JACOBI_EIGENVALUE
Eigenvalues and Eigenvectors of a Symmetric Matrix

JACOBI_EIGENVALUE is a Python 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:

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

Languages:

JACOBI_EIGENVALUE 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:

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

Reference:

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

Source Code:

• jacobi_eigenvalue.py, the source code.
• r8mat_diag_get_vector.py, returns the diagonal of an R8MAT as a vector.
• r8mat_identity.py, returns the identity matrix as an R8MAT.
• r8mat_is_eigen_right.py, determines the error in a right eigen system ||A*X-X*LAMBDA||.
• r8mat_mm.py, computes a matrix-matrix product.
• r8mat_norm_fro.py, returns the Frobenius norm of an R8MAT.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8vec_print.py, prints an R8VEC.
• timestamp.py, prints the current YMDHMS date as a timestamp.

Examples and Tests:

• jacobi_eigenvalue_test.py, calls all the tests.
• jacobi_eigenvalue_test.sh, runs all the tests.
• jacobi_eigenvalue_test.txt, the output file.

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