sgels.f(3)							      LAPACK								sgels.f(3)

NAME

       sgels.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgels (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
	    SGELS solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation
   subroutine sgels (characterTRANS, integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B,
       integerLDB, real, dimension( * )WORK, integerLWORK, integerINFO)
	SGELS solves overdetermined or underdetermined systems for GE matrices

       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.

       Parameters:
	   TRANS

		     TRANS is CHARACTER*1
		     = 'N': the linear system involves A;
		     = 'T': the linear system involves A**T.

	   M

		     M is INTEGER
		     The number of rows of the matrix A.  M >= 0.

	   N

		     N is INTEGER
		     The number of columns of the matrix A.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		     The number of right hand sides, i.e., the number of
		     columns of the matrices B and X. NRHS >=0.

	   A

		     A is 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

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

	   B

		     B is 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, 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
		     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

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

	   WORK

		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

	   LWORK

		     LWORK is 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

		     INFO is 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.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 183 of file sgels.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012							sgels.f(3)