SLATDF - use 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
SYNOPSIS
SUBROUTINE SLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL,
IPIV, JPIV )
INTEGER IJOB, LDZ, N
REAL RDSCAL, RDSUM
INTEGER IPIV( * ), JPIV( * )
REAL RHS( * ), Z( LDZ, * )
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.
ARGUMENTS
IJOB (input) INTEGER
IJOB = 2: First compute an approximative null-vec
tor 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 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 SGETC2: 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 acoording 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
STGSYL, 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 STGSY2 is called by STGSYL.
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 STGSY2 is called by STGSYL.
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 IMINF-95.05, Departement
Computing Science, Umea University, S-901 87 Umea,
Sweden, 1995.
Man(1) output converted with
man2html