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111 lines
3.9 KiB
Fortran
111 lines
3.9 KiB
Fortran
*DECK RSP
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SUBROUTINE RSP (NM, N, NV, A, W, MATZ, Z, FV1, FV2, IERR)
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C***BEGIN PROLOGUE RSP
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C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors
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C of a real symmetric matrix packed into a one dimensional
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C array.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4A1
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C***TYPE SINGLE PRECISION (RSP-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 PACKED 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 A. 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 NV is an INTEGER variable set equal to the dimension of the
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C array A as specified in the calling program. NV must not
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C be less than N*(N+1)/2.
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C
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C A contains the lower triangle, stored row-wise, of the real
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C symmetric packed matrix. A is a one-dimensional REAL
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C array, dimensioned A(NV).
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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 A has been destroyed.
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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. 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 20*N if NV is less than N*(N+1)/2,
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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 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 TQL2, TQLRAT, TRBAK3, TRED3
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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 RSP
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C
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INTEGER I,J,N,NM,NV,IERR,MATZ
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REAL A(*),W(*),Z(NM,*),FV1(*),FV2(*)
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C
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C***FIRST EXECUTABLE STATEMENT RSP
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IF (N .LE. NM) GO TO 5
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IERR = 10 * N
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GO TO 50
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5 IF (NV .GE. (N * (N + 1)) / 2) GO TO 10
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IERR = 20 * N
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GO TO 50
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C
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10 CALL TRED3(N,NV,A,W,FV1,FV2)
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IF (MATZ .NE. 0) GO TO 20
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C .......... FIND EIGENVALUES ONLY ..........
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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 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 TQL2(NM,N,W,FV1,Z,IERR)
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IF (IERR .NE. 0) GO TO 50
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CALL TRBAK3(NM,N,NV,A,N,Z)
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50 RETURN
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END
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