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TEST_EIGEN
Test Matrices for Eigenvalue Analysis {#test_eigen-test-matrices-for-eigenvalue-analysis align="center"}

TEST_EIGEN is a C++ library which generates eigenvalue tests.

The current version of the code can only generate a symmetric matrix with eigenvalues distributed according to a normal distribution whose mean and standard deviation are specified by the user in R8SYMM_GEN.

Licensing: {#licensing align="center"}

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

Languages: {#languages align="center"}

TEST_EIGEN 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: {#related-data-and-programs align="center"}

EISPACK, a C++ library which carries out eigenvalue computations. It includes a function to compute the singular value decomposition (SVD) of a rectangular matrix. superseded by LAPACK;

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

POWER_METHOD, a C++ library which carries out the power method for finding a dominant eigenvalue and its eigenvector.

TEST_MAT, a C++ library which defines test matrices.

TOMS343, a FORTRAN77 library which computes the eigenvalues and eigenvectors of a general real matrix;
this is a FORTRAN77 version of ACM TOMS algorithm 343.

TOMS384, a FORTRAN77 library which computes the eigenvalues and eigenvectors of a symmetric matrix;
this is a FORTRAN77 version of ACM TOMS algorithm 384.

Reference: {#reference align="center"}

  1. Robert Gregory, David Karney,
    A Collection of Matrices for Testing Computational Algorithms,
    Wiley, 1969,
    ISBN: 0882756494,
    LC: QA263.G68.
  2. Pete Stewart,
    Efficient Generation of Random Orthogonal Matrices With an Application to Condition Estimators,
    SIAM Journal on Numerical Analysis,
    Volume 17, Number 3, June 1980, pages 403-409.

Source Code: {#source-code align="center"}

Examples and Tests: {#examples-and-tests align="center"}

List of Routines: {#list-of-routines align="center"}

  • I4_MAX returns the maximum of two I4's.
  • I4_MIN returns the minimum of two I4's.
  • R8_ABS returns the absolute value of an R8.
  • R8_NORMAL_01 samples the standard normal probability distribution.
  • R8_SIGN returns the sign of an R8.
  • R8_UNIFORM_01 returns a unit pseudorandom R8.
  • R8BIN_PRINT prints the bins of a real vector.
  • R8MAT_COPY copies one R8MAT to another.
  • R8MAT_HOUSE_AXH_NEW computes A*H where H is a compact Householder matrix.
  • R8MAT_IDENTITY returns an identity matrix.
  • R8MAT_MM_NEW multiplies two matrices.
  • R8MAT_ORTH_UNIFORM returns a random orthogonal matrix.
  • R8MAT_PRINT prints an R8MAT.
  • R8MAT_PRINT_SOME prints some of an R8MAT.
  • R8SYMM_TEST determines a symmetric matrix with a certain eigenstructure.
  • R8VEC_BIN computes bins based on a given R8VEC.
  • R8VEC_COPY copies an R8VEC.
  • R8VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
  • R8VEC_MAX returns the value of the maximum element in an R8VEC.
  • R8VEC_MIN returns the value of the minimum element in an R8VEC.
  • R8VEC_NORM_L2 returns the L2 norm of an R8VEC.
  • R8VEC_NORMAL returns a scaled pseudonormal R8VEC.
  • R8VEC_PRINT prints an R8VEC.
  • R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
  • R8VEC_ZERO_NEW creates and zeroes an R8VEC.
  • R8VEC2_PRINT prints an R8VEC2.
  • TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

Last revised on 22 February 2012.