# cpbcon.f man page

cpbcon.f —

## Synopsis

### Functions/Subroutines

subroutinecpbcon(UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO)CPBCON

## Function/Subroutine Documentation

### subroutine cpbcon (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, realANORM, realRCOND, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

**CPBCON**

**Purpose:**

```
CPBCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by
CPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
```

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*KD*

```
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
```

*AB*

```
AB is COMPLEX array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
```

*LDAB*

```
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
```

*ANORM*

```
ANORM is REAL
The 1-norm (or infinity-norm) of the Hermitian band matrix A.
```

*RCOND*

```
RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.
```

*WORK*

`WORK is COMPLEX array, dimension (2*N)`

*RWORK*

`RWORK is REAL array, dimension (N)`

*INFO*

```
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 133 of file cpbcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

cpbcon(3) is an alias of cpbcon.f(3).