TEST_EIGEN
Test Matrices for Eigenvalue Analysis

TEST_EIGEN, a MATLAB 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, MATLAB programs which illustrate the use of the ARPACK libraruy to compute eigenvalues of large matrices.

EISPACK, a FORTRAN90 library which carries out eigenvalue computations; superseded by LAPACK;

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

LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.

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

test_eigen_test

TEST_MAT, a MATLAB library which defines test matrices.

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:

• r8_normal_01.m, returns a unit pseudonormal R8;
• r8_sign.m, returns the sign of an R8.
• r8_uniform_01.m, returns a unit pseudorandom R8;
• r8bin_print.m, prints the bins of a real vector.
• r8mat_house_axh.m, computes A*H, where H is a compact Householder matrix;
• r8mat_orth_uniform.m, returns a random orthogonal matrix;
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8nsymm_gen.m, determines a nonsymmetric matrix with a certain eigenstructure.
• r8symm_gen.m, determines a symmetric matrix with a certain eigenstructure.
• r8vec_bin.m, computes bins based on a given R8VEC.
• r8vec_house_column.m, defines a Householder premultiplier that "packs" a column;
• r8vec_normal_ab.m, returns a scaled pseudonormal R8VEC.
• r8vec_print.m, prints an R8VEC;
• r8vec_uniform_01.m, returns a unit pseudorandom R8VEC.
• timestamp.m, prints the current YMDHMS date as a timestamp;