# cpbcon.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cpbcon.f

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine cpbcon (character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real ANORM, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO)

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