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RedHat 9 (Linux i386) - man page for sgels (redhat section l)

SGELS(l)					)					 SGELS(l)

NAME
       SGELS  -  solve	overdetermined or underdetermined real linear systems involving an M-by-N
       matrix A, or its transpose, using a QR or LQ factorization of A

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

	   CHARACTER	 TRANS

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

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

PURPOSE
       SGELS solves overdetermined or underdetermined real linear  systems  involving  an  M-by-N
       matrix  A, or its transpose, using a QR or LQ factorization of A. It is assumed that A has
       full rank.  The following 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 = 'T' and m >= n:  find the minimum norm solution of
	  an undetermined system A**T * X = B.

       4. If TRANS = 'T' and m < n:  find the least squares solution of
	  an overdetermined system, i.e., solve the least squares problem
		       minimize || B - A**T * 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
	       = 'N': the linear system involves A;
	       = 'T': the linear system involves A**T.

       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) REAL array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, if M >= N, A is overwritten by details of
	       its QR factorization as returned by SGEQRF; if M <  N, A is overwritten by details
	       of its LQ factorization as returned by SGELQF.

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

       B       (input/output) REAL 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 = 'T'.  On exit, 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 elements N+1 to M in
	       that column; if TRANS = 'N' and m < n, rows 1 to N of B contain the  minimum  norm
	       solution  vectors; if TRANS = 'T' and m >= n, rows 1 to M of B contain the minimum
	       norm solution vectors; if TRANS = 'T' 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 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) REAL array, dimension (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 optimum 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

LAPACK version 3.0			   15 June 2000 				 SGELS(l)


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