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decuslib20-02
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decus/20-0026/eigen.doc
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SUBROUTINE EIGEN
PURPOSE
COMPUTE EIGENVALUES AND EIGENVECTORS OF A REAL SYMMETRIC
MATRIX
USAGE
CALL EIGEN(A,R,N,MV)
DESCRIPTION OF PARAMETERS
A - ORIGINAL MATRIX (SYMMETRIC), DESTROYED IN COMPUTATION.
RESULTANT EIGENVALUES ARE DEVELOPED IN DIAGONAL OF
MATRIX A IN DESCENDING ORDER.
R - RESULTANT MATRIX OF EIGENVECTORS (STORED COLUMNWISE,
IN SAME SEQUENCE AS EIGENVALUES)
N - ORDER OF MATRICES A AND R
MV- INPUT CODE
0 COMPUTE EIGENVALUES AND EIGENVECTORS
1 COMPUTE EIGENVALUES ONLY (R NEED NOT BE
DIMENSIONED BUT MUST STILL APPEAR IN CALLING
SEQUENCE)
REMARKS
ORIGINAL MATRIX A MUST BE REAL SYMMETRIC (STORAGE MODE=1)
MATRIX A CANNOT BE IN THE SAME LOCATION AS MATRIX R
SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE
METHOD
DIAGONALIZATION METHOD ORIGINATED BY JACOBI AND ADAPTED
BY VON NEUMANN FOR LARGE COMPUTERS AS FOUND IN 'MATHEMATICAL
METHODS FOR DIGITAL COMPUTERS', EDITED BY A. RALSTON AND
H.S. WILF, JOHN WILEY AND SONS, NEW YORK, 1962, CHAPTER 7