zpbtrf (l) - Linux Manuals

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

Command to display zpbtrf manual in Linux: $ man l zpbtrf

NAME

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

SYNOPSIS

SUBROUTINE ZPBTRF(: UPLO, N, KD, AB, LDAB, INFO )
: CHARACTER UPLO
: INTEGER INFO, KD, LDAB, N
: COMPLEX*16 AB( LDAB, * )

PURPOSE

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

A = U**H * U, if UPLO = aqUaq, or

A = L * L**H, if UPLO = aqLaq,
where U is an upper triangular matrix and L is lower triangular.

ARGUMENTS

UPLO (input) CHARACTER*1: = aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
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 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 = U**H*U or A = L*L**H 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 = -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.

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.
Contributed by
Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989