TEST_EIGEN
Test Matrices for Eigenvalue Analysis

TEST_EIGEN is a FORTRAN77 library which generates eigenvalue test.

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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

EISPACK, a FORTRAN77 library which can compute eigenvalues and eigenvectors.

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.

TEST_MAT, a FORTRAN77 library which defines a number of matrices with known properties. Examples with known eigenvalues and eigenvectors are included.

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

Examples and Tests:

• test_eigen_test.f, the calling program;
• test_eigen_test.txt, the output file.

List of Routines:

• GET_UNIT returns a free FORTRAN unit number.
• R4VEC_UNIFORM_01 returns a unit pseudorandom R4VEC.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• 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_TEST determines a nonsymmetric matrix with a certain eigenstructure.
• R8SYMM_TEST determines a symmetric matrix with a certain eigenstructure.
• 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.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.