# 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

Univ. of Colorado Denver

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