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).

Related Data and Programs:

ARPACK is an advanced and powerful library which uses Arnoldi iteration to compute eigenvalues and eigenvectors.

EISPACK is an obsolete library of FORTRAN90 routines which can compute eigenvalues and eigenvectors.

LAPACK is a modern library of FORTRAN90 routines which can compute eigenvalues and eigenvectors.

TEST_MAT is a library of FORTRAN90 routines which define 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.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.