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96 lines
3.7 KiB
Fortran
96 lines
3.7 KiB
Fortran
*DECK RSGAB
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SUBROUTINE RSGAB (NM, N, A, B, W, MATZ, Z, FV1, FV2, IERR)
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C***BEGIN PROLOGUE RSGAB
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C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
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C of a symmetric generalized eigenproblem.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4B1
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C***TYPE SINGLE PRECISION (RSGAB-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 for the REAL SYMMETRIC generalized eigenproblem ABx = (LAMBDA)x.
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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 parameters, A, B, and Z, as declared in the calling
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C program dimension statement. NM is an INTEGER variable.
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C
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C N is the order of the matrices A and B. N is an INTEGER
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C variable. N must be less than or equal to NM.
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C
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C A contains a real symmetric matrix. A is a two-dimensional
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C REAL array, dimensioned A(NM,N).
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C
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C B contains a positive definite real symmetric matrix. B is a
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C two-dimensional REAL array, dimensioned B(NM,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. W is a
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C one-dimensional REAL array, dimensioned W(N).
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C
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C Z contains the eigenvectors if MATZ is not zero. Z is a
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C two-dimensional REAL array, 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 7*N+1 if B is not positive definite,
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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 should be correct for indices
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C 1, 2, ..., IERR-1, but no eigenvectors are
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C computed.
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C
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C FV1 and FV2 are one-dimensional REAL arrays used for temporary
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C storage, dimensioned FV1(N) and FV2(N).
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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 REBAK, REDUC2, TQL2, TQLRAT, TRED1, TRED2
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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 RSGAB
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C
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INTEGER N,NM,IERR,MATZ
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REAL A(NM,*),B(NM,*),W(*),Z(NM,*),FV1(*),FV2(*)
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C
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C***FIRST EXECUTABLE STATEMENT RSGAB
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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 CALL REDUC2(NM,N,A,B,FV2,IERR)
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IF (IERR .NE. 0) GO TO 50
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IF (MATZ .NE. 0) GO TO 20
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C .......... FIND EIGENVALUES ONLY ..........
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CALL TRED1(NM,N,A,W,FV1,FV2)
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CALL TQLRAT(N,W,FV2,IERR)
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GO TO 50
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C .......... FIND BOTH EIGENVALUES AND EIGENVECTORS ..........
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20 CALL TRED2(NM,N,A,W,FV1,Z)
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CALL TQL2(NM,N,W,FV1,Z,IERR)
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IF (IERR .NE. 0) GO TO 50
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CALL REBAK(NM,N,B,FV2,N,Z)
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50 RETURN
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END
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