# cpbcon.f - Man Page

SRC/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** Ā

**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.

Definition at line **131** of file **cpbcon.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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