---
name: "cpbcon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cpbcon/3lapack"
---

# cpbcon(3lapack)

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

## NAME

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

## SYNOPSIS

- SUBROUTINE CPBCON(

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

- CHARACTER

  UPLO

- INTEGER

  INFO, KD, LDAB, N

- REAL

  ANORM, RCOND

- REAL

  RWORK( \* )

- COMPLEX

  AB( LDAB, \* ), WORK( \* )

## 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))).

## ARGUMENTS

- UPLO (input) CHARACTER\*1

  \= 'U':  Upper triangular factor stored in AB;\
   \= 'L':  Lower triangular factor stored in AB.

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- KD (input) INTEGER

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

- AB (input) 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 (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= KD+1.

- ANORM (input) REAL

  The 1-norm (or infinity-norm) of the Hermitian band matrix A.

- RCOND (output) 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 (workspace) COMPLEX array, dimension (2\*N)

  - RWORK (workspace) REAL array, dimension (N)

  - INFO (output) INTEGER

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