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

NAME

       LAPACK-3  -  uses  the  LU  factorization  of  the  n-by-n matrix Z computed by DGETC2 and
       computes a contribution to the reciprocal Dif-estimate by solving Z * x =  b  for  x,  and
       choosing the r.h.s

SYNOPSIS

       SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )

           INTEGER        IJOB, LDZ, N

           DOUBLE         PRECISION RDSCAL, RDSUM

           INTEGER        IPIV( * ), JPIV( * )

           DOUBLE         PRECISION RHS( * ), Z( LDZ, * )

PURPOSE

       DLATDF  uses the LU factorization of the n-by-n matrix Z computed by DGETC2 and computes a
       contribution to the reciprocal Dif-estimate by solving Z * x = b for x, and  choosing  the
       r.h.s. b such that
        the norm of x is as large as possible. On entry RHS = b holds the
        contribution from earlier solved sub-systems, and on return RHS = x.
        The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q,
        where P and Q are permutation matrices. L is lower triangular with
        unit diagonal elements and U is upper triangular.

ARGUMENTS

        IJOB    (input) INTEGER
                IJOB = 2: First compute an approximative null-vector e
                of Z using DGECON, e is normalized and solve for
                Zx = +-e - f with the sign giving the greater value
                of 2-norm(x). About 5 times as expensive as Default.
                IJOB .ne. 2: Local look ahead strategy where all entries of
                the r.h.s. b is choosen as either +1 or -1 (Default).

        N       (input) INTEGER
                The number of columns of the matrix Z.

        Z       (input) DOUBLE PRECISION array, dimension (LDZ, N)
                On entry, the LU part of the factorization of the n-by-n
                matrix Z computed by DGETC2:  Z = P * L * U * Q

        LDZ     (input) INTEGER
                The leading dimension of the array Z.  LDA >= max(1, N).

        RHS     (input/output) DOUBLE PRECISION array, dimension (N)
                On entry, RHS contains contributions from other subsystems.
                On exit, RHS contains the solution of the subsystem with
                entries acoording to the value of IJOB (see above).

        RDSUM   (input/output) DOUBLE PRECISION
                On entry, the sum of squares of computed contributions to
                the Dif-estimate under computation by DTGSYL, where the
                scaling factor RDSCAL (see below) has been factored out.
                On exit, the corresponding sum of squares updated with the
                contributions from the current sub-system.
                If TRANS = 'T' RDSUM is not touched.
                NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.

        RDSCAL  (input/output) DOUBLE PRECISION
                On entry, scaling factor used to prevent overflow in RDSUM.
                On exit, RDSCAL is updated w.r.t. the current contributions
                in RDSUM.
                If TRANS = 'T', RDSCAL is not touched.
                NOTE: RDSCAL only makes sense when DTGSY2 is called by
                DTGSYL.

        IPIV    (input) INTEGER array, dimension (N).
                The pivot indices; for 1 <= i <= N, row i of the
                matrix has been interchanged with row IPIV(i).

        JPIV    (input) INTEGER array, dimension (N).
                The pivot indices; for 1 <= j <= N, column j of the
                matrix has been interchanged with column JPIV(j).

FURTHER DETAILS

        Based on contributions by
           Bo Kagstrom and Peter Poromaa, Department of Computing Science,
           Umea University, S-901 87 Umea, Sweden.
        This routine is a further developed implementation of algorithm
        BSOLVE in [1] using complete pivoting in the LU factorization.
        [1] Bo Kagstrom and Lars Westin,
            Generalized Schur Methods with Condition Estimators for
            Solving the Generalized Sylvester Equation, IEEE Transactions
            on Automatic Control, Vol. 34, No. 7, July 1989, pp 745-751.
        [2] Peter Poromaa,
            On Efficient and Robust Estimators for the Separation
            between two Regular Matrix Pairs with Applications in
            Condition Estimation. Report IMINF-95.05, Departement of
            Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.

 LAPACK auxiliary routine (version 3.2.2)   April 2011                            DLATDF(3lapack)