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CGELSX(l)			       )			     CGELSX(l)

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       CGELSX - routine is deprecated and has been replaced by routine CGELSY

SYNOPSIS
       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( * )

PURPOSE
       This routine is deprecated and has been	replaced  by  routine  CGELSY.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 con‐
       dition 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 factor‐
	       ization 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 subma‐
	       trix 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  com‐
	       plete 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

LAPACK version 3.0		 15 June 2000			     CGELSX(l)
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