degree: int = 2
+
+ +
+
+coordinates: Float[Array, 'nn nd'] = Array([[0. , 0. , 0. ],        [1. , 0. , 0. ],        [0. , 1. , 0. ],        [0. , 0. , 1. ],        [0.5, 0. , 0. ],        [0.5, 0.5, 0. ],        [0. , 0.5, 0. ],        [0. , 0. , 0.5],        [0.5, 0. , 0.5],        [0. , 0.5, 0.5]], dtype=float32)
+
+ +
+
+vertexNodes: Int[Array, 'nn'] = Array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int32)
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = Array([[0, 4, 1, 8, 3, 7],        [1, 5, 2, 9, 3, 7],        [0, 7, 3, 9, 2, 6],        [0, 6, 2, 5, 1, 4]], dtype=int32)
+
+ +
+
+interiorNodes: Int[Array, 'nni'] = None
+
+ +
+
+__init__()[source]
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.fem.elements.tet4_element module

+
+
+class pancax.fem.elements.tet4_element.Tet4Element[source]
+

Bases: BaseElement

+
+
+elementType: str = 'tet4'
+
+ +
+
+degree: int = 1
+
+ +
+
+coordinates: Float[Array, 'nn nd'] = Array([[0., 0., 0.],        [1., 0., 0.],        [0., 1., 0.],        [0., 0., 1.]], dtype=float32)
+
+ +
+
+vertexNodes: Int[Array, 'nn'] = Array([0, 1, 2, 3], dtype=int32)
+
+ +
+
+faceNodes: Int[Array, 'nf nnpf'] = Array([[0, 1, 3],        [1, 2, 3],        [0, 3, 2],        [0, 2, 1]], dtype=int32)
+
+ +
+
+interiorNodes: Int[Array, 'nni'] = None
+
+ +
+
+__init__()[source]
+
+ +
+
+compute_shapes(nodalPoints, evaluationPoints)[source]
+

Method to be defined to calculate shape function values +and gradients given a list of nodal points (usually the vertexNodes) +and a list of evaluation points (usually the quadrature points).

+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.fem.html b/pancax.fem.html new file mode 100644 index 0000000..177783e --- /dev/null +++ b/pancax.fem.html @@ -0,0 +1,1491 @@ + + + + + + + + + pancax.fem package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.fem package

+
+

Subpackages

+
+ +
+
+
+

Submodules

+
+
+

pancax.fem.dof_manager module

+
+
+class pancax.fem.dof_manager.DofManager(mesh, dim: int, EssentialBCs: List[EssentialBC])[source]
+

Bases: object

+

Collection of arrays needed to differentiate between +fixed and free dofs for fem like calculations.

+

TODO better document the parameters in this guy

+
+
+__init__(mesh, dim: int, EssentialBCs: List[EssentialBC]) → None[source]
+
+
Parameters:
+
    +

  • functionSpace – FunctionSpace object

    • +

  • dim – The number of dims (really the number of active dofs for the physics)

    • +

  • EssentialBCs – A list of of EssentialBC objects

    • +
+
+
+
+ +
+
+get_bc_size() → int[source]
+
+
Returns:
+

the number of fixed dofs

+
+
+
+ +
+
+get_unknown_size() → int[source]
+
+
Returns:
+

the size of the unkowns vector

+
+
+
+ +
+
+create_field(Uu, Ubc=0.0) → Float[Array, 'nn nd'][source]
+
+
Parameters:
+
    +

  • Uu – Vector of unknown values

    • +

  • Ubc – Values for bc to apply

    • +
+
+
Returns:
+

U, a field of unknowns and bcs combined.

+
+
+
+ +
+
+get_bc_values(U) → Float[Array, 'nb'][source]
+
+
Parameters:
+

U – a nodal field

+
+
Returns:
+

the bc values in the field U

+
+
+
+ +
+
+get_unknown_values(U) → Float[Array, 'nu'][source]
+
+
Parameters:
+

U – a nodal field

+
+
Returns:
+

the unknown values in the field U

+
+
+
+ +
+
+slice_unknowns_with_dof_indices(Uu: Float[Array, 'nu'], dofIndexSlice: Int[Array, 'nn']) → Float[Array, 'nu_new'][source]
+
+ +
+
+_make_hessian_coordinates(conns: Int[Array, 'ne nnpe']) → Tuple[Int[Array, 'nn'], Int[Array, 'nn']][source]
+
+ +
+
+_make_hessian_bc_mask(conns: Int[Array, 'ne nnpe']) → Bool[Array, 'ne ndpe ndpe'][source]
+
+ +
+ +
+
+

pancax.fem.function_space module

+
+
+class pancax.fem.function_space.NonAllocatedFunctionSpace(mesh: pancax.fem.mesh.Mesh, q_rule: pancax.fem.quadrature_rules.QuadratureRule)[source]
+

Bases: Module

+
+
+__init__(mesh: Mesh, q_rule: QuadratureRule) → None[source]
+
+ +
+
+quadrature_rule: QuadratureRule
+
+ +
+
+shape_functions: ShapeFunctions
+
+ +
+
+compute_field_gradient(u, X)[source]
+

Takes in element level coordinates X and field u

+
+ +
+
+evaluate_on_element(U, X, state, dt, props, func)[source]
+

Takes in element level field, coordinates, states, etc. +and evaluates the function func

+
+ +
+
+integrate_on_element(U, X, state, dt, props, func)[source]
+
+ +
+
+integrate_on_elements(U, X, state, dt, props, func)[source]
+
+ +
+
+JxWs(X: Float[Array, 'nn nd']) → Float[Array, 'nq'][source]
+
+ +
+
+shape_function_values(X: Float[Array, 'nn nd']) → Float[Array, 'nq nnpe'][source]
+
+ +
+
+shape_function_gradients(X: Float[Array, 'nn nd']) → Float[Array, 'nq nnpe nd'][source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.fem.function_space.FunctionSpace(shapes: Float[Array, 'ne nqpe npe'], vols: Float[Array, 'ne nqpe'], shapeGrads: Float[Array, 'ne nqpe npe nd'], conns: Int[Array, 'ne nnpe'], quadratureRule: QuadratureRule, isAxisymmetric: bool)[source]
+

Bases: Module

+

Data needed for calculus on functions in the discrete function space.

+

In describing the shape of the attributes, ne is the number of +elements in the mesh, nqpe is the number of quadrature points per +element, npe is the number of nodes per element, and nd is the +spatial dimension of the domain.

+
+
Parameters:
+
    +

  • shapes – Shape function values on each element, shape (ne, nqpe, npe)

    • +

  • vols – Volume attributed to each quadrature point. That is, the +quadrature weight (on the parameteric element domain) multiplied by +the Jacobian determinant of the map from the parent element to the +element in the domain. Shape (ne, nqpe).

    • +

  • shapeGrads – Derivatives of the shape functions with respect to the +spatial coordinates of the domain. Shape (ne, nqpe, npe, nd).

    • +

  • mesh – The Mesh object of the domain.

    • +

  • quadratureRule – The QuadratureRule on which to sample the shape +functions.

    • +

  • isAxisymmetric – boolean indicating if the function space data are +axisymmetric.

    • +
+
+
+
+
+shapes: Float[Array, 'ne nqpe npe']
+
+ +
+
+vols: Float[Array, 'ne nqpe']
+
+ +
+
+shapeGrads: Float[Array, 'ne nqpe npe nd']
+
+ +
+
+conns: Int[Array, 'ne nnpe']
+
+ +
+
+quadratureRule: QuadratureRule
+
+ +
+
+isAxisymmetric: bool
+
+ +
+
+__init__(shapes: Float[Array, 'ne nqpe npe'], vols: Float[Array, 'ne nqpe'], shapeGrads: Float[Array, 'ne nqpe npe nd'], conns: Int[Array, 'ne nnpe'], quadratureRule: QuadratureRule, isAxisymmetric: bool) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+pancax.fem.function_space.construct_function_space(mesh, quadratureRule, mode2D='cartesian')[source]
+

Construct a discrete function space.

+

:param : +:type : param mesh: The mesh of the domain. +:param : +:type : param quadratureRule: The quadrature rule to be used for integrating on the +:param domain.: +:param : +:type : param mode2D: A string indicating how the 2D domain is interpreted for +:param integration. Valid values are cartesian and axisymmetric.: +:param Axisymetric mode will include the factor of 2*pi*r in the vols: +:param attribute.:

+
+
Return type:
+

The FunctionSpace object.

+
+
+
+ +
+
+pancax.fem.function_space.construct_function_space_from_parent_element(mesh, shapeOnRef, quadratureRule, mode2D='cartesian')[source]
+

Construct a function space with precomputed shape function data on the parent element.

+

This version of the function space constructor is Jax-transformable, +and in particular can be jitted. The computation of the shape function +values and derivatives on the parent element is not transformable in +general. However, the mapping of the shape function data to the elements in +the mesh is transformable. One can precompute the parent element shape +functions once and for all, and then use this special factory function to +construct the function space and avoid the non-transformable part of the +operation. The primary use case is for shape sensitivities: the coordinates +of the mesh change, and we want Jax to pick up the sensitivities of the +shape function derivatives in space to the coordinate changes +(which occurs through the mapping from the parent element to the spatial +domain).

+

:param : +:type : param mesh: The mesh of the domain. +:param : +:type : param shapeOnRef: A tuple of the shape function values and gradients on the +:param parent element: +:param evaluated at the quadrature points. The caller must: +:param take care to ensure the shape functions are evaluated at the same: +:param points as contained in the quadratureRule parameter.: +:param : domain. +:type : param quadratureRule: The quadrature rule to be used for integrating on the +:param : +:type : param mode2D: A string indicating how the 2D domain is interpreted for +:param integration. See the default factory function for details.:

+
+
Return type:
+

The FunctionSpace object.

+
+
+
+ +
+
+pancax.fem.function_space.map_element_shape_grads(coordField, nodeOrdinals, parentElement, shapeGradients)[source]
+
+ +
+
+pancax.fem.function_space.compute_element_volumes(coordField, nodeOrdinals, parentElement, shapes, shapeGradients, weights)[source]
+
+ +
+
+pancax.fem.function_space.compute_element_volumes_axisymmetric(coordField, nodeOrdinals, parentElement, shapes, shapeGradients, weights)[source]
+
+ +
+
+pancax.fem.function_space.default_modify_element_gradient(elemGrads, elemShapes, elemVols, elemNodalDisps, elemNodalCoords)[source]
+
+ +
+
+pancax.fem.function_space.compute_field_gradient(functionSpace, nodalField, nodalCoords, modify_element_gradient=<function default_modify_element_gradient>)[source]
+
+ +
+
+pancax.fem.function_space.interpolate_to_points(functionSpace, nodalField)[source]
+
+ +
+
+pancax.fem.function_space.integrate_over_block(functionSpace, U, X, stateVars, props, dt, func, block, *params, modify_element_gradient=<function default_modify_element_gradient>)[source]
+

Integrates a density function over a block of the mesh.

+
+
Parameters:
+
    +

  • functionSpace – Function space object to do the integration with.

    • +

  • U – The vector of dofs for the primal field in the functional.

    • +

  • X – Nodal coordinates

    • +

  • stateVars – Internal state variable array.

    • +

  • dt – Current time increment

    • +

  • func – Lagrangian density function to integrate, Must have the signature +func(u, dudx, q, x, *params) -> scalar, where u is the primal field, q is the +value of the internal variables, x is the current point coordinates, and *params is +a variadic set of additional parameters, which correspond to the *params argument. +block: Group of elements to integrate over. This is an array of element indices. For +performance, the elements within the block should be numbered consecutively.

    • +

  • modify_element_gradient – Optional function that modifies the gradient at the element level. +This can be to set the particular 2D mode, and additionally to enforce volume averaging +on the gradient operator. This is a keyword-only argument.

    • +
+
+
+

Returns +A scalar value for the integral of the density functional func integrated over the +block of elements.

+
+ +
+
+pancax.fem.function_space.evaluate_on_block(functionSpace, U, X, stateVars, dt, props, func, block, *params, modify_element_gradient=<function default_modify_element_gradient>)[source]
+

Evaluates a density function at every quadrature point in a block of the mesh.

+
+
Parameters:
+
    +

  • functionSpace – Function space object to do the evaluation with.

    • +

  • U – The vector of dofs for the primal field in the functional.

    • +

  • X – Nodal coordinates

    • +

  • stateVars – Internal state variable array.

    • +

  • dt – Current time increment

    • +

  • func – Lagrangian density function to evaluate, Must have the signature +`func(u, dudx, q, x, *params) -> scalar`, where `u` is the primal field, `q` is the +value of the internal variables, `x` is the current point coordinates, and `*params` is +a variadic set of additional parameters, which correspond to the `*params` argument.

    • +

  • block – Group of elements to evaluate over. This is an array of element indices. For +performance, the elements within the block should be numbered consecutively.

    • +

  • modify_element_gradient – Optional function that modifies the gradient at the element level. +This can be to set the particular 2D mode, and additionally to enforce volume averaging +on the gradient operator. This is a keyword-only argument.

    • +
+
+
+

Returns +An array of shape (numElements, numQuadPtsPerElement) that contains the scalar values of the +density functional `func` at every quadrature point in the block.

+
+ +
+
+pancax.fem.function_space.integrate_element_from_local_field(elemNodalField, elemNodalCoords, elemStates, dt, elemShapes, elemShapeGrads, elemVols, func, modify_element_gradient=<function default_modify_element_gradient>)[source]
+

Integrate over element with element nodal field as input. +This allows element residuals and element stiffness matrices to computed.

+
+ +
+
+pancax.fem.function_space.compute_element_field_gradient(U, coords, elemShapes, elemShapeGrads, elemVols, elemConnectivity, modify_element_gradient)[source]
+
+ +
+
+pancax.fem.function_space.compute_quadrature_point_field_gradient(u, shapeGrad)[source]
+
+ +
+
+pancax.fem.function_space.interpolate_to_point(elementNodalValues, shape)[source]
+
+ +
+
+pancax.fem.function_space.interpolate_to_element_points(U, elemShapes, elemConnectivity)[source]
+
+ +
+
+pancax.fem.function_space.integrate_element(U, coords, elemStates, elemShapes, elemShapeGrads, elemVols, elemConn, func, modify_element_gradient)[source]
+
+ +
+
+pancax.fem.function_space.evaluate_on_element(U, coords, elemStates, props, dt, elemShapes, elemShapeGrads, elemVols, elemConn, kernelFunc, modify_element_gradient, *params)[source]
+
+ +
+
+pancax.fem.function_space.project_quadrature_field_to_element_field(functionSpace, quadField)[source]
+
+ +
+
+pancax.fem.function_space.average_quadrature_field_over_element(elemQPData, vols)[source]
+
+ +
+
+pancax.fem.function_space.get_nodal_values_on_edge(functionSpace, nodalField, edge)[source]
+

Get nodal values of a field on an element edge.

+
+
Parameters:
+
    +

  • functionSpace – a FunctionSpace object

    • +

  • nodalField – The nodal vector defined over the mesh (shape is number of +nodes by number of field components)

    • +

  • edge – tuple containing the element number containing the edge and the +permutation (0, 1, or 2) of the edge within the triangle

    • +
+
+
+
+ +
+
+pancax.fem.function_space.interpolate_nodal_field_on_edge(functionSpace, U, interpolationPoints, edge)[source]
+

Interpolate a nodal field to specified points on an element edge.

+
+
Parameters:
+
    +

  • functionSpace – a FunctionSpace object

    • +

  • U – the nodal values array

    • +

  • interpolationPoints – coordinates of points (in the 1D parametric space) to +interpolate to

    • +

  • edge – tuple containing the element number containing the edge and the +permutation (0, 1, or 2) of the edge within the triangle

    • +
+
+
+
+ +
+
+pancax.fem.function_space.integrate_function_on_edge(functionSpace, func, U, quadRule, edge)[source]
+
+ +
+
+pancax.fem.function_space.integrate_function_on_edges(functionSpace, func, U, quadRule, edges)[source]
+
+ +
+
+

pancax.fem.mesh module

+
+
+class pancax.fem.mesh.Mesh(coords: Float[Array, 'nn nd'], conns: Float[Array, 'ne nnpe'], simplexNodesOrdinals: Float[Array, 'ne 3'], parentElement: any, parentElement1d: any, blocks: Dict[str, Float] | None = None, nodeSets: Dict[str, Float] | None = None, sideSets: Dict[str, Float] | None = None)[source]
+

Bases: Module

+

Triangle mesh representing a domain.

+
+
Parameters:
+
    +

  • coords – Coordinates of the nodes, shape (nNodes, nDim).

    • +

  • conns – Nodal connectivity table of the elements.

    • +

  • simplexNodesOrdinals – Indices of the nodes that are vertices.

    • +

  • parentElement – A ParentElement that is the element type in +parametric space. A mesh can contain only 1 element type.

    • +

  • parentElement1d

    • +

  • blocks – A dictionary mapping element block names to the indices of the +elements in the block.

    • +

  • nodeSets – A dictionary mapping node set names to the indices of the +nodes.

    • +

  • sideSets – A dictionary mapping side set names to the edges. The +edge data structure is a tuple of the element index and the local +number of the edge within that element. For example, triangle +elements will have edge 0, 1, or 2 for this entry.

    • +
+
+
+
+
+coords: Float[Array, 'nn nd']
+
+ +
+
+conns: Float[Array, 'ne nnpe']
+
+ +
+
+simplexNodesOrdinals: Float[Array, 'ne 3']
+
+ +
+
+parentElement: any
+
+ +
+
+parentElement1d: any
+
+ +
+
+blocks: Dict[str, Float] | None = None
+
+ +
+
+nodeSets: Dict[str, Float] | None = None
+
+ +
+
+sideSets: Dict[str, Float] | None = None
+
+ +
+
+get_blocks(blockNames: List[str])[source]
+
+ +
+
+property num_dimensions: int
+

dimension number of mesh

+
+
Type:
+

return

+
+
+
+ +
+
+property num_elements: int
+

number of elements in mesh

+
+
Type:
+

return

+
+
+
+ +
+
+property num_nodes: int
+

number of nodes in mesh

+
+ +
+
+__init__(coords: Float[Array, 'nn nd'], conns: Float[Array, 'ne nnpe'], simplexNodesOrdinals: Float[Array, 'ne 3'], parentElement: any, parentElement1d: any, blocks: Dict[str, Float] | None = None, nodeSets: Dict[str, Float] | None = None, sideSets: Dict[str, Float] | None = None) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+pancax.fem.mesh.create_structured_mesh_data(Nx, Ny, xExtent, yExtent)[source]
+
+ +
+
+pancax.fem.mesh.construct_mesh_from_basic_data(coords, conns, blocks, nodeSets=None, sideSets=None)[source]
+
+ +
+
+pancax.fem.mesh.construct_structured_mesh(Nx, Ny, xExtent, yExtent, elementOrder=1, useBubbleElement=False)[source]
+
+ +
+
+pancax.fem.mesh.combine_nodesets(set1, set2, nodeOffset)[source]
+
+ +
+
+pancax.fem.mesh.combine_sidesets(set1, set2, elemOffset)[source]
+
+ +
+
+pancax.fem.mesh.combine_blocks(set1, set2, elemOffset)[source]
+
+ +
+
+pancax.fem.mesh.combine_mesh(m1, m2)[source]
+
+ +
+
+pancax.fem.mesh.mesh_with_coords(mesh, coords)[source]
+
+ +
+
+pancax.fem.mesh.mesh_with_nodesets(mesh, nodeSets)[source]
+
+ +
+
+pancax.fem.mesh.mesh_with_blocks(mesh, blocks)[source]
+
+ +
+
+pancax.fem.mesh.create_edges(conns)[source]
+

Generate topological information about edges in a triangulation.

+
+
Parameters:
+

conns ((nTriangles, 3) array) – Connectivity table of the triangulation.

+
+
Returns:
+

    +

  • edgeConns ((nEdges, 2) array) – Vertices of each edge. Boundary edges are always in the +counter-clockwise sense, so that the interior of the body is on the left +side when walking from the first vertex to the second.

    • +

  • edges ((nEdges, 4) array) – Edge-to-triangle topological information. Each row provides the +follwing information for each edge: [leftT, leftP, rightT, rightP], +where leftT is the ID of the triangle to the left, leftP is the +permutation of the edge in the left triangle (edge 0, 1, or 2), rightT +is the ID of the triangle to the right, and rightP is the permutation +of the edge in the right triangle. If the edge is a boundary edge, the +values of rightT and rightP are -1.

    • +
+

+
+
+
+ +
+
+pancax.fem.mesh.create_higher_order_mesh_from_simplex_mesh(mesh, order, useBubbleElement=False, copyNodeSets=False, createNodeSetsFromSideSets=False)[source]
+
+ +
+
+pancax.fem.mesh.create_nodesets_from_sidesets(mesh)[source]
+
+ +
+
+pancax.fem.mesh.num_nodes(mesh)[source]
+
+ +
+
+pancax.fem.mesh.get_edge_node_indices(mesh: Mesh, edge)[source]
+
+ +
+
+pancax.fem.mesh.get_edge_field(mesh: Mesh, edge, field)[source]
+

Evaluate field on nodes of an element edge. +Arguments:

+
+
Parameters:
+
    +

  • mesh – a Mesh object

    • +

  • edge – tuple containing the element number containing the edge and the +permutation (0, 1, or 2) of the edge within the triangle

    • +
+
+
+
+ +
+
+pancax.fem.mesh.get_edge_coords(mesh: Mesh, edge)[source]
+
+ +
+
+pancax.fem.mesh.compute_edge_vectors(mesh: Mesh, edgeCoords)[source]
+

Get geometric vectors for an element edge.

+

Assumes that the edgs has a constant shape jacobian, that is, the +transformation from the parent element is affine.

+

Arguments +:param mesh: a Mesh object +:param edgeCoords: coordinates of all nodes on the edge, in the order +defined by the 1D parent element convention

+

Returns +tuple (t, n, j) with +:return t: the unit tangent vector +:return n: the outward unit normal vector +:return j: jacobian of the transformation from parent to physical space

+
+ +
+
+

pancax.fem.quadrature_rules module

+
+
+class pancax.fem.quadrature_rules.QuadratureRule(parentElement: BaseElement, degree: int)[source]
+

Bases: Module

+

Quadrature rule points and weights. +A namedtuple containing xigauss, a numpy array of the +coordinates of the sample points in the reference domain, and +wgauss, a numpy array with the weights.

+
+
Parameters:
+
    +

  • xigauss – coordinates of gauss points in reference element

    • +

  • wgauss – weights of gauss points in reference element

    • +
+
+
+
+
+__init__(parentElement: BaseElement, degree: int) → None[source]
+
+ +
+
+xigauss: Float[Array, 'nq nd']
+
+ +
+
+wgauss: Float[Array, 'nq']
+
+ +
+
+eval_at_iso_points(field)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+pancax.fem.quadrature_rules.create_quadrature_rule_1D(degree: int) → QuadratureRule[source]
+

Creates a Gauss-Legendre quadrature on the unit interval.

+

The rule can exactly integrate polynomials of degree up to +degree.

+
+
Parameters:
+

degree (Highest degree polynomial to be exactly integrated by the quadrature rule)

+
+
Returns:
+

    +

  • A QuadratureRule named tuple containing the quadrature point coordinates

    • +

  • and the weights.

    • +
+

+
+
+
+ +
+
+pancax.fem.quadrature_rules.eval_at_iso_points(xigauss, field)[source]
+
+ +
+
+pancax.fem.quadrature_rules.create_quadrature_rule_on_hex(quad_degree: int) → QuadratureRule[source]
+
+ +
+
+pancax.fem.quadrature_rules.create_quadrature_rule_on_quad(quad_degree: int) → QuadratureRule[source]
+
+
Parameters:
+

quad_degree – degree of quadrature rule to create

+
+
+
+ +
+
+pancax.fem.quadrature_rules.create_quadrature_rule_on_tet(degree: int) → QuadratureRule[source]
+
+ +
+
+pancax.fem.quadrature_rules.create_quadrature_rule_on_triangle(degree: int) → QuadratureRule[source]
+

Creates a Gauss-Legendre quadrature on the unit triangle.

+

The rule can exactly integrate 2D polynomials up to the value of +degree. The domain is the triangle between the vertices +(0, 0)-(1, 0)-(0, 1). The rules here are guaranteed to be +cyclically symmetric in triangular coordinates and to have strictly +positive weights.

+
+
Parameters:
+

degree (Highest degree polynomial to be exactly integrated by the quadrature rule)

+
+
Returns:
+

    +

  • A QuadratureRule named tuple containing the quadrature point coordinates

    • +

  • and the weights.

    • +
+

+
+
+
+ +
+
+pancax.fem.quadrature_rules.create_padded_quadrature_rule_1D(degree)[source]
+

Creates 1D Gauss quadrature rule data that are padded to maintain a +uniform size, which makes this function jit-able.

+

This function is inteded to be used only when jit compilation of calls to the +quadrature rules are needed. Otherwise, prefer to use the standard quadrature +rules. The standard rules do not contain extra 0s for padding, which makes +them more efficient when used repeatedly (such as in the global energy).

+
+
Parameters:
+

degree – degree of highest polynomial to be integrated exactly

+
+
+
+ +
+
+pancax.fem.quadrature_rules._gauss_quad_1D_1pt(_)[source]
+
+ +
+
+pancax.fem.quadrature_rules._gauss_quad_1D_2pt(_)[source]
+
+ +
+
+pancax.fem.quadrature_rules._gauss_quad_1D_3pt(_)[source]
+
+ +
+
+pancax.fem.quadrature_rules._gauss_quad_1D_4pt(_)[source]
+
+ +
+
+pancax.fem.quadrature_rules._gauss_quad_1D_5pt(_)[source]
+
+ +
+
+

pancax.fem.read_exodus_mesh module

+
+
+pancax.fem.read_exodus_mesh.read_exodus_mesh(fileName: str)[source]
+
+
Parameters:
+

fileName – file name of exodus mesh to read

+
+
Returns:
+

A mesh object

+
+
+
+ +
+
+pancax.fem.read_exodus_mesh._read_coordinates(exodusDataset)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_block_conns(exodusDataset, blockOrdinal)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_blocks(exodusDataset)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_node_sets(exodusDataset)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_side_sets(exodusDataset)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_element_type(exodusDataset)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._read_names_list(exodusDataset, recordName)[source]
+
+ +
+
+pancax.fem.read_exodus_mesh._get_vertex_nodes_from_exodus_tri6_mesh(conns)[source]
+
+ +
+
+

pancax.fem.sparse_matrix_assembler module

+
+
+pancax.fem.sparse_matrix_assembler.assemble_sparse_stiffness_matrix(kValues, conns, dofManager)[source]
+
+ +
+
+

pancax.fem.surface module

+
+
+pancax.fem.surface.create_edges(coords, conns, edge_is_potentially_in_contact)[source]
+
+ +
+
+pancax.fem.surface.get_coords(mesh, side)[source]
+
+ +
+
+pancax.fem.surface.integrate_values(quadratureRule, coords, gaussField)[source]
+
+ +
+
+pancax.fem.surface.integrate_function(quadratureRule, coords, field_func)[source]
+
+ +
+
+pancax.fem.surface.integrate_function_on_surface(quadratureRule, edges, mesh, func)[source]
+
+ +
+
+pancax.fem.surface.integrate_function_on_edge(quadratureRule, edge, mesh, func)[source]
+
+ +
+
+pancax.fem.surface.compute_normal(edgeCoords)[source]
+
+ +
+
+pancax.fem.surface.get_field_index(edge, conns)[source]
+
+ +
+
+pancax.fem.surface.eval_field(field, fieldIndex)[source]
+
+ +
+
+pancax.fem.surface.compute_edge_vectors(edgeCoords)[source]
+
+ +
+
+

pancax.fem.traction_bc module

+
+
+pancax.fem.traction_bc.interpolate_nodal_field_on_edge(conns, U, quadRule, edge)[source]
+
+ +
+
+pancax.fem.traction_bc.compute_traction_potential_energy_on_edge(coords, conns, U, quadRule, edge, load, time)[source]
+
+ +
+
+pancax.fem.traction_bc.compute_traction_potential_energy(coords, conns, U, quadRule, edges, load, time=0.0)[source]
+
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.html b/pancax.html new file mode 100644 index 0000000..cc4b2e7 --- /dev/null +++ b/pancax.html @@ -0,0 +1,1967 @@ + + + + + + + + + pancax package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax package

+
+

Subpackages

+
+ +
+
+
+

Submodules

+
+
+

pancax.__main__ module

+
+
+

pancax.history_writer module

+
+
+class pancax.history_writer.BaseHistoryWriter(log_every: int, write_every: int)[source]
+

Bases: Module

+
+
+log_every: int
+
+ +
+
+write_every: int
+
+ +
+
+abstract to_csv()[source]
+
+ +
+
+write_data(key: str, val: float) → None[source]
+
+ +
+
+abstract write_aux_values(loss)[source]
+
+ +
+
+abstract write_epoch(epoch)[source]
+
+ +
+
+write_history(loss, epoch: int)[source]
+
+ +
+
+abstract write_loss(loss)[source]
+
+ +
+
+__init__(log_every: int, write_every: int) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.history_writer.HistoryWriter(history_file: str, log_every: int, write_every: int)[source]
+

Bases: BaseHistoryWriter

+
+
+log_every: int
+
+ +
+
+write_every: int
+
+ +
+
+__init__(history_file: str, log_every: int, write_every: int) → None[source]
+
+ +
+
+history_file: Path
+
+ +
+
+data_dict: dict
+
+ +
+
+to_csv() → None[source]
+
+ +
+
+write_aux_values(loss)[source]
+
+ +
+
+write_epoch(epoch)[source]
+
+ +
+
+write_loss(loss)[source]
+
+ +
+
+_write_loss(loss, epoch: int, log_every=1, save_every=1000)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.history_writer.EnsembleHistoryWriter(base_name: str, n_pinns: int, log_every: int, write_every: int)[source]
+

Bases: BaseHistoryWriter

+
+
+log_every: int
+
+ +
+
+write_every: int
+
+ +
+
+__init__(base_name: str, n_pinns: int, log_every: int, write_every: int) → None[source]
+
+ +
+
+history_writers: List[HistoryWriter]
+
+ +
+
+to_csv()[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+write_aux_values(loss)[source]
+
+ +
+
+write_epoch(epoch)[source]
+
+ +
+
+write_loss(loss)[source]
+
+ +
+ +
+
+

pancax.kinematics module

+
+
+pancax.kinematics.create_field_methods(domain, bc_func)[source]
+
+ +
+
+pancax.kinematics.deformation_gradients(grad_us, formulation)[source]
+
+ +
+
+pancax.kinematics.invariants_old(grad_us, formulation)[source]
+
+ +
+
+pancax.kinematics.invariants(grad_u)[source]
+
+ +
+
+pancax.kinematics.plane_strain(F)[source]
+
+ +
+
+pancax.kinematics.incompressible_plane_stress(F)[source]
+
+ +
+
+

pancax.logging module

+
+
+pancax.logging.log_loss(loss, n, log_every)[source]
+
+ +
+
+class pancax.logging.BaseLogger(log_every: int)[source]
+

Bases: Module

+
+
+log_every: int
+
+ +
+
+abstract flush()[source]
+
+ +
+
+log_loss(loss, epoch)[source]
+
+ +
+
+abstract write_aux_values(loss)[source]
+
+ +
+
+abstract write_epoch_value(epoch)[source]
+
+ +
+
+abstract write_loss_value(loss)[source]
+
+ +
+
+__init__(log_every: int) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.logging.Logger(log_file_in: str, log_every: int)[source]
+

Bases: BaseLogger

+
+
+__init__(log_file_in: str, log_every: int) → None[source]
+
+ +
+
+log_file: any
+
+ +
+
+flush()[source]
+
+ +
+
+write_aux_values(loss)[source]
+
+ +
+
+write_epoch_value(epoch)[source]
+
+ +
+
+write_loss_value(loss)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.logging.EnsembleLogger(base_name: str, n_pinns: int, log_every: int)[source]
+

Bases: BaseLogger

+
+
+__init__(base_name: str, n_pinns: int, log_every: int) → None[source]
+
+ +
+
+loggers: List[Logger]
+
+ +
+
+flush()[source]
+
+ +
+
+write_aux_values(loss)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+write_epoch_value(epoch)[source]
+
+ +
+
+write_loss_value(loss)[source]
+
+ +
+ +
+
+

pancax.physics module

+
+
+pancax.physics.element_quantity(f, x, u, conn, N, grad_N, JxW, props)[source]
+
+ +
+
+pancax.physics.element_quantity_new(f, fspace, x_el, u_el, props)[source]
+
+ +
+
+pancax.physics.element_quantity_grad(f, fspace, x_el, u_el, props)
+

Jacobian of element_quantity_new with respect to positional argument(s) 3. Takes the same arguments as element_quantity_new but returns the jacobian of the output with respect to the arguments at positions 3.

+
+ +
+
+pancax.physics.element_quantity_hessian(f, fspace, x_el, u_el, props)
+

Jacobian of element_quantity_new with respect to positional argument(s) 3. Takes the same arguments as element_quantity_new but returns the jacobian of the output with respect to the arguments at positions 3.

+
+ +
+
+pancax.physics.potential_energy(domain, us, props)[source]
+
+ +
+
+pancax.physics.residual_mse(domain, us, props)[source]
+
+ +
+
+pancax.physics.mass_matrix(domain, us, props)[source]
+
+ +
+
+pancax.physics.stiffness_matrix(domain, us, props)[source]
+
+ +
+
+pancax.physics.traction_energy()[source]
+
+ +
+
+pancax.physics.internal_force(domain, us, props)
+

Gradient of potential_energy with respect to positional argument(s) 1. Takes the same arguments as potential_energy but returns the gradient, which has the same shape as the arguments at positions 1.

+
+ +
+
+pancax.physics.residual(x, y, z)
+
+ +
+
+pancax.physics.potential_energy_and_internal_force(domain, us, props)
+

Value and gradient of potential_energy with respect to positional argument(s) 1. Takes the same arguments as potential_energy but returns a two-element tuple where the first element is the value of potential_energy and the second element is the gradient, which has the same shape as the arguments at positions 1.

+
+ +
+
+pancax.physics.potential_energy_and_residual(domain, us, props)[source]
+
+ +
+
+pancax.physics.potential_energy_residual_and_reaction_force(domain, us, props)[source]
+
+ +
+
+pancax.physics.strong_form_residual(params, domain, t)[source]
+
+ +
+
+pancax.physics.nodal_incompressibility_constraint(params, domain, t)[source]
+
+ +
+
+pancax.physics.quadrature_incompressibility_constraint(domain, us, props)[source]
+
+ +
+
+pancax.physics.incompressible_energy(domain, us, props)[source]
+
+ +
+
+pancax.physics.incompressible_internal_force(domain, us, props)
+

Gradient of incompressible_energy with respect to positional argument(s) 1. Takes the same arguments as incompressible_energy but returns the gradient, which has the same shape as the arguments at positions 1.

+
+ +
+
+pancax.physics.incompressible_energy_and_internal_force(domain, us, props)
+

Value and gradient of incompressible_energy with respect to positional argument(s) 1. Takes the same arguments as incompressible_energy but returns a two-element tuple where the first element is the value of incompressible_energy and the second element is the gradient, which has the same shape as the arguments at positions 1.

+
+ +
+
+pancax.physics.incompressible_energy_and_residual(domain, us, props)[source]
+
+ +
+
+

pancax.post_processor module

+
+
+class pancax.post_processor.ExodusPostProcessor(mesh_file: str)[source]
+

Bases: object

+
+
+__init__(mesh_file: str) → None[source]
+
+ +
+
+check_variable_names(domain, variables) → None[source]
+
+ +
+
+close() → None[source]
+
+ +
+
+copy_mesh(output_file: str) → None[source]
+
+ +
+
+get_node_variable_number(domain, variables) → int[source]
+
+ +
+
+get_element_variable_number(domain, variables) → int[source]
+
+ +
+
+init(domain, output_file: str, node_variables: List[str], element_variables: List[str]) → None[source]
+
+ +
+
+index_to_component(index)[source]
+
+ +
+
+write_outputs(params, domain) → None[source]
+
+ +
+ +
+
+class pancax.post_processor.VtkPostProcessor(mesh_file: str)[source]
+

Bases: object

+
+
+__init__(mesh_file: str) → None[source]
+
+ +
+
+close()[source]
+
+ +
+
+init(domain, output_file: str, node_variables, element_variables) → None[source]
+
+ +
+
+write_outputs(params, domain) → None[source]
+
+ +
+
+convert_exodus_to_xml(exodus_file, xml_file)[source]
+

Converts an Exodus II file to a VTK XML MultiBlock dataset.

+
+ +
+
+get_vtk_cell_type(exodus_element_type)[source]
+

Map Exodus element types to VTK cell types.

+
+ +
+
+cell_type(vtk_cell_type, num_nodes_in_element)[source]
+
+ +
+ +
+
+class pancax.post_processor.PostProcessor(mesh_file: str, mesh_type='exodus')[source]
+

Bases: object

+
+
+__init__(mesh_file: str, mesh_type='exodus') → None[source]
+
+ +
+
+close()[source]
+
+ +
+
+init(domain, output_file, node_variables, element_variables=[])[source]
+
+ +
+
+write_outputs(params, domain)[source]
+
+ +
+ +
+
+

pancax.timer module

+
+
+exception pancax.timer.TimerError[source]
+

Bases: Exception

+

A custom exception used to report errors in use of Timer class

+
+ +
+
+class pancax.timer.Timer(name: str | None = None, text: str = 'Time in {name}: {:0.8f} seconds', logger: ~typing.Callable[[str], None] | None = <built-in function print>)[source]
+

Bases: ContextDecorator

+

Time your code using a class, context manager, or decorator

+
+
+timers: ClassVar[Dict[str, float]] = {}
+
+ +
+
+name: str | None = None
+
+ +
+
+text: str = 'Time in {name}: {:0.8f} seconds'
+
+ +
+
+logger(*, sep=' ', end='\n', file=None, flush=False)
+

Prints the values to a stream, or to sys.stdout by default.

+
+
sep

string inserted between values, default a space.

+
+
end

string appended after the last value, default a newline.

+
+
file

a file-like object (stream); defaults to the current sys.stdout.

+
+
flush

whether to forcibly flush the stream.

+
+
+
+ +
+
+_start_time: float | None = None
+
+ +
+
+start() → None[source]
+

Start a new timer

+
+ +
+
+stop() → float[source]
+

Stop the timer, and report the elapsed time

+
+ +
+
+__init__(name: str | None = None, text: str = 'Time in {name}: {:0.8f} seconds', logger: ~typing.Callable[[str], None] | None = <built-in function print>) → None
+
+ +
+ +
+
+

pancax.trainer module

+
+
+class pancax.trainer.Trainer(domain, opt, checkpoint_base='checkpoint', history_file='history.csv', log_file='pinn.log', output_file_base='output', output_node_variables=[], output_element_variables=[], log_every=1000, output_every=10000, serialise_every=10000, workdir='/__w/pancax/pancax/docs')[source]
+

Bases: object

+
+
+__init__(domain, opt, checkpoint_base='checkpoint', history_file='history.csv', log_file='pinn.log', output_file_base='output', output_node_variables=[], output_element_variables=[], log_every=1000, output_every=10000, serialise_every=10000, workdir='/__w/pancax/pancax/docs') → None[source]
+
+ +
+
+init(params)[source]
+
+ +
+
+serialise(params)[source]
+
+ +
+
+step(params, opt_st)[source]
+
+ +
+
+train(params, n_epochs)[source]
+
+ +
+
+write_outputs(params)[source]
+
+ +
+ +
+
+

pancax.utils module

+
+
+exception pancax.utils.DataFileNotFoundException[source]
+

Bases: Exception

+
+ +
+
+exception pancax.utils.MeshFileNotFoundException[source]
+

Bases: Exception

+
+ +
+
+pancax.utils.find_data_file(data_file_in: str)[source]
+
+ +
+
+pancax.utils.find_mesh_file(mesh_file_in: str)[source]
+
+ +
+
+pancax.utils.set_checkpoint_file(checkpoint_file_base: str)[source]
+
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.kernels.html b/pancax.kernels.html new file mode 100644 index 0000000..213998c --- /dev/null +++ b/pancax.kernels.html @@ -0,0 +1,642 @@ + + + + + + + + + pancax.kernels package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.kernels package

+
+

Submodules

+
+
+

pancax.kernels.base_kernel module

+
+
+pancax.kernels.base_kernel.vector_names(base_name: str, dim: int)[source]
+
+ +
+
+pancax.kernels.base_kernel.full_tensor_names(base_name: str)[source]
+

Provides a full list of tensorial variable component names +:param base_name: base name for a tensor variable e.g. base_name_xx

+
+ +
+
+pancax.kernels.base_kernel.full_tensor_names_2D(base_name: str)[source]
+

Provides a full list of tensorial variable component names +:param base_name: base name for a tensor variable e.g. base_name_xx

+
+ +
+
+pancax.kernels.base_kernel.element_pp(func, has_props=False, jit=True)[source]
+
+
Parameters:
+
    +

  • func – Function to use for an element property output variable

    • +

  • has_props – Whether or not this function need properties

    • +

  • jit – Whether or not to jit this function

    • +
+
+
+
+ +
+
+pancax.kernels.base_kernel.nodal_pp(func, has_props=False, jit=True)[source]
+
+
Parameters:
+
    +

  • func – Function to use for a nodal property output variable

    • +

  • has_props – Whether or not this function need properties

    • +

  • jit – Whether or not to jit this function

    • +
+
+
+
+ +
+
+pancax.kernels.base_kernel.standard_pp(physics)[source]
+
+ +
+
+class pancax.kernels.base_kernel.PhysicsKernel(mesh_file, bc_func, use_delta_pinn)[source]
+

Bases: ABC

+
+
+n_dofs: int
+
+ +
+
+field_value_names: List[str]
+
+ +
+
+var_name_to_method: Dict[str, Dict[str, Callable | List[str]]] = {}
+
+ +
+
+__init__(mesh_file, bc_func, use_delta_pinn) → None[source]
+
+ +
+
+bc_func: Callable
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.kernels.base_kernel.StrongFormPhysicsKernel(mesh_file, bc_func, use_delta_pinn)[source]
+

Bases: PhysicsKernel

+
+
+n_dofs: int
+
+ +
+
+field_value_names: List[str]
+
+ +
+
+bc_func: Callable
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+__init__(mesh_file, bc_func, use_delta_pinn) → None[source]
+
+ +
+
+field_gradients(field_network, x, t)[source]
+
+ +
+
+field_hessians(field_network, x, t)[source]
+
+ +
+
+field_laplacians(field_network, x, t)[source]
+
+ +
+
+field_time_derivatives(field_network, x, t)[source]
+
+ +
+
+field_second_time_derivatives(field_network, x, t)[source]
+
+ +
+
+abstract strong_form_neumann_bc(params, x, t, n)[source]
+
+ +
+
+abstract strong_form_residual(params, x, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.kernels.base_kernel.WeakFormPhysicsKernel(mesh_file, bc_func, use_delta_pinn)[source]
+

Bases: PhysicsKernel

+
+
+n_dofs: int
+
+ +
+
+field_value_names: List[str]
+
+ +
+
+bc_func: Callable
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+__init__(mesh_file, bc_func, use_delta_pinn) → None[source]
+
+ +
+
+element_field_gradient(params, domain, t)[source]
+
+ +
+
+element_quantity(f, fspace, x_el, u_el, props)[source]
+
+ +
+
+element_quantity_grad(f, fspace, x_el, u_el, props)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+element_quantity_hessian(f, fspace, x_el, u_el, props)[source]
+
+ +
+
+abstract energy(x_el, u_el, N, grad_N, JxW, props)[source]
+
+ +
+ +
+
+

pancax.kernels.laplace_beltrami module

+
+
+class pancax.kernels.laplace_beltrami.LaplaceBeltrami(mesh_file, bc_func, n_eigs: int, use_delta_pinn: bool | None = False)[source]
+

Bases: WeakFormPhysicsKernel

+
+
+n_dofs: int = 1
+
+ +
+
+field_names = ['eigenvector']
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+__init__(mesh_file, bc_func, n_eigs: int, use_delta_pinn: bool | None = False)[source]
+
+ +
+
+energy(x_el, u_el, N, grad_N, JxW, props)[source]
+
+ +
+
+kinetic_energy(x_el, u_el, N, grad_N, JxW, props)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.kernels.linear_elasticity module

+
+
+class pancax.kernels.linear_elasticity.LinearElasticity2D(mesh_file: str, bc_func: ~typing.Callable, body_force: ~typing.Callable = <function LinearElasticity2D.<lambda>>, use_delta_pinn: bool | None = False)[source]
+

Bases: StrongFormPhysicsKernel, WeakFormPhysicsKernel

+
+
+n_dofs: int = 2
+
+ +
+
+field_value_names: List[str] = ['displ_x', 'displ_y']
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+__init__(mesh_file: str, bc_func: ~typing.Callable, body_force: ~typing.Callable = <function LinearElasticity2D.<lambda>>, use_delta_pinn: bool | None = False) → None[source]
+
+ +
+
+energy(x_el, u_el, N, grad_N, JxW, props)[source]
+
+ +
+
+strong_form_residual(params, x, t)[source]
+
+ +
+
+strong_form_neumann_bc(params, x, t, n)[source]
+
+ +
+
+linear_strain(field_network, x, t)[source]
+
+ +
+
+cauchy_stress(params, x, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.kernels.poisson module

+
+
+class pancax.kernels.poisson.Poisson(mesh_file, bc_func: Callable, f: Callable, use_delta_pinn: bool | None = False)[source]
+

Bases: StrongFormPhysicsKernel, WeakFormPhysicsKernel

+
+
+n_dofs: int = 1
+
+ +
+
+field_value_names: List[str] = ['u']
+
+ +
+
+use_delta_pinn: bool
+
+ +
+
+__init__(mesh_file, bc_func: Callable, f: Callable, use_delta_pinn: bool | None = False)[source]
+
+ +
+
+energy(x_el, u_el, N, grad_N, JxW, props)[source]
+
+ +
+
+strong_form_residual(params, x, t)[source]
+
+ +
+
+strong_form_neumann_bc(params, x, t, n)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.kernels.solid_mechanics module

+
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.loss_functions.html b/pancax.loss_functions.html new file mode 100644 index 0000000..60cdac5 --- /dev/null +++ b/pancax.loss_functions.html @@ -0,0 +1,808 @@ + + + + + + + + + pancax.loss_functions package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.loss_functions package

+
+

Submodules

+
+
+

pancax.loss_functions.base_loss_function module

+
+
+class pancax.loss_functions.base_loss_function.BaseLossFunction[source]
+

Bases: Module

+

Base class for loss functions. +Currently does nothing but helps build a +type hierarchy.

+
+
+filtered_loss(diff_params, static_params, domain)[source]
+
+ +
+
+__init__() → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.base_loss_function.BCLossFunction[source]
+

Bases: BaseLossFunction

+

Base class for boundary condition loss functions.

+

A load_step method is expect with the following +type signature +load_step(self, params, domain, t)

+
+
+abstract load_step(params, domain, t)[source]
+
+ +
+
+__init__() → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.base_loss_function.PhysicsLossFunction[source]
+

Bases: BaseLossFunction

+

Base class for physics loss functions.

+

A load_step method is expect with the following +type signature +load_step(self, params, domain, t)

+
+
+abstract load_step(params, domain, t)[source]
+
+ +
+
+__init__() → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.loss_functions.bc_loss_functions module

+
+
+class pancax.loss_functions.bc_loss_functions.DirichletBCLoss(weight: float | None = 1.0)[source]
+

Bases: BCLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.bc_loss_functions.NeumannBCLoss(weight: float | None = 1.0)[source]
+

Bases: BCLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+ +
+
+

pancax.loss_functions.data_loss_functions module

+
+
+class pancax.loss_functions.data_loss_functions.FullFieldDataLoss(weight: float | None = 1.0)[source]
+

Bases: BaseLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.loss_functions.ic_loss_function module

+
+
+class pancax.loss_functions.ic_loss_function.ICLossFunction(weight: float = 1.0)[source]
+

Bases: BaseLossFunction

+
+
+weight: float = 1.0
+
+ +
+
+__init__(weight: float = 1.0) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.loss_functions.physics_loss_functions_strong_form module

+
+
+pancax.loss_functions.physics_loss_functions_strong_form.StrongFormResidualLoss(weight: float | None = 1.0)[source]
+
+ +
+
+pancax.loss_functions.physics_loss_functions_strong_form.StrongFormNeumannBCLoss(weight: float | None = 1.0)[source]
+
+ +
+
+pancax.loss_functions.physics_loss_functions_strong_form.StrongFormIncompressibilityConstraint(weight: bool | None = 1.0)[source]
+
+ +
+
+

pancax.loss_functions.strong_form_loss_functions module

+
+
+class pancax.loss_functions.strong_form_loss_functions.StrongFormResidualLoss(weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+ +
+
+

pancax.loss_functions.utils module

+
+
+class pancax.loss_functions.utils.CombineLossFunctions(*funcs, with_props=False)[source]
+

Bases: BaseLossFunction

+
+
+__init__(*funcs, with_props=False)[source]
+
+ +
+
+funcs: any
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+with_props: bool
+
+ +
+ +
+
+

pancax.loss_functions.weak_form_loss_functions module

+
+
+class pancax.loss_functions.weak_form_loss_functions.EnergyLoss(weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+

Energy loss function akin to the deep energy method.

+

Calculates the following quantity

+
+\[\mathcal{L} = w\Pi\left[u\right] = w\int_\Omega\psi\left(\mathbf{F}\right)\]
+
+
Parameters:
+

weight – weight for this loss function

+
+
+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.EnergyAndResidualLoss(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+

Energy and residual loss function used in Hamel et. al

+

Calculates the following quantity

+
+\[\mathcal{L} = w_1\Pi\left[u\right] + w_2\delta\Pi\left[u\right]_{free}\]
+
+
Parameters:
+
    +

  • energy_weight – Weight for the energy w_1

    • +

  • residual_weight – Weight for the residual w_2

    • +
+
+
+
+
+__init__(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0)[source]
+
+ +
+
+energy_weight: float
+
+ +
+
+residual_weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.EnergyResidualAndReactionLoss(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0, reaction_weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+
+
+__init__(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0, reaction_weight: float | None = 1.0)[source]
+
+ +
+
+energy_weight: float
+
+ +
+
+residual_weight: float
+
+ +
+
+reaction_weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.QuadratureIncompressibilityConstraint(weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.ResidualMSELoss(weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.IncompressibleEnergyLoss(weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+

Energy loss function akin to the deep energy method.

+

Calculates the following quantity

+
+\[\mathcal{L} = w\Pi\left[u\right] = w\int_\Omega\psi\left(\mathbf{F}\right)\]
+
+
Parameters:
+

weight – weight for this loss function

+
+
+
+
+__init__(weight: float | None = 1.0)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+ +
+
+class pancax.loss_functions.weak_form_loss_functions.IncompressibleEnergyAndResidualLoss(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0)[source]
+

Bases: PhysicsLossFunction

+

Energy and residual loss function used in Hamel et. al

+

Calculates the following quantity

+
+\[\mathcal{L} = w_1\Pi\left[u\right] + w_2\delta\Pi\left[u\right]_{free}\]
+
+
Parameters:
+
    +

  • energy_weight – Weight for the energy w_1

    • +

  • residual_weight – Weight for the residual w_2

    • +
+
+
+
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+__init__(energy_weight: float | None = 1.0, residual_weight: float | None = 1.0)[source]
+
+ +
+
+energy_weight: float
+
+ +
+
+residual_weight: float
+
+ +
+
+load_step(params, domain, t)[source]
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.math.html b/pancax.math.html new file mode 100644 index 0000000..3eb640e --- /dev/null +++ b/pancax.math.html @@ -0,0 +1,426 @@ + + + + + + + + + pancax.math package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.math package

+
+

Submodules

+
+
+

pancax.math.math module

+
+
+pancax.math.math.safe_sqrt_jvp(xt, vt)[source]
+
+ +
+
+pancax.math.math.sum2(a)[source]
+

Sum a vector to much higher accuracy than numpy.sum.

+
+
Parameters:
+

a (ndarray, with only one axis (shape [n,]))

+
+
Returns:
+

sum – The sum of the numbers in the array

+
+
Return type:
+

real

+
+
+

This special sum method computes the result as accurate as if +computed in quadruple precision.

+

Reference: +T. Ogita, S. M. Rump, and S. Oishi. Accurate sum and dot product. +SIAM J. Sci. Comput., Vol 26, No 6, pp. 1955-1988. +doi: 10.1137/030601818

+
+ +
+
+pancax.math.math._two_sum(a, b)[source]
+
+ +
+
+pancax.math.math.dot2(x, y)[source]
+

Compute inner product of 2 vectors to much higher accuracy than numpy.dot.

+

:param : +:type : param x: ndarray, with only one axis (shape [n,]) +:param : +:type : param y: ndarray, with only one axis (shape [n,])

+
+
Returns:
+

The inner product of the input vectors.

+
+
Return type:
+

return dotprod: real

+
+
+

This special inner product method computes the result as accurate +as if computed in quadruple precision. This algorithm is useful to +computing objective functions from numerical integration. It avoids +accumulation of floating point cancellation error that can obscure +whether an objective function has truly decreased.

+

The environment variable setting +‘XLA_FLAGS = “–xla_cpu_enable_fast_math=false”’ +is critical for this function to work on the CPU. Otherwise, xla +apparently sets a flag for LLVM that allows unsafe floating point +optimizations that can change associativity.

+

Reference +T. Ogita, S. M. Rump, and S. Oishi. Accurate sum and dot product. +SIAM J. Sci. Comput., Vol 26, No 6, pp. 1955-1988. +doi 10.1137/030601818

+
+ +
+
+pancax.math.math._two_product(a, b)[source]
+
+ +
+
+pancax.math.math._float_split(a)[source]
+
+ +
+
+

pancax.math.tensor_math module

+
+
+pancax.math.tensor_math.if_then_else(cond, val1, val2)[source]
+
+ +
+
+pancax.math.tensor_math.compute_deviatoric_tensor(strain)[source]
+
+ +
+
+pancax.math.tensor_math.dev(strain)[source]
+
+ +
+
+pancax.math.tensor_math.tensor_norm(tensor)[source]
+
+ +
+
+pancax.math.tensor_math.norm_of_deviator_squared(tensor)[source]
+
+ +
+
+pancax.math.tensor_math.norm_of_deviator(tensor)[source]
+
+ +
+
+pancax.math.tensor_math.mises_equivalent_stress(stress)[source]
+
+ +
+
+pancax.math.tensor_math.triaxiality(A)[source]
+
+ +
+
+pancax.math.tensor_math.sym(A)[source]
+
+ +
+
+pancax.math.tensor_math.logh(A)[source]
+
+ +
+
+pancax.math.tensor_math.logh_from_eigen(eVals, eVecs)[source]
+
+ +
+
+pancax.math.tensor_math.tensor_2D_to_3D(H)[source]
+
+ +
+
+pancax.math.tensor_math.eigen_sym33_non_unit(tensor)[source]
+
+ +
+
+pancax.math.tensor_math.eigen_sym33_unit(tensor)[source]
+
+ +
+
+pancax.math.tensor_math.cos_of_acos_divided_by_3(x)[source]
+
+ +
+
+pancax.math.tensor_math.mtk_log_sqrt_jvp(Cpack, Hpack)[source]
+
+ +
+
+pancax.math.tensor_math.mtk_pow_jvp(m, Cpack, Hpack)[source]
+
+ +
+
+pancax.math.tensor_math.relative_log_difference_taylor(lam1, lam2)[source]
+
+ +
+
+pancax.math.tensor_math.relative_log_difference_no_tolerance_check(lam1, lam2)[source]
+
+ +
+
+pancax.math.tensor_math.relative_log_difference(lam1, lam2)[source]
+
+ +
+
+pancax.math.tensor_math.log_jvp(Cpack, Hpack)[source]
+
+ +
+
+pancax.math.tensor_math.jvp_sqrtm(primals, tangents)[source]
+
+ +
+
+pancax.math.tensor_math.sqrtm_dbp(A)[source]
+

Matrix square root by product form of Denman-Beavers iteration.

+

Translated from the Matrix Function Toolbox +http://www.ma.man.ac.uk/~higham/mftoolbox +Nicholas J. Higham, Functions of Matrices: Theory and Computation, +SIAM, Philadelphia, PA, USA, 2008. ISBN 978-0-898716-46-7,

+
+ +
+
+pancax.math.tensor_math.logm_jvp(primals, tangents)[source]
+
+ +
+
+pancax.math.tensor_math._logm_iss(A)[source]
+

Logarithmic map by inverse scaling and squaring and Padé approximants

+

Translated from the Matrix Function Toolbox +http://www.ma.man.ac.uk/~higham/mftoolbox +Nicholas J. Higham, Functions of Matrices: Theory and Computation, +SIAM, Philadelphia, PA, USA, 2008. ISBN 978-0-898716-46-7,

+
+ +
+
+pancax.math.tensor_math.log_pade_pf(A, n)[source]
+

Logarithmic map by Padé approximant and partial fractions

+
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.networks.html b/pancax.networks.html new file mode 100644 index 0000000..92da32b --- /dev/null +++ b/pancax.networks.html @@ -0,0 +1,629 @@ + + + + + + + + + pancax.networks package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.networks package

+
+

Submodules

+
+
+

pancax.networks.elm module

+
+
+pancax.networks.elm.activation(x)[source]
+
+ +
+
+class pancax.networks.elm.ELM(n_inputs, n_outputs, n_neurons, key)[source]
+

Bases: Module

+
+
+__init__(n_inputs, n_outputs, n_neurons, key)[source]
+
+ +
+
+layer: any
+
+ +
+
+beta: any
+
+ +
+
+n_outputs: int
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.networks.elm.ELM2(layer: <built-in function any>, beta: <built-in function any>, n_outputs: int)[source]
+

Bases: Module

+
+
+layer: any
+
+ +
+
+__init__(layer: any, beta: any, n_outputs: int) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+beta: any
+
+ +
+
+n_outputs: int
+
+ +
+ +
+
+

pancax.networks.field_property_pair module

+
+
+class pancax.networks.field_property_pair.BasePancaxModel[source]
+

Bases: Module

+

Base class for pancax model parameters.

+

This includes a few helper methods

+
+
+serialise(base_name, epoch)[source]
+
+ +
+
+__init__() → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.networks.field_property_pair.FieldPropertyPair(fields: Module, properties: Module)[source]
+

Bases: BasePancaxModel

+

Data structure for storing a set of field network +parameters and a set of material properties

+
+
Parameters:
+
    +

  • fields – field network parameters object

    • +

  • properties – property parameters object

    • +
+
+
+
+
+fields: Module
+
+ +
+
+properties: Module
+
+ +
+
+freeze_fields_filter()[source]
+
+ +
+
+freeze_props_filter()[source]
+
+ +
+
+__init__(fields: Module, properties: Module) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.networks.initialization module

+
+
+pancax.networks.initialization.zero_init(key: PRNGKey, shape) → Float[Array, 'no ni'][source]
+
+
Parameters:
+
    +

  • weight – current weight array for sizing

    • +

  • key – rng key

    • +
+
+
Returns:
+

A new set of weights

+
+
+
+ +
+
+pancax.networks.initialization.trunc_init(key: PRNGKey, shape) → Float[Array, 'no ni'][source]
+
+
Parameters:
+
    +

  • weight – current weight array for sizing

    • +

  • key – rng key

    • +
+
+
Returns:
+

A new set of weights

+
+
+
+ +
+
+pancax.networks.initialization.init_linear_weight(model: Module, init_fn: Callable, key: PRNGKey) → Module[source]
+
+
Parameters:
+
    +

  • model – equinox model

    • +

  • init_fn – function to initialize weigth with

    • +

  • key – rng key

    • +
+
+
Returns:
+

a new equinox model

+
+
+
+ +
+
+pancax.networks.initialization.init_linear(model: Module, init_fn: Callable, key: PRNGKey)[source]
+
+
Parameters:
+
    +

  • model – equinox model

    • +

  • init_fn – function to initialize weigth with

    • +

  • key – rng key

    • +
+
+
Returns:
+

a new equinox model

+
+
+
+ +
+
+pancax.networks.initialization.box_init(layer: Linear, key: PRNGKey)[source]
+
+ +
+
+

pancax.networks.mlp module

+
+
+pancax.networks.mlp.Linear(n_inputs: int, n_outputs: int, key: PRNGKey)[source]
+
+
Parameters:
+
    +

  • n_inputs – Number of inputs to linear layer

    • +

  • n_outputs – Number of outputs of the linear layer

    • +

  • key – rng key

    • +
+
+
Returns:
+

Equinox Linear layer

+
+
+
+ +
+
+pancax.networks.mlp.MLP(n_inputs: int, n_outputs: int, n_neurons: int, n_layers: int, activation: ~typing.Callable, key: ~jax._src.random.PRNGKey, use_final_bias: bool | None = False, init_func: ~typing.Callable | None = <function trunc_init>)[source]
+
+
Parameters:
+
    +

  • n_inputs – Number of inputs to the MLP

    • +

  • n_outputs – Number of outputs of the MLP

    • +

  • n_neurons – Number of neurons in each hidden layer of the MLP

    • +

  • n_layers – Number of hidden layers in the MLP

    • +

  • activation – Activation function, e.g. tanh or relu

    • +

  • key – rng key

    • +

  • use_final_bias – Boolean for whether or not to use a bias +vector in the final layer

    • +
+
+
Returns:
+

Equinox MLP layer

+
+
+
+ +
+
+pancax.networks.mlp.MLPBasis(n_inputs: int, n_neurons: int, n_layers: int, activation: ~typing.Callable, key: ~jax._src.random.PRNGKey, init_func: ~typing.Callable | None = <function trunc_init>)[source]
+
+ +
+
+

pancax.networks.properties module

+
+
+class pancax.networks.properties.Properties(prop_mins: ~jax.Array, prop_maxs: ~jax.Array, key: ~jax._src.random.PRNGKey, activation_func: ~typing.Callable | None = <PjitFunction of <function sigmoid>>)[source]
+

Bases: Module

+
+
Parameters:
+
    +

  • prop_mins – Minimum allowable properties

    • +

  • prop_maxs – Maximum allowable properties

    • +

  • prop_params – Actual tunable parameters

    • +
+
+
+
+
+__init__(prop_mins: ~jax.Array, prop_maxs: ~jax.Array, key: ~jax._src.random.PRNGKey, activation_func: ~typing.Callable | None = <PjitFunction of <function sigmoid>>) → None[source]
+
+
Parameters:
+
    +

  • prop_mins – Minimum allowable properties

    • +

  • prop_maxs – Maximum allowable properties

    • +

  • key – rng key

    • +
+
+
+
+ +
+
+prop_mins: Array
+
+ +
+
+prop_maxs: Array
+
+ +
+
+prop_params: Array
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+activation_func: Callable
+
+ +
+ +
+
+class pancax.networks.properties.FixedProperties(props: jax.Array)[source]
+

Bases: Properties

+
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+__init__(props: Array) → None[source]
+
+
Parameters:
+

props – Property values to be fixed

+
+
+
+ +
+ +
+
+

pancax.networks.rbf module

+
+
+class pancax.networks.rbf.RBFBasis(n_inputs: int, n_neurons: int, key: <function PRNGKey at 0x7f76547353a0>)[source]
+

Bases: Module

+
+
+__init__(n_inputs: int, n_neurons: int, key: PRNGKey) → None[source]
+
+ +
+
+center: Array
+
+ +
+
+sigma: Array
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+pancax.networks.rbf.rbf_normalization(hidden)[source]
+
+ +
+
+

Module contents

+
+
+pancax.networks.Network(network_type, *args, **kwargs)[source]
+
+ +
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.optimizers.html b/pancax.optimizers.html new file mode 100644 index 0000000..e99178e --- /dev/null +++ b/pancax.optimizers.html @@ -0,0 +1,307 @@ + + + + + + + + + pancax.optimizers package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.optimizers package

+
+

Submodules

+
+
+

pancax.optimizers.adam module

+
+
+class pancax.optimizers.adam.Adam(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = True, learning_rate: float | None = 0.001, transition_steps: int | None = 500, decay_rate: float | None = 0.99, clip_gradients: bool | None = False, filter_spec: Callable | None = None)[source]
+

Bases: Optimizer

+
+
+__init__(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = True, learning_rate: float | None = 0.001, transition_steps: int | None = 500, decay_rate: float | None = 0.99, clip_gradients: bool | None = False, filter_spec: Callable | None = None) → None[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+make_step_method()[source]
+
+ +
+ +
+
+

pancax.optimizers.base module

+
+
+class pancax.optimizers.base.Optimizer(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = True)[source]
+

Bases: ABC

+
+
+__init__(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = True) → None[source]
+
+ +
+
+abstract make_step_method(params)[source]
+
+ +
+
+ensemble_init(params)[source]
+
+ +
+
+ensemble_step_old(params, domain, opt_st)[source]
+
+ +
+
+init(params)[source]
+
+ +
+
+train(params, domain, times, opt, logger, history, pp, n_epochs, log_every: int | None = 100, serialise_every: int | None = 10000, postprocess_every: int | None = 10000)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.optimizers.lbfgs module

+
+
+pancax.optimizers.lbfgs.value_and_grad_from_state(value_fn)[source]
+
+ +
+
+class pancax.optimizers.lbfgs.LBFGS(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = False, learning_rate: float | None = 0.1)[source]
+

Bases: Optimizer

+
+
+__init__(loss_function: Callable, has_aux: bool | None = False, jit: bool | None = False, learning_rate: float | None = 0.1) → None[source]
+
+ +
+
+make_step_method()[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.optimizers.utils module

+
+
+pancax.optimizers.utils.trainable_filter(params: any, freeze_properties: bool | None = True, freeze_basis: bool | None = False)[source]
+
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.physics_kernels.html b/pancax.physics_kernels.html new file mode 100644 index 0000000..f1ad80a --- /dev/null +++ b/pancax.physics_kernels.html @@ -0,0 +1,702 @@ + + + + + + + + + pancax.physics_kernels package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.physics_kernels package

+
+

Submodules

+
+
+

pancax.physics_kernels.base module

+
+
+pancax.physics_kernels.base.nodal_pp(func, has_props=False, jit=True)[source]
+
+
Parameters:
+
    +

  • func – Function to use for a nodal property output variable

    • +

  • has_props – Whether or not this function need properties

    • +

  • jit – Whether or not to jit this function

    • +
+
+
+
+ +
+
+pancax.physics_kernels.base.standard_pp(physics)[source]
+
+ +
+
+class pancax.physics_kernels.base.BasePhysics(field_value_names: tuple[str, ...])[source]
+

Bases: Module

+
+
+__init__(field_value_names: tuple[str, ...]) → None[source]
+
+ +
+
+field_value_names: tuple[str, ...]
+
+ +
+
+var_name_to_method: Dict[str, Callable]
+
+ +
+
+dirichlet_bc_func: Callable
+
+ +
+
+x_mins: Float[Array, 'nd']
+
+ +
+
+x_maxs: Float[Array, 'nd']
+
+ +
+
+field_values(field, x, t, *args)[source]
+
+ +
+
+field_gradients(field, x, t, *args)[source]
+
+ +
+
+field_hessians(field, x, t, *args)[source]
+
+ +
+
+field_laplacians(field, x, t, *args)[source]
+
+ +
+
+field_time_derivatives(field, x, t, *args)[source]
+
+ +
+
+field_second_time_derivatives(field, x, t, *args)[source]
+
+ +
+
+update_dirichlet_bc_func(bc_func: Callable)[source]
+
+ +
+
+update_normalization(domain)[source]
+
+ +
+
+update_var_name_to_method()[source]
+
+ +
+
+vmap_field_values(field, xs, t, *args)[source]
+
+ +
+
+vmap_field_gradients(field, xs, t, *args)[source]
+
+ +
+
+property n_dofs
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.base.BaseVariationalFormPhysics(field_value_names: tuple[str, ...])[source]
+

Bases: BasePhysics

+
+
+__init__(field_value_names: tuple[str, ...]) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.base.BaseEnergyFormPhysics(field_value_names: tuple[str, ...])[source]
+

Bases: BaseVariationalFormPhysics

+
+
+field_value_names: tuple[str, ...]
+
+ +
+
+element_energy(params, x, t, u, fspace, *args)[source]
+
+ +
+
+element_kinetic_energy(params, x, t, u, fspace, *args)[source]
+
+ +
+
+abstract energy(params, x, t, u, grad_u, *args)[source]
+
+ +
+
+potential_energy_on_block(params, x, t, us, fspace, conns, *args)[source]
+
+ +
+
+potential_energy(params, domain, t, us, *args)[source]
+
+ +
+
+potential_energy_and_internal_force(params, domain, t, us, *args)[source]
+
+ +
+
+potential_energy_and_residual(params, domain, t, us, *args)[source]
+
+ +
+
+potential_energy_residual_and_reaction_force(params, domain, t, us, *args)[source]
+
+ +
+
+mass_matrix(params, domain, t, us, *args)[source]
+
+ +
+
+stiffness_matrix(params, domain, t, us, *args)[source]
+
+ +
+
+__init__(field_value_names: tuple[str, ...]) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+vmap_element_energy(params, x, t, u, fspace, conns, *args)[source]
+
+ +
+ +
+
+class pancax.physics_kernels.base.BaseStrongFormPhysics(field_value_names: tuple[str, ...])[source]
+

Bases: BasePhysics

+
+
+__init__(field_value_names: tuple[str, ...]) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+field_value_names: tuple[int, ...]
+
+ +
+
+strong_form_neumann_bc(params, x, t, n, *args)[source]
+
+ +
+
+abstract strong_form_residual(params, x, t, *args)[source]
+
+ +
+ +
+
+

pancax.physics_kernels.burgers_equation module

+
+
+class pancax.physics_kernels.burgers_equation.BurgersEquation[source]
+

Bases: BaseStrongFormPhysics

+
+
+field_value_names: tuple[int, ...]
+
+ +
+
+__init__()[source]
+
+ +
+
+strong_form_residual(params, x, t, *args)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.physics_kernels.heat_equation module

+
+
+class pancax.physics_kernels.heat_equation.HeatEquation[source]
+

Bases: BaseStrongFormPhysics

+
+
+field_value_names: tuple[int]
+
+ +
+
+__init__()[source]
+
+ +
+
+strong_form_residual(params, x, t, *args)[source]
+
+ +
+
+strong_form_neumann_bc(params, x, t, n, *args)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.physics_kernels.laplace_beltrami module

+
+
+class pancax.physics_kernels.laplace_beltrami.LaplaceBeltrami[source]
+

Bases: BaseEnergyFormPhysics

+
+
+field_value_names: tuple[int, ...] = 'u'
+
+ +
+
+__init__()[source]
+
+ +
+
+energy(params, x, t, u, grad_u, *args)[source]
+
+ +
+
+kinetic_energy(params, x, t, u, grad_u, *args)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+

pancax.physics_kernels.poisson module

+
+
+class pancax.physics_kernels.poisson.Poisson(f: Callable)[source]
+

Bases: BaseEnergyFormPhysics, BaseStrongFormPhysics

+
+
+field_value_names: tuple[str, ...] = 'u'
+
+ +
+
+__init__(f: Callable) → None[source]
+
+ +
+
+f: Callable
+
+ +
+
+energy(params, x, t, u, grad_u, *args)[source]
+
+ +
+
+strong_form_neumann_bc(params, x, t, n, *args)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+strong_form_residual(params, x, t, *args)[source]
+
+ +
+ +
+
+

pancax.physics_kernels.solid_mechanics module

+
+
+class pancax.physics_kernels.solid_mechanics.BaseMechanicsFormulation(n_dimensions: int)[source]
+

Bases: Module

+
+
+n_dimensions: int
+
+ +
+
+abstract modify_field_gradient(grad_u)[source]
+
+ +
+
+__init__(n_dimensions: int) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.solid_mechanics.IncompressiblePlaneStress[source]
+

Bases: BaseMechanicsFormulation

+
+
+n_dimensions: int = 2
+
+ +
+
+__init__() → None[source]
+
+ +
+
+deformation_gradient(grad_u)[source]
+
+ +
+
+modify_field_gradient(grad_u)[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.solid_mechanics.PlaneStrain(n_dimensions: int = 2)[source]
+

Bases: BaseMechanicsFormulation

+
+
+n_dimensions: int = 2
+
+ +
+
+extract_stress(P)[source]
+
+ +
+
+modify_field_gradient(grad_u)[source]
+
+ +
+
+__init__(n_dimensions: int = 2) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.solid_mechanics.ThreeDimensional(n_dimensions: int = 3)[source]
+

Bases: BaseMechanicsFormulation

+
+
+n_dimensions: int = 3
+
+ +
+
+modify_field_gradient(grad_u)[source]
+
+ +
+
+__init__(n_dimensions: int = 3) → None
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+ +
+
+class pancax.physics_kernels.solid_mechanics.SolidMechanics(constitutive_model, formulation)[source]
+

Bases: BaseEnergyFormPhysics

+
+
+__init__(constitutive_model, formulation) → None[source]
+
+ +
+
+field_value_names: tuple[str, ...]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+constitutive_model: any
+
+ +
+
+formulation: BaseMechanicsFormulation
+
+ +
+
+energy(params, x, t, u, grad_u, *args)[source]
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/pancax.problems.html b/pancax.problems.html new file mode 100644 index 0000000..627dfae --- /dev/null +++ b/pancax.problems.html @@ -0,0 +1,274 @@ + + + + + + + + + pancax.problems package — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+ +
+
+
+
+ +
+

pancax.problems package

+
+

Submodules

+
+
+

pancax.problems.forward_problem module

+
+
+exception pancax.problems.forward_problem.DomainPhysicsCompatabilityError[source]
+

Bases: Exception

+
+ +
+
+class pancax.problems.forward_problem.ForwardProblem(domain: pancax.domains.base.BaseDomain, physics: pancax.physics_kernels.base.BasePhysics, ics: List[Callable], essential_bcs: List[pancax.bcs.essential_bc.EssentialBC], natural_bcs: List[pancax.bcs.natural_bc.NaturalBC])[source]
+

Bases: Module

+
+
+__init__(domain: BaseDomain, physics: BasePhysics, ics: List[Callable], essential_bcs: List[EssentialBC], natural_bcs: List[NaturalBC]) → None[source]
+
+ +
+
+domain: BaseDomain
+
+ +
+
+physics: BasePhysics
+
+ +
+
+ics: List[Callable]
+
+ +
+
+essential_bcs: List[EssentialBC]
+
+ +
+
+natural_bcs: List[NaturalBC]
+
+ +
+
+property conns
+
+ +
+
+property coords
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+property dof_manager
+
+ +
+
+property fspace
+
+ +
+
+property mesh
+
+ +
+
+property mesh_file
+
+ +
+
+property times
+
+ +
+ +
+
+

pancax.problems.inverse_problem module

+
+
+class pancax.problems.inverse_problem.InverseProblem(domain: pancax.domains.base.BaseDomain, physics: pancax.physics_kernels.base.BasePhysics, ics: List[Callable], essential_bcs: List[pancax.bcs.essential_bc.EssentialBC], natural_bcs: List[pancax.bcs.natural_bc.NaturalBC], field_data: pancax.data.full_field_data.FullFieldData, global_data: pancax.data.global_data.GlobalData)[source]
+

Bases: ForwardProblem

+
+
+__init__(domain: BaseDomain, physics: BasePhysics, ics: List[Callable], essential_bcs: List[EssentialBC], natural_bcs: List[NaturalBC], field_data: FullFieldData, global_data: GlobalData) → None[source]
+
+ +
+
+_abc_impl = <_abc._abc_data object>
+
+ +
+
+field_data: FullFieldData
+
+ +
+
+global_data: GlobalData
+
+ +
+ +
+
+

Module contents

+
+
+ + +
+
+ +
+
+
+
+ + + + \ No newline at end of file diff --git a/py-modindex.html b/py-modindex.html new file mode 100644 index 0000000..5993a44 --- /dev/null +++ b/py-modindex.html @@ -0,0 +1,573 @@ + + + + + + + + Python Module Index — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Python Module Index
    • +
  • +
    • +
+
+
+
+
+ + +

Python Module Index

+ +
+ p +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
 
+ p
+ pancax +
    + pancax.bcs +
    + pancax.bcs.distance_functions +
    + pancax.bcs.essential_bc +
    + pancax.bcs.natural_bc +
    + pancax.bvps +
    + pancax.bvps.biaxial_tension +
    + pancax.bvps.simple_shear +
    + pancax.bvps.uniaxial_tension +
    + pancax.constitutive_models +
    + pancax.constitutive_models.base +
    + pancax.constitutive_models.blatz_ko +
    + pancax.constitutive_models.gent +
    + pancax.constitutive_models.neohookean +
    + pancax.constitutive_models.properties +
    + pancax.constitutive_models.swanson +
    + pancax.data +
    + pancax.data.full_field_data +
    + pancax.data.global_data +
    + pancax.domains +
    + pancax.domains.base +
    + pancax.domains.collocation_domain +
    + pancax.domains.delta_pinn_domain +
    + pancax.domains.variational_domain +
    + pancax.fem +
    + pancax.fem.dof_manager +
    + pancax.fem.elements +
    + pancax.fem.elements.base_element +
    + pancax.fem.elements.hex8_element +
    + pancax.fem.elements.line_element +
    + pancax.fem.elements.quad4_element +
    + pancax.fem.elements.quad9_element +
    + pancax.fem.elements.simplex_tri_element +
    + pancax.fem.elements.tet10_element +
    + pancax.fem.elements.tet4_element +
    + pancax.fem.function_space +
    + pancax.fem.mesh +
    + pancax.fem.quadrature_rules +
    + pancax.fem.read_exodus_mesh +
    + pancax.fem.sparse_matrix_assembler +
    + pancax.fem.surface +
    + pancax.fem.traction_bc +
    + pancax.history_writer +
    + pancax.kernels +
    + pancax.kernels.base_kernel +
    + pancax.kernels.laplace_beltrami +
    + pancax.kernels.linear_elasticity +
    + pancax.kernels.poisson +
    + pancax.kinematics +
    + pancax.logging +
    + pancax.loss_functions +
    + pancax.loss_functions.base_loss_function +
    + pancax.loss_functions.bc_loss_functions +
    + pancax.loss_functions.data_loss_functions +
    + pancax.loss_functions.ic_loss_function +
    + pancax.loss_functions.physics_loss_functions_strong_form +
    + pancax.loss_functions.strong_form_loss_functions +
    + pancax.loss_functions.utils +
    + pancax.loss_functions.weak_form_loss_functions +
    + pancax.math +
    + pancax.math.math +
    + pancax.math.tensor_math +
    + pancax.networks +
    + pancax.networks.elm +
    + pancax.networks.field_property_pair +
    + pancax.networks.initialization +
    + pancax.networks.mlp +
    + pancax.networks.properties +
    + pancax.networks.rbf +
    + pancax.optimizers +
    + pancax.optimizers.adam +
    + pancax.optimizers.base +
    + pancax.optimizers.lbfgs +
    + pancax.optimizers.utils +
    + pancax.physics +
    + pancax.physics_kernels +
    + pancax.physics_kernels.base +
    + pancax.physics_kernels.burgers_equation +
    + pancax.physics_kernels.heat_equation +
    + pancax.physics_kernels.laplace_beltrami +
    + pancax.physics_kernels.poisson +
    + pancax.physics_kernels.solid_mechanics +
    + pancax.post_processor +
    + pancax.problems +
    + pancax.problems.forward_problem +
    + pancax.problems.inverse_problem +
    + pancax.timer +
    + pancax.trainer +
    + pancax.utils +
+ + +
+
+
+ +
+ +
+

© Copyright 2024, Craig M. Hamel.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + \ No newline at end of file diff --git a/search.html b/search.html new file mode 100644 index 0000000..cfa701a --- /dev/null +++ b/search.html @@ -0,0 +1,133 @@ + + + + + + + + Search — pancax 0.0.2 documentation + + + + + + + + + + + + + + + + + + + + + +
+ + +
+ +
+
+
+
    +
    • +
  • Search
    • +
  • +
    • +
+
+
+
+
+ + + + +
+ +
+ +
+
+
+ +
+ +
+

© Copyright 2024, Craig M. Hamel.

+
+ + Built with Sphinx using a + theme + provided by Read the Docs. + + +
+
+
+
+
+ + + + + + + + + \ No newline at end of file diff --git a/searchindex.js b/searchindex.js new file mode 100644 index 0000000..b20b285 --- /dev/null +++ b/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"alltitles": {"Indices and tables": [[0, "indices-and-tables"]], "Module contents": [[2, "module-pancax"], [3, "module-pancax.bcs"], [4, "module-pancax.bvps"], [5, "module-pancax.constitutive_models"], [6, "module-pancax.data"], [7, "module-pancax.domains"], [8, "module-pancax.fem"], [9, "module-pancax.fem.elements"], [10, "module-pancax.kernels"], [11, "module-pancax.loss_functions"], [12, "module-pancax.math"], [13, "module-pancax.networks"], [14, "module-pancax.optimizers"], [15, "module-pancax.physics_kernels"], [16, "module-pancax.problems"]], "Pancax": [[0, null]], "Submodules": [[2, "submodules"], [3, "submodules"], [4, "submodules"], [5, "submodules"], [6, "submodules"], [7, "submodules"], [8, "submodules"], [9, "submodules"], [10, "submodules"], [11, "submodules"], [12, "submodules"], [13, "submodules"], [14, "submodules"], [15, "submodules"], [16, "submodules"]], "Subpackages": [[2, "subpackages"], [8, "subpackages"]], "pancax": [[1, null]], "pancax package": [[2, null]], "pancax.__main__ module": [[2, "pancax-main-module"]], "pancax.bcs package": [[3, null]], "pancax.bcs.distance_functions module": [[3, "module-pancax.bcs.distance_functions"]], "pancax.bcs.essential_bc module": [[3, "module-pancax.bcs.essential_bc"]], "pancax.bcs.natural_bc module": [[3, "module-pancax.bcs.natural_bc"]], "pancax.bvps package": [[4, null]], "pancax.bvps.biaxial_tension module": [[4, "module-pancax.bvps.biaxial_tension"]], "pancax.bvps.simple_shear module": [[4, "module-pancax.bvps.simple_shear"]], "pancax.bvps.uniaxial_tension module": [[4, "module-pancax.bvps.uniaxial_tension"]], "pancax.constitutive_models package": [[5, null]], "pancax.constitutive_models.base module": [[5, "module-pancax.constitutive_models.base"]], "pancax.constitutive_models.blatz_ko module": [[5, "module-pancax.constitutive_models.blatz_ko"]], "pancax.constitutive_models.gent module": [[5, "module-pancax.constitutive_models.gent"]], "pancax.constitutive_models.neohookean module": [[5, "module-pancax.constitutive_models.neohookean"]], "pancax.constitutive_models.properties module": [[5, "module-pancax.constitutive_models.properties"]], "pancax.constitutive_models.swanson module": [[5, "module-pancax.constitutive_models.swanson"]], "pancax.data package": [[6, null]], "pancax.data.full_field_data module": [[6, "module-pancax.data.full_field_data"]], "pancax.data.global_data module": [[6, "module-pancax.data.global_data"]], "pancax.domains package": [[7, null]], "pancax.domains.base module": [[7, "module-pancax.domains.base"]], "pancax.domains.collocation_domain module": [[7, "module-pancax.domains.collocation_domain"]], "pancax.domains.delta_pinn_domain module": [[7, "module-pancax.domains.delta_pinn_domain"]], "pancax.domains.variational_domain module": [[7, "module-pancax.domains.variational_domain"]], "pancax.fem package": [[8, null]], "pancax.fem.dof_manager module": [[8, "module-pancax.fem.dof_manager"]], "pancax.fem.elements package": [[9, null]], "pancax.fem.elements.base_element module": [[9, "module-pancax.fem.elements.base_element"]], "pancax.fem.elements.hex8_element module": [[9, "module-pancax.fem.elements.hex8_element"]], "pancax.fem.elements.line_element module": [[9, "module-pancax.fem.elements.line_element"]], "pancax.fem.elements.quad4_element module": [[9, "module-pancax.fem.elements.quad4_element"]], "pancax.fem.elements.quad9_element module": [[9, "module-pancax.fem.elements.quad9_element"]], "pancax.fem.elements.simplex_tri_element module": [[9, "module-pancax.fem.elements.simplex_tri_element"]], "pancax.fem.elements.tet10_element module": [[9, "module-pancax.fem.elements.tet10_element"]], "pancax.fem.elements.tet4_element module": [[9, "module-pancax.fem.elements.tet4_element"]], "pancax.fem.function_space module": 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pancax.fem.function_space)": [[8, "pancax.fem.function_space.construct_function_space", false]], "construct_function_space_from_parent_element() (in module pancax.fem.function_space)": [[8, "pancax.fem.function_space.construct_function_space_from_parent_element", false]], "construct_mesh_from_basic_data() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.construct_mesh_from_basic_data", false]], "construct_structured_mesh() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.construct_structured_mesh", false]], "convert_exodus_to_xml() (pancax.post_processor.vtkpostprocessor method)": [[2, "pancax.post_processor.VtkPostProcessor.convert_exodus_to_xml", false]], "coordinates (pancax.fem.elements.base_element.baseelement attribute)": [[9, "pancax.fem.elements.base_element.BaseElement.coordinates", false]], "coordinates (pancax.fem.elements.hex8_element.hex8element attribute)": [[9, "pancax.fem.elements.hex8_element.Hex8Element.coordinates", false]], "coordinates (pancax.fem.elements.line_element.lineelement attribute)": [[9, "pancax.fem.elements.line_element.LineElement.coordinates", false]], "coordinates (pancax.fem.elements.quad4_element.quad4element attribute)": [[9, "pancax.fem.elements.quad4_element.Quad4Element.coordinates", false]], "coordinates (pancax.fem.elements.quad9_element.quad9element attribute)": [[9, "pancax.fem.elements.quad9_element.Quad9Element.coordinates", false]], "coordinates (pancax.fem.elements.simplex_tri_element.simplextrielement attribute)": [[9, "pancax.fem.elements.simplex_tri_element.SimplexTriElement.coordinates", false]], "coordinates (pancax.fem.elements.tet10_element.tet10element attribute)": [[9, "pancax.fem.elements.tet10_element.Tet10Element.coordinates", false]], "coordinates (pancax.fem.elements.tet4_element.tet4element attribute)": [[9, "pancax.fem.elements.tet4_element.Tet4Element.coordinates", false]], "coordinates() (pancax.bcs.essential_bc.essentialbc method)": [[3, "pancax.bcs.essential_bc.EssentialBC.coordinates", false]], "coordinates() (pancax.bcs.natural_bc.naturalbc method)": [[3, "pancax.bcs.natural_bc.NaturalBC.coordinates", false]], "coords (pancax.domains.base.basedomain attribute)": [[7, "pancax.domains.base.BaseDomain.coords", false]], "coords (pancax.domains.collocation_domain.collocationdomain attribute)": [[7, "pancax.domains.collocation_domain.CollocationDomain.coords", false]], "coords (pancax.domains.variational_domain.variationaldomain attribute)": [[7, "pancax.domains.variational_domain.VariationalDomain.coords", false]], "coords (pancax.fem.mesh.mesh attribute)": [[8, "pancax.fem.mesh.Mesh.coords", false]], "coords (pancax.problems.forward_problem.forwardproblem property)": [[16, "pancax.problems.forward_problem.ForwardProblem.coords", false]], "copy_mesh() (pancax.post_processor.exoduspostprocessor method)": [[2, "pancax.post_processor.ExodusPostProcessor.copy_mesh", false]], "cos_of_acos_divided_by_3() (in module pancax.math.tensor_math)": [[12, "pancax.math.tensor_math.cos_of_acos_divided_by_3", false]], "create_edges() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.create_edges", false]], "create_edges() (in module pancax.fem.surface)": [[8, "pancax.fem.surface.create_edges", false]], "create_field() (pancax.fem.dof_manager.dofmanager method)": [[8, "pancax.fem.dof_manager.DofManager.create_field", false]], "create_field_methods() (in module pancax.kinematics)": [[2, "pancax.kinematics.create_field_methods", false]], "create_higher_order_mesh_from_simplex_mesh() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.create_higher_order_mesh_from_simplex_mesh", false]], "create_nodesets_from_sidesets() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.create_nodesets_from_sidesets", false]], "create_padded_quadrature_rule_1d() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_padded_quadrature_rule_1D", false]], "create_quadrature_rule_1d() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_quadrature_rule_1D", false]], "create_quadrature_rule_on_hex() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_quadrature_rule_on_hex", false]], "create_quadrature_rule_on_quad() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_quadrature_rule_on_quad", false]], "create_quadrature_rule_on_tet() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_quadrature_rule_on_tet", false]], "create_quadrature_rule_on_triangle() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.create_quadrature_rule_on_triangle", false]], "create_structured_mesh_data() (in module pancax.fem.mesh)": [[8, "pancax.fem.mesh.create_structured_mesh_data", false]], "cutoff_strain (pancax.constitutive_models.swanson.swanson attribute)": [[5, "pancax.constitutive_models.swanson.Swanson.cutoff_strain", false]], "data_dict (pancax.history_writer.historywriter attribute)": [[2, "pancax.history_writer.HistoryWriter.data_dict", false]], "datafilenotfoundexception": [[2, "pancax.utils.DataFileNotFoundException", false]], "default_modify_element_gradient() (in module pancax.fem.function_space)": [[8, "pancax.fem.function_space.default_modify_element_gradient", false]], "deformation_gradient() (pancax.physics_kernels.solid_mechanics.incompressibleplanestress method)": [[15, "pancax.physics_kernels.solid_mechanics.IncompressiblePlaneStress.deformation_gradient", false]], "deformation_gradients() (in module pancax.kinematics)": [[2, "pancax.kinematics.deformation_gradients", false]], "degree (pancax.fem.elements.base_element.baseelement attribute)": [[9, "pancax.fem.elements.base_element.BaseElement.degree", false]], "degree (pancax.fem.elements.hex8_element.hex8element attribute)": [[9, "pancax.fem.elements.hex8_element.Hex8Element.degree", false]], "degree (pancax.fem.elements.line_element.lineelement attribute)": [[9, "pancax.fem.elements.line_element.LineElement.degree", false]], "degree (pancax.fem.elements.quad4_element.quad4element attribute)": [[9, "pancax.fem.elements.quad4_element.Quad4Element.degree", false]], "degree (pancax.fem.elements.quad9_element.quad9element attribute)": [[9, "pancax.fem.elements.quad9_element.Quad9Element.degree", false]], "degree (pancax.fem.elements.simplex_tri_element.simplextrielement attribute)": [[9, "pancax.fem.elements.simplex_tri_element.SimplexTriElement.degree", false]], "degree (pancax.fem.elements.tet10_element.tet10element attribute)": [[9, "pancax.fem.elements.tet10_element.Tet10Element.degree", false]], "degree (pancax.fem.elements.tet4_element.tet4element attribute)": [[9, "pancax.fem.elements.tet4_element.Tet4Element.degree", false]], "deltapinndomain (class in pancax.domains.delta_pinn_domain)": [[7, "pancax.domains.delta_pinn_domain.DeltaPINNDomain", false]], "dev() (in module pancax.math.tensor_math)": [[12, "pancax.math.tensor_math.dev", false]], "dirichlet_bc_func (pancax.physics_kernels.base.basephysics attribute)": [[15, "pancax.physics_kernels.base.BasePhysics.dirichlet_bc_func", false]], "dirichletbcloss (class in pancax.loss_functions.bc_loss_functions)": [[11, "pancax.loss_functions.bc_loss_functions.DirichletBCLoss", false]], "displacements (pancax.data.global_data.globaldata attribute)": [[6, "pancax.data.global_data.GlobalData.displacements", false]], "distance() (in module pancax.bcs.distance_functions)": [[3, "pancax.bcs.distance_functions.distance", false]], "distance_function() (in module pancax.bcs.distance_functions)": [[3, "pancax.bcs.distance_functions.distance_function", false]], "dof_manager (pancax.domains.variational_domain.variationaldomain attribute)": [[7, "pancax.domains.variational_domain.VariationalDomain.dof_manager", false]], "dof_manager (pancax.problems.forward_problem.forwardproblem property)": [[16, "pancax.problems.forward_problem.ForwardProblem.dof_manager", false]], "dofmanager (class in pancax.fem.dof_manager)": [[8, "pancax.fem.dof_manager.DofManager", false]], "domain (pancax.problems.forward_problem.forwardproblem attribute)": [[16, "pancax.problems.forward_problem.ForwardProblem.domain", false]], "domainphysicscompatabilityerror": [[16, "pancax.problems.forward_problem.DomainPhysicsCompatabilityError", false]], "dot2() (in module pancax.math.math)": [[12, "pancax.math.math.dot2", false]], "eigen_modes (pancax.domains.delta_pinn_domain.deltapinndomain attribute)": [[7, "pancax.domains.delta_pinn_domain.DeltaPINNDomain.eigen_modes", false]], "eigen_sym33_non_unit() (in module pancax.math.tensor_math)": [[12, "pancax.math.tensor_math.eigen_sym33_non_unit", false]], "eigen_sym33_unit() (in module pancax.math.tensor_math)": [[12, "pancax.math.tensor_math.eigen_sym33_unit", false]], "element_energy() (pancax.physics_kernels.base.baseenergyformphysics method)": [[15, "pancax.physics_kernels.base.BaseEnergyFormPhysics.element_energy", false]], "element_field_gradient() (pancax.kernels.base_kernel.weakformphysicskernel method)": [[10, "pancax.kernels.base_kernel.WeakFormPhysicsKernel.element_field_gradient", false]], "element_kinetic_energy() (pancax.physics_kernels.base.baseenergyformphysics method)": [[15, "pancax.physics_kernels.base.BaseEnergyFormPhysics.element_kinetic_energy", false]], "element_pp() (in module pancax.kernels.base_kernel)": [[10, "pancax.kernels.base_kernel.element_pp", false]], "element_quantity() (in module pancax.physics)": [[2, "pancax.physics.element_quantity", false]], "element_quantity() (pancax.kernels.base_kernel.weakformphysicskernel method)": [[10, "pancax.kernels.base_kernel.WeakFormPhysicsKernel.element_quantity", false]], "element_quantity_grad() (in module pancax.physics)": [[2, "pancax.physics.element_quantity_grad", false]], "element_quantity_grad() (pancax.kernels.base_kernel.weakformphysicskernel method)": [[10, "pancax.kernels.base_kernel.WeakFormPhysicsKernel.element_quantity_grad", false]], "element_quantity_hessian() (in module pancax.physics)": [[2, "pancax.physics.element_quantity_hessian", false]], "element_quantity_hessian() (pancax.kernels.base_kernel.weakformphysicskernel method)": [[10, "pancax.kernels.base_kernel.WeakFormPhysicsKernel.element_quantity_hessian", false]], "element_quantity_new() (in module pancax.physics)": [[2, "pancax.physics.element_quantity_new", false]], "elementtype (pancax.fem.elements.base_element.baseelement attribute)": [[9, "pancax.fem.elements.base_element.BaseElement.elementType", false]], "elementtype (pancax.fem.elements.hex8_element.hex8element attribute)": [[9, "pancax.fem.elements.hex8_element.Hex8Element.elementType", false]], "elementtype (pancax.fem.elements.line_element.lineelement attribute)": [[9, "pancax.fem.elements.line_element.LineElement.elementType", false]], "elementtype (pancax.fem.elements.quad4_element.quad4element attribute)": [[9, "pancax.fem.elements.quad4_element.Quad4Element.elementType", false]], "elementtype (pancax.fem.elements.quad9_element.quad9element attribute)": [[9, "pancax.fem.elements.quad9_element.Quad9Element.elementType", false]], "elementtype (pancax.fem.elements.simplex_tri_element.simplextrielement attribute)": [[9, "pancax.fem.elements.simplex_tri_element.SimplexTriElement.elementType", false]], "elementtype (pancax.fem.elements.tet10_element.tet10element attribute)": [[9, "pancax.fem.elements.tet10_element.Tet10Element.elementType", false]], "elementtype (pancax.fem.elements.tet4_element.tet4element attribute)": [[9, "pancax.fem.elements.tet4_element.Tet4Element.elementType", false]], "elm (class in pancax.networks.elm)": [[13, "pancax.networks.elm.ELM", false]], "elm2 (class in pancax.networks.elm)": [[13, "pancax.networks.elm.ELM2", false]], "energy() (pancax.constitutive_models.base.baseconstitutivemodel method)": [[5, "pancax.constitutive_models.base.BaseConstitutiveModel.energy", false]], "energy() (pancax.constitutive_models.blatz_ko.blatzko method)": [[5, "pancax.constitutive_models.blatz_ko.BlatzKo.energy", false]], "energy() (pancax.constitutive_models.gent.gent method)": [[5, "pancax.constitutive_models.gent.Gent.energy", false]], "energy() (pancax.constitutive_models.neohookean.neohookean method)": [[5, "pancax.constitutive_models.neohookean.NeoHookean.energy", false]], "energy() (pancax.constitutive_models.swanson.swanson method)": [[5, "pancax.constitutive_models.swanson.Swanson.energy", false]], "energy() (pancax.kernels.base_kernel.weakformphysicskernel method)": [[10, "pancax.kernels.base_kernel.WeakFormPhysicsKernel.energy", false]], "energy() (pancax.kernels.laplace_beltrami.laplacebeltrami method)": [[10, "pancax.kernels.laplace_beltrami.LaplaceBeltrami.energy", false]], "energy() (pancax.kernels.linear_elasticity.linearelasticity2d method)": [[10, "pancax.kernels.linear_elasticity.LinearElasticity2D.energy", false]], "energy() (pancax.kernels.poisson.poisson method)": [[10, "pancax.kernels.poisson.Poisson.energy", false]], "energy() (pancax.physics_kernels.base.baseenergyformphysics method)": [[15, "pancax.physics_kernels.base.BaseEnergyFormPhysics.energy", false]], "energy() (pancax.physics_kernels.laplace_beltrami.laplacebeltrami method)": [[15, "pancax.physics_kernels.laplace_beltrami.LaplaceBeltrami.energy", false]], "energy() (pancax.physics_kernels.poisson.poisson method)": [[15, "pancax.physics_kernels.poisson.Poisson.energy", false]], "energy() (pancax.physics_kernels.solid_mechanics.solidmechanics method)": [[15, "pancax.physics_kernels.solid_mechanics.SolidMechanics.energy", false]], "energy_weight (pancax.loss_functions.weak_form_loss_functions.energyandresidualloss attribute)": [[11, "pancax.loss_functions.weak_form_loss_functions.EnergyAndResidualLoss.energy_weight", false]], "energy_weight (pancax.loss_functions.weak_form_loss_functions.energyresidualandreactionloss attribute)": [[11, "pancax.loss_functions.weak_form_loss_functions.EnergyResidualAndReactionLoss.energy_weight", false]], "energy_weight (pancax.loss_functions.weak_form_loss_functions.incompressibleenergyandresidualloss attribute)": [[11, "pancax.loss_functions.weak_form_loss_functions.IncompressibleEnergyAndResidualLoss.energy_weight", false]], "energyandresidualloss (class in pancax.loss_functions.weak_form_loss_functions)": [[11, "pancax.loss_functions.weak_form_loss_functions.EnergyAndResidualLoss", false]], "energyloss (class in pancax.loss_functions.weak_form_loss_functions)": [[11, "pancax.loss_functions.weak_form_loss_functions.EnergyLoss", false]], "energyresidualandreactionloss (class in pancax.loss_functions.weak_form_loss_functions)": [[11, "pancax.loss_functions.weak_form_loss_functions.EnergyResidualAndReactionLoss", false]], "ensemble_init() (pancax.optimizers.base.optimizer method)": [[14, "pancax.optimizers.base.Optimizer.ensemble_init", false]], "ensemble_step_old() (pancax.optimizers.base.optimizer method)": [[14, "pancax.optimizers.base.Optimizer.ensemble_step_old", false]], "ensemblehistorywriter (class in pancax.history_writer)": [[2, "pancax.history_writer.EnsembleHistoryWriter", false]], "ensemblelogger (class in pancax.logging)": [[2, "pancax.logging.EnsembleLogger", false]], "essential_bcs (pancax.problems.forward_problem.forwardproblem attribute)": [[16, "pancax.problems.forward_problem.ForwardProblem.essential_bcs", false]], "essentialbc (class in pancax.bcs.essential_bc)": [[3, "pancax.bcs.essential_bc.EssentialBC", false]], "essentialbcset (class in pancax.bcs.essential_bc)": [[3, "pancax.bcs.essential_bc.EssentialBCSet", false]], "eval_at_iso_points() (in module pancax.fem.quadrature_rules)": [[8, "pancax.fem.quadrature_rules.eval_at_iso_points", false]], "eval_at_iso_points() (pancax.fem.quadrature_rules.quadraturerule method)": [[8, "pancax.fem.quadrature_rules.QuadratureRule.eval_at_iso_points", false]], "eval_field() (in module pancax.fem.surface)": [[8, "pancax.fem.surface.eval_field", false]], "evaluate_on_block() (in module pancax.fem.function_space)": [[8, "pancax.fem.function_space.evaluate_on_block", false]], "evaluate_on_element() (in module pancax.fem.function_space)": [[8, "pancax.fem.function_space.evaluate_on_element", false]], "evaluate_on_element() (pancax.fem.function_space.nonallocatedfunctionspace method)": [[8, "pancax.fem.function_space.NonAllocatedFunctionSpace.evaluate_on_element", false]], "exoduspostprocessor (class in pancax.post_processor)": [[2, "pancax.post_processor.ExodusPostProcessor", false]], "extract_stress() (pancax.physics_kernels.solid_mechanics.planestrain method)": [[15, "pancax.physics_kernels.solid_mechanics.PlaneStrain.extract_stress", false]], "f (pancax.physics_kernels.poisson.poisson attribute)": [[15, "pancax.physics_kernels.poisson.Poisson.f", false]], "facenodes (pancax.fem.elements.base_element.baseelement attribute)": [[9, "pancax.fem.elements.base_element.BaseElement.faceNodes", false]], "facenodes (pancax.fem.elements.hex8_element.hex8element attribute)": [[9, "pancax.fem.elements.hex8_element.Hex8Element.faceNodes", false]], "facenodes (pancax.fem.elements.line_element.lineelement attribute)": [[9, "pancax.fem.elements.line_element.LineElement.faceNodes", false]], "facenodes (pancax.fem.elements.quad4_element.quad4element attribute)": [[9, "pancax.fem.elements.quad4_element.Quad4Element.faceNodes", false]], "facenodes (pancax.fem.elements.quad9_element.quad9element attribute)": [[9, "pancax.fem.elements.quad9_element.Quad9Element.faceNodes", false]], "facenodes (pancax.fem.elements.simplex_tri_element.simplextrielement attribute)": [[9, "pancax.fem.elements.simplex_tri_element.SimplexTriElement.faceNodes", false]], "facenodes (pancax.fem.elements.tet10_element.tet10element attribute)": [[9, "pancax.fem.elements.tet10_element.Tet10Element.faceNodes", false]], "facenodes (pancax.fem.elements.tet4_element.tet4element attribute)": [[9, "pancax.fem.elements.tet4_element.Tet4Element.faceNodes", false]], "field_data (pancax.problems.inverse_problem.inverseproblem attribute)": [[16, "pancax.problems.inverse_problem.InverseProblem.field_data", false]], "field_gradients() (pancax.kernels.base_kernel.strongformphysicskernel method)": [[10, "pancax.kernels.base_kernel.StrongFormPhysicsKernel.field_gradients", false]], "field_gradients() (pancax.physics_kernels.base.basephysics method)": [[15, "pancax.physics_kernels.base.BasePhysics.field_gradients", false]], "field_hessians() (pancax.kernels.base_kernel.strongformphysicskernel method)": [[10, "pancax.kernels.base_kernel.StrongFormPhysicsKernel.field_hessians", false]], "field_hessians() (pancax.physics_kernels.base.basephysics method)": [[15, "pancax.physics_kernels.base.BasePhysics.field_hessians", false]], "field_laplacians() (pancax.kernels.base_kernel.strongformphysicskernel method)": [[10, 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