
NAMEzlatdf.f SYNOPSISFunctions/Subroutinessubroutine zlatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV) Function/Subroutine Documentationsubroutine zlatdf (integerIJOB, integerN, complex*16, dimension( ldz, * )Z, integerLDZ, complex*16, dimension( * )RHS, double precisionRDSUM, double precisionRDSCAL, integer, dimension( * )IPIV, integer, dimension( * )JPIV)ZLATDF uses the LU factorization of the nbyn matrix computed by sgetc2 and computes a contribution to the reciprocal Difestimate. Purpose:ZLATDF computes the contribution to the reciprocal Difestimate 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 ZGETC2. On entry RHS = f holds the contribution from earlier solved subsystems, and on return RHS = x. The factorization of Z returned by ZGETC2 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
Author:
IJOB is INTEGER IJOB = 2: First compute an approximative nullvector e of Z using ZGECON, 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 ZGETC2: Z = P * L * U * QLDZ 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 according 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 ZTGSYL, 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 ZTGSY2 is called by CTGSYL.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 ZTGSY2 is called by ZTGSYL.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). 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.
Definition at line 169 of file zlatdf.f.
[2] Peter Poromaa, On Efficient and Robust Estimators for the Separation between two Regular Matrix Pairs with Applications in Condition Estimation. Report UMINF95.05, Department of Computing Science, Umea University, S901 87 Umea, Sweden,
AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Visit the GSP FreeBSD Man Page Interface. 