slatdf(3)

NAME

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 tri

angular 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).

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 contribu

tions to the Dif-estimate under computation by STGSYL, where the

scaling factor RDSCAL (see below) has been factored out. On ex

it, 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 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 contri

butions 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 al

gorithm BSOLVE in [1] using complete pivoting in the LU factor

ization.

[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 version 3.0 15 June 2000

SLATDF(3)