zlatdf.f man page

zlatdf.f —

Synopsis

Functions/Subroutines

subroutine zlatdf (IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV)
ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.

Function/Subroutine Documentation

subroutine zlatdf (integer IJOB, integer N, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) RHS, double precision RDSUM, double precision RDSCAL, integer, dimension( * ) IPIV, integer, dimension( * ) JPIV)

ZLATDF uses the LU factorization of the n-by-n matrix computed by sgetc2 and computes a contribution to the reciprocal Dif-estimate.  

Purpose:

 ZLATDF 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 ZGETC2. On entry RHS = f holds the
 contribution from earlier solved sub-systems, 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.
Parameters:

IJOB

          IJOB is INTEGER
          IJOB = 2: First compute an approximative null-vector e
              of Z using ZGECON, 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*16 array, dimension (LDZ, N)
          On entry, the LU part of the factorization of the n-by-n
          matrix Z computed by ZGETC2:  Z = P * L * U * Q

LDZ

          LDZ is INTEGER
          The leading dimension of the array Z.  LDA >= max(1, N).

RHS

          RHS is COMPLEX*16 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 Dif-estimate 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 sub-system.
          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).
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

June 2016

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.

Definition at line 171 of file zlatdf.f.

Author

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Referenced By

The man page zlatdf(3) is an alias of zlatdf.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK