# CentOS 7.0 - man page for cpbtrf (centos section 3)

```cpbtrf.f(3)							      LAPACK							       cpbtrf.f(3)

NAME
cpbtrf.f -

SYNOPSIS
Functions/Subroutines
subroutine cpbtrf (UPLO, N, KD, AB, LDAB, INFO)
CPBTRF

Function/Subroutine Documentation
subroutine cpbtrf (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, integerINFO)
CPBTRF

Purpose:

CPBTRF computes the Cholesky factorization of a complex Hermitian
positive definite band matrix A.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.

Parameters:
UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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 subdiagonals if UPLO = 'L'.  KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
On entry, the upper or lower triangle of the Hermitian 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).

On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**H*U or A = L*L**H of the band
matrix A, in the same storage format as A.

LDAB

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

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
November 2011

Further Details:

The band storage scheme is illustrated by the following example, when
N = 6, KD = 2, and UPLO = 'U':

On entry:			     On exit:

*    *   a13  a24  a35  a46	  *    *   u13	u24  u35  u46
*   a12  a23  a34  a45  a56	  *   u12  u23	u34  u45  u56
a11  a22  a33  a44  a55  a66	 u11  u22  u33	u44  u55  u66

Similarly, if UPLO = 'L' the format of A is as follows:

On entry:			     On exit:

a11  a22  a33  a44  a55  a66	 l11  l22  l33	l44  l55  l66
a21  a32  a43  a54  a65   *	 l21  l32  l43	l54  l65   *
a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *    *

Array elements marked * are not used by the routine.

Contributors:
Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989

Definition at line 143 of file cpbtrf.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       cpbtrf.f(3)```