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97 lines
3.4 KiB
Fortran
97 lines
3.4 KiB
Fortran
*DECK RST
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SUBROUTINE RST (NM, N, W, E, MATZ, Z, IERR)
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C***BEGIN PROLOGUE RST
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C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
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C of a real symmetric tridiagonal matrix.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4A5
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C***TYPE SINGLE PRECISION (RST-S)
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C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
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C***AUTHOR Smith, B. T., et al.
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C***DESCRIPTION
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C
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C This subroutine calls the recommended sequence of
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C subroutines from the eigensystem subroutine package (EISPACK)
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C to find the eigenvalues and eigenvectors (if desired)
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C of a REAL SYMMETRIC TRIDIAGONAL matrix.
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C
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C On Input
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C
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C NM must be set to the row dimension of the two-dimensional
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C array parameter, Z, as declared in the calling program
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C dimension statement. NM is an INTEGER variable.
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C
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C N is the order of the matrix. N is an INTEGER variable.
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C N must be less than or equal to NM.
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C
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C W contains the diagonal elements of the real symmetric
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C tridiagonal matrix. W is a one-dimensional REAL array,
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C dimensioned W(N).
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C
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C E contains the subdiagonal elements of the matrix in its last
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C N-1 positions. E(1) is arbitrary. E is a one-dimensional
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C REAL array, dimensioned E(N).
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C
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C MATZ is an INTEGER variable set equal to zero if only
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C eigenvalues are desired. Otherwise, it is set to any
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C non-zero integer for both eigenvalues and eigenvectors.
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C
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C On Output
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C
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C W contains the eigenvalues in ascending order.
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C
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C Z contains the eigenvectors if MATZ is not zero. The eigen-
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C vectors are orthonormal. Z is a two-dimensional REAL array,
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C dimensioned Z(NM,N).
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C
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C IERR is an INTEGER flag set to
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C Zero for normal return,
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C 10*N if N is greater than NM,
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C J if the J-th eigenvalue has not been
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C determined after 30 iterations.
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C The eigenvalues and eigenvectors in the W and Z
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C arrays should be correct for indices
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C 1, 2, ..., IERR-1.
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C
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C Questions and comments should be directed to B. S. Garbow,
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C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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C ------------------------------------------------------------------
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C
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C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
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C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
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C system Routines - EISPACK Guide, Springer-Verlag,
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C 1976.
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C***ROUTINES CALLED IMTQL1, IMTQL2
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C***REVISION HISTORY (YYMMDD)
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C 760101 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE RST
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C
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INTEGER I,J,N,NM,IERR,MATZ
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REAL W(*),E(*),Z(NM,*)
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C
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C***FIRST EXECUTABLE STATEMENT RST
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IF (N .LE. NM) GO TO 10
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IERR = 10 * N
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GO TO 50
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C
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10 IF (MATZ .NE. 0) GO TO 20
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C .......... FIND EIGENVALUES ONLY ..........
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CALL IMTQL1(N,W,E,IERR)
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GO TO 50
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C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
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20 DO 40 I = 1, N
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C
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DO 30 J = 1, N
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Z(J,I) = 0.0E0
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30 CONTINUE
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C
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Z(I,I) = 1.0E0
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40 CONTINUE
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C
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CALL IMTQL2(NM,N,W,E,Z,IERR)
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50 RETURN
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END
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