SUBROUTINE MINFIT(NM,M,N,A,W,IP,B,IERR,RV1)
C***BEGIN PROLOGUE  MINFIT
C***DATE WRITTEN   760101   (YYMMDD)
C***REVISION DATE  830518   (YYMMDD)
C***CATEGORY NO.  D9,D9
C***KEYWORDS  EIGENVALUES,EIGENVECTORS,EISPACK
C***AUTHOR  SMITH, B. T., ET AL.
C***PURPOSE  Compute Singular Value Decomposition of rectangular
C            matrix and solve related Linear Least Squares problem
C***DESCRIPTION
C
C     This subroutine is a translation of the ALGOL procedure MINFIT,
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, towards the solution of the linear
C                                                        T
C     system AX=B, the singular value decomposition A=USV  of a real
C                                         T
C     M by N rectangular matrix, forming U B rather than U.  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 B.
C
C        N is the number of columns of A and the order of V.
C
C        A contains the rectangular coefficient matrix of the system.
C
C        IP is the number of columns of B.  IP can be zero.
C
C        B contains the constant column matrix of the system
C          if IP is not zero.  Otherwise B is not referenced.
C
C     On OUTPUT
C
C        A has been overwritten by the matrix V (orthogonal) of the
C          decomposition in its first N rows and columns.  If an
C          error exit is made, the columns of V corresponding to
C          indices of correct singular values should be correct.
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                                   T
C        B has been overwritten by U B.  If an error exit is made,
C                       T
C          the rows of U B corresponding to indices of correct
C          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***REFERENCES  B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW,
C                 Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN-
C                 SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG,
C                 1976.
C***ROUTINES CALLED  PYTHAG
C***END PROLOGUE  MINFIT