test_eigen

test_eigen, a MATLAB code which generates random real symmetric and nonsymmetric matrices with known eigenvalues and eigenvectors, to test eigenvalue algorithms.

The current version of the code can only generate a symmetric or nonsymmetric matrix of arbitrary size, with real eigenvalues distributed according to a normal distribution whose mean and standard deviation are specified by the user in routines R8SYMM_GEN() and R8NSYMM_GEN().

Licensing:

The information on this web page is distributed under the MIT 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 and an Octave version and a Python version.

Related Data and Programs:

test_eigen_test

arpack_test, a MATLAB code which uses arpack() to compute eigenvalues of large matrices.

eigs_test a MATLAB code which calls eigs(), which is a built-in system function which computes the eigenvalues and eigenvectors of a matrix.

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

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

test_matrix, a MATLAB code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.

web_matrix, a MATLAB code which stores sample matrices describing a web page network. These matrices are typically very sparse, and the examples here are stored using the sparse triplet (ST) format. They can be used to demonstrate pagerank and other graph algorithms.

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:

• 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.
• r8triangular_upper_gen.m, generates an upper triangular matrix with random entries.
• r8vec_bin.m, computes bins based on a given R8VEC.
• r8vec_house_column.m, defines a Householder premultiplier that "packs" a column;
• r8vec_print.m, prints an R8VEC;
• r8vec2_print.m, prints a pair of R8VEC's;