NAME

cpbtrf - compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

SYNOPSIS

  SUBROUTINE CPBTRF( UPLO, N, NDIAG, A, LDA, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*)
  INTEGER N, NDIAG, LDA, INFO

  SUBROUTINE CPBTRF_64( UPLO, N, NDIAG, A, LDA, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*)
  INTEGER*8 N, NDIAG, LDA, INFO

F95 INTERFACE

  SUBROUTINE PBTRF( UPLO, [N], NDIAG, A, [LDA], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INFO

  SUBROUTINE PBTRF_64( UPLO, [N], NDIAG, A, [LDA], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INFO

C INTERFACE

#include <sunperf.h>

void cpbtrf(char uplo, int n, int ndiag, complex *a, int lda, int *info);

void cpbtrf_64(char uplo, long n, long ndiag, complex *a, long lda, long *info);

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.

ARGUMENTS

UPLO (input)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The order of the matrix A. N > = 0.
NDIAG (input)
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG > = 0.
A (input/output)
On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first NDIAG+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd) < =i < =j; if UPLO = 'L', A(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.
LDA (input)
The leading dimension of the array A. LDA > = NDIAG+1.

INFO (output)

 = 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, NDIAG = 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.

Contributed by

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