CLATDF(l) ) CLATDF(l)
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
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, * )
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.
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
strategy where all entries of the r.h.s. b is choosen as either +1 or -1.
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
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 fac-
tored out. On exit, the corresponding 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
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).
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  using com-
plete pivoting in the LU factorization.
 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.
 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,
LAPACK version 3.0 15 June 2000 CLATDF(l)