Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - computes the minimum norm solution to a real linear least squares problem

SYNOPSIS

       SUBROUTINE SGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO )

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

           REAL           RCOND

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

PURPOSE

       SGELSS 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.

ARGUMENTS

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

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

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

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

        LWORK   (input) 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    (output) 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.

 LAPACK driver routine (version 3.2)        April 2011                            SGELSS(3lapack)