mirror of
https://git.planet-casio.com/Lephenixnoir/OpenLibm.git
synced 2025-01-01 06:23:39 +01:00
90 lines
3.3 KiB
Fortran
90 lines
3.3 KiB
Fortran
*DECK RS
|
|
SUBROUTINE RS (NM, N, A, W, MATZ, Z, FV1, FV2, IERR)
|
|
C***BEGIN PROLOGUE RS
|
|
C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
|
|
C of a real symmetric matrix.
|
|
C***LIBRARY SLATEC (EISPACK)
|
|
C***CATEGORY D4A1
|
|
C***TYPE SINGLE PRECISION (RS-S, CH-C)
|
|
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
|
|
C***AUTHOR Smith, B. T., et al.
|
|
C***DESCRIPTION
|
|
C
|
|
C This subroutine calls the recommended sequence of
|
|
C subroutines from the eigensystem subroutine package (EISPACK)
|
|
C to find the eigenvalues and eigenvectors (if desired)
|
|
C of a REAL SYMMETRIC matrix.
|
|
C
|
|
C On Input
|
|
C
|
|
C NM must be set to the row dimension of the two-dimensional
|
|
C array parameters, A and Z, as declared in the calling
|
|
C program dimension statement. NM is an INTEGER variable.
|
|
C
|
|
C N is the order of the matrix A. N is an INTEGER variable.
|
|
C N must be less than or equal to NM.
|
|
C
|
|
C A contains the real symmetric matrix. A is a two-dimensional
|
|
C REAL array, dimensioned A(NM,N).
|
|
C
|
|
C MATZ is an INTEGER variable set equal to zero if only
|
|
C eigenvalues are desired. Otherwise, it is set to any
|
|
C non-zero integer for both eigenvalues and eigenvectors.
|
|
C
|
|
C On Output
|
|
C
|
|
C A is unaltered.
|
|
C
|
|
C W contains the eigenvalues in ascending order. W is a one-
|
|
C dimensional REAL array, dimensioned W(N).
|
|
C
|
|
C Z contains the eigenvectors if MATZ is not zero. The
|
|
C eigenvectors are orthonormal. Z is a two-dimensional
|
|
C REAL array, dimensioned Z(NM,N).
|
|
C
|
|
C IERR is an INTEGER flag set to
|
|
C Zero for normal return,
|
|
C 10*N if N is greater than NM,
|
|
C J if the J-th eigenvalue has not been
|
|
C determined after 30 iterations.
|
|
C The eigenvalues, and eigenvectors if requested,
|
|
C should be correct for indices 1, 2, ..., IERR-1.
|
|
C
|
|
C FV1 and FV2 are one-dimensional REAL arrays used for temporary
|
|
C storage, dimensioned FV1(N) and FV2(N).
|
|
C
|
|
C Questions and comments should be directed to B. S. Garbow,
|
|
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
|
|
C ------------------------------------------------------------------
|
|
C
|
|
C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
|
|
C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
|
|
C system Routines - EISPACK Guide, Springer-Verlag,
|
|
C 1976.
|
|
C***ROUTINES CALLED TQL2, TQLRAT, TRED1, TRED2
|
|
C***REVISION HISTORY (YYMMDD)
|
|
C 760101 DATE WRITTEN
|
|
C 890831 Modified array declarations. (WRB)
|
|
C 890831 REVISION DATE from Version 3.2
|
|
C 891214 Prologue converted to Version 4.0 format. (BAB)
|
|
C 920501 Reformatted the REFERENCES section. (WRB)
|
|
C***END PROLOGUE RS
|
|
C
|
|
INTEGER N,NM,IERR,MATZ
|
|
REAL A(NM,*),W(*),Z(NM,*),FV1(*),FV2(*)
|
|
C
|
|
C***FIRST EXECUTABLE STATEMENT RS
|
|
IF (N .LE. NM) GO TO 10
|
|
IERR = 10 * N
|
|
GO TO 50
|
|
C
|
|
10 IF (MATZ .NE. 0) GO TO 20
|
|
C .......... FIND EIGENVALUES ONLY ..........
|
|
CALL TRED1(NM,N,A,W,FV1,FV2)
|
|
CALL TQLRAT(N,W,FV2,IERR)
|
|
GO TO 50
|
|
C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
|
|
20 CALL TRED2(NM,N,A,W,FV1,Z)
|
|
CALL TQL2(NM,N,W,FV1,Z,IERR)
|
|
50 RETURN
|
|
END
|