# ctbcon.f - Man Page

SRC/ctbcon.f

## Synopsis

### Functions/Subroutines

subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
CTBCON

## Function/Subroutine Documentation

### subroutine ctbcon (character norm, character uplo, character diag, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CTBCON

Purpose:

``` CTBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).```
Parameters

NORM

```          NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= '1' or 'O':  1-norm;
= 'I':         Infinity-norm.```

UPLO

```          UPLO is CHARACTER*1
= 'U':  A is upper triangular;
= 'L':  A is lower triangular.```

DIAG

```          DIAG is CHARACTER*1
= 'N':  A is non-unit triangular;
= 'U':  A is unit triangular.```

N

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

KD

```          KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A.  KD >= 0.```

AB

```          AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.```

LDAB

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

RCOND

```          RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).```

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

NAG Ltd.

Definition at line 141 of file ctbcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK