cpbtf2 (l) - Linux Manuals

cpbtf2: computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

NAME

CPBTF2 - computes the Cholesky factorization of a complex Hermitian positive definite band matrix A

SYNOPSIS

SUBROUTINE CPBTF2(

UPLO, N, KD, AB, LDAB, INFO )

    

CHARACTER UPLO

    

INTEGER INFO, KD, LDAB, N

    

COMPLEX AB( LDAB, * )

PURPOSE

CPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form

A = Uaq * U ,  if UPLO = aqUaq, or

A = L  * Laq,  if UPLO = aqLaq,
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 super-diagonals of the matrix A if UPLO = aqUaq, or the number of sub-diagonals if UPLO = aqLaq. KD >= 0.

AB (input/output) 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = aqLaq, 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 = 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 k-th 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:

 *    *   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 = aqLaq 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.