# zla_gbrcond_x.f - Man Page

## Synopsis

### Functions/Subroutines

double precision function **zla_gbrcond_x** (TRANS, **N**, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK)**ZLA_GBRCOND_X** computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

## Function/Subroutine Documentation

### double precision function zla_gbrcond_x (character TRANS, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldafb, * ) AFB, integer LDAFB, integer, dimension( * ) IPIV, complex*16, dimension( * ) X, integer INFO, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK)

**ZLA_GBRCOND_X** computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

**Purpose:**

ZLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector.

**Parameters:***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose)

*N*N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.

*KL*KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

*KU*KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

*AB*AB is COMPLEX*16 array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

*LDAB*LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.

*AFB*AFB is COMPLEX*16 array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.

*LDAFB*LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

*IPIV*IPIV is INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by ZGBTRF; row i of the matrix was interchanged with row IPIV(i).

*X*X is COMPLEX*16 array, dimension (N) The vector X in the formula op(A) * diag(X).

*INFO*INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.

*WORK*WORK is COMPLEX*16 array, dimension (2*N). Workspace.

*RWORK*RWORK is DOUBLE PRECISION array, dimension (N). Workspace.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 157 of file zla_gbrcond_x.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK