# cla_gbrcond_x.f (3) - Linux Manuals

## NAME

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 (characterTRANS, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, complex, dimension( * )X, integerINFO, 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