CLATDF(l) ) CLATDF(l)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, * )
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 strat‐
egy 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.
LAPACK version 3.0 15 June 2000 CLATDF(l)
