zpbtf2 (l)  Linux Man Pages
zpbtf2: computes the Cholesky factorization of a complex Hermitian positive definite band matrix A
NAME
ZPBTF2  computes the Cholesky factorization of a complex Hermitian positive definite band matrix ASYNOPSIS
 SUBROUTINE ZPBTF2(
 UPLO, N, KD, AB, LDAB, INFO )
 CHARACTER UPLO
 INTEGER INFO, KD, LDAB, N
 COMPLEX*16 AB( LDAB, * )
PURPOSE
ZPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the formA
A
where U is an upper triangular matrix, Uaq is the conjugate transpose of U, and L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
ARGUMENTS
 UPLO (input) CHARACTER*1

Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= aqUaq: Upper triangular
= aqLaq: Lower triangular  N (input) INTEGER
 The order of the matrix A. N >= 0.
 KD (input) INTEGER
 The number of superdiagonals of the matrix A if UPLO = aqUaq, or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
 AB (input/output) 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 = aqUaq, AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = aqLaq, 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 = Uaq*U or A = L*Laq of the band matrix A, in the same storage format as A.
 LDAB (input) INTEGER
 The leading dimension of the array AB. LDAB >= KD+1.
 INFO (output) 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.
FURTHER DETAILS
The band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = aqUaq:On entry: On exit:
a11
On entry: On exit:
a11
a21
a31