Mac binaries

[jabaws.git] / website / archive / binaries / mac / src / disembl / Tisean_3.0.1 / source_f / slatec / rs.f

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+*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