CXML
        	    
LAPACK version 3.0
cgelsx(3)

PURPOSE
  CGELSX - routine is deprecated and has been replaced by routine CGELSY

SYNTAX
  SUBROUTINE CGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK,
		     RWORK, INFO )

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

      REAL	     RCOND

      INTEGER	     JPVT( * )

      REAL	     RWORK( * )

      COMPLEX	     A( LDA, * ), B( LDB, * ), WORK( * )

DESCRIPTION
  This routine is deprecated and has been replaced by routine CGELSY.  CGELSX
  computes the minimum-norm solution to a complex linear least squares
  problem:
      minimize || A * X - B ||
  using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:
      A * P = Q * [ R11 R12 ]
		  [  0	R22 ]
  with R11 defined as the largest leading submatrix whose estimated condition
  number is less than 1/RCOND.	The order of R11, RANK, is the effective rank
  of A.

  Then, R22 is considered to be negligible, and R12 is annihilated by unitary
  transformations from the right, arriving at the complete orthogonal
  factorization:
     A * P = Q * [ T11 0 ] * Z
		 [  0  0 ]
  The minimum-norm solution is then
     X = P * Z' [ inv(T11)*Q1'*B ]
		[	 0	 ]
  where Q1 consists of the first RANK columns of Q.

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
	  matrices B and X. NRHS >= 0.

  A	  (input/output) COMPLEX array, dimension (LDA,N)
	  On entry, the M-by-N matrix A.  On exit, A has been overwritten by
	  details of its complete orthogonal factorization.

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

  B	  (input/output) COMPLEX array, dimension (LDB,NRHS)
	  On entry, the M-by-NRHS right hand side matrix B.  On exit, 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,M,N).

  JPVT	  (input/output) INTEGER array, dimension (N)
	  On entry, if JPVT(i) .ne. 0, the i-th column of A is an initial
	  column, otherwise it is a free column.  Before the QR factorization
	  of A, all initial columns are permuted to the leading positions;
	  only the remaining free columns are moved as a result of column
	  pivoting during the factorization.  On exit, if JPVT(i) = k, then
	  the i-th column of A*P was the k-th column of A.

  RCOND	  (input) REAL
	  RCOND is used to determine the effective rank of A, which is
	  defined as the order of the largest leading triangular submatrix
	  R11 in the QR factorization with pivoting of A, whose estimated
	  condition number < 1/RCOND.

  RANK	  (output) INTEGER
	  The effective rank of A, i.e., the order of the submatrix R11.
	  This is the same as the order of the submatrix T11 in the complete
	  orthogonal factorization of A.

  WORK	  (workspace) COMPLEX array, dimension
	  (min(M,N) + max( N, 2*min(M,N)+NRHS )),

  RWORK	  (workspace) REAL array, dimension (2*N)

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value