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CGELS(1)	      LAPACK driver routine (version 3.2)	      CGELS(1)

NAME
       CGELS - solves overdetermined or underdetermined complex linear systems
       involving an M-by-N matrix A, or its conjugate-transpose, using a QR or
       LQ factorization of A

SYNOPSIS
       SUBROUTINE CGELS( TRANS,	 M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO
			 )

	   CHARACTER	 TRANS

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

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

PURPOSE
       CGELS solves overdetermined or underdetermined complex  linear  systems
       involving an M-by-N matrix A, or its conjugate-transpose, using a QR or
       LQ factorization of A.  It is assumed that A has full rank.   The  fol‐
       lowing options are provided:
       1. If TRANS = 'N' and m >= n:  find the least squares solution of
	  an overdetermined system, i.e., solve the least squares problem
		       minimize || B - A*X ||.
       2. If TRANS = 'N' and m < n:  find the minimum norm solution of
	  an underdetermined system A * X = B.
       3. If TRANS = 'C' and m >= n:  find the minimum norm solution of
	  an undetermined system A**H * X = B.
       4. If TRANS = 'C' and m < n:  find the least squares solution of
	  an overdetermined system, i.e., solve the least squares problem
		       minimize || B - A**H * X ||.
       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.

ARGUMENTS
       TRANS   (input) CHARACTER*1
	       = 'N': the linear system involves A;
	       = 'C': the linear system involves A**H.

       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.  if M >= N, A is overwritten  by
	       details	of  its QR factorization as returned by CGEQRF; if M <
	       N, A is overwritten by  details	of  its	 LQ  factorization  as
	       returned by CGELQF.

       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	matrix	B  of  right hand side vectors, stored
	       columnwise; B is M-by-NRHS if TRANS  =  'N',  or	 N-by-NRHS  if
	       TRANS  =	 'C'.	On  exit, if INFO = 0, B is overwritten by the
	       solution vectors, stored columnwise: if TRANS = 'N' and m >= n,
	       rows  1	to  n of B contain the least squares solution vectors;
	       the residual sum of squares for the solution in each column  is
	       given by the sum of squares of the modulus of elements N+1 to M
	       in that column; if TRANS = 'N' and m < n, rows 1 to N of B con‐
	       tain the minimum norm solution vectors; if TRANS = 'C' and m >=
	       n, rows 1 to M of B contain the minimum norm solution  vectors;
	       if  TRANS  =  'C' and m < n, rows 1 to M of B contain the least
	       squares solution vectors; the residual sum of squares  for  the
	       solution	 in  each column is given by the sum of squares of the
	       modulus of elements M+1 to N in that column.

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

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

       LWORK   (input) INTEGER
	       The dimension of the array WORK.	 LWORK >= max( 1,  MN  +  max(
	       MN,  NRHS  ) ).	For optimal performance, LWORK >= max( 1, MN +
	       max( MN, NRHS )*NB ).  where MN = min(M,N) and NB is the	 opti‐
	       mum  block  size.   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:  if INFO =	i, the i-th diagonal element of the triangular
	       factor of A is zero, so that A does not	have  full  rank;  the
	       least squares solution could not be computed.

 LAPACK driver routine (version 3November 2008			      CGELS(1)
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