MINFIT(3F)

NAME
     MINFIT, SMINFIT  -  EISPACK routine.  This subroutine determines, towards
     the solution of the linear
        T system AX=B, the singular value decomposition A=USV  of a real
        T M by N rectangular matrix, forming U B rather than U.  Householder
     bidiagonalization and a variant of the QR algorithm are used.


SYNOPSYS
          subroutine  minfit(nm, m, n, a, w, ip, b, ierr, rv1)
          integer          nm, m, n, ip, ierr
          double precision a(nm,n), w(n), b(nm,ip), rv1(n)

          subroutine sminfit(nm, m, n, a, w, ip, b, ierr, rv1)
          integer          nm, m, n, ip, ierr
          real             a(nm,n), w(n), b(nm,ip), rv1(n)



DESCRIPTION
     On INPUT

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.  Note that NM
     must be at least as large as the maximum of M and N.

     M is the number of rows of A and B.

     N is the number of columns of A and the order of V.

     A contains the rectangular coefficient matrix of the system.

     IP is the number of columns of B.  IP can be zero.

     B contains the constant column matrix of the system if IP is not zero.
     Otherwise B is not referenced.  On OUTPUT

     A has been overwritten by the matrix V (orthogonal) of the decomposition
     in its first N rows and columns.  If an error exit is made, the columns
     of V corresponding to indices of correct singular values should be
     correct.

     W contains the N (non-negative) singular values of A (the diagonal
     elements of S).  They are UNORDERED.  If an error exit is made, the
     singular values should be correct for indices IERR+1,IERR+2,...,N.
        T

     B has been overwritten by U B.  If an error exit is made,
        T the rows of U B corresponding to indices of correct singular values
     should be correct.

     IERR is set to Zero       for normal return, K          if the K-th
     singular value has not been
        determined after 30 iterations.

     RV1 is a temporary storage array. Calls PYTHAG(A,B) for sqrt(A**2 +
     B**2).  Questions and comments should be directed to B. S. Garbow,
     APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY