JACOBI_EIGENVALUE
Eigenvalues and Eigenvectors of a Symmetric Matrix

JACOBI_EIGENVALUE is a FORTRAN90 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:

ARPACK, a FORTRAN90 library which uses Arnoldi methods to compute some eigenvalues and eigenvectors of matrices, which may be very large.

EISPACK, a FORTRAN90 library which carries out eigenvalue computations; superseded by LAPACK;

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

TEST_EIGEN, a FORTRAN90 library which implements test matrices for eigenvalue analysis.

TEST_MAT, a FORTRAN90 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.f90, the source code.

Examples and Tests:

• jacobi_eigenvalue_test.f90, a sample calling program.
• jacobi_eigenvalue_test.txt, the output file.

List of Routines:

• 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 FORTRAN90 source codes.