dgelsx.f(3)							      LAPACK							       dgelsx.f(3)

NAME

       dgelsx.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dgelsx (M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, INFO)
	    DGELSX solves overdetermined or underdetermined systems for GE matrices

Function/Subroutine Documentation
   subroutine dgelsx (integerM, integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B,
       integerLDB, integer, dimension( * )JPVT, double precisionRCOND, integerRANK, double precision, dimension( * )WORK, integerINFO)
	DGELSX solves overdetermined or underdetermined systems for GE matrices

       Purpose:

	    This routine is deprecated and has been replaced by routine DGELSY.

	    DGELSX computes the minimum-norm solution to a real 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
	    condition 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 orthogonal 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**T [ inv(T11)*Q1**T*B ]
			    [	     0	       ]
	    where Q1 consists of the first RANK columns of Q.

       Parameters:
	   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 matrices B and X. NRHS >= 0.

	   A

		     A is DOUBLE PRECISION 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

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

	   B

		     B is DOUBLE PRECISION 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

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

	   JPVT

		     JPVT is 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 factorization 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

		     RCOND is DOUBLE PRECISION
		     RCOND is used to determine the effective rank of A, which
		     is defined as the order of the largest leading triangular
		     submatrix R11 in the QR factorization with pivoting of A,
		     whose estimated condition number < 1/RCOND.

	   RANK

		     RANK is 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 complete orthogonal factorization of A.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension
				 (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 178 of file dgelsx.f.

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

Version 3.4.1							  Sun May 26 2013						       dgelsx.f(3)