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CGELSS(l)			       )			     CGELSS(l)

NAME
       CGELSS  -  compute  the minimum norm solution to a complex linear least
       squares problem

SYNOPSIS
       SUBROUTINE CGELSS( M, N, NRHS, A, LDA, B, LDB, S,  RCOND,  RANK,	 WORK,
			  LWORK, RWORK, INFO )

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

	   REAL		  RCOND

	   REAL		  RWORK( * ), S( * )

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

PURPOSE
       CGELSS  computes	 the  minimum  norm solution to a complex 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 singu‐
       lar 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) COMPLEX 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) COMPLEX 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,M,N).

       S       (output) REAL 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) REAL
	       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) COMPLEX 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 >=
	       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.

       RWORK   (workspace) REAL array, dimension (5*min(M,N))

       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 bidiag‐
	       onal form did not converge to zero.

LAPACK version 3.0		 15 June 2000			     CGELSS(l)
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