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 or nonsymmetric matrix of arbitrary size, with eigenvalues distributed according to a normal distribution whose mean and standard deviation are specified by the user (subroutines R8SYMM_GEN and R8NSYMM_GEN).

Licensing:

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

Languages:

TEST_EIGEN 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 FORTRAN90 library which computes eigenvalues for large matrices;

EISPACK, a FORTRAN90 library which carries out eigenvalue computations; superseded by LAPACK;

JACOBI_EIGENVALUE, a FORTRAN90 library which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.

LAPACK_EIGEN_TEST, a FORTRAN90 program which tests some of the LAPACK eigenvalue functions.

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

TEST_MAT, 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.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:

• test_eigen.f90, the source code;

Examples and Tests:

• test_eigen_test.f90, the calling program;
• test_eigen_test.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.
• 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.
• R8NSYMM_GEN generates a nonsymmetric matrix with a certain eigenstructure.
• R8SYMM_GEN generates 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.