NAME

       slatdf.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
           SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes
           a contribution to the reciprocal Dif-estimate.

Function/Subroutine Documentation

   subroutine slatdf (integer IJOB, integer N, real, dimension( ldz, * ) Z, integer LDZ, real,
       dimension( * ) RHS, real RDSUM, real RDSCAL, integer, dimension( * ) IPIV, integer,
       dimension( * ) JPIV)
       SLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a
       contribution to the reciprocal Dif-estimate.

       Purpose:

            SLATDF uses the LU factorization of the n-by-n matrix Z computed by
            SGETC2 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 SGETC2 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.

       Parameters:
           IJOB

                     IJOB is INTEGER
                     IJOB = 2: First compute an approximative null-vector e
                         of Z using SGECON, 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 chosen as either +1 or -1 (Default).

           N

                     N is INTEGER
                     The number of columns of the matrix Z.

           Z

                     Z is REAL array, dimension (LDZ, N)
                     On entry, the LU part of the factorization of the n-by-n
                     matrix Z computed by SGETC2:  Z = P * L * U * Q

           LDZ

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

           RHS

                     RHS is REAL 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

                     RDSUM is REAL
                     On entry, the sum of squares of computed contributions to
                     the Dif-estimate under computation by STGSYL, 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 STGSY2 is called by STGSYL.

           RDSCAL

                     RDSCAL is REAL
                     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 STGSY2 is called by
                           STGSYL.

           IPIV

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

           JPIV

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Further Details:
           This routine is a further developed implementation of algorithm BSOLVE in [1] using
           complete pivoting in the LU factorization.

       Contributors:
           Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901
           87 Umea, Sweden.

       References:

             [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.

Author

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