
dlatdf.f(3) LAPACK dlatdf.f(3)
NAME
dlatdf.f 
SYNOPSIS
Functions/Subroutines
subroutine dlatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
DLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes
a contribution to the reciprocal Difestimate.
Function/Subroutine Documentation
subroutine dlatdf (integerIJOB, integerN, double precision, dimension( ldz, * )Z, integerLDZ,
double precision, dimension( * )RHS, double precisionRDSUM, double precisionRDSCAL,
integer, dimension( * )IPIV, integer, dimension( * )JPIV)
DLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a
contribution to the reciprocal Difestimate.
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
contribution 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 permutation matrices. L is lower triangular with
unit diagonal elements and U is upper triangular.
Parameters:
IJOB
IJOB is 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
N is INTEGER
The number of columns of the matrix Z.
Z
Z is 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
LDZ is INTEGER
The leading dimension of the array Z. LDA >= max(1, N).
RHS
RHS is 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
RDSUM is 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 factored out.
On exit, the corresponding sum of squares updated with the
contributions from the current subsystem.
If TRANS = 'T' RDSUM is not touched.
NOTE: RDSUM only makes sense when DTGSY2 is called by STGSYL.
RDSCAL
RDSCAL is 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
IPIV is INTEGER array, dimension (N).
The pivot indices; for 1 <= i <= N, row i of the
matrix has been interchanged with row IPIV(i).
JPIV
JPIV is INTEGER array, dimension (N).
The pivot indices; for 1 <= j <= N, column j of the
matrix has been interchanged with column JPIV(j).
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Further Details:
This routine is a further developed implementation of algorithm BSOLVE in [1] using
complete pivoting in the LU factorization.
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S901
87 Umea, Sweden.
References:
[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.
Definition at line 171 of file dlatdf.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dlatdf.f(3) 
