CXML
        	    
LAPACK version 3.0
dgelss(3)

PURPOSE
  DGELSS - compute the minimum norm solution to a real linear least squares
  problem

SYNTAX
  SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK,
		     INFO )

      INTEGER	     INFO, LDA, LDB, LWORK, M, N, NRHS, RANK

      DOUBLE	     PRECISION RCOND

      DOUBLE	     PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( * )

DESCRIPTION
  DGELSS computes the minimum norm solution to a real linear least squares
  problem: Minimize 2-norm(| b - A*x |).

  using the singular value decomposition (SVD) of A. A is an M-by-N matrix
  which may be rank-deficient.

  Several right hand side vectors b and solution vectors x can be handled in
  a single call; they are stored as the columns of the M-by-NRHS right hand
  side matrix B and the N-by-NRHS solution matrix X.

  The effective rank of A is determined by treating as zero those singular
  values which are less than RCOND times the largest singular value.

ARGUMENTS
  M	  (input) INTEGER
	  The number of rows of the matrix A. M >= 0.

  N	  (input) INTEGER
	  The number of columns of the matrix A. N >= 0.

  NRHS	  (input) INTEGER
	  The number of right hand sides, i.e., the number of columns of the
	  matrices B and X. NRHS >= 0.

  A	  (input/output) DOUBLE PRECISION array, dimension (LDA,N)
	  On entry, the M-by-N matrix A.  On exit, the first min(m,n) rows of
	  A are overwritten with its right singular vectors, stored rowwise.

  LDA	  (input) INTEGER
	  The leading dimension of the array A.	 LDA >= max(1,M).

  B	  (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
	  On entry, the M-by-NRHS right hand side matrix B.  On exit, B is
	  overwritten by the N-by-NRHS solution matrix X.  If m >= n and RANK
	  = n, the residual sum-of-squares for the solution in the i-th
	  column is given by the sum of squares of elements n+1:m in that
	  column.

  LDB	  (input) INTEGER
	  The leading dimension of the array B. LDB >= max(1,max(M,N)).

  S	  (output) DOUBLE PRECISION array, dimension (min(M,N))
	  The singular values of A in decreasing order.	 The condition number
	  of A in the 2-norm = S(1)/S(min(m,n)).

  RCOND	  (input) DOUBLE PRECISION
	  RCOND is used to determine the effective rank of A.  Singular
	  values S(i) <= RCOND*S(1) are treated as zero.  If RCOND < 0,
	  machine precision is used instead.

  RANK	  (output) INTEGER
	  The effective rank of A, i.e., the number of singular values which
	  are greater than RCOND*S(1).

  WORK	  (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
	  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK	  (input) INTEGER
	  The dimension of the array WORK. LWORK >= 1, and also: LWORK >=
	  3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) For good
	  performance, LWORK should generally be larger.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value.
	  > 0:	the algorithm for computing the SVD failed to converge; if
	  INFO = i, i off-diagonal elements of an intermediate bidiagonal
	  form did not converge to zero.