CLATDF(3S)CLATDF(3S)NAME
CLATDF - compute 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
SYNOPSIS
SUBROUTINE CLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )
INTEGER IJOB, LDZ, N
REAL RDSCAL, RDSUM
INTEGER IPIV( * ), JPIV( * )
COMPLEX RHS( * ), Z( LDZ, * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
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.
ARGUMENTS
IJOB (input) 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.
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CLATDF(3S)CLATDF(3S)
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 CGETC2: 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
according to the value of IJOB (see above).
RDSUM (input/output) 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 (input/output) 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 (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 algorithm BSOLVE in
[1] using complete pivoting in the LU factorization.
[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
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CLATDF(3S)CLATDF(3S)
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.
SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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