
zpbtf2.f(3) LAPACK zpbtf2.f(3)
NAME
zpbtf2.f 
SYNOPSIS
Functions/Subroutines
subroutine zpbtf2 (UPLO, N, KD, AB, LDAB, INFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite
band matrix (unblocked algorithm).
Function/Subroutine Documentation
subroutine zpbtf2 (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB,
integerLDAB, integerINFO)
ZPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band
matrix (unblocked algorithm).
Purpose:
ZPBTF2 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, U**H is the conjugate transpose
of U, and L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
Parameters:
UPLO
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
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*16 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
jth column of A is stored in the jth column of the array AB
as follows:
if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO = 'L', AB(1+ij,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 = k, the kth argument had an illegal value
> 0: if INFO = k, the leading minor of order k is not
positive definite, and the factorization could not be
completed.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
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.
Definition at line 143 of file zpbtf2.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 zpbtf2.f(3) 
