SUBROUTINE SVD(NM,M,N,A,W,MATU,U,MATV,V,IERR,RV1)
C***BEGIN PROLOGUE  SVD
C***REFER TO  EISDOC
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 two-dimensional
C          array parameters as declared in the calling program
C          dimension statement.  Note that NM must be at least
C          as large as the maximum 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.
C
C        MATU should be set to .TRUE. if the U matrix in the
C          decomposition is desired, and to .FALSE. otherwise.
C
C        MATV should be set to .TRUE. if the V matrix in the
C          decomposition is desired, and to .FALSE. otherwise.
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.
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
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 is not needed.  If an error
C          exit is made, the columns of V corresponding to indices of
C          correct singular values should be correct.
C
C        IERR is 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 temporary storage array.
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***ROUTINES CALLED  PYTHAG
C***END PROLOGUE  SVD