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

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