# cla_gbrcond_x.f man page

cla_gbrcond_x.f

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

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

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

Purpose:

```    CLA_GBRCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX 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 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 array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by CGBTRF.  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 CGBTRF; row i of the matrix was interchanged
with row IPIV(i).```

X

```          X is COMPLEX 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 array, dimension (2*N).
Workspace.```

RWORK

```          RWORK is REAL array, dimension (N).
Workspace.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 155 of file cla_gbrcond_x.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK