clatdf(3S)

NAME
     CLATDF - compute 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 CLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )

         INTEGER        IJOB, LDZ, N

         REAL           RDSCAL, RDSUM

         INTEGER        IPIV( * ), JPIV( * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLATDF 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 CGETC2. On entry RHS = f holds the contribution from earlier
     solved sub-systems, and on return RHS = x.

     The factorization of Z returned by CGETC2 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
             CGECON, 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) REAL array, dimension (LDZ, N)
             On entry, the LU part of the factorization of the n-by-n matrix Z
             computed by CGETC2:  Z = P * L * U * Q

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

     RHS     (input/output) REAL 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) REAL
             On entry, the sum of squares of computed contributions to the
             Dif-estimate under computation by CTGSYL, 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 CTGSY2 is called by CTGSYL.

     RDSCAL  (input/output) 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 CTGSY2 is called by CTGSYL.

     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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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