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 ear
lier 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-vec
tor 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).
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 contribu
tions to the Dif-estimate under computation by
CTGSYL, where the scaling factor RDSCAL (see
below) has been factored out. On exit, the corre
sponding sum of squares updated with the contribu
tions 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 Separa
tion
between two Regular Matrix Pairs with Applications
Condition Estimation. Report UMINF-95.05, Depart
ment of
Computing Science, Umea University, S-901 87 Umea,
Sweden,
1995.
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