subroutine clatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
CLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.
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.
Parameters:
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 chosen as either +1 or -1. Default.
N
N is INTEGER The number of columns of the matrix Z.
Z
Z is COMPLEX 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
LDZ is INTEGER The leading dimension of the array Z. LDA >= max(1, N).
RHS
RHS is COMPLEX 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 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
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
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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Further Details:
Contributors:
References:
[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,
Definition at line 171 of file clatdf.f.
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