zlatdf.f - Man Page

SRC/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

NAG Ltd.

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 167 of file zlatdf.f.

Author

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Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK