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

NAME

       LAPACK-3  - computes the contribution to the reciprocal Dif-estimate by solving for x in Z
       * x = b, where b is chosen such that the norm of x is as large as possible

SYNOPSIS

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

           INTEGER        IJOB, LDZ, N

           DOUBLE         PRECISION RDSCAL, RDSUM

           INTEGER        IPIV( * ), JPIV( * )

           COMPLEX*16     RHS( * ), Z( LDZ, * )

PURPOSE

       ZLATDF computes the contribution to the reciprocal Dif-estimate by solving for x in Z *  x
       = b, where b is chosen such that the norm of x is as large as possible. It is assumed that
       LU decomposition
        of Z has been computed by ZGETC2. On entry RHS = f holds the
        contribution from earlier solved sub-systems, and on return RHS = x.
        The factorization of Z returned by ZGETC2 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 ZGECON, 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 ZGETC2:  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 according 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 ZTGSYL, 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 ZTGSY2 is called by CTGSYL.

        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 ZTGSY2 is called by
                ZTGSYL.

        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 UMINF-95.05, Department of
               Computing Science, Umea University, S-901 87 Umea, Sweden,
               1995.

 LAPACK auxiliary routine (version 3.2)     April 2011                            ZLATDF(3lapack)