TEST_EIGEN
Test Matrices for Eigenvalue Analysis

TEST_EIGEN is a FORTRAN90 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 (subroutine SYMM_TEST).

Licensing:

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

Related Data and Programs:

ARPACK, a FORTRAN90 library which computes eigenvalues for large matrices;

EISPACK a FORTRAN90 library which carries out eigenvalue computations; superseded by LAPACK;

LAPACK is a FORTRAN90 library which factors and solves systems of linear equations in a variety of formats and arithmetic types. It supersedes LINPACK and EISPAK.

POWER_METHOD is a FORTRAN90 library which carries out the power method for finding a dominant eigenvalue and its eigenvector.

TEST_EIGEN is available in a FORTRAN77 version and a FORTRAN90 version.

TEST_MAT is a FORTRAN90 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:

1. Robert Gregory, David Karney,
   A Collection of Matrices for Testing Computational Algorithms,
   Wiley, 1969,
   ISBN: 0882756494,
   LC: QA263 G862.
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:

• test_eigen.f90, the source code;
• test_eigen.csh, commands to compile the source code;

Examples and Tests:

• test_eigen_prb.f90, the calling program;
• test_eigen_prb.csh, commands to compile, link and run the calling program;
• test_eigen_prb_output.txt, the output file.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• HISTOGRAM_FILE_WRITE creates a plot file of histogram data.
• R4_NORMAL_01 returns a unit pseudonormal R4.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R4BIN_PRINT prints the bins of an R4VEC.
• R4MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.
• R4MAT_ORTH_UNIFORM returns a random orthogonal R4MAT.
• R4MAT_PRINT prints an R4MAT.
• R4MAT_PRINT_SOME prints some of an R4MAT.
• R4SYMM_TEST determines a symmetric matrix with a certain eigenstructure.
• R4VEC_BIN computes bins based on a given R4VEC.
• R4VEC_NORMAL returns a scaled pseudonormal R4VEC.
• R4VEC_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
• R4VEC_PRINT prints an R4VEC.
• R4VEC_UNIFORM_01 returns a unit pseudorandom R4VEC.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_TO_S_LEFT writes a real into a left justified character string.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8BIN_PRINT prints the bins of a real vector.
• R8MAT_HOUSE_AXH computes A*H where H is a compact Householder matrix.
• R8MAT_ORTH_UNIFORM returns a random orthogonal R8MAT.
• 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_HOUSE_COLUMN defines a Householder premultiplier that "packs" a column.
• R8VEC_NORMAL returns a scaled pseudonormal R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• RANDOM_INITIALIZE initializes the FORTRAN 90 random number seed.
• S_LEFT flushes a string left.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.