SLATEC Routines --- SVD ---

*DECK SVD
      SUBROUTINE SVD (NM, M, N, A, W, MATU, U, MATV, V, IERR, RV1)
C***BEGIN PROLOGUE  SVD
C***SUBSIDIARY
C***PURPOSE  Perform the singular value decomposition of a rectangular
C            matrix.
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (SVD-S)
C***AUTHOR  (UNKNOWN)
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure SVD,
C     NUM. MATH. 14, 403-420(1970) by Golub and Reinsch.
C     HANDBOOK FOR AUTO. COMP., VOL II-LINEAR ALGEBRA, 134-151(1971).
C
C     This subroutine determines the singular value decomposition
C          T
C     A=USV  of a REAL M by N rectangular matrix.  Householder
C     bidiagonalization and a variant of the QR algorithm are used.
C
C     On Input
C
C        NM must be set to the row dimension of the two-dimensional
C          array parameters, A, U and V, as declared in the calling
C          program dimension statement.  NM is an INTEGER variable.
C          Note that NM must be at least as large as the maximum
C          of M and N.
C
C        M is the number of rows of A and U.
C
C        N is the number of columns of A and U and the order of V.
C
C        A contains the rectangular input matrix to be decomposed.  A is
C          a two-dimensional REAL array, dimensioned A(NM,N).
C
C        MATU should be set to .TRUE. if the U matrix in the
C          decomposition is desired, and to .FALSE. otherwise.
C          MATU is a LOGICAL variable.
C
C        MATV should be set to .TRUE. if the V matrix in the
C          decomposition is desired, and to .FALSE. otherwise.
C          MATV is a LOGICAL variable.
C
C     On Output
C
C        A is unaltered (unless overwritten by U or V).
C
C        W contains the N (non-negative) singular values of A (the
C          diagonal elements of S).  They are unordered.  If an
C          error exit is made, the singular values should be correct
C          for indices IERR+1, IERR+2, ..., N.  W is a one-dimensional
C          REAL array, dimensioned W(N).
C
C        U contains the matrix U (orthogonal column vectors) of the
C          decomposition if MATU has been set to .TRUE.  Otherwise,
C          U is used as a temporary array.  U may coincide with A.
C          If an error exit is made, the columns of U corresponding
C          to indices of correct singular values should be correct.
C          U is a two-dimensional REAL array, dimensioned U(NM,N).
C
C        V contains the matrix V (orthogonal) of the decomposition if
C          MATV has been set to .TRUE.  Otherwise, V is not referenced.
C          V may also coincide with A if U does not.  If an error
C          exit is made, the columns of V corresponding to indices of
C          correct singular values should be correct.  V is a two-
C          dimensional REAL array, dimensioned V(NM,N).
C
C        IERR is an INTEGER flag set to
C          Zero       for normal return,
C          K          if the K-th singular value has not been
C                     determined after 30 iterations.
C
C        RV1 is a one-dimensional REAL array used for temporary storage,
C          dimensioned RV1(N).
C
C     CALLS PYTHAG(A,B) for sqrt(A**2 + B**2).
C
C     Questions and comments should be directed to B. S. Garbow,
C     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C     ------------------------------------------------------------------
C
C***SEE ALSO  EISDOC
C***ROUTINES CALLED  PYTHAG
C***REVISION HISTORY  (YYMMDD)
C   811101  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900402  Added TYPE section.  (WRB)
C***END PROLOGUE  SVD