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<html>
<head>
<title>
R4LIB - A Single Precision Real Arithmetic Utility Library
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
R4LIB <br> A Single Precision Real Arithmetic Utility Library
</h1>
<hr>
<p>
<b>R4LIB</b>
is a C++ library which
contains a number of utility routines for "R4" or "single precision real"
arithmetic.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>R4LIB</b> is available in
<a href = "../../c_src/r4lib/r4lib.html">a C version</a> and
<a href = "../../cpp_src/r4lib/r4lib.html">a C++ version</a> and
<a href = "../../f77_src/r4lib/r4lib.html">a FORTRAN77 version</a> and
<a href = "../../f_src/r4lib/r4lib.html">a FORTRAN90 version</a> and
<a href = "../../m_src/r4lib/r4lib.html">a MATLAB version</a> and
<a href = "../../py_src/r4lib/r4lib.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/c4lib/c4lib.html">
C4LIB</a>,
a C++ library which
implements certain elementary functions for "C4" or
single precision complex variables;
</p>
<p>
<a href = "../../cpp_src/c8lib/c8lib.html">
C8LIB</a>,
a C++ library which
implements certain elementary functions for "C8" or
double precision complex variables;
</p>
<p>
<a href = "../../cpp_src/i4lib/i4lib.html">
I4LIB</a>,
a C++ library which
contains many utility routines, using "I4" or "single precision integer"
arithmetic.
</p>
<p>
<a href = "../../cpp_src/i8lib/i8lib.html">
I8LIB</a>,
a C++ library which
contains many utility routines, using "I8" or "double precision integer"
arithmetic.
</p>
<p>
<a href = "../../cpp_src/r8lib/r8lib.html">
R8LIB</a>,
a C++ library which
contains many utility routines, using "R8" or
"double precision real" arithmetic.
</p>
<p>
<a href = "../../cpp_src/subpak/subpak.html">
SUBPAK</a>,
a C++ library which
contains many utility routines;
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "r4lib.cpp">r4lib.cpp</a>, the source code;
</li>
<li>
<a href = "r4lib.hpp">r4lib.hpp</a>, the header file.
</li>
<li>
<a href = "r4lib.sh">r4lib.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "r4lib_prb.cpp">r4lib_prb.cpp</a>, a sample calling
program;
</li>
<li>
<a href = "r4lib_prb.sh">r4lib_prb.sh</a>, commands to
compile, link and run the sample calling program;
</li>
<li>
<a href = "r4lib_prb_output.txt">r4lib_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>C4_ARGUMENT</b> returns the argument of a C4.
</li>
<li>
<b>C4_MAGNITUDE</b> returns the magnitude of a C4.
</li>
<li>
<b>C4_SQRT</b> returns the principal square root of a C4.
</li>
<li>
<b>I4_LOG_10</b> returns the integer part of the logarithm base 10 of an I4.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>I4_SIGN</b> returns the sign of an I4.
</li>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4INT_TO_R4INT</b> maps an I4 interval to an R4 interval.
</li>
<li>
<b>I4VEC_COPY</b> copies an I4VEC.
</li>
<li>
<b>I4VEC_INDICATOR_NEW</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_PERMUTE</b> permutes an I4VEC in place.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_ZERO</b> zeroes an I4VEC.
</li>
<li>
<b>I4VEC_ZERO_NEW</b> creates and zeroes an I4VEC.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_UNIFORM_NEW</b> selects a random permutation of N objects.
</li>
<li>
<b>R4_ABS</b> returns the absolute value of an R4.
</li>
<li>
<b>R4_ADD</b> adds two R4's.
</li>
<li>
<b>R4_ATAN</b> computes the inverse tangent of the ratio Y / X.
</li>
<li>
<b>R4_CAS</b> returns the "casine" of an R4.
</li>
<li>
<b>R4_CEILING</b> rounds an R4 "up" (towards +oo) to the next integer.
</li>
<li>
<b>R4_CHOOSE</b> computes the binomial coefficient C(N,K) as an R4.
</li>
<li>
<b>R4_CHOP</b> chops an R4 to a given number of binary places.
</li>
<li>
<b>R4_CSQRT</b> returns the complex square root of an R4.
</li>
<li>
<b>R4_CUBE_ROOT</b> returns the cube root of an R4.
</li>
<li>
<b>R4_DIFF</b> computes (X-Y) to a specified accuracy.
</li>
<li>
<b>R4_DIGIT</b> returns a particular decimal digit of an R4.
</li>
<li>
<b>R4_EPSILON</b> returns the R4 roundoff unit.
</li>
<li>
<b>R4_EXP</b> computes the exponential function, avoiding overflow and underflow.
</li>
<li>
<b>R4_FACTORIAL</b> computes the factorial of N.
</li>
<li>
<b>R4_FACTORIAL2</b> computes the float factorial function.
</li>
<li>
<b>R4_FLOOR</b> rounds an R4 "down" (towards -oo) to the next integer.
</li>
<li>
<b>R4_FRACTION</b> uses real arithmetic on an integer ratio.
</li>
<li>
<b>R4_FRACTIONAL</b> returns the fractional part of an R4.
</li>
<li>
<b>R4_HUGE</b> returns a "huge" R4.
</li>
<li>
<b>R4_IN_01</b> is TRUE if an R4 is in the range [0,1].
</li>
<li>
<b>R4_IS_INT</b> determines if an R4 represents an integer value.
</li>
<li>
<b>R4_LOG_10</b> returns the logarithm base 10 of the absolute value of an R4.
</li>
<li>
<b>R4_LOG_2</b> returns the logarithm base 2 of the absolute value of an R4.
</li>
<li>
<b>R4_LOG_B</b> returns the logarithm base B of an R4.
</li>
<li>
<b>R4_MANT</b> computes the "mantissa" or "fraction part" of an R4.
</li>
<li>
<b>R4_MAX</b> returns the maximum of two R4's.
</li>
<li>
<b>R4_MIN</b> returns the minimum of two R4's..
</li>
<li>
<b>R4_MOD</b> returns the remainder of R4 division.
</li>
<li>
<b>R4_MODP</b> returns the nonnegative remainder of R4 division.
</li>
<li>
<b>R4_MOP</b> returns the I-th power of -1 as an R4 value.
</li>
<li>
<b>R4_NINT</b> returns the nearest integer to an R4.
</li>
<li>
<b>R4_NORMAL</b> returns a scaled pseudonormal R4.
</li>
<li>
<b>R4_NORMAL_01</b> returns a unit pseudonormal R4.
</li>
<li>
<b>R4_PI</b> returns the value of PI as an R4.
</li>
<li>
<b>R4_POWER</b> computes an integer power of an R4.
</li>
<li>
<b>R4_POWER_FAST</b> computes the P-th power of R, for real R and integer P.
</li>
<li>
<b>R4_PYTHAG</b> computes sqrt ( A*A + B*B ), avoiding overflow and underflow.
</li>
<li>
<b>R4_REVERSE_BYTES</b> reverses the four bytes in an R4.
</li>
<li>
<b>R4_ROUND2</b> rounds an R4 in base 2.
</li>
<li>
<b>R4_ROUNDB</b> rounds an R4 in a given base.
</li>
<li>
<b>R4_ROUNDX</b> rounds an R4 in base 10.
</li>
<li>
<b>R4_SIGN</b> returns the sign of an R4.
</li>
<li>
<b>R4_SIGN_OPPOSITE</b> is TRUE if two R4's are not of the same sign.
</li>
<li>
<b>R4_SIGN_OPPOSITE_STRICT</b> is TRUE if two R4's are strictly of opposite sign.
</li>
<li>
<b>R4_SWAP</b> switches two R4's.
</li>
<li>
<b>R4_SWAP3</b> swaps three R4's.
</li>
<li>
<b>R4_TINY</b> returns a "tiny" R4.
</li>
<li>
<b>R4_TO_DHMS</b> converts an R4 day value into days, hours, minutes, seconds.
</li>
<li>
<b>R4_TO_I4</b> maps real X in [XMIN, XMAX] to integer IX in [IXMIN, IXMAX].
</li>
<li>
<b>R4_TO_R4_DISCRETE</b> maps R to RD in [RMIN, RMAX] with NR possible values.
</li>
<li>
<b>R4_UNIFORM</b> returns a scaled pseudorandom R4.
</li>
<li>
<b>R4_UNIFORM_01</b> returns a unit pseudorandom R4.
</li>
<li>
<b>R4_UNSWAP3</b> unswaps three R4's.
</li>
<li>
<b>R4_WALSH_1D</b> evaluates the Walsh function of a real scalar argument.
</li>
<li>
<b>R4MAT_BORDER_ADD</b> adds a "border" to an R4MAT.
</li>
<li>
<b>R4MAT_BORDER_CUT</b> cuts the "border" of an R4MAT.
</li>
<li>
<b>R4MAT_CHOLESKY_FACTOR</b> computes the Cholesky factor of a symmetric R4MAT.
</li>
<li>
<b>R4MAT_CHOLESKY_SOLVE</b> solves a Cholesky factored linear system A * x = b.
</li>
<li>
<b>R4MAT_CHORESKY_FACTOR</b> computes the "Choresky" factor of a symmetric R4MAT.
</li>
<li>
<b>R4MAT_COPY</b> copies one R4MAT to another.
</li>
<li>
<b>R4MAT_COPY_NEW</b> copies one R4MAT to a "new" R4MAT.
</li>
<li>
<b>R4MAT_DET</b> computes the determinant of an R4MAT.
</li>
<li>
<b>R4MAT_DET_2D</b> computes the determinant of a 2 by 2 R4MAT.
</li>
<li>
<b>R4MAT_DET_3D</b> computes the determinant of a 3 by 3 R4MAT.
</li>
<li>
<b>R4MAT_DET_4D</b> computes the determinant of a 4 by 4 R4MAT.
</li>
<li>
<b>R4MAT_DET_5D</b> computes the determinant of a 5 by 5 R4MAT.
</li>
<li>
<b>R4MAT_DIAG_ADD_SCALAR</b> adds a scalar to the diagonal of an R4MAT.
</li>
<li>
<b>R4MAT_DIAG_ADD_VECTOR</b> adds a vector to the diagonal of an R4MAT.
</li>
<li>
<b>R4MAT_DIAG_GET_VECTOR</b> gets the value of the diagonal of an R4MAT.
</li>
<li>
<b>R4MAT_DIAG_SET_SCALAR</b> sets the diagonal of an R4MAT to a scalar value.
</li>
<li>
<b>R4MAT_DIAG_SET_VECTOR</b> sets the diagonal of an R4MAT to a vector.
</li>
<li>
<b>R4MAT_EXPAND_LINEAR</b> linearly interpolates new data into an R4MAT.
</li>
<li>
<b>R4MAT_EXPAND_LINEAR2</b> expands an R4MAT by linear interpolation.
</li>
<li>
<b>R4MAT_FLIP_COLS</b> swaps the columns of an R4MAT.
</li>
<li>
<b>R4MAT_FLIP_ROWS</b> swaps the rows of an R4MAT.
</li>
<li>
<b>R4MAT_GIVENS_POST</b> computes the Givens postmultiplier rotation matrix.
</li>
<li>
<b>R4MAT_GIVENS_PRE</b> computes the Givens premultiplier rotation matrix.
</li>
<li>
<b>R4MAT_HESS</b> approximates a Hessian matrix via finite differences.
</li>
<li>
<b>R4MAT_HOUSE_AXH</b> computes A*H where H is a compact Householder matrix.
</li>
<li>
<b>R4MAT_HOUSE_AXH_NEW</b> computes A*H where H is a compact Householder matrix.
</li>
<li>
<b>R4MAT_HOUSE_FORM</b> constructs a Householder matrix from its compact form.
</li>
<li>
<b>R4MAT_HOUSE_HXA</b> computes H*A where H is a compact Householder matrix.
</li>
<li>
<b>R4MAT_HOUSE_POST</b> computes a Householder post-multiplier matrix.
</li>
<li>
<b>R4MAT_HOUSE_PRE</b> computes a Householder pre-multiplier matrix.
</li>
<li>
<b>R4MAT_IDENTITY</b> sets the square matrix A to the identity.
</li>
<li>
<b>R4MAT_IN_01</b> is TRUE if the entries of an R4MAT are in the range [0,1].
</li>
<li>
<b>R4MAT_INDICATOR_NEW</b> sets up an "indicator" R4MAT.
</li>
<li>
<b>R4MAT_INVERSE_2D</b> inverts a 2 by 2 matrix using Cramer's rule.
</li>
<li>
<b>R4MAT_INVERSE_3D</b> inverts a 3 by 3 matrix using Cramer's rule.
</li>
<li>
<b>R4MAT_INVERSE_4D</b> inverts a 4 by 4 matrix using Cramer's rule.
</li>
<li>
<b>R4MAT_JAC</b> estimates a dense jacobian matrix of the function FX.
</li>
<li>
<b>R4MAT_L_INVERSE</b> inverts a lower triangular R4MAT.
</li>
<li>
<b>R4MAT_L_PRINT</b> prints a lower triangular R4MAT.
</li>
<li>
<b>R4MAT_L_SOLVE</b> solves a lower triangular linear system.
</li>
<li>
<b>R4MAT_L1_INVERSE</b> inverts a unit lower triangular R4MAT.
</li>
<li>
<b>R4MAT_LT_SOLVE</b> solves a transposed lower triangular linear system.
</li>
<li>
<b>R4MAT_LU</b> computes the LU factorization of a rectangular R4MAT.
</li>
<li>
<b>R4MAT_MAX</b> returns the maximum entry of an R4MAT.
</li>
<li>
<b>R4MAT_MAX_INDEX</b> returns the location of the maximum entry of an R4MAT.
</li>
<li>
<b>R4MAT_MAXCOL_MINROW</b> gets the maximum column minimum row of an M by N matrix.
</li>
<li>
<b>R4MAT_MAXROW_MINCOL</b> gets the maximum row minimum column of an M by N matrix.
</li>
<li>
<b>R4MAT_MIN</b> returns the minimum entry of an R4MAT.
</li>
<li>
<b>R4MAT_MIN_INDEX</b> returns the location of the minimum entry of an R4MAT.
</li>
<li>
<b>R4MAT_MINCOL_MAXROW</b> gets the minimum column maximum row of an M by N matrix.
</li>
<li>
<b>R4MAT_MINROW_MAXCOL</b> gets the minimum row maximum column of an M by N matrix.
</li>
<li>
<b>R4MAT_MM</b> multiplies two matrices.
</li>
<li>
<b>R4MAT_MM_NEW</b> multiplies two matrices.
</li>
<li>
<b>R4MAT_MTV</b> multiplies a transposed matrix times a vector.
</li>
<li>
<b>R4MAT_MTXV</b> multiplies a transposed matrix times a vector.
</li>
<li>
<b>R4MAT_MV</b> multiplies a matrix times a vector.
</li>
<li>
<b>R4MAT_MXM</b> multiplies two matrices.
</li>
<li>
<b>R4MAT_MXM_NEW</b> multiplies two matrices.
</li>
<li>
<b>R4MAT_MXV</b> multiplies a matrix times a vector.
</li>
<li>
<b>R4MAT_NINT</b> rounds the entries of an R4MAT.
</li>
<li>
<b>R4MAT_NORM_EIS</b> returns the EISPACK norm of an R4MAT.
</li>
<li>
<b>R4MAT_NORM_FRO</b> returns the Frobenius norm of an R4MAT.
</li>
<li>
<b>R4MAT_NULLSPACE</b> computes the nullspace of a matrix.
</li>
<li>
<b>R4MAT_NULLSPACE_SIZE</b> computes the size of the nullspace of a matrix.
</li>
<li>
<b>R4MAT_ORTH_UNIFORM_NEW</b> returns a random orthogonal matrix.
</li>
<li>
<b>R4MAT_PLOT</b> "plots" an R4MAT.
</li>
<li>
<b>R4MAT_PLOT_SYMBOL</b> returns a symbol for entries of an R4MAT.
</li>
<li>
<b>R4MAT_POLY_CHAR</b> computes the characteristic polynomial of an R4MAT.
</li>
<li>
<b>R4MAT_POWER</b> computes a nonnegative power of an R4MAT.
</li>
<li>
<b>R4MAT_POWER_METHOD</b> applies the power method to a matrix.
</li>
<li>
<b>R4MAT_PRINT</b> prints an R4MAT.
</li>
<li>
<b>R4MAT_PRINT_SOME</b> prints some of an R4MAT.
</li>
<li>
<b>R4MAT_REF</b> computes the row echelon form of a matrix.
</li>
<li>
<b>R4MAT_RREF</b> computes the reduced row echelon form of a matrix.
</li>
<li>
<b>R4MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R4MAT_SOLVE_2D</b> solves a 2 by 2 linear system using Cramer's rule.
</li>
<li>
<b>R4MAT_SOLVE_3D</b> solves a 3 by 3 linear system using Cramer's rule.
</li>
<li>
<b>R4MAT_SOLVE2</b> computes the solution of an N by N linear system.
</li>
<li>
<b>R4MAT_SYMM_EIGEN</b> returns a symmetric matrix with given eigensystem.
</li>
<li>
<b>R4MAT_SYMM_JACOBI</b> applies Jacobi eigenvalue iteration to a symmetric matrix.
</li>
<li>
<b>R4MAT_TO_R4PLU</b> factors a general matrix.
</li>
<li>
<b>R4MAT_TRACE</b> computes the trace of an R4MAT.
</li>
<li>
<b>R4MAT_TRANSPOSE</b> returns the transpose of an R4MAT.
</li>
<li>
<b>R4MAT_TRANSPOSE_IN_PLACE</b> transposes a square R4MAT in place.
</li>
<li>
<b>R4MAT_TRANSPOSE_PRINT</b> prints an R4MAT, transposed.
</li>
<li>
<b>R4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R4MAT, transposed.
</li>
<li>
<b>R4MAT_U_INVERSE</b> inverts an upper triangular R4MAT.
</li>
<li>
<b>R4MAT_U1_INVERSE</b> inverts a unit upper triangular R4MAT.
</li>
<li>
<b>R4MAT_UNIFORM_01</b> returns a unit pseudorandom R4MAT.
</li>
<li>
<b>R4MAT_UNIFORM_NEW</b> returns a scaled pseudorandom R4MAT.
</li>
<li>
<b>R4MAT_UNIFORM_01_NEW</b> returns a unit pseudorandom R4MAT.
</li>
<li>
<b>R4MAT_VAND2</b> returns the N by N row Vandermonde matrix A.
</li>
<li>
<b>R4MAT_ZERO</b> zeroes an R4MAT.
</li>
<li>
<b>R4MAT_ZERO_NEW</b> returns a new zeroed R4MAT.
</li>
<li>
<b>R4ROW_SWAP</b> swaps two rows of an R4ROW.
</li>
<li>
<b>R4VEC_AMAX</b> returns the maximum absolute value in an R4VEC.
</li>
<li>
<b>R4VEC_AMAX_INDEX</b> returns the index of the maximum absolute value in an R4VEC.
</li>
<li>
<b>R4VEC_AMIN</b> returns the minimum absolute value in an R4VEC.
</li>
<li>
<b>R4VEC_AMIN_INDEX</b> returns the index of the minimum absolute value in an R4VEC.
</li>
<li>
<b>R4VEC_COPY</b> copies an R4VEC.
</li>
<li>
<b>R4VEC_COPY_NEW</b> copies an R4VEC to a "new" R4VEC.
</li>
<li>
<b>R4VEC_HOUSE_COLUMN</b> defines a Householder premultiplier that "packs" a column.
</li>
<li>
<b>R4VEC_IS_INT</b> is TRUE if an R4VEC is integral.
</li>
<li>
<b>R4VEC_MAX</b> returns the value of the maximum element in an R4VEC.
</li>
<li>
<b>R4VEC_MEAN</b> returns the mean of an R4VEC.
</li>
<li>
<b>R4VEC_MIN</b> returns the value of the minimum element in an R4VEC.
</li>
<li>
<b>R4VEC_NORM</b> returns the L2 norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORM_AFFINE</b> returns the affine L2 norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORM_L1</b> returns the L1 norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORM_L2</b> returns the L2 norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORM_LI</b> returns the L-oo norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORM_LP</b> returns the LP norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORMAL_01</b> returns a unit pseudonormal R4VEC.
</li>
<li>
<b>R4VEC_NORMALIZE</b> normalizes an R4VEC.
</li>
<li>
<b>R4VEC_NORMALIZE_L1</b> normalizes an R4VEC to have unit sum.
</li>
<li>
<b>R4VEC_NORMSQ</b> returns the squared L2 norm of an R4VEC.
</li>
<li>
<b>R4VEC_NORMSQ_AFFINE</b> returns the squared affine L2 norm of an R4VEC.
</li>
<li>
<b>R4VEC_PERMUTE_CYCLIC</b> performs a cyclic permutation of an R4VEC.
</li>
<li>
<b>R4VEC_PRINT_PART</b> prints "part" of an R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM</b> returns a scaled pseudorandom R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_NEW</b> returns a scaled pseudorandom R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_01</b> returns a unit unit pseudorandom R4VEC.
</li>
<li>
<b>R4VEC_UNIFORM_01_NEW</b> returns a unit unit pseudorandom R4VEC.
</li>
<li>
<b>R4VEC_VARIANCE</b> returns the variance of an R4VEC.
</li>
<li>
<b>R4VEC_ZERO</b> zeroes an R4VEC.
</li>
<li>
<b>R4VEC_ZERO_NEW</b> creates and zeroes an R4VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 20 May 2011.
</i>
<!-- John Burkardt -->
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