SLATDF(1) LAPACK auxiliary routine (version 3.2) SLATDF(1)NAME
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
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 factoriza‐
tion 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 ele‐
ments and U is upper triangular.
ARGUMENTS
IJOB (input) INTEGER
IJOB = 2: First compute an approximative null-vector 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 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 SGETC2: 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
acoording 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 STGSYL, 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 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 of
Computing Science, Umea University, S-901 87 Umea, Sweden, 1995.
LAPACK auxiliary routine (versioNovember 2008 SLATDF(1)
