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

NAME

       LAPACK-3 - routine i deprecated and has been replaced by routine SGELSY

SYNOPSIS

       SUBROUTINE SGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, WORK, INFO )

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

           REAL           RCOND

           INTEGER        JPVT( * )

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

PURPOSE

       This routine is deprecated and has been replaced by routine SGELSY.
        SGELSX 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.

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 matrices B and X. NRHS >= 0.

        A       (input/output) REAL 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     (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, 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,M,N).

        JPVT    (input/output) 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   (input) REAL
                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    (output) 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    (workspace) REAL array, dimension
                (max( min(M,N)+3*N, 2*min(M,N)+NRHS )),

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

 LAPACK driver routine (version 3.3.1)      April 2011                            SGELSX(3lapack)