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dgelss.f(3)			    LAPACK			   dgelss.f(3)

NAME
       dgelss.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dgelss (M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,
	   LWORK, INFO)
	    DGELSS solves overdetermined or underdetermined systems for GE
	   matrices

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

       Purpose:

	    DGELSS computes the minimum norm solution to a real 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
	    singular values which are less than RCOND times the largest singular
	    value.

       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 the 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, the first min(m,n) rows of A are overwritten with
		     its right singular vectors, stored rowwise.

	   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, 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

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

	   S

		     S is DOUBLE PRECISION 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

		     RCOND is DOUBLE PRECISION
		     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

		     RANK is INTEGER
		     The effective rank of A, i.e., the number of singular values
		     which are greater than RCOND*S(1).

	   WORK

		     WORK is DOUBLE PRECISION 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 >= 1, and also:
		     LWORK >= 3*min(M,N) + max( 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.

	   INFO

		     INFO is 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
			   bidiagonal form did not converge to zero.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 172 of file dgelss.f.

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

Version 3.4.2			Sat Nov 16 2013			   dgelss.f(3)
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