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JACOBI_EIGENVALUE\ Eigenvalues and Eigenvectors of a Symmetric Matrix {#jacobi_eigenvalue-eigenvalues-and-eigenvectors-of-a-symmetric-matrix align=”center”} ==================================================

JACOBI_EIGENVALUE is a C++ library which computes the eigenvalues and eigenvectors of a real symmetric matrix.

Given a real symmetric NxN matrix A, JACOBI_EIGENVALUE carries out an iterative procedure known as Jacobi’s iteration, to determine a N-vector D of real, positive eigenvalues, and an NxN matrix V whose columns are the corresponding eigenvectors, so that, for each column J of the eigenmatrix:

        A * Vj = Dj * Vj

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

JACOBI_EIGENVALUE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs: {#related-data-and-programs align=”center”}

TEST_EIGEN, a C++ library which implements test matrices for eigenvalue analysis.

TEST_MAT, a C++ library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Reference: {#reference align=”center”}

1. Gene Golub, Charles VanLoan,\ Matrix Computations, Third Edition,\ Johns Hopkins, 1996,\ ISBN: 0-8018-4513-X,\ LC: QA188.G65.

Source Code: {#source-code align=”center”}

• jacobi_eigenvalue.cpp, the source code.
• jacobi_eigenvalue.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• jacobi_eigenvalue_prb.cpp, a sample calling program.
• jacobi_eigenvalue_prb_output.txt, the output file.

List of Routines: {#list-of-routines align=”center”}

• JACOBI_EIGENVALUE carries out the Jacobi eigenvalue iteration.
• R8MAT_DIAG_GET_VECTOR gets the value of the diagonal of an R8MAT.
• R8MAT_IDENTITY stores the identity matrix in an R8MAT.
• R8MAT_IS_EIGEN_RIGHT determines the error in a (right) eigensystem.
• R8MAT_NORM_FRO returns the Frobenius norm of an M by N R8MAT.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_PRINT prints an R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.

Last revised on 15 July 2013.