
DLATDF(l) ) DLATDF(l)
NAME
DLATDF  use the LU factorization of the nbyn matrix Z computed by DGETC2 and computes a
contribution to the reciprocal Difestimate by solving Z * x = b for x, and choosing the
r.h.s
SYNOPSIS
SUBROUTINE DLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )
INTEGER IJOB, LDZ, N
DOUBLE PRECISION RDSCAL, RDSUM
INTEGER IPIV( * ), JPIV( * )
DOUBLE PRECISION RHS( * ), Z( LDZ, * )
PURPOSE
DLATDF uses the LU factorization of the nbyn matrix Z computed by DGETC2 and computes a
contribution to the reciprocal Difestimate 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 con
tribution from earlier solved subsystems, and on return RHS = x.
The factorization of Z returned by DGETC2 has the form Z = P*L*U*Q, where P and Q are per
mutation matrices. L is lower triangular with unit diagonal elements and U is upper trian
gular.
ARGUMENTS
IJOB (input) INTEGER
IJOB = 2: First compute an approximative nullvector e of Z using DGECON, e is
normalized and solve for Zx = +e  f with the sign giving the greater value of
2norm(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) DOUBLE PRECISION array, dimension (LDZ, N)
On entry, the LU part of the factorization of the nbyn matrix Z computed by
DGETC2: Z = P * L * U * Q
LDZ (input) INTEGER
The leading dimension of the array Z. LDA >= max(1, N).
RHS (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
On entry, the sum of squares of computed contributions to the Difestimate under
computation by DTGSYL, 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 subsystem. If TRANS = 'T' RDSUM is not touched. NOTE:
RDSUM only makes sense when DTGSY2 is called by STGSYL.
RDSCAL (input/output) DOUBLE PRECISION
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 DTGSY2 is called by DTGSYL.
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, S901 87 Umea, Sweden.
This routine is a further developed implementation of algorithm BSOLVE in [1] using com
plete 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 745751.
[2] Peter Poromaa,
On Efficient and Robust Estimators for the Separation
between two Regular Matrix Pairs with Applications in
Condition Estimation. Report IMINF95.05, Departement of
Computing Science, Umea University, S901 87 Umea, Sweden, 1995.
LAPACK version 3.0 15 June 2000 DLATDF(l) 
