TEST_MAT
Test Matrices

TEST_MAT is a FORTRAN77 library which defines test matrices for which some of the determinant, eigenvalues, inverse, null vectors, P*L*U factorization or linear system solution are already known, including the Vandermonde and Wathen matrix.

A wide range of matrix dimensions, forms and properties are available. These matrices may be useful in testing an algorithm for correctness on a variety of problems.

Many of the matrices can be rectangular, with the user specifying the number of rows and columns. Almost all the matrices can be made of arbitrary size, with the user specifying the dimension.

Many different matrix zero structures are available, including diagonal, bidiagonal, tridiagonal, pentadiagonal, banded, upper and lower triangular, and Hessenberg.

Many different matrix symmetry patterns are available, including symmetric, antisymmetric, persymmetric, circulant, Toeplitz, and Hankel.

Matrices are available with known inverses, condition numbers, determinants, rank, eigenvalues, and characteristic polynomials. Other matrix properties include positive definiteness, positivity, zero/one, and adjacency matrices.

Many of the matrices come from a MATLAB M file collection developed by Nicholas Higham, Department of Mathematics, University of Manchester.

An earlier version of the collection is available, again as MATLAB M files, in ACM TOMS Algorithm 694, in the TOMS directory of the NETLIB web site.

Many of these matrices, and many other matrices, are available at http://math.nist.gov, the Matrix Market web site.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TEST_MAT is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CG, a FORTRAN77 library which implements a simple version of the conjugate gradient (CG) method for solving a system of linear equations of the form A*x=b, suitable for situations in which the matrix A is positive definite (only real, positive eigenvalues) and symmetric.

EISPACK, a FORTRAN77 library which carries out eigenvalue computations;

EXPOKIT, a FORTRAN77 library which solves various forms of the matrix exponential problem, by Roger Sidje.

JACOBI_EIGENVALUE, a FORTRAN77library which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.

LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.

LINPACK, a FORTRAN77 library which factors and solves systems of linear equations in a variety of formats and arithmetic types.

TEST_EIGEN, a FORTRAN77 library which implements test matrices for eigenvalue analysis.

WATHEN, a FORTRAN77 library which compares storage schemes (full, banded, sparse triplet) and solution strategies (Linpack full, Linpack banded, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

Source Code:

• test_mat.f, the source code;
• test_mat.sh, commands to compile the source code;

Examples and Tests:

• test_mat_prb.f, the calling program;
• test_mat_prb.sh, commands to compile, link and run the calling program;
• test_mat_prb_output.txt, the output file.

List of Routines:

• A123 returns the A123 matrix.
• A123_DETERMINANT returns the determinant of the A123 matrix.
• A123_EIGEN_LEFT returns left eigenvectors of the A123 matrix.
• A123_EIGEN_RIGHT returns right eigenvectors of the A123 matrix.
• A123_EIGENVALUES returns the eigenvalues of the A123 matrix.
• A123_INVERSE returns the pseudo-inverse of the A123 matrix.
• A123_NULL_LEFT returns a left null vector of the A123 matrix.
• A123_NULL_RIGHT returns a right null vector of the A123 matrix.
• A123_PLU returns the PLU factors of the A123 matrix.
• A123_QR returns the QR factors of the A123 matrix.
• A123_RHS returns the A123 right hand side.
• A123_SOLUTION returns the A123_SOLUTION
• A123_SVD returns the SVD factors of the A123 matrix.
• AEGERTER returns the AEGERTER matrix.
• AEGERTER_CONDITION returns the L1 condition of the AEGERTER matrix.
• AEGERTER_DETERMINANT returns the determinant of the AEGERTER matrix.
• AEGERTER_EIGENVALUES returns the eigenvalues of the AEGERTER matrix.
• AEGERTER_INVERSE returns the inverse of the AEGERTER matrix.
• ANTICIRCULANT returns an ANTICIRCULANT matrix.
• ANTICIRCULANT_DETERMINANT returns the determinant of the ANTICIRCULANT matrix.
• ANTIHADAMARD returns an approximate ANTIHADAMARD matrix.
• ANTIHADAMARD_DETERMINANT returns the determinant of the ANTIHADAMARD matrix.
• ANTISYMM_RANDOM returns an ANTISYMMETRIC matrix.
• ARCHIMEDES returns the ARCHIMEDES matrix.
• ARCHIMEDES_NULL_RIGHT returns a right null vector for the ARCHIMEDES matrix.
• BAB returns the BAB matrix.
• BAB_CONDITION returns the L1 condition of the BAB matrix.
• BAB_DETERMINANT returns the determinant of the BAB matrix.
• BAB_EIGEN_RIGHT returns right eigenvectors of the BAB matrix.
• BAB_EIGENVALUES returns the eigenvalues of the BAB matrix.
• BAB_INVERSE returns the inverse of the BAB matrix.
• BALANC balances a real matrix before eigenvalue calculations.
• BAUER returns the BAUER matrix.
• BAUER_CONDITION returns the L1 condition of the BAUER matrix.
• BAUER_DETERMINANT returns the determinant of the BAUER matrix.
• BAUER_INVERSE returns the inverse of the BAUER matrix.
• BERNSTEIN returns the BERNSTEIN matrix.
• BERNSTEIN_DETERMINANT returns the determinant of the BERNSTEIN matrix.
• BERNSTEIN_INVERSE returns the inverse BERNSTEIN matrix.
• BIMARKOV_RANDOM returns a BIMARKOV matrix.
• BIS returns the BIS matrix.
• BIS_CONDITION returns the L1 condition of the BIS matrix.
• BIS_DETERMINANT returns the determinant of the BIS matrix.
• BIS_EIGENVALUES returns the eigenvalues of the BIS matrix.
• BIS_INVERSE returns the inverse of the BIS matrix.
• BIW returns the BIW matrix.
• BIW_CONDITION computes the L1 condition of the BIW matrix.
• BIW_DETERMINANT computes the determinant of the BIW matrix.
• BIW_INVERSE returns the inverse of the BIW matrix.
• BODEWIG returns the BODEWIG matrix.
• BODEWIG_CONDITION returns the L1 condition of the BODEWIG matrix.
• BODEWIG_DETERMINANT returns the determinant of the BODEWIG matrix.
• BODEWIG_EIGENVALUES returns the eigenvalues of the BODEWIG matrix.
• BODEWIG_INVERSE returns the inverse of the BODEWIG matrix.
• BODEWIG_PLU returns the PLU factors of the BODEWIG matrix.
• BODEWIG_RHS returns the BODEWIG right hand side.
• BODEWIG_EIGEN_RIGHT returns right eigenvectors of the BODEWIG matrix.
• BODEWIG_SOLUTION returns the BODEWIG_SOLUTION
• BOOTHROYD returns the BOOTHROYD matrix.
• BOOTHROYD_CONDITION returns the L1 condition of the BOOTHROYD matrix.
• BOOTHROYD_DETERMINANT returns the determinant of the BOOTHROYD matrix.
• BOOTHROYD_INVERSE returns the inverse of the BOOTHROYD matrix.
• BORDERBAND returns the BORDERBAND matrix.
• BORDERBAND_DETERMINANT returns the determinant of the BORDERBAND matrix.
• BORDERBAND_INVERSE returns the inverse of the BORDERBAND matrix.
• BORDERBAND_PLU returns the PLU factors of the BORDERBAND matrix.
• BVEC_NEXT_GRLEX generates the next binary vector in GRLEX order.
• C8_I returns the value of the imaginary unit, i.
• C8_LE_L2 := X <= Y for complex values, and the L2 norm.
• C8_NORMAL_01 returns a unit pseudonormal C8.
• C8_ONE returns the value of complex 1.
• C8_SWAP swaps two C8's.
• C8_UNIFORM_01 returns a unit pseudorandom C8.
• C8_ZERO returns the value of complex 0.
• C8MAT_HOUSE constructs a complex Householder elementary reflector matrix.
• C8MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.
• C8MAT_HOUSE_FORM constructs a Householder matrix from its compact form.
• C8MAT_IDENTITY sets a C8MAT to the identity.
• C8MAT_PRINT prints a C8MAT.
• C8MAT_PRINT_SOME prints some of a C8MAT.
• C8MAT_UNIFORM_01 returns a unit pseudorandom C8MAT.
• C8VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
• C8VEC_NORM_L2 returns the L2 norm of a C8VEC.
• C8VEC_NORM_SQUARED returns the square of the L2 norm of a C8VEC.
• C8VEC_PRINT prints a C8VEC, with an optional title.
• C8VEC_PRINT_SOME prints some of a C8VEC.
• C8VEC_SORT_A_L2 ascending sorts a C8VEC by L2 norm.
• C8VEC_UNIFORM_01 returns a unit pseudorandom C8VEC.
• C8VEC_UNITY returns the N roots of unity.
• CARRY returns the CARRY matrix.
• CARRY_DETERMINANT returns the determinant of the CARRY matrix.
• CARRY_EIGEN_LEFT returns the left eigenvectors of the CARRY matrix.
• CARRY_EIGEN_RIGHT returns right eigenvectors of the CARRY matrix.
• CARRY_EIGENVALUES returns the eigenvalues of the CARRY matrix.
• CARRY_INVERSE returns the inverse of the CARRY matrix.
• CAUCHY returns the CAUCHY matrix.
• CAUCHY_DETERMINANT returns the determinant of the CAUCHY matrix.
• CAUCHY_INVERSE returns the inverse of the CAUCHY matrix.
• CHEBY_DIFF1 returns the CHEBY_DIFF1 matrix.
• CHEBY_DIFF1_NULL_LEFT returns a left null vector of the CHEBY_DIFF1 matrix.
• CHEBY_DIFF1_NULL_RIGHT returns a right null vector of the CHEBY_DIFF1 matrix.
• CHEBY_T returns the CHEBY_T matrix.
• CHEBY_T_DETERMINANT returns the determinant of the CHEBY_T matrix.
• CHEBY_T_EIGENVALUES returns the eigenvalues of the CHEBY_T matrix.
• CHEBY_T_INVERSE returns the inverse of the CHEBY_T matrix.
• CHEBY_U returns the CHEBY_U matrix.
• CHEBY_U_DETERMINANT returns the determinant of the CHEBY_U matrix.
• CHEBY_U_EIGENVALUES returns the eigenvalues of the CHEBY_U matrix.
• CHEBY_U_INVERSE returns the inverse of the CHEBY_U matrix.
• CHEBY_U_POLYNOMIAL evaluates the Chebyshev polynomials of the second kind.
• CHEBY_VAN1 returns the CHEBY_VAN1 matrix.
• CHEBY_VAN2 returns the CHEBY_VAN2 matrix.
• CHEBY_VAN2_DETERMINANT returns the determinant of the CHEBY_VAN2 matrix.
• CHEBY_VAN2_INVERSE returns the inverse of the CHEBY_VAN2 matrix.
• CHEBY_VAN3 returns the CHEBY_VAN3 matrix.
• CHEBY_VAN3_DETERMINANT returns the determinant of the CHEBY_VAN3 matrix.
• CHEBY_VAN3_INVERSE returns the inverse of the CHEBY_VAN3 matrix.
• CHOW returns the CHOW matrix.
• CHOW_DETERMINANT returns the determinant of the CHOW matrix.
• CHOW_EIGENVALUES returns the eigenvalues of the CHOW matrix.
• CHOW_INVERSE returns the inverse of the CHOW matrix.
• CHOW_EIGEN_LEFT returns the left eigenvectors for the CHOW matrix.
• CHOW_EIGEN_RIGHT returns right eigenvectors for the CHOW matrix.
• CIRCULANT returns the CIRCULANT matrix.
• CIRCULANT_DETERMINANT returns the determinant of the CIRCULANT matrix.
• CIRCULANT_EIGENVALUES returns the eigenvalues of the CIRCULANT matrix.
• CIRCULANT2 returns the CIRCULANT2 matrix.
• CIRCULANT2_DETERMINANT returns the determinant of the CIRCULANT2 matrix.
• CIRCULANT2_EIGENVALUES returns the eigenvalues of the CIRCULANT2 matrix.
• CIRCULANT2_INVERSE returns the inverse of the CIRCULANT2 matrix.
• CLEMENT1 returns the CLEMENT1 matrix.
• CLEMENT1_DETERMINANT returns the determinant of the CLEMENT1 matrix.
• CLEMENT1_EIGENVALUES returns the eigenvalues of the CLEMENT1 matrix.
• CLEMENT1_INVERSE returns the inverse of the CLEMENT1 matrix.
• CLEMENT2 returns the CLEMENT2 matrix.
• CLEMENT2_DETERMINANT returns the determinant of the CLEMENT2 matrix.
• CLEMENT2_INVERSE returns the inverse of the CLEMENT2 matrix.
• COLLEAGUE returns the COLLEAGUE matrix.
• COMBIN returns the COMBIN matrix.
• COMBIN_CONDITION returns the L1 condition of the COMBIN matrix.
• COMBIN_DETERMINANT returns the determinant of the COMBIN matrix.
• COMBIN_EIGENVALUES returns the eigenvalues of the COMBIN matrix.
• COMBIN_INVERSE returns the inverse of the COMBIN matrix.
• COMBIN_EIGEN_RIGHT returns right eigenvectors of the COMBIN matrix.
• COMPANION returns the COMPANION matrix.
• COMPANION_CONDITION returns the L1 condition of the COMPANION matrix.
• COMPANION_DETERMINANT returns the determinant of the COMPANION matrix.
• COMPANION_INVERSE returns the inverse of the COMPANION matrix.
• COMPLETE_SYMMETRIC_POLY evaluates a complete symmetric polynomial.
• COMPLEX3 returns the COMPLEX3 matrix.
• COMPLEX3_INVERSE returns the inverse of the COMPLEX3 matrix.
• COMPLEX_I returns the COMPLEX_I matrix.
• COMPLEX_I_DETERMINANT returns the determinant of the COMPLEX_I matrix.
• COMPLEX_I_INVERSE returns the inverse of the COMPLEX_I matrix.
• CONEX1 returns the CONEX1 matrix.
• CONEX1_CONDITION returns the L1 condition of the CONEX1 matrix.
• CONEX1_DETERMINANT returns the determinant of the CONEX1 matrix.
• CONEX1_INVERSE returns the inverse of the CONEX1 matrix.
• CONEX2 returns the CONEX2 matrix.
• CONEX2_CONDITION returns the L1 condition of the CONEX2 matrix.
• CONEX2_DETERMINANT returns the determinant of the CONEX2 matrix.
• CONEX2_INVERSE returns the inverse of the CONEX2 matrix.
• CONEX3 returns the CONEX3 matrix.
• CONEX3_CONDITION returns the L1 condition of the CONEX3 matrix.
• CONEX3_DETERMINANT returns the determinant of the CONEX3 matrix.
• CONEX3_INVERSE returns the inverse of the CONEX3 matrix.
• CONEX4 returns the CONEX4 matrix.
• CONEX4_CONDITION returns the L1 condition of the CONEX4 matrix.
• CONEX4_DETERMINANT returns the determinant of the CONEX4 matrix.
• CONEX4_INVERSE returns the inverse CONEX4 matrix.
• CONFERENCE returns the CONFERENCE matrix.
• CONFERENCE_DETERMINANT returns the determinant of the CONFERENCE matrix.
• CONFERENCE_INVERSE returns the inverse of the CONFERENCE matrix.
• COVAR returns the covariance matrix for a square nonsingular matrix.
• COVAR2 returns the covariance matrix for a rectangular matrix.
• CREATION returns the CREATION matrix.
• CREATION_DETERMINANT returns the determinant of the CREATION matrix.
• CREATION_EIGENVALUES returns the eigenvalues of the CREATION matrix.
• CREATION_NULL_LEFT returns a left null vector of the CREATION matrix.
• CREATION_NULL_RIGHT returns a right null vector of the CREATION matrix.
• CYCOL_RANDOM returns the CYCOL_RANDOM matrix.
• DAUB2 returns the DAUB2 matrix.
• DAUB2_CONDITION returns the L1 condition of the DAUB2 matrix.
• DAUB2_DETERMINANT returns the determinant of the DAUB2 matrix.
• DAUB2_INVERSE returns the inverse of the DAUB2 matrix.
• DAUB4 returns the DAUB4 matrix.
• DAUB4_CONDITION returns the L1 condition of the DAUB4 matrix.
• DAUB4_DETERMINANT returns the determinant of the DAUB4 matrix.
• DAUB4_INVERSE returns the inverse of the DAUB4 matrix.
• DAUB6 returns the DAUB6 matrix.
• DAUB6_CONDITION returns the L1 condition of the DAUB6 matrix.
• DAUB6_DETERMINANT returns the determinant of the DAUB6 matrix.
• DAUB6_INVERSE returns the inverse of the DAUB6 matrix.
• DAUB8 returns the DAUB8 matrix.
• DAUB8_CONDITION returns the L1 condition of the DAUB8 matrix.
• DAUB8_DETERMINANT returns the determinant of the DAUB8 matrix.
• DAUB8_INVERSE returns the inverse of the DAUB8 matrix.
• DAUB10 returns the DAUB10 matrix.
• DAUB10_CONDITION returns the L1 condition of the DAUB10 matrix.
• DAUB10_DETERMINANT returns the determinant of the DAUB10 matrix.
• DAUB10_INVERSE returns the inverse of the DAUB10 matrix.
• DAUB12 returns the DAUB12 matrix.
• DAUB12_CONDITION returns the L1 condition of the DAUB12 matrix.
• DAUB12_DETERMINANT returns the determinant of the DAUB12 matrix.
• DAUB12_INVERSE returns the inverse of the DAUB12 matrix.
• DIAGONAL returns the DIAGONAL matrix.
• DIAGONAL_CONDITION returns the L1 condition of the DIAGONAL matrix.
• DIAGONAL_DETERMINANT returns the determinant of the DIAGONAL matrix.
• DIAGONAL_EIGEN_LEFT returns left eigenvectors of the DIAGONAL matrix.
• DIAGONAL_EIGEN_RIGHT returns right eigenvectors of the DIAGONAL matrix.
• DIAGONAL_EIGENVALUES returns the eigenvalues of the DIAGONAL matrix.
• DIAGONAL_INVERSE returns the inverse of the DIAGONAL matrix.
• DIF1 returns the DIF1 matrix.
• DIF1_DETERMINANT returns the determinant of the DIF1 matrix.
• DIF1_EIGENVALUES returns the eigenvalues of the DIF1 matrix.
• DIF1_INVERSE returns the inverse of the DIF1 matrix.
• DIF1_NULL_LEFT returns a left null vector of the DIF1 matrix.
• DIF1_NULL_RIGHT returns a right null vector of the DIF1 matrix.
• DIF1CYCLIC returns the DIF1CYCLIC matrix.
• DIF1CYCLIC_DETERMINANT: determinant of the DIF1CYCLIC matrix.
• DIF1CYCLIC_NULL_LEFT returns a left null vector of the DIF1CYCLIC matrix.
• DIF1CYCLIC_NULL_RIGHT returns a right null vector of the DIF1CYCLIC matrix.
• DIF2 returns the DIF2 matrix.
• DIF2_CONDITION returns the L1 condition of the DIF2 matrix.
• DIF2_DETERMINANT returns the determinant of the DIF2 matrix.
• DIF2_EIGEN_RIGHT returns right eigenvectors of the DIF2 matrix.
• DIF2_EIGENVALUES returns the eigenvalues of the DIF2 matrix.
• DIF2_INVERSE returns the inverse of the DIF2 matrix.
• DIF2_LLT returns the Cholesky factor of the DIF2 matrix.
• DIF2_PLU returns the PLU factors of the DIF2 matrix.
• DIF2_RHS returns the DIF2 right hand side.
• DIF2_SOLUTION returns the DIF2 solution matrix.
• DIF2CYCLIC returns the DIF2CYCLIC matrix.
• DIF2CYCLIC_DETERMINANT: determinant of the DIF2CYCLIC matrix.
• DIF2CYCLIC_NULL_LEFT returns a left null vector of the DIF2CYCLIC matrix.
• DIF2CYCLIC_NULL_RIGHT returns a right null vector of the DIF2CYCLIC matrix.
• DORR returns the DORR matrix.
• DORR_DETERMINANT computes the determinant of the DORR matrix.
• DORR_INVERSE returns the inverse of the DORR matrix.
• DOWNSHIFT returns the DOWNSHIFT matrix.
• DOWNSHIFT_CONDITION returns the L1 condition of the DOWNSHIFT matrix.
• DOWNSHIFT_DETERMINANT returns the determinant of the DOWNSHIFT matrix.
• DOWNSHIFT_EIGENVALUES returns the eigenvalues of the DOWNSHIFT matrix.
• DOWNSHIFT_INVERSE returns the inverse of the DOWNSHIFT matrix.
• DRMAC returns the DRMAC matrix.
• DRMAC_INVERSE returns the inverse of the DRMAC matrix.
• EBERLEIN returns the EBERLEIN matrix.
• EBERLEIN_DETERMINANT returns the determinant of the EBERLEIN matrix.
• EBERLEIN_EIGENVALUES returns the eigenvalues of the EBERLEIN matrix.
• EBERLEIN_NULL_RIGHT returns a left null vector of the EBERLEIN matrix.
• ELMHES transforms a real general matrix to upper Hessenberg form.
• EULERIAN returns the EULERIAN matrix.
• EULERIAN_DETERMINANT returns the determinant of the EULERIAN matrix.
• EULERIAN_INVERSE computes the inverse of the EULERIAN matrix.
• EXCHANGE returns the EXCHANGE matrix.
• EXCHANGE_CONDITION returns the L1 condition of the EXCHANGE matrix.
• EXCHANGE_DETERMINANT returns the determinant of the EXCHANGE matrix.
• EXCHANGE_EIGENVALUES returns the eigenvalues of the EXCHANGE matrix.
• EXCHANGE_INVERSE returns the inverse of the EXCHANGE matrix.
• EXCHANGE_EIGEN_RIGHT returns right eigenvectors of the EXCHANGE matrix.
• FIBONACCI1 returns the FIBONACCI1 matrix.
• FIBONACCI1_DETERMINANT returns the determinant of the FIBONACCI1 matrix.
• FIBONACCI1_NULL_LEFT returns a left null vector of the FIBONACCI1 matrix.
• FIBONACCI1_NULL_RIGHT returns a right null vector of the FIBONACCI1 matrix.
• FIBONACCI2 returns the FIBONACCI2 matrix.
• FIBONACCI2_CONDITION returns the L1 condition of the FIBONACCI2 matrix.
• FIBONACCI2_DETERMINANT returns the determinant of the FIBONACCI2 matrix.
• FIBONACCI2_EIGENVALUES returns the eigenvalues of the FIBONACCI2 matrix.
• FIBONACCI2_INVERSE returns the inverse of the FIBONACCI2 matrix.
• FIBONACCI3 returns the FIBONACCI3 matrix.
• FIBONACCI3_DETERMINANT returns the determinant of the FIBONACCI3 matrix.
• FIBONACCI3_EIGENVALUES returns the eigenvalues of the FIBONACCI3 matrix.
• FIBONACCI3_INVERSE returns the inverse of the FIBONACCI3 matrix.
• FIEDLER returns the FIEDLER matrix.
• FIEDLER_DETERMINANT returns the determinant of the FIEDLER matrix.
• FIEDLER_INVERSE returns the inverse of the FIEDLER matrix.
• FORSYTHE returns the FORSYTHE matrix.
• FORSYTHE_DETERMINANT returns the determinant of the FORSYTHE matrix.
• FORSYTHE_EIGENVALUES returns the eigenvalues of the FORSYTHE matrix.
• FORSYTHE_INVERSE returns the inverse of the Forsythe matrix.
• FOURIER returns the FOURIER matrix.
• FOURIER_DETERMINANT returns the determinant of the FOURIER matrix.
• FOURIER_EIGENVALUES returns the eigenvalues of the FOURIER matrix.
• FOURIER_INVERSE returns the inverse of the FOURIER matrix.
• FOURIER_COSINE returns the FOURIER_COSINE matrix.
• FOURIER_COSINE_DETERMINANT: determinant of the FOURIER_COSINE matrix.
• FOURIER_COSINE_INVERSE returns the inverse of the FOURIER_COSINE matrix.
• FOURIER_SINE returns the FOURIER_SINE matrix.
• FOURIER_SINE_DETERMINANT returns the determinant of the FOURIER_SINE matrix.
• FOURIER_SINE_INVERSE returns the inverse of the FOURIER_SINE matrix.
• FRANK returns the FRANK matrix.
• FRANK_DETERMINANT returns the determinant of the FRANK matrix.
• FRANK_EIGENVALUES returns the eigenvalues of the FRANK matrix.
• FRANK_INVERSE returns the inverse of the FRANK matrix.
• FRANK_RHS returns the FRANK right hand side.
• FRANK_SOLUTION returns the FRANK solution matrix.
• GEAR returns the GEAR matrix.
• GEAR_DETERMINANT returns the determinant of the GEAR matrix.
• GEAR_EIGENVALUES returns the eigenvalues of the GEAR matrix.
• GFPP returns the GFPP matrix.
• GFPP_CONDITION returns the L1 condition of the GFPP matrix.
• GFPP_DETERMINANT returns the determinant of the GFPP matrix.
• GFPP_INVERSE returns the inverse of the GFPP matrix.
• GFPP_PLU returns the PLU factorization of the GFPP matrix.
• GIVENS returns the GIVENS matrix.
• GIVENS_CONDITION returns the L1 condition of the GIVENS matrix.
• GIVENS_DETERMINANT returns the determinant of the GIVENS matrix.
• GIVENS_EIGENVALUES returns the eigenvalues of the GIVENS matrix.
• GIVENS_INVERSE returns the inverse of the GIVENS matrix.
• GIVENS_LLT returns the Cholesky factor of the GIVENS matrix.
• GIVENS_PLU returns the PLU factors of the GIVENS matrix.
• GK316 returns the GK316 matrix.
• GK316_DETERMINANT returns the determinant of the GK316 matrix.
• GK316_EIGENVALUES returns the eigenvalues of the GK316 matrix.
• GK316_INVERSE returns the inverse of the GK316 matrix.
• GK323 returns the GK323 matrix.
• GK323_DETERMINANT returns the determinant of the GK323 matrix.
• GK323_INVERSE returns the inverse of the GK323 matrix.
• GK324 returns the GK324 matrix.
• GK324_DETERMINANT returns the determinant of the GK324 matrix.
• GK324_INVERSE returns the inverse of the GK324 matrix.
• GRCAR returns the GRCAR matrix.
• HADAMARD returns the HADAMARD matrix.
• HAMMING computes the HAMMING matrix.
• HAMMING_NULL_RIGHT returns a right null vector of the HAMMING matrix.
• HANKEL returns the HANKEL matrix.
• HANKEL_N returns the HANKEL_N matrix.
• HANKEL_N_CONDITION returns the L1 condition of the HANKEL_N matrix.
• HANKEL_N_DETERMINANT returns the determinant of the HANKEL_N matrix.
• HANKEL_N_INVERSE returns the inverse of the HANKEL_N matrix.
• HANOWA returns the HANOWA matrix.
• HANOWA_DETERMINANT returns the determinant of the HANOWA matrix.
• HANOWA_EIGENVALUES returns the eigenvalues of the HANOWA matrix.
• HANOWA_INVERSE returns the inverse of the Hanowa matrix.
• HARMAN returns the HARMAN matrix.
• HARMAN_CONDITION returns the L1 condition of the HARMAN matrix.
• HARMAN_DETERMINANT returns the determinant of the HARMAN matrix.
• HARMAN_EIGENVALUES returns the eigenvalues of the HARMAN matrix.
• HARMAN_INVERSE returns the inverse of the HARMAN matrix.
• HARTLEY returns the HARTLEY matrix.
• HARTLEY_CONDITION returns the L1 condition of the HARTLEY matrix.
• HARTLEY_DETERMINANT returns the determinant of the HARTLEY matrix.
• HARTLEY_EIGENVALUES returns the eigenvalues of the HARTLEY matrix.
• HARTLEY_INVERSE returns the inverse of the HARTLEY matrix.
• HELMERT returns the HELMERT matrix.
• HELMERT_DETERMINANT returns the determinant of the HELMERT matrix.
• HELMERT_INVERSE returns the inverse of the HELMERT matrix.
• HELMERT2 returns the HELMERT2 matrix.
• HELMERT2_INVERSE returns the inverse of the HELMERT2 matrix.
• HERMITE returns the HERMITE matrix.
• HERMITE_DETERMINANT returns the determinant of the HERMITE matrix.
• HERMITE_INVERSE returns the inverse of the HERMITE matrix.
• HERMITE_ROOTS computes the roots of a Hermite polynomial.
• HERNDON returns the HERNDON matrix.
• HERNDON_DETERMINANT returns the determinant of the HERNDON matrix.
• HERNDON_EIGENVALUES returns the eigenvalues of the HERNDON matrix.
• HERNDON_INVERSE returns the inverse of the HERNDON matrix.
• HILBERT returns the HILBERT matrix.
• HILBERT_DETERMINANT returns the determinant of the HILBERT matrix.
• HILBERT_INVERSE returns the inverse of the Hilbert matrix.
• HOFFMAN computes the HOFFMAN matrix.
• HOFFMAN_RHS returns the HOFFMAN right hand side.
• HOFFMAN_OPTIMUM returns the HOFFMAN optimum solution.
• HOUSEHOLDER constructs a HOUSEHOLDER matrix.
• HOUSEHOLDER_DETERMINANT returns the determinant of a HOUSEHOLDER matrix.
• HOUSEHOLDER_EIGENVALUES returns the eigenvalues of a HOUSEHOLDER matrix.
• HOUSEHOLDER_INVERSE returns the inverse of a HOUSEHOLDER matrix.
• HQR computes all eigenvalues of a real upper Hessenberg matrix.
• I4_FACTOR factors an I4 into prime factors.
• I4_IS_EVEN returns TRUE if an I4 is even.
• I4_IS_ODD returns TRUE if an I4 is odd.
• I4_IS_PRIME reports whether an I4 is prime.
• I4_LOG_10 returns the integer part of the logarithm base 10 of ABS(X).
• I4_MODP returns the nonnegative remainder of integer division.
• I4_RISE computes the rising factorial function [X]^N.
• I4_SIGN evaluates the sign of an I4.
• I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
• I4_WRAP forces an I4 to lie between given limits by wrapping.
• I4MAT_PRINT prints an I4MAT.
• I4MAT_PRINT_SOME prints some of an I4MAT.
• I4VEC_INDEX returns the location of the first occurrence of a given value.
• I4VEC_INDICATOR sets an I4VEC to the indicator vector.
• I4VEC_MIN computes the minimum element of an I4VEC.
• I4VEC_PRINT prints an I4VEC.
• IDEM_RANDOM returns the IDEM_RANDOM matrix.
• IDEM_RANDOM_DETERMINANT returns the determinant of the IDEM_RANDOM matrix.
• IDEM_RANDOM_EIGENVALUES returns the eigenvalues of the IDEM_RANDOM matrix.
• IDEM_RANDOM_EIGEN_RIGHT returns right eigenvectors of the IDEM_RANDOM matrix.
• IDENTITY returns the IDENTITY matrix.
• IDENTITY_CONDITION returns the L1 condition of the IDENTITY matrix.
• IDENTITY_DETERMINANT returns the determinant of the IDENTITY matrix.
• IDENTITY_EIGENVALUES returns the eigenvalues of the IDENTITY matrix.
• IDENTITY_INVERSE returns the inverse of the IDENTITY matrix.
• IDENTITY_EIGEN_LEFT returns the left eigenvectors of the IDENTITY matrix.
• IDENTITY_EIGEN_RIGHT returns right eigenvectors of the IDENTITY matrix.
• IJFACT1 returns the IJFACT1 matrix.
• IJFACT1_DETERMINANT returns the determinant of the IJFACT1 matrix.
• IJFACT2 returns the IJFACT2 matrix.
• IJFACT2_DETERMINANT returns the determinant of the IJFACT2 matrix.
• ILL3 returns the ILL3 matrix.
• ILL3_CONDITION returns the L1 condition of the ILL3 matrix.
• ILL3_DETERMINANT returns the determinant of the ILL3 matrix.
• ILL3_EIGENVALUES returns the eigenvalues of the ILL3 matrix.
• ILL3_INVERSE returns the inverse of the ILL3 matrix.
• ILL3_EIGEN_RIGHT returns right eigenvectors of the ILL3 matrix.
• INDICATOR returns the INDICATOR matrix.
• INTEGRATION returns the INTEGRATION matrix.
• INTEGRATION_DETERMINANT returns the determinant of the INTEGRATION matrix.
• INTEGRATION_EIGENVALUES returns the eigenvalues of the INTEGRATION matrix.
• INTEGRATION_INVERSE returns the inverse of the INTEGRATION matrix.
• INVOL returns the INVOL matrix.
• INVOL_DETERMINANT returns the determinant of the INVOL matrix.
• INVOL_EIGENVALUES returns the eigenvalues of the INVOL matrix.
• INVOL_INVERSE returns the inverse of the INVOL matrix.
• INVOL_RANDOM returns the INVOL_RANDOM matrix.
• JACOBI returns the JACOBI matrix.
• JACOBI_DETERMINANT returns the determinant of the JACOBI matrix.
• JACOBI_EIGENVALUES returns the eigenvalues of the JACOBI matrix.
• JACOBI_INVERSE returns the inverse of the JACOBI matrix.
• JACOBI_ITERATE applies the Jacobi eigenvalue iteration to a symmetric matrix.
• JACOBI_SYMBOL evaluates the Jacobi symbol (Q/P).
• JORDAN returns the JORDAN matrix.
• JORDAN_CONDITION returns the L1 condition of the JORDAN matrix.
• JORDAN_DETERMINANT returns the determinant of the JORDAN matrix.
• JORDAN_EIGENVALUES returns the eigenvalues of the JORDAN matrix.
• JORDAN_INVERSE returns the inverse of the JORDAN matrix.
• KAHAN returns the KAHAN matrix.
• KAHAN_DETERMINANT returns the determinant of the KAHAN matrix.
• KAHAN_INVERSE returns the inverse of the KAHAN matrix.
• KERSHAW returns the KERSHAW matrix.
• KERSHAW_CONDITION returns the L1 condition of the KERSHAW matrix.
• KERSHAW_DETERMINANT returns the determinant of the KERSHAW matrix.
• KERSHAW_EIGEN_RIGHT returns the right eigenvectors of the KERSHAW matrix.
• KERSHAW_EIGENVALUES returns the eigenvalues of the KERSHAW matrix.
• KERSHAW_INVERSE returns the inverse of the KERSHAW matrix.
• KERSHAW_LLT returns the Cholesky factor of the KERSHAW matrix.
• KERSHAWTRI returns the KERSHAWTRI matrix.
• KERSHAWTRI_DETERMINANT returns the determinant of the KERSHAWTRI matrix.
• KERSHAWTRI_INVERSE returns the inverse of the KERSHAWTRI matrix.
• KMS returns the KMS matrix.
• KMS_DETERMINANT returns the determinant of the KMS matrix.
• KMS_EIGENVALUES returns the eigenvalues of the KMS matrix.
• KMS_EIGENVALUES_THETA returns data needed to compute KMS eigenvalues.
• KMS_EIGENVALUES_THETA_F evaluates a function for KMS eigenvalues.
• KMS_INVERSE returns the inverse of the KMS matrix.
• KMS_LDL returns the LDL factorization of the KMS matrix.
• KMS_PLU returns the PLU factors of the KMS matrix.
• KMS_EIGEN_RIGHT returns right eigenvectors of the KMS matrix.
• KRYLOV returns the KRYLOV matrix.
• LAGUERRE returns the LAGUERRE matrix.
• LAGUERRE_DETERMINANT returns the determinant of the LAGUERRE matrix.
• LAGUERRE_INVERSE returns the inverse of the LAGUERRE matrix.
• LAUCHLI returns the LAUCHLI matrix.
• LAUCHLI_NULL_LEFT returns a left null vector of the LAUCHLI matrix.
• LEGENDRE returns the LEGENDRE matrix.
• LEGENDRE_DETERMINANT returns the determinant of the LEGENDRE matrix.
• LEGENDRE_INVERSE returns the inverse of the LEGENDRE matrix.
• LEGENDRE_SYMBOL evaluates the Legendre symbol (Q/P).
• LEGENDRE_VAN returns the LEGENDRE_VAN matrix.
• LEGENDRE_ZEROS computes the zeros of the Legendre polynomial.
• LEHMER returns the LEHMER matrix.
• LEHMER_DETERMINANT returns the determinant of the LEHMER matrix.
• LEHMER_INVERSE returns the inverse of the LEHMER matrix.
• LEHMER_LLT returns the Cholesky factor of the LEHMER matrix.
• LEHMER_PLU returns the PLU factors of the LEHMER matrix.
• LESLIE returns the LESLIE matrix.
• LESLIE_DETERMINANT returns the determinant of the LESLIE matrix.
• LESP returns the LESP matrix.
• LESP_DETERMINANT computes the determinant of the LESP matrix.
• LESP_INVERSE returns the inverse of the LESP matrix.
• LIETZKE returns the LIETZKE matrix.
• LIETZKE_CONDITION returns the L1 condition of the LIETZKE matrix.
• LIETZKE_DETERMINANT returns the determinant of the LIETZKE matrix.
• LIETZKE_INVERSE returns the inverse of the LIETZKE matrix.
• LIGHTS_OUT returns the LIGHTS_OUT matrix.
• LINE_ADJ returns the LINE_ADJ matrix.
• LINE_ADJ_DETERMINANT returns the determinant of the LINE_ADJ matrix.
• LINE_ADJ_EIGEN_RIGHT returns right eigenvectors of the LINE_ADJ matrix.
• LINE_ADJ_EIGENVALUES returns the eigenvalues of the LINE_ADJ matrix.
• LINE_ADJ_NULL_LEFT returns a left null vector of the LINE_ADJ matrix.
• LINE_ADJ_NULL_RIGHT returns a right null vector of the LINE_ADJ matrix.
• LINE_LOOP_ADJ returns the LINE_LOOP_ADJ matrix.
• LINE_LOOP_ADJ_DETERMINANT: the determinant of the LINE_LOOP_ADJ matrix.
• LINE_LOOP_ADJ_EIGEN_RIGHT:right eigenvectors of the LINE_LOOP_ADJ matrix.
• LINE_LOOP_ADJ_EIGENVALUES: the eigenvalues of the LINE_LOOP_ADJ matrix.
• LOEWNER returns the LOEWNER matrix.
• LOTKIN returns the LOTKIN matrix.
• LOTKIN_DETERMINANT returns the determinant of the LOTKIN matrix.
• LOTKIN_INVERSE returns the inverse of the LOTKIN matrix.
• MAGIC returns a magic matrix.
• MAGIC_A is a utility routine for magic square computations.
• MAGIC_B is a utility routine for magic square computations.
• MAGIC_BIMARKOV returns a magic biMarkov matrix.
• MAGIC_C is a utility routine for magic square computations.
• MAGIC_EVEN constructs a magic square for the case where N is even.
• MAGIC_ODD constructs a magic square for the case where N is odd.
• MARKOV_RANDOM returns the MARKOV_RANDOM matrix.
• MAXIJ returns the MAXIJ matrix.
• MAXIJ_CONDITION returns the L1 condition of the MAXIJ matrix.
• MAXIJ_DETERMINANT returns the determinant of the MAXIJ matrix.
• MAXIJ_INVERSE returns the inverse of the MAXIJ matrix.
• MAXIJ_PLU returns the PLU factors of the MAXIJ matrix.
• MERTENS evaluates the Mertens function.
• MERTENS_VALUES returns some values of the Mertens function.
• MILNES returns the MILNES matrix.
• MILNES_DETERMINANT returns the determinant of the MILNES matrix.
• MILNES_INVERSE returns the inverse of the MILNES matrix.
• MINIJ returns the MINIJ matrix.
• MINIJ_CONDITION returns the L1 condition of the MINIJ matrix.
• MINIJ_DETERMINANT returns the determinant of the MINIJ matrix.
• MINIJ_EIGENVALUES returns the eigenvalues of the MINIJ matrix.
• MINIJ_INVERSE returns the inverse of the MINIJ matrix.
• MINIJ_LLT returns the Cholesky factor of the MINIJ matrix.
• MINIJ_PLU returns the PLU factors of the MINIJ matrix.
• MOEBIUS returns the value of MU(N), the Moebius function of N.
• MOEBIUS_VALUES returns some values of the Moebius function.
• MOLER1 returns the MOLER1 matrix.
• MOLER1_DETERMINANT returns the determinant of the MOLER1 matrix.
• MOLER1_INVERSE returns the inverse of the MOLER1 matrix.
• MOLER1_LLT returns the lower triangular Cholesky factor of the MOLER1 matrix.
• MOLER1_PLU returns the PLU factors of the MOLER1 matrix.
• MOLER2 returns the MOLER2 matrix.
• MOLER2_DETERMINANT returns the determinant of the MOLER2 matrix.
• MOLER2_EIGENVALUES returns the eigenvalues of the MOLER2 matrix.
• MOLER2_NULL_LEFT returns a left null vector for the MOLER2 matrix.
• MOLER2_NULL_RIGHT returns a right null vector for the MOLER2 matrix.
• MOLER3 returns the MOLER3 matrix.
• MOLER3_DETERMINANT returns the determinant of the MOLER3 matrix.
• MOLER3_INVERSE returns the inverse of the MOLER3 matrix.
• MOLER3_LLT returns the Cholesky factor of the MOLER3 matrix.
• MOLER3_PLU returns the PLU factors of the MOLER3 matrix.
• MOLER4 returns the MOLER4 matrix.
• MOLER4_CONDITION returns the L1 condition of the MOLER4 matrix.
• MOLER4_DETERMINANT returns the determinant of the MOLER4 matrix.
• MOLER4_EIGENVALUES returns the eigenvalues of the MOLER4 matrix.
• MOLER4_INVERSE returns the inverse of the MOLER4 matrix.
• NEUMANN returns the NEUMANN matrix.
• NEUMANN_DETERMINANT returns the determinant of the NEUMANN matrix.
• NEUMANN_NULL_RIGHT returns a right null vector of the NEUMANN matrix.
• ONE returns the ONE matrix.
• ONE_DETERMINANT returns the determinant of the ONE matrix.
• ONE_EIGENVALUES returns the eigenvalues of the ONE matrix.
• ONE_NULL_LEFT returns a left null vector of the ONE matrix.
• ONE_NULL_RIGHT returns a right null vector of the ONE matrix.
• ONE_EIGEN_RIGHT returns right eigenvectors of the ONE matrix.
• ORTEGA returns the ORTEGA matrix.
• ORTEGA_DETERMINANT returns the determinant of the ORTEGA matrix.
• ORTEGA_EIGENVALUES returns the eigenvalues of the ORTEGA matrix.
• ORTEGA_INVERSE returns the inverse of the ORTEGA matrix.
• ORTEGA_EIGEN_RIGHT returns right eigenvectors of the ORTEGA matrix.
• ORTH_RANDOM returns the ORTH_RANDOM matrix.
• ORTH_RANDOM_DETERMINANT returns the determinant of the ORTH_RANDOM matrix.
• ORTH_RANDOM_INVERSE returns the inverse of the ORTH_RANDOM matrix.
• ORTH_SYMM returns the ORTH_SYMM matrix.
• ORTH_SYMM_CONDITION returns the L1 condition of the ORTH_SYMM matrix.
• ORTH_SYMM_DETERMINANT returns the determinant of the ORTH_SYMM matrix.
• ORTH_SYMM_EIGENVALUES returns eigenvalues of the ORTH_SYMM matrix.
• ORTH_SYMM_INVERSE returns the inverse of the ORTH_SYMM matrix.
• OTO returns the OTO matrix.
• OTO_CONDITION returns the L1 condition of the OTO matrix.
• OTO_DETERMINANT returns the determinant of the OTO matrix.
• OTO_EIGENVALUES returns the eigenvalues of the OTO matrix.
• OTO_INVERSE returns the inverse of the OTO matrix.
• OTO_LLT returns the Cholesky factor of the OTO matrix.
• OTO_PLU returns the PLU factors of the OTO matrix.
• OTO_EIGEN_RIGHT returns right eigenvectors of the OTO matrix.
• PARLETT returns the PARLETT matrix.
• PARLETT_EIGENVALUES returns the eigenvalues of the PARLETT matrix.
• PARTER returns the PARTER matrix.
• PARTER_DETERMINANT returns the determinant of the PARTER matrix.
• PARTER_INVERSE returns the inverse of the PARTER matrix.
• PASCAL1 returns the PASCAL1 matrix.
• PASCAL1_CONDITION returns the L1 condition of the PASCAL1 matrix.
• PASCAL1_DETERMINANT returns the determinant of the PASCAL1 matrix.
• PASCAL1_EIGENVALUES returns eigenvalues of the PASCAL1 matrix.
• PASCAL1_INVERSE returns the inverse of the PASCAL1 matrix.
• PASCAL2 returns the PASCAL2 matrix.
• PASCAL2_DETERMINANT returns the determinant of the PASCAL2 matrix.
• PASCAL2_INVERSE returns the inverse of the PASCAL2 matrix.
• PASCAL2_LLT returns the Cholesky factor of the PASCAL2 matrix.
• PASCAL2_PLU returns the PLU factors of the PASCAL2 matrix.
• PASCAL3 returns the PASCAL3 matrix.
• PASCAL3_CONDITION returns the L1 condition of the PASCAL3 matrix.
• PASCAL3_DETERMINANT returns the determinant of the PASCAL3 matrix.
• PASCAL3_INVERSE returns the inverse of the PASCAL3 matrix.
• PDS_RANDOM returns the PDS_RANDOM matrix.
• PDS_RANDOM_DETERMINANT returns the determinant of the PDS_RANDOM matrix.
• PDS_RANDOM_EIGENVALUES returns the eigenvalues of the PDS_RANDOM matrix.
• PDS_RANDOM_INVERSE returns the inverse of the PDS_RANDOM matrix.
• PDS_RANDOM_EIGEN_RIGHT returns right eigenvectors of the PDS_RANDOM matrix.
• PEI returns the PEI matrix.
• PEI_CONDITION returns the L1 condition of the PEI matrix.
• PEI_DETERMINANT returns the determinant of the PEI matrix.
• PEI_EIGENVALUES returns the eigenvalues of the PEI matrix.
• PEI_INVERSE returns the inverse of the PEI matrix.
• PEI_EIGEN_RIGHT returns right eigenvectors of the PEI matrix.
• PERM_CHECK checks that a vector represents a permutation.
• PERM_INVERSE inverts a permutation "in place".
• PERM_MAT_TO_VEC returns a permutation from a permutation matrix.
• PERM_SIGN returns the sign of a permutation.
• PERM_VEC_TO_MAT returns a permutation matrix.
• PERMUTATION_DETERMINANT returns the determinant of a PERMUTATION matrix.
• PERMUTATION_RANDOM returns the PERMUTATION_RANDOM matrix.
• PERMUTATION_RANDOM_DETERMINANT: determinant of PERMUTATION_RANDOM matrix.
• PERMUTATION_RANDOM_INVERSE: inverse of PERMUTATION_RANDOM matrix.
• PICK returns the PICK matrix.
• PLU returns a PLU matrix.
• PLU_DETERMINANT returns the determinant of the PLU matrix.
• PLU_INVERSE returns the inverse of a PLU matrix.
• PLU_PLU returns the PLU factors of the PLU matrix.
• POISSON returns the POISSON matrix.
• POISSON_DETERMINANT returns the determinant of the POISSON matrix.
• POISSON_EIGENVALUES returns the eigenvalues of the POISSON matrix.
• POISSON_RHS returns the right hand side of a Poisson linear system.
• POISSON_SOLUTION returns the solution of a Poisson linear system.
• PRIME returns any of the first PRIME_MAX prime numbers.
• PROLATE returns the PROLATE matrix.
• PROPA_NO_RANDOM returns a PROPA_NO_RANDOM matrix.
• PROPA_YES_RANDOM returns a PROPA_YES_RANDOM matrix.
• QUATERNION_I returns a 4 by 4 matrix that behaves like the quaternion unit I.
• QUATERNION_J returns a 4 by 4 matrix that behaves like the quaternion unit J.
• QUATERNION_K returns a 4 by 4 matrix that behaves like the quaternion unit K.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.
• R8_EPSILON returns the R8 roundoff unit.
• R8_FACTORIAL computes the factorial of N.
• R8_HUGE returns a "huge" R8.
• R8_MOP returns the I-th power of -1 as an R8 value.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_PI returns the value of pi as an R8.
• R8_SWAP switches two R8's.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8_UNIFORM_AB returns a pseudorandom R8 scaled to [A,B].
• R8COL_SWAP swaps columns I and J of an R8COL.
• R8COL_TO_R8VEC converts an R8COL to an R8VEC.
• R8MAT_CHOLESKY_FACTOR computes the Cholesky factor of a symmetric matrix.
• R8MAT_COPY copies an R8MAT.
• R8MAT_DETERMINANT computes the determinant of a square R8MAT.
• R8MAT_DIAG_GET_VECTOR gets the value of the diagonal of an R8MAT.
• R8MAT_EIGENVALUES computes the eigenvalues of a square R8MAT.
• R8MAT_GEDET computes the determinant of an R8MAT factored by R8MAT_GEFA.
• R8MAT_GEFA factors an R8MAT.
• R8MAT_GEINVERSE computes the inverse of an R8MAT factored by R8MAT_GEFA.
• R8MAT_GEPLU produces the PLU factors of an R8MAT.
• R8MAT_GESL solves a system factored by R8MAT_GEFA.
• R8MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.
• R8MAT_HOUSE_FORM constructs a Householder matrix from its compact form.
• R8MAT_IDENTITY stores the identity matrix in an R8MAT.
• R8MAT_INVERSE computes the inverse of an R8MAT.
• R8MAT_IS_ADJACENCY checks whether an R8MAT is an adjacency matrix.
• R8MAT_IS_ANTICIRCULANT checks whether an R8MAT is an anticirculant matrix.
• R8MAT_IS_ANTIPERSYMM checks an R8MAT for antipersymmetry.
• R8MAT_IS_ANTISYMM checks an R8MAT for antisymmetry.
• R8MAT_IS_BAND determines whether an R8MAT is banded.
• R8MAT_IS_CENTROSYMM checks an R8MAT for centrosymmetry.
• R8MAT_IS_CIRCULANT checks whether an R8MAT is a circulant matrix.
• R8MAT_IS_COLUMN_ORTHOGONAL checks whether an R8MAT is column orthogonal.
• R8MAT_IS_CYCLIC_TRIDIAGONAL determines if an R8MAT is cyclic tridiagonal.
• R8MAT_IS_DIAG2 counts the number of nonzero diagonals in an R8MAT.
• R8MAT_IS_DIAGDOM checks whether an R8MAT is diagonally dominant.
• R8MAT_IS_EIGEN_LEFT determines the error in a left eigensystem.
• R8MAT_IS_EIGEN_RIGHT determines the error in a right eigensystem.
• R8MAT_IS_HANKEL checks whether an R8MAT is Hankel.
• R8MAT_IS_IDENTITY determines if an R8MAT is the identity.
• R8MAT_IS_INVERSE determines if one R8MAT is the inverse of another.
• R8MAT_IS_LLT measures the error in a lower Cholesky factorization.
• R8MAT_IS_NULL_LEFT determines if x is a left null vector of an R8MAT.
• R8MAT_IS_NULL_RIGHT determines if x is a right null vector of an R8MAT.
• R8MAT_IS_PERM checks whether an R8MAT is a permutation matrix.
• R8MAT_IS_PLU measures the error in a PLU factorization.
• R8MAT_IS_SOLUTION measures the error in a linear system solution.
• R8MAT_IS_SYMMETRIC checks an R8MAT for symmetry.
• R8MAT_IS_TRANSITION checks whether an R8MAT is a transition matrix.
• R8MAT_IS_ZERO_ONE checks whether an R8MAT is a zero/one matrix.
• R8MAT_MM multiplies two R8MAT's.
• R8MAT_MMT multiplies computes C = A * B' for two R8MAT's.
• R8MAT_MTM multiplies computes C = A' * B for two R8MAT's.
• R8MAT_MV multiplies a matrix times a vector.
• R8MAT_NORM_EIS returns the EISPACK norm of an R8MAT.
• R8MAT_NORM_FRO returns the Frobenius norm of an R8MAT.
• R8MAT_NORM_L1 returns the matrix L1 norm of an R8MAT.
• R8MAT_NORM_L2 returns the matrix L2 norm of an M by N R8MAT.
• R8MAT_NORM_LI returns the matrix L-oo norm of an R8MAT.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8MAT_TRACE computes the trace of an R8MAT.
• R8MAT_TRANSPOSE makes a transposed copy of a matrix.
• R8MAT_TRANSPOSE_IN_PLACE transposes a square matrix in place.
• R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
• R8MAT_UNIFORM_AB returns a scaled pseudorandom R8MAT.
• R8POLY_DEGREE returns the degree of a polynomial in power sum form.
• R8POLY_PRINT prints out a polynomial.
• R8ROW_SWAP swaps two rows of an R8ROW.
• R8ROW_TO_R8VEC converts an R8ROW into an R8VEC.
• R8VEC_AMAX returns the maximum absolute value in an R8VEC.
• R8VEC_AMIN returns the minimum absolute value in an R8VEC.
• R8VEC_ASUM sums the absolute values of the entries of an R8VEC.
• R8VEC_COPY copies an R8VEC.
• R8VEC_DOT_PRODUCT finds the dot product of a pair of R8VEC's.
• R8VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
• R8VEC_INDICATOR sets an R8VEC to the indicator vector.
• R8VEC_LINSPACE creates a vector of linearly spaced values.
• R8VEC_NORM_L2 returns the L2 norm of an R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_PRODUCT multiplies the entries of an R8VEC.
• R8VEC_SORT_BUBBLE_A ascending sorts an R8VEC using bubble sort.
• R8VEC_SUM sums the entries of an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• R8VEC_UNIFORM_AB returns a scaled pseudorandom R8VEC.
• R8VEC2_PRINT prints a pair of real vectors.
• RAYLEIGH returns the Rayleigh quotient of the matrix A and the vector X.
• RAYLEIGH2 returns the generalized Rayleigh quotient.
• RECTANGLE_ADJ returns the RECTANGLE_ADJ matrix.
• RECTANGLE_ADJ_DETERMINANT: the determinant of the RECTANGLE_ADJ matrix.
• REDHEFFER returns the REDHEFFER matrix.
• REDHEFFER_DETERMINANT returns the determinant of the REDHEFFER matrix.
• REF_RANDOM returns a REF_RANDOM matrix.
• REF_RANDOM_DETERMINANT: determinant of a REF_RANDOM matrix.
• RIEMANN returns the RIEMANN matrix.
• RING_ADJ returns the RING_ADJ matrix.
• RING_ADJ_DETERMINANT returns the determinant of the RING_ADJ matrix.
• RING_ADJ_NULL_LEFT returns a left null vector of the RING_ADJ matrix.
• RING_ADJ_NULL_RIGHT returns a right null vector of the RING_ADJ matrix.
• RIS returns the RIS matrix.
• RIS_DETERMINANT returns the determinant of the RIS matrix.
• RIS_INVERSE returns the inverse of the RIS matrix.
• RODMAN returns the RODMAN matrix.
• RODMAN_CONDITION returns the L1 condition of the RODMAN matrix.
• RODMAN_DETERMINANT returns the determinant of the RODMAN matrix.
• RODMAN_EIGEN_RIGHT returns right eigenvectors of the RODMAN matrix.
• RODMAN_EIGENVALUES returns the eigenvalues of the RODMAN matrix.
• RODMAN_INVERSE returns the inverse of the RODMAN matrix.
• ROSSER1 returns the ROSSER1 matrix.
• ROSSER1_DETERMINANT returns the determinant of the ROSSER1 matrix.
• ROSSER1_EIGEN_LEFT returns left eigenvectors of the ROSSER1 matrix.
• ROSSER1_EIGEN_RIGHT returns right eigenvectors of the ROSSER1 matrix.
• ROSSER1_EIGENVALUES returns the eigenvalues of the ROSSER1 matrix.
• ROSSER1_NULL_LEFT returns a left null vector of the ROSSER1 matrix.
• ROSSER1_NULL_RIGHT returns a right null vector of the ROSSER1 matrix.
• ROUTH returns the ROUTH matrix.
• ROUTH_DETERMINANT returns the determinant of the ROUTH matrix.
• ROWCOLSUM_MATRIX returns the ROWCOLSUM matrix.
• RUTIS1 returns the RUTIS1 matrix.
• RUTIS1_CONDITION returns the L1 condition of the RUTIS1 matrix.
• RUTIS1_DETERMINANT returns the determinant of the RUTIS1 matrix.
• RUTIS1_EIGENVALUES returns the eigenvalues of the RUTIS1 matrix.
• RUTIS1_INVERSE returns the inverse of the RUTIS1 matrix.
• RUTIS1_EIGEN_RIGHT returns right eigenvectors of the RUTIS1 matrix.
• RUTIS2 returns the RUTIS2 matrix.
• RUTIS2_CONDITION returns the L1 condition of the RUTIS2 matrix.
• RUTIS2_DETERMINANT returns the determinant of the RUTIS2 matrix.
• RUTIS2_EIGENVALUES returns the eigenvalues of the RUTIS2 matrix.
• RUTIS2_INVERSE returns the inverse of the RUTIS2 matrix.
• RUTIS2_EIGEN_RIGHT returns right eigenvectors of the RUTIS2 matrix.
• RUTIS3 returns the RUTIS3 matrix.
• RUTIS3_CONDITION returns the L1 condition of the RUTIS3 matrix.
• RUTIS3_DETERMINANT returns the determinant of the RUTIS3 matrix.
• RUTIS3_EIGENVALUES returns the eigenvalues of the RUTIS3 matrix.
• RUTIS3_INVERSE returns the inverse of the RUTIS3 matrix.
• RUTIS3_EIGEN_LEFT returns the left eigenvectors of the RUTIS3 matrix.
• RUTIS3_EIGEN_RIGHT returns right eigenvectors of the RUTIS3 matrix.
• RUTIS4 returns the RUTIS4 matrix.
• RUTIS4_DETERMINANT returns the determinant of the RUTIS4 matrix.
• RUTIS4_EIGENVALUES returns the eigenvalues of the RUTIS4 matrix.
• RUTIS4_INVERSE returns the inverse of the RUTIS4 matrix.
• RUTIS5 returns the RUTIS5 matrix.
• RUTIS5_CONDITION returns the L1 condition of the RUTIS5 matrix.
• RUTIS5_DETERMINANT returns the determinant of the RUTIS5 matrix.
• RUTIS5_EIGENVALUES returns the eigenvalues of the RUTIS5 matrix.
• RUTIS5_INVERSE returns the inverse of the RUTIS5 matrix.
• RUTIS5_EIGEN_RIGHT returns right eigenvectors of the RUTIS5 matrix.
• SCHUR_BLOCK returns the SCHUR_BLOCK matrix.
• SCHUR_BLOCK_DETERMINANT returns the determinant of the SCHUR_BLOCK matrix.
• SCHUR_BLOCK_EIGENVALUES returns the eigenvalues of the SCHUR_BLOCK matrix.
• SCHUR_BLOCK_INVERSE returns the inverse of the SCHUR_BLOCK matrix.
• SKEW_CIRCULANT returns a SKEW_CIRCULANT matrix.
• SKEW_CIRCULANT_DETERMINANT: the determinant of the SKEW_CIRCULANT matrix.
• SKEW_CIRCULANT_EIGENVALUES returns eigenvalues of the SKEW_CIRCULANT matrix.
• SMOKE1 returns the SMOKE1 matrix.
• SMOKE1_DETERMINANT returns the determinant of the SMOKE1 matrix.
• SMOKE1_EIGENVALUES returns the eigenvalues of the SMOKE1 matrix.
• SMOKE2 returns the SMOKE2 matrix.
• SMOKE2_DETERMINANT returns the determinant of the SMOKE2 matrix.
• SMOKE2_EIGENVALUES returns the eigenvalues of the SMOKE2 matrix.
• SNAKES returns the Snakes and Ladders transition matrix.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• SPLINE returns the SPLINE matrix.
• SPLINE_DETERMINANT computes the determinant of the SPLINE matrix.
• SPLINE_INVERSE returns the inverse of the SPLINE matrix.
• STIRLING returns the STIRLING matrix.
• STIRLING_DETERMINANT returns the determinant of the STIRLING matrix.
• STIRLING_EIGENVALUES returns the eigenvalues of the STIRLING matrix.
• STIRLING_INVERSE returns the inverse of the STIRLING matrix.
• STRIPE returns the STRIPE matrix.
• SUBSET_RANDOM selects a random subset of an N-set.
• SUMMATION returns the SUMMATION matrix.
• SUMMATION_CONDITION: L1 condition of the SUMMATION matrix.
• SUMMATION_DETERMINANT returns the determinant of the SUMMATION matrix.
• SUMMATION_EIGENVALUES returns the eigenvalues of the SUMMATION matrix.
• SUMMATION_INVERSE returns the inverse of the SUMMATION matrix.
• SWEET1 returns the SWEET1 matrix.
• SWEET1_CONDITION: L1 condition of the SWEET1 matrix.
• SWEET1_DETERMINANT returns the determinant of the SWEET1 matrix.
• SWEET1_INVERSE returns the inverse of the SWEET1 matrix.
• SWEET2 returns the SWEET2 matrix.
• SWEET2_CONDITION returns the L1 condition of the SWEET2 matrix.
• SWEET2_DETERMINANT returns the determinant of the SWEET2 matrix.
• SWEET2_INVERSE returns the inverse of the SWEET2 matrix.
• SWEET3 returns the SWEET3 matrix.
• SWEET3_CONDITION returns the L1 condition of the SWEET3 matrix.
• SWEET3_DETERMINANT returns the determinant of the SWEET3 matrix.
• SWEET3_INVERSE returns the inverse of the SWEET3 matrix.
• SWEET4 returns the SWEET4 matrix.
• SWEET4_CONDITION returns the L1 condition of the SWEET4 matrix.
• SWEET4_DETERMINANT returns the determinant of the SWEET4 matrix.
• SWEET4_INVERSE returns the inverse of the SWEET4 matrix.
• SYLVESTER returns the SYLVESTER matrix.
• SYLVESTER_KAC returns the SYLVESTER_KAC matrix.
• SYLVESTER_KAC_DETERMINANT: determinant of the SYLVESTER_KAC matrix.
• SYLVESTER_KAC_EIGEN_RIGHT: right eigenvectors of the SYLVESTER_KAC matrix.
• SYLVESTER_KAC_EIGENVALUES: eigenvalues of the SYLVESTER_KAC matrix.
• SYLVESTER_KAC_INVERSE returns the inverse of the CLEMENT1 matrix.
• SYMM_RANDOM returns the SYMM_RANDOM matrix.
• SYMM_RANDOM_DETERMINANT returns the determinant of the SYMM_RANDOM matrix.
• SYMM_RANDOM_EIGEN_LEFT returns left eigenvectors of the SYMM_RANDOM matrix.
• SYMM_RANDOM_EIGEN_RIGHT returns right eigenvectors of the SYMM_RANDOM matrix.
• SYMM_RANDOM_EIGENVALUES returns the eigenvalues of the SYMM_RANDOM matrix.
• SYMM_RANDOM_INVERSE returns the inverse of the SYMM_RANDOM matrix.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TOEPLITZ returns a TOEPLITZ matrix.
• TOEPLITZ_5DIAG returns the TOEPLITZ_5DIAG matrix.
• TOEPLITZ_5S returns the TOEPLITZ_5S matrix.
• TOEPLITZ_5S_DETERMINANT returns the determinant of the TOEPLITZ_5S matrix.
• TOEPLITZ_5S_EIGENVALUES returns the eigenvalues of the TOEPLITZ_5S matrix.
• TOEPLITZ_PDS returns the TOEPLITZ_PDS matrix.
• TOURNAMENT_RANDOM returns the TOURNAMENT_RANDOM matrix.
• TOURNAMENT_RANDOM_DETERMINANT: determinant of the TOURNAMENT_RANDOM matrix.
• TRANSITION_RANDOM returns the TRANSITION_RANDOM matrix.
• TRENCH returns the TRENCH matrix.
• TRI_L1_INVERSE inverts a unit lower triangular R8MAT.
• TRI_U_INVERSE inverts an upper triangular R8MAT.
• TRI_UPPER returns the TRI_UPPER matrix.
• TRI_UPPER_CONDITION returns the L1 condition of the TRI_UPPER matrix.
• TRI_UPPER_DETERMINANT returns the determinant of the TRI_UPPER matrix.
• TRI_UPPER_EIGENVALUES returns the eigenvalues of the TRI_UPPER matrix.
• TRI_UPPER_INVERSE returns the inverse of the TRI_UPPER matrix.
• TRIDIAGONAL_DETERMINANT computes the determinant of a tridiagonal matrix.
• TRIS returns the TRIS matrix.
• TRIS_DETERMINANT returns the determinant of the TRIS matrix.
• TRIS_EIGENVALUES returns the eigenvalues of the TRIS matrix.
• TRIS_INVERSE returns the inverse of the TRIS matrix.
• TRIV returns the TRIV matrix.
• TRIV_DETERMINANT computes the determinant of the TRIV matrix.
• TRIV_INVERSE returns the inverse of the TRIV matrix.
• TRIW returns the TRIW matrix.
• TRIW_DETERMINANT returns the determinant of the TRIW matrix.
• TRIW_EIGENVALUES returns the eigenvalues of the TRIW matrix.
• TRIW_INVERSE sets the inverse of the TRIW matrix.
• UNITARY_RANDOM returns the UNITARY_RANDOM matrix.
• UNITARY_RANDOM_DETERMINANT: determinant of a UNITARY_RANDOM matrix.
• UNITARY_RANDOM_INVERSE returns the inverse of the UNITARY_RANDOM matrix.
• UPSHIFT returns the UPSHIFT matrix.
• UPSHIFT_CONDITION returns the L1 condition of the UPSHIFT matrix.
• UPSHIFT_DETERMINANT returns the determinant of the UPSHIFT matrix.
• UPSHIFT_EIGENVALUES returns the eigenvalues of the UPSHIFT matrix.
• UPSHIFT_INVERSE returns the inverse of the UPSHIFT matrix.
• VAND1 returns the VAND1 matrix.
• VAND1_DETERMINANT returns the determinant of the VAND1 matrix.
• VAND1_INVERSE returns the inverse of the VAND1 matrix.
• VAND1_INVERSE_UL returns the UL factors of the Vandermonde1 inverse.
• VAND2 returns the VAND2 matrix.
• VAND2_DETERMINANT returns the determinant of the VAND2 matrix.
• VAND2_INVERSE returns the inverse of the VAND2 matrix.
• VAND2_INVERSE_UL returns the UL factors of the Vandermonde2 inverse.
• VAND2_LU returns the LU factors of the Vandermonde2 matrix.
• VAND2_PLU returns the PLU factors of the Vandermonde2 matrix.
• WATHEN returns the WATHEN matrix.
• WATHEN_ORDER returns the order of the WATHEN matrix.
• WILK03 returns the WILK03 matrix.
• WILK03_CONDITION returns the L1 condition of the WILK03 matrix.
• WILK03_DETERMINANT returns the determinant of the WILK03 matrix.
• WILK03_EIGENVALUES returns the eigenvalues of the WILK03 matrix.
• WILK03_INVERSE returns the inverse of the WILK03 matrix.
• WILK03_RHS returns the right hand side of the WILK03 linear system.
• WILK03_SOLUTION returns the solution of the WILK03 linear system.
• WILK04 returns the WILK04 matrix.
• WILK04_CONDITION returns the L1 condition of the WILK04 matrix.
• WILK04_DETERMINANT returns the determinant of the WILK04 matrix.
• WILK04_EIGENVALUES returns the eigenvalues of the WILK04 matrix.
• WILK04_INVERSE returns the inverse of the WILK04 matrix.
• WILK04_RHS returns the right hand side of the WILK04 linear system.
• WILK04_SOLUTION returns the solution of the WILK04 linear system.
• WILK05 returns the WILK05 matrix.
• WILK05_CONDITION returns the L1 condition of the WILK05 matrix.
• WILK05_DETERMINANT returns the determinant of the WILK05 matrix.
• WILK05_INVERSE returns the inverse of the WILK05 matrix.
• WILK12 returns the WILK12 matrix.
• WILK12_DETERMINANT returns the determinant of the WILK12 matrix.
• WILK12_EIGENVALUES returns the eigenvalues of the WILK12 matrix.
• WILK12_EIGEN_RIGHT returns right eigenvectors of the WILK12 matrix.
• WILK20 returns the WILK20 matrix.
• WILK21 returns the WILK21 matrix.
• WILK21_DETERMINANT computes the determinant of the WILK21 matrix.
• WILK21_INVERSE returns the inverse of the WILK21 matrix.
• WILSON returns the WILSON matrix.
• WILSON_CONDITION returns the L1 condition of the WILSON matrix.
• WILSON_DETERMINANT returns the determinant of the WILSON matrix.
• WILSON_EIGEN_RIGHT returns right eigenvectors of the WILSON matrix.
• WILSON_EIGENVALUES returns the eigenvalues of the WILSON matrix.
• WILSON_INVERSE returns the inverse of the WILSON matrix.
• WILSON_LLT returns the lower Cholesky factor of the WILSON matrix.
• WILSON_PLU returns the PLU factors of the WILSON matrix.
• WILSON_RHS returns the WILSON right hand side.
• WILSON_SOLUTION returns the WILSON solution.
• ZERO returns the ZERO matrix.
• ZERO_DETERMINANT returns the determinant of the ZERO matrix.
• ZERO_EIGEN_RIGHT returns right eigenvectors of the ZERO matrix.
• ZERO_EIGENVALUES returns the eigenvalues of the ZERO matrix.
• ZERO_NULL_LEFT returns a left null vector of the ZERO matrix.
• ZERO_NULL_RIGHT returns a right null vector of the ZERO matrix.
• ZIELKE returns the ZIELKE matrix.

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