SRC/clatdf.f(3)            Library Functions Manual            SRC/clatdf.f(3)

NAME
       SRC/clatdf.f

SYNOPSIS
   Functions/Subroutines
       subroutine clatdf (ijob, n, z, ldz, rhs, rdsum, rdscal, ipiv, jpiv)
           CLATDF 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 clatdf (integer ijob, integer n, complex, dimension( ldz, * ) z,
       integer ldz, complex, dimension( * ) rhs, real rdsum, real rdscal,
       integer, dimension( * ) ipiv, integer, dimension( * ) jpiv)
       CLATDF uses the LU factorization of the n-by-n matrix computed by
       sgetc2 and computes a contribution to the reciprocal Dif-estimate.

       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.
           !>

       Parameters
           IJOB

           !>          IJOB is 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 chosen as either +1 or
           !>              -1.  Default.
           !>

           N

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

           Z

           !>          Z is COMPLEX 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

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

           RHS

           !>          RHS is COMPLEX 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

           !>          RDSUM is 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

           !>          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 CTGSY2 is called by
           !>          CTGSYL.
           !>

           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.

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

       Definition at line 167 of file clatdf.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/clatdf.f(3)