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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes the contribution to the reciprocal Dif-estimate by solving for x in Z * x = b, where b is chosen such that the

```NAME
LAPACK-3  - 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

SYNOPSIS
SUBROUTINE ZLATDF( IJOB, N, Z, LDZ, RHS, RDSUM, RDSCAL, IPIV, JPIV )

INTEGER        IJOB, LDZ, N

DOUBLE         PRECISION RDSCAL, RDSUM

INTEGER        IPIV( * ), JPIV( * )

COMPLEX*16     RHS( * ), Z( LDZ, * )

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.

ARGUMENTS
IJOB    (input) 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 choosen as either +1 or
-1.  Default.

N       (input) INTEGER
The number of columns of the matrix Z.

Z       (input) DOUBLE PRECISION 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     (input) INTEGER
The leading dimension of the array Z.  LDA >= max(1, N).

RHS     (input/output) 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   (input/output) 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  (input/output) 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    (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
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.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
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