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clatdf.f(3) | LAPACK | clatdf.f(3) |
NAME¶
clatdf.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine clatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
Function/Subroutine Documentation¶
subroutine clatdf (integerIJOB, integerN, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )RHS, realRDSUM, realRDSCAL, integer, dimension( * )IPIV, integer, dimension( * )JPIV)¶
CLATDF Purpose: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
N
Z
LDZ
RHS
RDSUM
RDSCAL
IPIV
JPIV
Author:
IJOB is 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. Default.
N is INTEGER The number of columns of the matrix Z.
Z is 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 is INTEGER The leading dimension of the array Z. LDA >= max(1, N).
RHS is 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 above).
RDSUM is 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 factored out. On exit, the corresponding sum of squares updated with the contributions from the current sub-system. If TRANS = 'T' RDSUM is not touched. NOTE: RDSUM only makes sense when CTGSY2 is called by CTGSYL.
RDSCAL 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 CTGSY2 is called by CTGSYL.
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 is INTEGER array, dimension (N). The pivot indices; for 1 <= j <= N, column j of the matrix has been interchanged with column JPIV(j).
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
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, S-901 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 745-751.
[2] 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,
- 1995.
-
Author¶
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