TEST_MAT
Test Matrices
TEST_MAT,
a MATLAB 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 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 FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
ARPACK,
a MATLAB library which
uses Arnoldi methods
to compute some eigenvalues and eigenvectors of matrices,
which may be very large.
CG,
a MATLAB 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.
CONDITION,
a MATLAB library which
implements methods of computing or estimating the condition number
of a matrix.
JACOBI_EIGENVALUE,
a MATLAB library which
implements the Jacobi iteration for the iterative determination
of the eigenvalues and eigenvectors of a real symmetric matrix.
LAPACK_EXAMPLES,
a FORTRAN90 program which
demonstrates the use of the LAPACK linear algebra library.
LINPACK,
a MATLAB library which
factors matrices,
computes determinants and inverses, solves linear systems,
for real and complex arithmetic, single and double precision,
and for general, banded, symmetric, tridiagonal, or triangular
matrices.
MATRIX_EXPONENTIAL,
a MATLAB library which
demonstrates some simple approaches to the problem of computing the
exponential of a matrix.
TEST_EIGEN,
a MATLAB library which
implements test matrices for eigenvalue analysis.
test_mat,
a MATLAB 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.
test_mat_test
TEST_MATRIX.
a MATLAB library which
contains Nick Higham's collection of test matrices.
TEST_MATRIX_EXPONENTIAL,
a MATLAB library which
defines a set of test cases for computing the matrix exponential.
WATHEN,
a MATLAB library which
compares storage schemes (full, banded, sparse triplet, sparse) and
solution strategies (A\x, Linpack, conjugate gradient) for linear systems
involving the Wathen matrix, which can arise when solving a
problem using the finite element method (FEM).
Source Code:
-
a123.m
returns the A123 matrix.
-
a123_determinant.m
returns the determinant of the A123 matrix.
-
a123_eigen_right.m
returns the right eigenvectors of the A123 matrix.
-
a123_eigenvalues.m
returns the eigenvalues of the A123 matrix.
-
a123_inverse.m
returns the inverse of the A123 matrix.
-
a123_null_left.m
returns a left null vector of the A123 matrix.
-
a123_right_left.m
returns a right null vector of the A123 matrix.
-
a123_plu.m
returns the PLU factors of the A123 matrix.
-
a123_qr.m
returns the QR factors of the A123 matrix.
-
a123_rhs.m
returns the right hand side of the A123 matrix.
-
a123_solution.m
returns the solution of the A123 matrix.
-
a123_svd.m
returns the SVD factors of the A123 matrix.
-
aegerter.m
returns the AEGERTER matrix.
-
aegerter_condition.m
returns the L1 condition number of the AEGERTER matrix.
-
aegerter_determinant.m
returns the determinant of the AEGERTER matrix.
-
aegerter_eigenvalues.m
returns the eigenvalues of the AEGERTER matrix.
-
aegerter_inverse.m
returns the inverse of the AEGERTER matrix.
-
anticirculant.m
returns the ANTICIRCULANT matrix.
-
anticirculant_determinant.m
returns the determinant of the ANTICIRCULANT matrix.
-
antihadamard.m
returns the ANTIHADAMARD matrix.
-
antihadamard_determinant.m
returns the determinant of the ANTIHADAMARD matrix.
-
antisymm_random.m
returns a random antisymmetric matrix.
-
archimedes.m
returns the ARCHIMEDES matrix.
-
archimedes_null_right.m
returns a right null vector for the ARCHIMEDES matrix.
-
bab.m
returns the BAB matrix.
-
bab_condition.m
returns the L1 condition number of the BAB matrix.
-
bab_determinant.m
returns the determinant of the BAB matrix.
-
bab_eigen_right.m
returns the right eigenvectors of the BAB matrix.
-
bab_eigenvalues.m
returns the eigenvalues of the BAB matrix.
-
bab_inverse.m
returns the inverse of the BAB matrix.
-
bernstein.m,
returns the BERNSTEIN matrix.
-
bernstein_determinant.m,
returns the determinant of the BERNSTEIN matrix.
-
bernstein_inverse.m,
returns the inverse of the BERNSTEIN matrix.
-
bernstein_poly_01.m,
evaluates the Bernstein polynomials based in [0,1].
-
bernstein_vandermonde.m,
returns the BERNSTEIN Vandermonde matrix.
-
bimarkov_random.m
returns a BIMARKOV_RANDOM matrix.
-
bis.m
returns the BIS matrix.
-
bis_condition.m
returns the condition of the BIS matrix.
-
bis_determinant.m
returns the determinant of the BIS matrix.
-
bis_eigenvalues.m
returns the eigenvalues of the BIS matrix.
-
bis_inverse.m
returns the inverse of the BIS matrix.
-
biw.m
returns the BIW matrix.
-
biw_condition.m
returns the L1 condition of the BIW matrix.
-
biw_determinant.m
returns the determinant of the BIW matrix.
-
biw_inverse.m
returns the inverse of the BIW matrix.
-
bodewig.m
returns the BODEWIG matrix.
-
bodewig_condition.m
returns the L1 condition of the BODEWIG matrix.
-
bodewig_determinant.m
returns the determinant of the BODEWIG matrix.
-
bodewig_eigen_right.m
returns the right eigenvectors of the BODEWIG matrix.
-
bodewig_eigenvalues.m
returns the eigenvalues of the BODEWIG matrix.
-
bodewig_inverse.m
returns the inverse of the BODEWIG matrix.
-
bodewig_plu.m
returns the PLU factors of the BODEWIG matrix.
-
bodewig_rhs.m
returns the right hand side of the BODEWIG matrix.
-
bodewig_solution.m
returns the solution of the BODEWIG matrix.
-
boothroyd.m
returns the BOOTHROYD matrix.
-
boothroyd_condition.m
returns the L1 condition of the BOOTHROYD matrix.
-
boothroyd_determinant.m
returns the determinant of the BOOTHROYD matrix.
-
boothroyd_inverse.m
returns the inverse of the BOOTHROYD matrix.
-
borderband.m
returns the BORDERBAND matrix.
-
borderband_determinant.m
returns the determinant of the BORDERBAND matrix.
-
borderband_inverse.m
returns the inverse of the BORDERBAND matrix.
-
borderband_plu.m
returns the P*L*U factors of the BORDERBAND matrix.
-
bvec_next_grlex.m
returns the next binary vector in GRLEX order.
-
c8_i.m
returns the value of the imaginary unit, i.
-
c8_le_l2.m
:= X <= Y for complex values, and the L2 norm.
-
c8_normal_01.m
returns a unit pseudonormal C8.
-
c8_one.m
returns the value of complex 1.
-
c8_swap.m
swaps two complex values.
-
c8_uniform_01.m
returns a unit pseudorandom C8.
-
c8_zero.m
returns the value of complex 0.
-
c8mat_house.m
constructs a complex Householder elementary reflector matrix.
-
c8mat_house_axh.m
computes A*H where H is a compact Householder matrix.
-
c8mat_house_form.m
constructs a Householder matrix from its compact form.
-
c8mat_identity.m
sets the square matrix A to the identity.
-
c8mat_indicator.m,
returns the C8MAT indicator matrix.
-
c8mat_is_column_orthogonal.m
checks if a C8MAT is column orthogonal.
-
c8mat_is_hermitian.m
checks if a C8MAT is hermitian.
-
c8mat_is_inverse.m
determines if one matrix is the inverse of another.
-
c8mat_is_row_orthogonal.m
checks if a C8MAT is row orthogonal.
-
c8mat_is_square.m,
determines if an C8MAT is square.
-
c8mat_is_symmetric.m
checks a C8MAT for symmetry.
-
c8mat_is_unit_column.m
checks whether A has columns of unit Euclidean norm.
-
c8mat_is_unit_unit_row.m
checks whether A has rows of unit Euclidean norm.
-
c8mat_is_unitary.m
checks whether a complex matrix is unitary.
-
c8mat_norm_fro.m
returns the Frobenius norm of an M by N matrix.
-
c8mat_print.m
prints a complex matrix, with an optional title.
-
c8mat_print_some.m
prints some of a complex matrix, with an optional title.
-
c8mat_uniform_01.m
returns a unit pseudorandom C8MAT.
-
c8vec_house_column.m
defines a Householder premultiplier that "packs" a column.
-
c8vec_norm_l2.m
returns the L2 norm of a complex vector.
-
c8vec_print.m
prints a complex vector, with an optional title.
-
c8vec_print_some.m
prints some of a complex vector.
-
c8vec_sort_a2.m
ascending sorts a complex array by L2 norm.
-
c8vec_uniform_01.m
returns a unit pseudorandom C8VEC.
-
c8vec_unity.m
returns the N roots of unity.
-
carry.m
returns the CARRY matrix.
-
carry_determinant.m
returns the determinant of the CARRY matrix.
-
carry_eigen_left.m
returns the left eigenvectors of the CARRY matrix.
-
carry_eigen_right.m
returns the right eigenvectors of the CARRY matrix.
-
carry_eigenvalues.m
returns the eigenvalues of the CARRY matrix.
-
carry_inverse.m
returns the inverse of the CARRY matrix.
-
cauchy.m
returns the CAUCHY matrix.
-
cauchy_determinant.m
returns the determinant of the CAUCHY matrix.
-
cauchy_inverse.m
returns the inverse of the CAUCHY matrix.
-
cheby_diff1.m
returns the CHEBY_DIFF1 matrix.
-
cheby_diff1_determinant.m
returns the determinant of the CHEBY_DIFF1 matrix.
-
cheby_diff1_null_left.m
returns a left null vector for the CHEBY_DIFF1 matrix.
-
cheby_diff1_null_right.m
returns a right null vector for the CHEBY_DIFF1 matrix.
-
cheby_t.m
returns the CHEBY_T matrix.
-
cheby_t_determinant.m
returns the determinant of the CHEBY_T matrix.
-
cheby_t_inverse.m
returns the inverse of the CHEBY_T matrix.
-
cheby_u.m
returns the CHEBY_U matrix.
-
cheby_u_determinant.m
returns the determinant of the CHEBY_U matrix.
-
cheby_u_inverse.m
returns the inverse of the CHEBY_U matrix.
-
cheby_u_polynomial.m
evaluates the Chebyshev polynomials of the second kind.
-
cheby_van1.m
returns the CHEBY_VAN1 matrix.
-
cheby_van2.m
returns the CHEBY_VAN2 matrix.
-
cheby_van2_determinant.m
returns the determinant of the CHEBY_VAN2 matrix.
-
cheby_van2_inverse.m
returns the inverse of the CHEBY_VAN2 matrix.
-
cheby_van3.m
returns the CHEBY_VAN3 matrix.
-
cheby_van3_determinant.m
inverts the determinant of the CHEBY_VAN3 marix.
-
cheby_van3_inverse.m
inverts the inverse of the CHEBY_VAN3 marix.
-
chow.m
returns the CHOW matrix.
-
chow_determinant.m
returns the determinant of the CHOW matrix.
-
chow_eigen_left.m
returns the left eigenvector matrix for the CHOW matrix.
-
chow_eigen_right.m
returns the right eigenvector matrix for the CHOW matrix.
-
chow_eigenvalues.m
returns the eigenvalues of the CHOW matrix.
-
chow_inverse.m
returns the inverse of the CHOW matrix.
-
circulant.m
returns the CIRCULANT matrix.
-
circulant_determinant.m
returns the determinant of the CIRCULANT matrix.
-
circulant_eigenvalues.m
returns the eigenvalues of the CIRCULANT matrix.
-
circulant_inverse.m
returns the inverse of the CIRCULANT matrix.
-
circulant2.m
returns the CIRCULANT2 matrix.
-
circulant2_determinant.m
returns the determinant of the CIRCULANT2 matrix.
-
circulant2_eigenvalues.m
returns the eigenvalues of the CIRCULANT2 matrix.
-
circulant2_inverse.m
returns the inverse of the CIRCUlANT2 matrix.
-
clement1.m
returns the CLEMENT1 matrix.
-
clement1__determinant.m
returns the determinant of the CLEMENT1 matrix.
-
clement1_eigenvalues.m
returns the eigenvalues of the CLEMENT1 matrix.
-
clement1_inverse.m
returns the inverse of the CLEMENT1 matrix.
-
clement2.m
returns the CLEMENT2 matrix.
-
clement2_determinant.m
returns the determinant of the CLEMENT2 matrix.
-
clement2_inverse.m
returns the inverse of the CLEMENT2 matrix.
-
colleague.m
returns the COLLEAGUE matrix.
-
combin.m
returns the COMBIN matrix.
-
combinant_condition.m
returns the condition of the COMBIN matrix.
-
combinant_determinant.m
returns the determinant of the COMBIN matrix.
-
combin_eigen_right.m
returns the right eigenvectors of the COMBIN matrix.
-
combin_eigenvalues.m
returns the eigenvalues of the COMBIN matrix.
-
combin_inverse.m
returns the inverse of the COMBIN matrix A.
-
companion.m
returns the COMPANION matrix.
-
companion_determinant.m
returns the determinant of the COMPANION matrix.
-
companion_inverse.m
returns the inverse of the COMPANION matrix.
-
complete_symmetric_poly.m
evaluates the complete symmetric polynomial for given variable
values.
-
complex3.m
returns the COMPLEX3 matrix.
-
complex3_inverse.m
returns the inverse of the COMPLEX3 matrix.
-
complex_i.m
returns the COMPLEX_I matrix.
-
complex_i_determinant.m
returns the determinant of the COMPLEX_I matrix.
-
complex_i_inverse.m
returns the inverse of the COMPLEX_I matrix.
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conex1.m
returns the CONEX1 matrix.
-
conex1_condition.m
returns the L1 condition of the CONEX1 matrix.
-
conex1_determinant.m
returns the determinant of the CONEX1 matrix.
-
conex1_inverse.m
returns the inverse of the CONEX1 matrix.
-
conex2.m
returns the CONEX2 matrix.
-
conex2_condition.m
returns the L1 condition of the CONEX2 matrix.
-
conex2_determinant.m
returns the determinant of the CONEX2 matrix.
-
conex2_inverse.m
returns the inverse of the CONEX2 matrix.
-
conex3.m
returns the CONEX3 matrix.
-
conex3_conditioni.m
returns the condition of the CONEX3 matrix.
-
conex3_determinant.m
returns the determinant of the CONEX3 matrix.
-
conex3_inverse.m
returns the inverse of the CONEX3 matrix.
-
conex4.m
returns the CONEX4 matrix.
-
conex4_conditioni.m
returns the condition of the CONEX4 matrix.
-
conex4_determinant.m
returns the determinant of the CONEX4 matrix.
-
conex4_inverse.m
returns the inverse of the CONEX4 matrix.
-
conference.m
returns the CONFERENCE matrix.
-
conference_determinant.m
returns the determinant of the CONFERENCE matrix.
-
conference_inverse.m
returns the inverse of the CONFERENCE matrix.
-
covar.m
returns the covariance matrix for a square nonsingular matrix.
-
covar2.m
returns the covariance matrix for a rectangular matrix.
-
creation.m
returns the CREATION matrix.
-
creation_determinant.m
returns the determinant of the CREATION matrix.
-
creation_null_left.m
returns a left null vector of the CREATION matrix.
-
creation_null_right.m
returns a right null vector of the CREATION matrix.
-
cycol_random.m
returns the K-cyclical column matrix.
-
daub2.m
returns the DAUB2 matrix.
-
daub2_condition.m
returns the L1 determinant of the DAUB2 matrix.
-
daub2_determinant.m
returns the determinant of the DAUB2 matrix.
-
daub2_inverse.m
returns the inverse of the DAUB2 matrix.
-
daub4.m
returns the DAUB4 matrix.
-
daub4_condition.m
returns the L1 determinant of the DAUB4 matrix.
-
daub4_determinant.m
returns the determinant of the DAUB4 matrix.
-
daub4_inverse.m
returns the inverse of the DAUB4 matrix.
-
daub6.m
returns the DAUB6 matrix.
-
daub6_condition.m
returns the L1 determinant of the DAUB6 matrix.
-
daub6_determinant.m
returns the determinant of the DAUB6 matrix.
-
daub6_inverse.m
returns the inverse of the DAUB6 matrix.
-
daub8.m
returns the DAUB8 matrix.
-
daub8_condition.m
returns the L1 determinant of the DAUB8 matrix.
-
daub8_determinant.m
returns the determinant of the DAUB8 matrix.
-
daub8_inverse.m
returns the inverse of the DAUB8 matrix.
-
daub10.m
returns the DAUB10 matrix.
-
daub10_condition.m
returns the L1 determinant of the DAUB10 matrix.
-
daub10_determinant.m
returns the determinant of the DAUB10 matrix.
-
daub10_inverse.m
returns the inverse of the DAUB10 matrix.
-
daub12.m
returns the DAUB12 matrix.
-
daub12_condition.m
returns the L1 determinant of the DAUB12 matrix.
-
daub12_determinant.m
returns the determinant of the DAUB12 matrix.
-
daub12_inverse.m
returns the inverse of the DAUB12 matrix.
-
diagonal.m
returns the DIAGONAL matrix.
-
diagonal_condition.m
returns the condition of the DIAGONAL matrix.
-
diagonal_determinant.m
returns the determinant of the DIAGONAL matrix.
-
diagonal_eigen_left.m
returns left eigenvectors of the DIAGONAL matrix.
-
diagonal_eigen_right.m
returns right eigenvectors of the DIAGONAL matrix.
-
diagonal_eigenvalues.m
returns the eigenvalues of the DIAGONAL matrix.
-
diagonal_inverse.m
returns the inverse of the DIAGONAL matrix.
-
dif1.m
returns the DIF1 matrix.
-
dif1_determinant.m
determinant of the DIF1 matrix.
-
dif1_eigenvalues.m
eigenvalues of the DIF1 matrix.
-
dif1_inverse.m
inverse of the DIF1 matrix.
-
dif1_null_left.m
returns a left null vector of the DIF1 matrix.
-
dif1_null_right.m
returns a right null vector of the DIF1 matrix.
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dif1cyclic.m
returns the DIF1CYCLIC matrix.
-
dif1cyclic_determinant.m
determinant of the DIF1CYCLIC matrix.
-
dif1cyclic_null_left.m
returns a left null vector of the DIF1CYCLIC matrix.
-
dif1cyclic_null_right.m
returns a right null vector of the DIF1CYCLIC matrix.
-
dif2.m
returns the DIF2 matrix.
-
dif2_condition.m
returns the L1 condition of the DIF2 matrix.
-
dif2_determinant.m
returns the determinant of the DIF2 matrix.
-
dif2_eigen_right.m
returns the right eigenvectors of the DIF2 matrix.
-
dif2_eigenvalues.m
returns the eigenvalues of the DIF2 matrix.
-
dif2_inverse.m
returns the inverse of the DIF2 matrix.
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dif2_llt.m
returns the Cholesky factor of the DIF2 matrix.
-
dif2_plu.m
returns the PLU factors of the DIF2 matrix.
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dif2_rhs.m
returns the right hand side of the DIF2 matrix.
-
dif2_solution.m
returns the solution of the DIF2 matrix.
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dif2cyclic.m
returns the DIF2CYCLIC matrix.
-
dif2cyclic_determinant.m
determinant of the DIF2CYCLIC matrix.
-
dif2cyclic_null_left.m
left null vector of the DIF2CYCLIC matrix.
-
dif2cyclic_null_right.m
right null vector of the DIF2CYCLIC matrix.
-
dorr.m
returns the DORR matrix.
-
dorr_determinant.m
returns the determinant of the DORR matrix.
-
dorr_inverse.m
returns the inverse of the DORR matrix.
-
downshift.m
returns the DOWNSHIFT matrix.
-
downshift_condition.m
returns the L1 condition of the DOWNSHIFT matrix.
-
downshift_determinant.m
returns the determinant of the DOWNSHIFT matrix.
-
downshift_eigenvalues.m
returns the eigenvalues of the DOWNSHIFT matrix.
-
downshift_inverse.m
returns the inverse of the DOWNSHIFT matrix.
-
drmac.m
returns the DRMAC matrix.
-
drmac_inverse.m
returns the inverse of the DRMAC matrix.
-
eberlein.m
returns the EBERLEIN matrix.
-
eberlein_determinant.m
returns the determinant of the EBERLEIN matrix.
-
eberlein_eigenvalues.m
returns the eigenvalues of the EBERLEIN matrix.
-
eberlein_null_left.m
returns a left null vector of the EBERLEIN matrix.
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eulerian.m
returns the EULERIAN matrix.
-
eulerian_determinant.m
returns the determinant of the EULERIAN matrix.
-
eulerian_inverse.m
computes the inverse of the EULERIAN matrix.
-
exchange.m
returns the EXCHANGE matrix.
-
exchange_condition.m,
returns the condition of the EXCHANGE matrix.
-
exchange_determinant.m
returns the determinant of the EXCHANGE matrix.
-
exchangev.m
returns the right eigenvectors of the EXCHANGE matrix.
-
exchange_eigenvalues.m
returns the eigenvalues of the EXCHANGE matrix.
-
exchange_inverse.m
returns the inverse of the EXCHANGE matrix.
-
fibonacci1.m
returns the FIBONACCI1 matrix.
-
fibonacci1_determinant.m
returns the determinant of the FIBONACCI1 matrix.
-
fibonacci1_null_left.m
returns a left null vector of the FIBONACCI1 matrix.
-
fibonacci1_null_right.m
returns a right null vector of the FIBONACCI1 matrix.
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fibonacci2.m
returns the FIBONACCI2 matrix.
-
fibonacci2_condition.m
returns the L1 condition of the FIBONACCI2 matrix.
-
fibonacci2_determinant.m
returns the determinant of the FIBONACCI2 matrix.
-
fibonacci2_eigenvalues.m
returns the eigenvalues of the FIBONACCI2 matrix.
-
fibonacci2_inverse.m
returns the inverse of the FIBONACCI2 matrix.
-
fibonacci3.m
returns the FIBONACCI3 matrix.
-
fibonacci3_determinant.m
returns the determinant of the FIBONACCI3 matrix.
-
fibonacci3_eigenvalues.m
returns the eigenvalues of the FIBONACCI3 matrix.
-
fibonacci3_inverse.m
returns the inverse of the FIBONACCI3 matrix.
-
fiedler.m
returns the FIEDLER matrix.
-
fiedler_determinant.m
returns the determinant of the FIEDLER matrix.
-
fiedler_inverse.m
returns the inverse of the FIEDLER matrix.
-
forsythe.m
returns the FORSYTHE matrix.
-
forsythe_determinant.m
returns the determinant of the FORSYTHE matrix.
-
forsythe_eigenvalues.m
returns the eigenvalues of the FORSYTHE matrix.
-
forsythe_inverse.m
returns the inverse of the FORSYTHE matrix.
-
fourier.m
returns the FOURIER matrix.
-
fourier_determinant.m
returns the determinant of the FOURIER matrix.
-
fourier_eigenvalues.m
returns the eigenvalues of the FOURIER matrix.
-
fourier_inverse.m
returns the inverse of the FOURIER matrix.
-
fourier_cosine.m
returns the FOURIER COSINE matrix.
-
fourier_cosine_determinant.m
returns the determinant of the FOURIER COSINE matrix.
-
fourier_cosine_inverse.m
returns the inverse of the FOURIER COSINE matrix.
-
fourier_sine.m
returns the FOURIER_SINE matrix.
-
fourier_sine_determinant.m
returns the determinant of the FOURIER_SINE matrix.
-
fourier_sine_inverse.m
returns the inverse of the FOURIER_SINE matrix.
-
frank.m
returns the FRANK matrix.
-
frank_determinant.m
returns the determinant of the FRANK matrix.
-
frank_eigenvalues.m
returns the eigenvalues of the FRANK matrix.
-
frank_inverse.m
returns the inverse of the FRANK matrix.
-
frank_rhs.m
returns the right hand side of the FRANK matrix.
-
frank_solution.m
returns the solution of the FRANK matrix.
-
gear.m
returns the GEAR matrix.
-
gear_determinant.m
returns the determinant of the GEAR matrix.
-
gear_eigenvalues.m
returns the eigenvalues of the GEAR matrix.
-
gfpp.m
returns the GFPP matrix.
-
gfpp_condition.m
returns the L1 condition of the GFPP matrix.
-
gfpp_determinant.m
returns the determinant of the GFPP matrix.
-
gfpp_inverse.m
returns the inverse of the GFPP matrix.
-
gfpp_plu.m
returns the PLU factorization of the GFPP matrix.
-
givens.m
returns the GIVENS matrix.
-
givens_condition.m
returns the L1 condition of the GIVENS matrix.
-
givens_determinant.m
returns the determinant of the GIVENS matrix.
-
givens_eigenvalues.m
returns the eigenvalues of the GIVENS matrix.
-
givens_inverse.m
returns the inverse of the GIVENS matrix.
-
givens_llt.m
returns the Cholesky factor of the GIVENS matrix.
-
givens_plu.m
returns the PLU factors of the GIVENS matrix.
-
gk316.m
returns the GK316 matrix, a Gregory and Karney test matrix.
-
gk316_determinant.m
returns the determinant of GK316.
-
gk316_eigenvalues.m
returns the eigenvalues of GK316.
-
gk316_inverse.m
returns the inverse of the GK316 matrix.
-
gk323.m
returns the GK323 matrix.
-
gk323_determinant.m
returns the determinant of the GK323 matrix.
-
gk323_inverse.m
returns the inverse of the GK323 matrix.
-
gk324.m
returns the GK324 matrix.
-
gk324_determinant.m
returns the determinant of the GK324 matrix.
-
gk324_inverse.m
returns the inverse of the GK324 matrix.
-
grcar.m
returns the GRCAR matrix.
-
hadamard.m
returns the HADAMARD matrix.
-
hamming.m
computes the HAMMING matrix.
-
hankel.m
returns the HANKEL matrix.
-
hankel_n.m
returns the HANKEL_N matrix.
-
hankel_n_condition.m
returns the L1 condition of the HANKEL_N matrix.
-
hankel_n_determinant.m
returns the determinant of the HANKEL_N matrix.
-
hankel_n_inverse.m
returns the inverse of the HANKEL_N matrix.
-
hanowa.m
returns the HANOWA matrix.
-
hanowa_determinant.m
returns the determinant of the HANOWA matrix.
-
hanowa_eigenvalues.m
returns the eigenvalues of the HANOWA matrix.
-
hanowa_inverse.m
returns the inverse of the HANOWA matrix.
-
harman.m
returns the HARMAN matrix.
-
harman_condition.m
returns the L1 condition of the HARMAN matrix.
-
harman_determinant.m
returns the determinant of the HARMAN matrix.
-
harman_inverse.m
returns the inverse of the HARMAN matrix.
-
hartley.m
returns the HARTLEY matrix.
-
hartley_condition.m
returns the L1 condition of the HARTLEY matrix.
-
hartley_determinant.m
returns the determinant of the HARTLEY matrix.
-
hartley_inverse.m
returns the inverse of the HARTLEY matrix.
-
helmert.m
returns the HELMERT matrix.
-
helmert_determinant.m
returns the determinant of the HELMERT matrix.
-
helmert_inverse.m
returns the inverse of the HELMERT matrix.
-
helmert2.m
returns the HELMERT2 matrix.
-
helmert2_inverse.m
returns the inverse of the HELMERT2 matrix.
-
hermite.m
returns the HERMITE matrix.
-
hermite_determinant.m
returns the determinant of the HERMITE matrix.
-
hermite_inverse.m
returns the inverse of the HERMITE matrix.
-
hermite_roots.m
returns the roots of a Hermite polynomial.
-
herndon.m
returns the HERNDON matrix.
-
herndon_determinant.m
returns the determinant of the HERNDON matrix.
-
herndon_eigenvalues.m
returns the eigenvalues of the HERNDON matrix.
-
herndon_inverse.m
returns the inverse of the HERNDON matrix.
-
hess4.m
returns the HESS4 matrix.
-
hess4_determinant.m
returns the determinant of the HESS4 matrix.
-
hess4_eigen_right.m
returns the right eigenvectors of the HESS4 matrix.
-
hess4_eigenvalues.m
returns the eigenvalues of the HESS4 matrix.
-
hess4_inverse.m
returns the inverse of the HESS4 matrix.
-
hess5.m
returns the HESS5 matrix.
-
hess5_determinant.m
returns the determinant of the HESS5 matrix.
-
hess5_eigen_right.m
returns the right eigenvectors of the HESS5 matrix.
-
hess5_eigenvalues.m
returns the eigenvalues of the HESS5 matrix.
-
hess5_inverse.m
returns the inverse of the HESS5 matrix.
-
hilbert.m
returns the HILBERT matrix.
-
hilbert_determinant.m
returns the determinant of the HILBERT matrix.
-
hilbert_inverse.m
returns the inverse of the HILBERT matrix.
-
hoffman.m
computes the HOFFMAN matrix.
-
hoffman_optimum.m
returns the Hoffman optimum solution.
-
hoffman_rhs.m
returns the right hand side for the HOFFMAN matrix.
-
householder.m
constructs a HOUSEHOLDER matrix.
-
householder_determinant.m
returns the determinant of a HOUSEHOLDER matrix.
-
householder_eigenvalues.m
returns the eigenvalues of a HOUSEHOLDER matrix.
-
householder_inverse.m
returns the inverse of a HOUSEHOLDER matrix.
-
i4_factor.m
factors an integer into prime factors.
-
i4_is_even.m
returns TRUE if I is even.
-
i4_is_odd.m
returns TRUE if I is odd.
-
i4_is_prime.m
reports whether an integer is prime.
-
i4_log_10.m
returns the integer part of the logarithm base 10 of abs ( X ).
-
i4_modp.m
returns the nonnegative remainder of integer division.
-
i4_rise.m
computes the integer rising factorial function.
-
i4_sign.m
returns the sign of an I4.
-
i4_swap.m
switches two integer values.
-
i4_uniform_ab.m
returns a scaled pseudorandom I4.
-
i4_wrap.m
forces an integer to lie between given limits by wrapping.
-
i4mat_print.m
prints an I4MAT.
-
i4mat_print_some.m
prints some of an I4MAT.
-
i4vec_index.m
returns the location of the first occurrence of a given value.
-
i4vec_indicator.m
sets an integer vector to the indicator vector.
-
i4vec_print.m
prints an integer vector, with an optional title.
-
idem_random.m
returns the IDEM_RANDOM matrix.
-
idem_random_determinant.m
returns the determinant of the IDEM_RANDOM matrix.
-
idem_random_eigen_right.m
returns the right eigenvectors of the IDEM_RANDOM matrix.
-
idem_random_eigenvalues.m
returns the eigenvalues of the IDEM_RANDOM matrix.
-
identity.m
returns the IDENTITY matrix.
-
identity_condition.m
returns the L1 condition of the IDENTITY matrix.
-
identity_determinant.m
returns the determinant of the IDENTITY matrix.
-
identity_eigen_left.m
returns the left eigenvectors of the IDENTITY matrix.
-
identity_eigen_right.m
returns the right eigenvectors of the IDENTITY matrix.
-
identity_eigenvalues.m
returns the eigenvalues of the IDENTITY matrix.
-
identity_inverse.m
returns the inverse of the IDENTITY matrix.
-
ijfact1.m
returns the IJFACT1 matrix.
-
ijfact1_determinant.m
returns the determinant of the IJFACT1 matrix.
-
ijfact2.m
returns the IFJACT2 matrix.
-
ijfact2_determinant.m
returns the determinant of the IJFACT2 matrix.
-
ill3.m
returns the ILL3 matrix, an ill conditioned 3 by 3 matrix.
-
ill3_condition.m
returns the condition of the ILL3 matrix.
-
ill3_determinant.m
returns the determinant of the ILL3 matrix.
-
ill3_eigen_right.m
returns the right eigenvectors of the ILL3 matrix.
-
ill3_eigenvalues.m
returns the eigenvalues of the ILL3 matrix.
-
ill3_inverse.m
returns the inverse of the ILL3 matrix.
-
indicator.m
sets the INDICATOR matrix.
-
integration.m
returns the INTEGRATION matrix.
-
integration_determinant.m
returns the determinant of the INTEGRATION matrix.
-
integration_eigenvalues.m
returns the eigenvalues of the INTEGRATION matrix.
-
integration_inverse.m
returns the inverse of the INTEGRATION matrix.
-
invol.m
returns the INVOL matrix.
-
invol_determinant.m
returns the determinant of the INVOL matrix.
-
invol_eigenvalues.m
returns the eigenvalues of the INVOL matrix.
-
invol_inverse.m
returns the inverse of the INVOL matrix.
-
invol_random.m
returns an INVOL_RANDOM matrix.
-
jacobi.m
returns the JACOBI matrix.
-
jacobi_determinant.m
returns the determinant of the JACOBI matrix.
-
jacobi_eigenvalues.m
returns the eigenvalues of the JACOBI matrix.
-
jacobi_inverse.m
returns the inverse of the JACOBI matrix.
-
jacobi_iterate.m
applies the Jacobi eigenvalue iteration to a symmetric matrix.
-
jacobi_symbol.m
evaluates the Jacobi symbol (Q/P).
-
jordan.m
returns the JORDAN matrix.
-
jordan_condition.m
returns the L1 condition of a JORDAN matrix.
-
jordan_determinant.m
returns the determinant of a JORDAN matrix.
-
jordan_eigenvalues.m
returns the eigenvalues of a JORDAN matrix.
-
jordan_inverse.m
returns the inverse of the JORDAN matrix.
-
kahan.m
returns the KAHAN matrix.
-
kahan_determinant.m
returns the determinant of the KAHAN matrix.
-
kahan_inverse.m
returns the inverse of the KAHAN matrix.
-
kershaw.m
returns the KERSHAW matrix.
-
kershaw_condition.m
returns the L1 condition of the KERSHAW matrix.
-
kershaw_determinant.m
returns the determinant of the KERSHAW matrix.
-
kershaw_eigenright.m
returns right eigenvalues of the KERSHAW matrix.
-
kershaw_eigenvalues.m
returns the eigenvalues of the KERSHAW matrix.
-
kershaw_inverse.m
returns the inverse of the KERSHAW matrix.
-
kershaw_llt.m
returns the Cholesky factor of the KERSHAW matrix.
-
kershawtri.m
returns the KERSHAWTRI matrix.
-
kershawtri_determinant.m
returns the determinant of the KERSHAWTRI matrix.
-
kershawtri_inverse.m
returns the inverse of the KERSHAWTRI matrix.
-
kms.m
returns the KMS matrix.
-
kms_determinant.m
returns the determinant of the KMS matrix.
-
kms_eigenvalues.m
returns the eigenvalues of the KMS matrix.
-
kms_eigenvalues_theta.m
returns data needed to compute the eigenvalues of the KMS matrix.
-
kms_eigenvalues_theta_f.m
evaluates a function for eigenvalues of the KMS matrix.
-
kms_inverse.m
returns the inverse of the KMS matrix.
-
kms_ldl.m
returns the LDL factorization of the KMS matrix.
-
kms_plu.m
returns the PLU factorization of the KMS matrix.
-
krylov.m
returns a KRYLOV matrix.
-
laguerre.m
returns the LAGUERRE matrix.
-
laguerre_determinant.m
returns the determinant of the LAGUERRE matrix.
-
laguerre_inverse.m
returns the inverse of the LAGUERRE matrix.
-
lauchli.m
returns the LAUCHLI matrix.
-
lauchli_null_left.m
returns a left null vector for the LAUCHLI matrix.
-
legendre.m
returns the LEGENDRE matrix.
-
legendre_determinant.m
returns the determinant of the LEGENDRE matrix.
-
legendre_inverse.m
returns the inverse of the LEGENDRE matrix.
-
legendre_symbol.m
evaluates the Legendre symbol (Q/P).
-
legendre_van.m
returns the LEGENDRE_VAN matrix.
-
legendre_zeros.m
computes the zeros of the Legendre polynomial.
-
lehmer.m
returns the LEHMER matrix.
-
lehmer_determinant.m
returns the determinant of the LEHMER matrix.
-
lehmer_inverse.m
returns the inverse of the LEHMER matrix.
-
lehmer_llt.m
returns the lower triangular Cholesky factor of the LEHMER matrix.
-
lehmer_plu.m
returns the PLU factors of the LEHMER matrix.
-
leslie.m
returns the LESLIE matrix, for population dynamics.
-
leslie_determinant.m
returns the determinant of the LESLIE matrix.
-
lesp.m
returns the LESP matrix.
-
lesp_determinant.m
returns the determinant of the LESP matrix.
-
lesp_inverse.m
returns the inverse of the LESP matrix.
-
lietzke.m
returns the LIETZKE matrix.
-
lietzke_condition.m
returns the L1 condition of the LIETZKE matrix.
-
lietzke_determinant.m
returns the determinant of the LIETZKE matrix.
-
lietzke_inverse.m
returns the inverse of the LIETZKE matrix.
-
lights_out.m
returns the LIGHTS_OUT matrix.
-
line_adj.m
returns the LINE_ADJ matrix.
-
line_adj_determinant.m
returns the determinant of the LINE_ADJ matrix.
-
line_adj_eigen_right.m
returns the right eigenvectors of the LINE_ADJ matrix.
-
line_adj_eigenvalues.m
returns the eigenvalues of the LINE_ADJ matrix.
-
line_adj_inverse.m
returns the inverse of the LINE_ADJ matrix.
-
line_adj_null_left.m
returns a right null vector of the LINE_ADJ matrix.
-
line_adj_null_right.m
returns a right null vector of the LINE_ADJ matrix.
-
line_loop_adj.m
returns the LINE_LOOP_ADJ matrix.
-
line_loop_adj_determinant.m
returns the detereminant of the LINE_LOOP_ADJ matrix.
-
line_loop_adj_eigen_right.m
returns the right eigenvectors of the LINE_LOOP_ADJ matrix.
-
line_loop_adj_eigenvalues.m
returns the eigenvalues of the LINE_LOOP_ADJ matrix.
-
loewner.m
returns the LOEWNER matrix.
-
lotkin.m
returns the LOTKIN matrix.
-
lotkin_determinant.m
returns the determinant of the LOTKIN matrix.
-
lotkin_inverse.m
returns the inverse of the LOTKIN matrix.
-
markov_random.m
returns a random Markov matrix.
-
maxij.m
returns the MAXIJ matrix.
-
maxij_condition.m
returns the L1 condition of the MAXIJ matrix.
-
maxij_determinant.m
returns the determinant of the MAXIJ matrix.
-
maxij_inverse.m
returns the inverse of the MAXIJ matrix.
-
maxij_plu.m
returns the PLU factors of the MAXIJ matrix.
-
mertens.m
evaluates the Mertens function.
-
mertens_values.m
returns some values of the Mertens function.
-
milnes.m
returns the MILNES matrix.
-
milnes_determinant.m
returns the determinant of the MILNES matrix.
-
milnes_inverse.m
returns the inverse of the MILNES matrix.
-
minij.m
returns the MINIJ matrix.
-
minij_condition.m
returns the L1 condition of the MINIJ matrix.
-
minij_determinant.m
returns the determinant of the MINIJ matrix.
-
minij_eigenvalues.m
returns the eigenvalues of the MINIJ matrix.
-
minij_inverse.m
returns the inverse of the MINIJ matrix.
-
minij_llt.m
returns the Cholesky factor of the MINIJ matrix.
-
minij_plu.m
returns the P*L*U factors of the MINIJ matrix.
-
moebius.m
returns the value of MU(N), the Moebius function of N.
-
moebius_values.m
returns some values of the Moebius function.
-
moler1.m
returns the MOLER1 matrix.
-
moler1_determinant.m
returns the determinant of the MOLER1 matrix.
-
moler1_inverse.m
returns the inverse of the MOLER1 matrix.
-
moler1_llt.m
returns the lower triangular Cholesky factor of the MOLER1 matrix.
-
moler1_plu.m
returns the P*L*U factors of the MOLER1 matrix.
-
moler2.m
returns the MOLER2 matrix.
-
moler2_determinant.m
returns the determinant of the MOLER2 matrix.
-
moler2_eigenvalues.m
returns the eigenvalues of the MOLER2 matrix.
-
moler2_null_left.m
returns a left null vector of the MOLER2 matrix.
-
moler2_null_right.m
returns a right null vector of the MOLER2 matrix.
-
moler3.m
returns the MOLER3 matrix.
-
moler3_determinant.m
returns the determinant of the MOLER3 matrix.
-
moler3_inverse.m
returns the inverse of the MOLER3 matrix.
-
moler3_llt.m
returns the Cholesky factor of the MOLER3 matrix.
-
moler3_plu.m
returns the PLU factors of the MOLER3 matrix.
-
moler4.m
returns the MOLER4 matrix.
-
moler4_condition.m
returns the L1 condition of the MOLER4 matrix.
-
moler4_determinant.m
returns the determinant of the MOLER4 matrix.
-
moler4_eigenvalues.m
returns the eigenvalues of the MOLER4 matrix.
-
moler4_inverse.m
returns the inverse of the MOLER4 matrix.
-
neumann.m
returns the NEUMANN matrix.
-
neumann_determinant.m
returns the determinant of the NEUMANN matrix.
-
neumann_null_right.m
returns a right null vector of the NEUMANN matrix.
-
one.m
returns the ONE matrix.
-
one_determinant.m
returns the determinant of the ONE matrix.
-
one_eigen_right.m
returns the right eigenvectors of the ONE matrix.
-
one_eigenvalues.m
returns the eigenvalues of the ONE matrix.
-
one_null_left.m
returns a left null vector of the ONE matrix.
-
one_null_right.m
returns a right null vector of the ONE matrix.
-
ortega.m
returns the ORTEGA matrix.
-
ortega_determinant.m
returns the determinant of the ORTEGA matrix.
-
ortega_eigen_right.m
returns the right eigenvectors of the ORTEGA matrix.
-
ortega_eigenvalues.m
returns the eigenvalues of the ORTEGA matrix.
-
ortega_inverse.m
returns the inverse of the ORTEGA matrix.
-
orth_random.m
returns the ORTH_RANDOM matrix.
-
orth_random_determinant.m
returns the determinant of the ORTH_RANDOM matrix.
-
orth_symm.m
returns the ORTH_SYMM matrix.
-
orth_symm_condition.m
returns the L1 condition of the ORTH_SYMM matrix.
-
orth_symm_determinant.m
returns the determinant of the ORTH_SYMM matrix.
-
orth_symm_eigenvalues.m
returns eigenvalues of the orthogonal symmetric matrix.
-
orth_symm_inverse.m
returns the inverse of the ORTH_SYMM matrix.
-
oto.m
returns the OTO matrix.
-
oto_condition.m
returns the L1 condition of the OTO matrix.
-
oto_determinant.m
returns the determinant of the OTO matrix.
-
oto_eigen_right.m
returns the right eigenvectors of the OTO matrix.
-
oto_eigenvalues.m
returns the eigenvalues of the OTO matrix.
-
oto_inverse.m
returns the inverse of the OTO matrix.
-
oto_llt.m
returns the lower triangular Cholesky factor of the OTO matrix.
-
oto_plu.m
returns the P*L*U factors of the OTO matrix.
-
parlett.m
returns the PARLETT matrix.
-
parlett_eigenvalues.m
returns the eigenvalues of the PARLETT matrix.
-
parter.m
returns the PARTER matrix.
-
parter_determinant.m
returns the determinant of the PARTER matrix.
-
parter_inverse.m
returns the inverse of the PARTER matrix.
-
pascal1.m
returns the PASCAL1 matrix.
-
pascal1_condition.m
returns the L1 condition of the PASCAL1 matrix.
-
pascal1_determinant.m
returns the determinant of the PASCAL1 matrix.
-
pascal1_eigenvalues.m
returns eigenvalues of the PASCAL1 matrix.
-
pascal1_inverse.m
returns the inverse of the PASCAL1 matrix.
-
pascal2.m
returns the PASCAL2 matrix.
-
pascal2_determinant.m
returns the determinant of the PASCAL2 matrix.
-
pascal2_inverse.m
returns the inverse of the PASCAL2 matrix.
-
pascal2_llt.m
returns the Cholesky factor of the PASCAL2 matrix.
-
pascal2_plu.m
returns the P*L*U factors of the PASCAL2 matrix.
-
pascal3.m
returns the PASCAL3 matrix.
-
pascal3_condition.m
returns the L1 condition of the PASCAL3 matrix.
-
pascal3_determinant.m
returns the determinant of the PASCAL3 matrix.
-
pascal3_inverse.m
returns the inverse of the PASCAL3 matrix.
-
pds_random.m
returns the PDS_RANDOM matrix.
-
pds_random_determinant.m
returns the determinant of the PDS_RANDOM matrix.
-
pds_random_eigen_right.m
returns the right eigenvectors of the PDS_RANDOM matrix.
-
pds_random_eigenvalues.m
returns the eigenvalues of the PDS_RANDOM matrix.
-
pds_random_inverse.m
returns the inverse of the PDS_RANDOM matrix.
-
pei.m
returns the PEI matrix.
-
pei_condition.m
returns the L1 condition of the PEI matrix.
-
pei_determinant.m
returns the determinant of the PEI matrix.
-
pei_eigen_right.m
returns the right eigenvectors of the PEI matrix.
-
pei_eigenvalues.m
returns the eigenvalues of the PEI matrix.
-
pei_inverse.m
returns the inverse of the PEI matrix.
-
perm_check.m
checks that a vector represents a permutation.
-
perm_inverse.m
checks that a vector represents a permutation.
-
perm_mat_to_vec.m
converts a permutation from matrix to vector form.
-
perm_sign.m
returns the sign of a permutation.
-
perm_vec_to_mat.m
converts a permutation from vector to matrix form.
-
permutation_determinant.m
returns the determinant of a permutation matrix.
-
permutation_random.m
returns the PERMUTATION_RANDOM matrix.
-
permutation_random_determinant.m
returns the determinant of the PERMUTATION_RANDOM matrix.
-
permutation_random_inverse.m
returns the inverse of the PERMUTATION_RANDOM matrix.
-
pick.m
returns the PICK matrix.
-
plu.m
returns the PLU matrix.
-
plu_determinant.m
returns the determinant of the PLU matrix.
-
plu_inverse.m
returns the inverse of the PLU matrix.
-
plu_plu.m
returns the PLU factors of the PLU matrix.
-
poisson.m
returns the POISSON matrix.
-
poisson_determinant.m
returns the determinant of the POISSON matrix.
-
poisson_eigenvalues.m
returns the eigenvalues of the POISSON matrix.
-
poisson_rhs.m
returns the right hand side of a linear system involving the POISSON matrix.
-
poisson_solution.m
returns the solution of a linear system involving the POISSON matrix.
-
prime.m
returns any of the first PRIME_MAX prime numbers.
-
prolate.m
returns the PROLATE matrix.
-
propa_no_random.m
returns a random matrix that does not have property A.
-
propa_yes_random.m
returns a random matrix with property A.
-
quaternion_i.m
returns the QUATERNION_I matrix.
-
quaternion_j.m
returns the QUATERNION_J matrix.
-
quaternion_k.m
returns the QUATERNION_K matrix.
-
r8_choose.m,
returns Choose(N,K) as an R8;
-
r8_factorial.m,
returns N! as an R8;
-
r8_mop.m,
returns a minus-one-power as an R8;
-
r8_normal_01.m,
returns a unit pseudonormal R8;
-
r8_pi.m,
returns the value of Pi as an R8;
-
r8_sign.m,
returns the sign of an R8.
-
r8_uniform_01.m,
returns a unit pseudorandom R8;
-
r8_uniform_ab.m,
returns a scaled pseudorandom R8;
-
r8col_swap.m,
swaps two columns of an R8COL;
-
r8col_to_r8vec.m,
converts an R8COL to a R8VEC;
-
r8mat_cholesky_factor.m,
computes the Cholesky factor of a symmetric real matrix.
-
r8mat_determinant.m,
computes the determinant of a real matrix.
-
r8mat_diag_add_scalar.m,
adds a scalar to the diagonal of a R8MAT;
-
r8mat_diag_get_vector.m,
gets the diagonal of a R8MAT;
-
r8mat_diag_set_scalar.m,
sets the diagonal of a R8MAT to a scalar;
-
r8mat_geco.m,
factors a real matrix and estimates its condition number.
-
r8mat_gedet.m,
computes the determinant of a matrix factored by R8MAT_GEFA.
-
r8mat_gefa.m,
factors a general matrix.
-
r8mat_geinverse.m,
computes the inverse of a matrix factored by R8MAT_GEFA.
-
r8mat_geplu.m,
produces the PLU factors of a real rectangular matrix.
-
r8mat_gesl.m,
solves a system factored by R8MAT_GEFA.
-
r8mat_house_axh.m,
computes A*H, where H is a compact Householder matrix;
-
r8mat_house_form.m,
constructs a Householder matrix from its compact form;
-
r8mat_identity.m,
sets a R8MAT to the identity matrix;
-
r8mat_inverse.m,
computes the inverse of an R8MAT;
-
r8mat_is_adjacency.m,
is TRUE if an R8MAT is an adjacency matrix.
-
r8mat_is_anticirculant.m,
is TRUE if an R8MAT is an anticirculant matrix.
-
r8mat_is_antipersymmetric.m,
is TRUE if an R8MAT is an antipersymmetric matrix.
-
r8mat_is_antisymmetric.m,
is TRUE if an R8MAT is an antisymmetric matrix.
-
r8mat_is_banded.m,
is TRUE if an R8MAT is a banded matrix.
-
r8mat_is_centrosymmetric.m,
is TRUE if an R8MAT is a centrosymmetric matrix.
-
r8mat_is_circulant.m,
is TRUE if an R8MAT is a circulant matrix.
-
r8mat_is_cyclic_tridiagonal.m,
is TRUE if an R8MAT is a cyclic tridiagonal matrix.
-
r8mat_is_diag2.m,
returns the number of nonzero diagonals.
-
r8mat_is_diagonally_dominant.m,
is TRUE if an R8MAT is diagonally dominant.
-
r8mat_is_diagonally_dominant_column.m,
is TRUE if an R8MAT is column diagonally dominant.
-
r8mat_is_diagonally_dominant_row.m,
is TRUE if an R8MAT is row diagonally dominant.
-
r8mat_is_eigen_left.m,
determines the error in a left eigensystem.
-
r8mat_is_eigen_right.m,
determines the error in a right eigensystem.
-
r8mat_is_hankel.m,
is TRUE if an R8MAT is a Hankel matrix.
-
r8mat_is_identity.m,
determines if a matrix is the identity matrix.
-
r8mat_is_integer.m,
is TRUE if an R8MAT is an integer matrix.
-
r8mat_is_inverse.m,
determines if one matrix is the inverse of another.
-
r8mat_is_inverse_left.m,
determines if one matrix is the left inverse of another.
-
r8mat_is_inverse_right.m,
determines if one matrix is the right inverse of another.
-
r8mat_is_irreducible.m,
is TRUE if an R8MAT is an irreducible matrix.
-
r8mat_is_l.m,
is TRUE if an R8MAT is an L matrix.
-
r8mat_is_llt.m,
determines the error in a lower triangular Cholesky factorization,
||A-LL'||.
-
r8mat_is_m.m,
is TRUE if an R8MAT is an M matrix.
-
r8mat_is_negative.m,
is TRUE if an R8MAT is a negative matrix.
-
r8mat_is_normal.m,
is TRUE if an R8MAT is a normal matrix.
-
r8mat_is_null_left.m,
determines the error in a left null vector, ||x'*A'||.
-
r8mat_is_null_right.m,
determines the error in a right null vector, ||A*x||.
-
r8mat_is_orthogonal.m,
is TRUE if an R8MAT is orthogonal.
-
r8mat_is_orthogonal_column.m,
is TRUE if an R8MAT is column orthogonal.
-
r8mat_is_orthogonal_row.m,
is TRUE if an R8MAT is row orthogonal.
-
r8mat_is_pds.m,
is TRUE if an R8MAT is a positive definite symmetric matrix.
-
r8mat_is_permutation.m,
is TRUE if an R8MAT is a permutation matrix.
-
r8mat_is_persymmetric.m,
is TRUE if an R8MAT is a persymmetric matrix.
-
r8mat_is_plu.m,
determines the error in a P*L*U factorization of a matrix.
-
r8mat_is_positive.m,
is TRUE if an R8MAT is a positive matrix.
-
r8mat_is_propa.m,
is TRUE if an R8MAT is a property A matrix.
-
r8mat_is_ref.m,
is TRUE if an R8MAT is a row echelon form matrix.
-
r8mat_is_scalar.m,
is TRUE if an R8MAT is a scalar matrix.
-
r8mat_is_solution.m,
measures the error in solutions of A*X-B.
-
r8mat_is_sparse.m,
returns the relative sparseness of a matrix.
-
r8mat_is_square.m,
determines if an R8MAT is square.
-
r8mat_is_sum.m,
is TRUE if an R8MAT has constant row or column sums.
-
r8mat_is_symmetric.m,
determines if an R8MAT is symmetric.
-
r8mat_is_toeplitz.m,
is TRUE if an R8MAT is a Toeplitz matrix.
-
r8mat_is_tournament.m,
is TRUE if an R8MAT is a tournament matrix.
-
r8mat_is_transition.m,
determines if a matrix is a transition matrix.
-
r8mat_is_triangular.m,
is TRUE if an R8MAT is a triangular matrix.
-
r8mat_is_unit_column.m,
is TRUE if an R8MAT has columns of unit norm.
-
r8mat_is_unit_row.m,
is TRUE if an R8MAT has rows of unit norm.
-
r8mat_is_zero_one.m,
is TRUE if an R8MAT is a zero-one matrix.
-
r8mat_norm_eis.m,
computes the EISPACK norm of a matrix;
-
r8mat_norm_fro.m,
computes the Frobenius norm of a R8MAT;
-
r8mat_norm_l1.m,
computes the L1 norm of a R8MAT;
-
r8mat_norm_l2.m,
computes the L2 norm of a R8MAT;
-
r8mat_norm_li.m,
computes the L-infinity norm of a R8MAT;
-
r8mat_plot.m,
plots a R8MAT, with an optional title;
-
r8mat_plot_symbol.m,
returns a symbol for a double precision number;
-
r8mat_poly_char.m,
computes the characteristic polynomial of a R8MAT;
-
r8mat_print.m
prints a matrix.
-
r8mat_print_some.m
prints SOME of a matrix.
-
r8mat_symm_jacobi.m,
applies Jacobi eigenvalue iteration to a symmetric matrix.
-
r8mat_trace.m,
returns the trace of a R8MAT;
-
r8mat_uniform_01.m,
returns a unit pseudorandom R8MAT;
-
r8mat_uniform_ab.m,
returns an R8MAT of scaled pseudorandom numbers;
-
r8poly_order.m,
returns the order of a polynomial.
-
r8poly_print.m,
prints a polynomial;
-
r8row_swap.m,
swaps two rows of an R8ROW.
-
r8row_to_r8vec.m,
converts an R8ROW into an R8VEC.
-
r8vec_house_column.m,
defines a Householder premultiplier that "packs" a column;
-
r8vec_indicator.m,
sets a R8VEC to the indicator vector;
-
r8vec_linspace.m,
returns evenly spaced data as an R8VEC.
-
r8vec_norm_l2.m,
returns the L2 norm of a R8VEC.
-
r8vec_print.m,
prints a R8VEC;
-
r8vec_uniform_01.m,
returns a unit pseudorandom R8VEC.
-
r8vec_uniform_ab.m,
returns a vector of scaled pseudorandom values;
-
r8vec2_print.m,
prints a pair of R8VEC's;
-
rayleigh.m,
returns the Rayleigh quotient of the matrix A and the vector X.
-
rayleigh2.m,
returns the generalized Rayleigh quotient.
-
rectangle_adj.m,
returns the RECTANGLE_ADJ matrix.
-
rectangle_adj_determinant.m,
returns the determinant of the RECTANGLE_ADJ matrix.
-
redheffer.m,
returns the REDHEFFER matrix.
-
redheffer_determinant.m,
returns the determinant of the REDHEFFER matrix.
-
ref_random.m,
returns the REF_RANDOM matrix, a random row echelon matrix.
-
ref_random.m,
returns the determinant of the REF_RANDOM matrix,
a random row echelon matrix.
-
riemann.m,
returns the RIEMANN matrix.
-
ring_adj.m,
returns the RING_ADJ matrix.
-
ring_adj_determinant.m,
returns the determinant of the RING_ADJ matrix.
-
ris.m,
returns the RIS matrix.
-
ris_determinant.m,
returns the determinant of the RIS matrix.
-
ris_inverse.m,
returns the inverse of the RIS matrix.
-
rodman.m,
returns the RODMAN matrix.
-
rodman_condition.m,
returns the L1 condition of the RODMAN matrix.
-
rodman_determinant.m,
returns the determinant of the RODMAN matrix.
-
rodman_eigen_right.m
returns the right eigenvectors of the RODMAN matrix.
-
rodman_eigenvalues.m,
returns the eigenvalues of the RODMAN matrix.
-
rodman_inverse.m,
returns the inverse of the RODMAN matrix.
-
rosser1.m,
returns the ROSSER1 matrix.
-
rosser1_determinant.m,
returns the determinant of the ROSSER1 matrix.
-
rosser1_eigen_left.m,
returns the left eigenvectors of the ROSSER1 matrix.
-
rosser1_eigen_right.m,
returns the right eigenvectors of the ROSSER1 matrix.
-
rosser1_eigenvalues.m,
returns the eigenvalues of the ROSSER1 matrix.
-
rosser1_null_left.m,
returns a left null vector of the ROSSER1 matrix.
-
rosser1_null_right.m,
returns a right null vector of the ROSSER1 matrix.
-
routh.m,
returns the ROUTH matrix.
-
routh_determinant.m,
returns the determinant of the ROUTH matrix.
-
rowcolsum_matrix.m,
returns the ROWCOLSUM matrix.
-
rutis1.m,
returns the RUTIS1 matrix.
-
rutis1_condition.m,
returns the condition of the RUTIS1 matrix.
-
rutis1_determinant.m,
returns the determinant of the RUTIS1 matrix.
-
rutis1_eigen_right.m,
returns the right eigenvectors of the RUTIS1 matrix.
-
rutis1_eigenvalues.m,
returns the eigenvalues of the RUTIS1 matrix.
-
rutis1_inverse.m,
returns the inverse of the RUTIS1 matrix.
-
rutis2.m,
returns the RUTIS2 matrix.
-
rutis2_condition.m,
returns the condition of the RUTIS2 matrix.
-
rutis2_determinant.m,
returns the determinant of the RUTIS2 matrix.
-
rutis2_eigen_right.m,
returns the right eigenvectors of the RUTIS2 matrix.
-
rutis2_eigenvalues.m,
returns the eigenvalues of the RUTIS2 matrix.
-
rutis2_inverse.m,
returns the inverse of the RUTIS2 matrix.
-
rutis3.m,
returns the RUTIS3 matrix.
-
rutis3_condition.m,
returns the condition of the RUTIS3 matrix.
-
rutis3_determinant.m,
returns the determinant of the RUTIS3 matrix.
-
rutis3_eigen_left.m,
returns the left eigenvectors of the RUTIS3 matrix.
-
rutis3_eigen_right.m,
returns the right eigenvectors of the RUTIS3 matrix.
-
rutis3_eigenvalues.m,
returns the eigenvalues of the RUTIS3 matrix.
-
rutis3_inverse.m,
returns the inverse of the RUTIS3 matrix.
-
rutis4.m,
returns the RUTIS4 matrix.
-
rutis4_determinant.m,
returns the determinant of the RUTIS4 matrix.
-
rutis4_eigenvalues.m,
returns the eigenvalues of the Rutishauser4 matrix.
-
rutis5.m,
returns the RUTIS5 matrix.
-
rutis5_condition.m,
returns the L1 condition of the RUTIS5 matrix.
-
rutis5_determinant.m,
returns the determinant of the RUTIS5 matrix.
-
rutis5_eigen_right.m,
returns the right eigenvectors of the RUTIS5 matrix.
-
rutis5_eigenvalues.m,
returns the eigenvalues of the RUTIS5 matrix.
-
rutis5_inverse.m,
returns the inverse of the RUTIS5 matrix.
-
s_len_trim.m
returns the length of a string to the last nonblank.
-
schur_block.m
returns the SCHUR_BLOCK matrix.
-
schur_block_determinant.m
returns the determinant of the SCHUR_BLOCK matrix.
-
schur_block_eigenvalues.m
returns the eigenvalues of the SCHUR_BLOCK matrix.
-
schur_block_inverse.m
returns the inverse of the SCHUR_BLOCK matrix.
-
skew_circulant.m
returns a SKEW_CIRCULANT matrix.
-
skew_circulant_determinant.m
returns the determinant of the SKEW_CIRCULANT matrix.
-
skew_circulant_eigenvalues.m
returns eigenvalues of the SKEW_CIRCULANT matrix.
-
smoke.m
returns the SMOKE matrix.
-
smoke_determinant.m
returns the determinant of the SMOKE matrix.
-
smoke_eigenvalues.m
returns the eigenvalues of the SMOKE matrix.
-
snakes.m
returns the SNAKES matrix.
-
sort_heap_external.m,
externally sorts a list of values into ascending order;
-
spline.m
returns the SPLINE matrix.
-
spline_determinant.m
returns the determinant of the SPLINE matrix.
-
spline_inverse.m
returns the inverse of the SPLINE matrix.
-
stirling.m
returns the STIRLING matrix.
-
stirling_determinant.m
returns the determinant of the STIRLING matrix.
-
stirling_inverse.m
returns the inverse of the STIRLING matrix.
-
stripe.m
returns the STRIPE matrix.
-
sub_random.m
selects a random subset of an N-set.
-
sudoku_adj.m
returns the SUDOKU_ADJ matrix.
-
summation.m
returns the SUMMATION matrix.
-
summation_condition.m
returns the L1 condition of the SUMMATION matrix.
-
summation_determinant.m
returns the determinant of the SUMMATION matrix.
-
summation_eigenvalues.m
returns the eigenvalues of the SUMMATION matrix.
-
summation_inverse.m
returns the inverse of the SUMMATION matrix.
-
sweet1.m
returns the SWEET1 matrix.
-
sweet1_condition.m
returns the L1 condition of the SWEET1 matrix.
-
sweet1_determinant.m
returns the determinant of the SWEET1 matrix.
-
sweet1_inverse.m
returns the inverse of the SWEET1 matrix.
-
sweet2.m
returns the SWEET2 matrix.
-
sweet2_condition.m
returns the L1 condition of the SWEET2 matrix.
-
sweet2_determinant.m
returns the determinant of the SWEET2 matrix.
-
sweet2_inverse.m
returns the inverse of the SWEET2 matrix.
-
sweet3.m
returns the SWEET3 matrix.
-
sweet3_condition.m
returns the L1 condition of the SWEET3 matrix.
-
sweet3_determinant.m
returns the determinant of the SWEET3 matrix.
-
sweet3_inverse.m
returns the inverse of the SWEET3 matrix.
-
sweet4.m
returns the SWEET4 matrix.
-
sweet4_condition.m
returns the L1 condition of the SWEET4 matrix.
-
sweet4_determinant.m
returns the determinant of the SWEET4 matrix.
-
sweet4_inverse.m
returns the inverse of the SWEET4 matrix.
-
sylvester.m
returns the SYLVESTER matrix.
-
sylvester_kac.m
returns the SYLVESTER_KAC matrix.
-
sylvester_kac_determinant.m
returns the determinant of the SYLVESTER_KAC matrix.
-
sylvester_kac_eigen_right.m
returns the right eigenvectors of the SYLVESTER_KAC matrix.
-
sylvester_kac_eigenvalues.m
returns the eigenvalues of the SYLVESTER_KAC matrix.
-
sylvester_kac_inverse.m
returns the inverse of the SYLVESTER_KAC matrix.
-
symm_random.m
returns the SYMM_RANDOM matrix.
-
symm_random_determinant.m
returns the determinant of the SYMM_RANDOM matrix.
-
symm_random_eigen_left.m
returns the left eigenvectors of the SYMM_RANDOM matrix.
-
symm_random_eigen_right.m
returns the right eigenvectors of the SYMM_RANDOM matrix.
-
symm_random_eigenvalues.m
returns the eigenvalues of the SYMM_RANDOM matrix.
-
symm_random_inverse.m
returns the inverse of the SYMM_RANDOM matrix.
-
timestamp.m
returns the YMDHMS date as a timestamp.
-
toeplitz.m
returns a TOEPLITZ matrix.
-
toeplitz_5diag.m
returns a pentadiagonal Toeplitz matrix.
-
toeplitz_5s.m
returns the TOEPLITZ_5S matrix.
-
toeplitz_5s_determinant.m
returns the determinant of the TOEPLITZ_5S matrix.
-
toeplitz_5s_eigenvalues.m
returns the eigenvalues of the TOEPLITZ_5S matrix.
-
toeplitz_pds.m
returns the TOEPLITZ_PDS matrix.
-
tournament_random.m
returns the TOURNAMENT_RANDOM matrix.
-
tournament_random_determinant.m
returns the determinant of the TOURNAMENT_RANDOM matrix.
-
transition_random.m
returns a random transition matrix.
-
trench.m
returns the TRENCH matrix.
-
tri_l1_inverse.m
returns the inverse of a unit lower triangular matrix.
-
tri_u_inverse.m
returns the inverse of an upper triangular matrix.
-
tri_upper.m
returns the TRI_UPPER matrix.
-
tri_upper_condition.m
returns the L1 condition of the TRI_UPPER matrix.
-
tri_upper_determinant.m
returns the determinant of the TRI_UPPER matrix.
-
tri_upper_eigenvalues.m
returns the eigenvalues of the TRI_UPPER matrix.
-
tri_upper_inverse.m
returns the inverse of the TRI_UPPER matrix.
-
tridiagonal_determinant.m
returns the determinant of a tridiagonal matrix.
-
tris.m
returns the TRIS matrix.
-
tris_determinant.m
returns the determinant of the TRIS matrix.
-
tris_eigenvalues.m
returns the eigenvalues of the TRIS matrix.
-
tris_inverse.m
returns the inverse of the TRIS matrix.
-
triv.m
returns the TRIV matrix.
-
triv_determinant.m
returns the determinant of the TRIV matrix.
-
triv_inverse.m
returns the inverse of the TRIV matrix.
-
triw.m
returns the TRIW matrix.
-
triw_determinant.m
returns the determinant of the TRIW matrix.
-
triw_eigenvalues.m
returns the eigenvalues of the TRIW matrix.
-
triw_inverse.m
sets the inverse of the TRIW matrix.
-
unitary_random.m
returns a UNITARY_RANDOM matrix.
-
unitary_random_determinant.m
returns the determinant of a random unitary matrix.
-
unitary_random_inverse.m
returns the inverse of a random unitary matrix.
-
upshift.m
returns the UPSHIFT matrix.
-
upshift_condition.m
returns the L1 condition of the UPSHIFT matrix.
-
upshift_determinant.m
returns the determinant of the UPSHIFT matrix.
-
upshift_eigenvalues.m
returns the eigenvalues of the UPSHIFT matrix.
-
upshift_inverse.m
returns the inverse of the UPSHIFT matrix.
-
vand1.m
returns the VAND1 matrix.
-
vand1_determinant.m
returns the determinant of the VAND1 matrix.
-
vand1_inverse.m
returns the inverse of the VAND1 matrix.
-
vand1_inverse_ul.m
returns the UL factors of the inverse of the VAND1 matrix.
-
vand2.m
returns the VAND2 matrix.
-
vand2_determinant.m
returns the determinant of the VAND2 matrix.
-
vand2_inverse.m
returns the inverse of the VAND2 matrix.
-
vand2_inverse_ul.m
returns the UL factors of the inverse of the VAND2 matrix.
-
vand2_lu.m
returns the LU factors of the VAND2 matrix.
-
vand2_plu.m
returns the PLU factors of the VAND2 matrix.
-
wathen.m
returns the WATHEN matrix.
-
wathen_order.m
returns the order of the WATHEN matrix.
-
wilk03.m
returns the WILK03 matrix.
-
wilk03_condition.m
returns the condition of the WILK03 matrix.
-
wilk03_determinant.m
returns the determinant of the WILK03 matrix.
-
wilk03_inverse.m
returns the inverse of the WILK03 matrix.
-
wilk03_rhs.m
returns the right hand side of the WILK03 linear system.
-
wilk03_solution.m
returns the solution of the WILK03 linear system.
-
wilk04.m
returns the WILK04 matrix.
-
wilk04_condition.m
returns the L1 condition of the WILK04 matrix.
-
wilk04_determinant.m
returns the determinant of the WILK04 matrix.
-
wilk04_eigenvalues.m
returns the eigenvalues of the WILK04 matrix.
-
wilk04_rhs.m
returns the right hand side of the WILK04 linear system.
-
wilk04_solution.m
returns the solution of the WILK04 linear system.
-
wilk05.m
returns the WILK05 matrix.
-
wilk05_condition.m
returns the L1 condition of the WILK05 matrix.
-
wilk05_determinant.m
returns the determinant of the WILK05 matrix.
-
wilk05_inverse.m
returns the determinant of the WILK05 matrix.
-
wilk12.m
returns the WILK12 matrix.
-
wilk12_condition.m
returns the L1 condition of the WILK12 matrix.
-
wilk12_determinant.m
returns the determinant of the WILK12 matrix.
-
wilk12_eigen_right.m
returns the right eigenvectors of the WILK12 matrix.
-
wilk12_eigenvalues.m
returns the eigenvalues of the WILK12 matrix.
-
wilk20.m
returns the WILK20 matrix.
-
wilk21.m
returns the WILK21 matrix.
-
wilk21_determinant.m
returns the determinant of the WILK21 matrix.
-
wilk21_inverse.m
returns the inverse of the WILK21 matrix.
-
wilson.m
returns the WILSON matrix.
-
wilson_condition.m
returns the L1 condition of the WILSON matrix.
-
wilson_determinant.m
returns the determinant of the WILSON matrix.
-
wilson_eigen_right.m
returns the right eigenvectors of the WILSON matrix.
-
wilson_eigenvalues.m
returns the eigenvalues of the WILSON matrix.
-
wilson_inverse.m
returns the inverse of the WILSON matrix.
-
wilson_llt.m
returns the lower triangular Cholesky factor of the WILSON matrix.
-
wilson_plu.m
returns the PLU factors of the WILSON matrix.
-
wilson_rhs.m
returns the WILSON right hand side.
-
wilson_solution.m
returns the WILSON solution.
-
zero.m
returns the ZERO matrix.
-
zero_determinant.m
returns the determinant of the ZERO matrix.
-
zero_eigen_right.m
returns the right eigenvectors of the ZERO matrix.
-
zero_eigenvalues.m
returns the eigenvalues of the ZERO matrix.
-
zero_null_left.m
returns a left null vector of the ZERO matrix.
-
zero_null_right.m
returns a right null vector of the ZERO matrix.
-
zielke.m
returns the ZIELKE matrix.
-
test_condition.m,
tests the condition number evaluation routines.
-
test_determinant.m,
tests the determinant evaluation routines.
-
test_eigen_left.m,
tests the left eigensystem routines.
-
test_eigen_right.m,
tests the right eigensystem routines.
-
test_inverse.m,
tests the inverse evaluation routines.
-
test_llt.m,
tests the lower triangular Cholesky factor routines.
-
test_null_left.m,
tests the left null vector routines.
-
test_null_right.m,
tests the right null vector routines.
-
test_plu.m,
tests the P*L*U factor routines.
-
test_solution.m,
tests the linear system solution routines.
-
test_type.m,
tests functions which determine the linear algebraic type of
a matrix.
Last revised on 29 March 2019.