slatdf.f (3)  Linux Manuals
NAME
slatdf.f 
SYNOPSIS
Functions/Subroutines
subroutine slatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
SLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate.
Function/Subroutine Documentation
subroutine slatdf (integerIJOB, integerN, real, dimension( ldz, * )Z, integerLDZ, real, dimension( * )RHS, realRDSUM, realRDSCAL, integer, dimension( * )IPIV, integer, dimension( * )JPIV)
SLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate.
Purpose:

SLATDF uses the LU factorization of the nbyn matrix Z computed by SGETC2 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 SGETC2 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 SGECON, 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).
NN is INTEGER The number of columns of the matrix Z.
ZZ is REAL array, dimension (LDZ, N) On entry, the LU part of the factorization of the nbyn matrix Z computed by SGETC2: Z = P * L * U * Q
LDZLDZ is INTEGER The leading dimension of the array Z. LDA >= max(1, N).
RHSRHS is 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).
RDSUMRDSUM is REAL On entry, the sum of squares of computed contributions to the Difestimate 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 subsystem. If TRANS = 'T' RDSUM is not touched. NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.
RDSCALRDSCAL is 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.
IPIVIPIV is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix has been interchanged with row IPIV(i).
JPIVJPIV 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 slatdf.f.
Author
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