# 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

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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