cpbtrf(3P) Sun Performance Library cpbtrf(3P)NAMEcpbtrf - compute the Cholesky factorization of a complex Hermitian pos‐
itive definite band matrix A
SYNOPSIS
SUBROUTINE CPBTRF(UPLO, N, KD, A, LDA, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*)
INTEGER N, KD, LDA, INFO
SUBROUTINE CPBTRF_64(UPLO, N, KD, A, LDA, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*)
INTEGER*8 N, KD, LDA, INFO
F95 INTERFACE
SUBROUTINE PBTRF(UPLO, [N], KD, A, [LDA], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, KD, LDA, INFO
SUBROUTINE PBTRF_64(UPLO, [N], KD, A, [LDA], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, KD, LDA, INFO
C INTERFACE
#include <sunperf.h>
void cpbtrf(char uplo, int n, int kd, complex *a, int lda, int *info);
void cpbtrf_64(char uplo, long n, long kd, complex *a, long lda, long
*info);
PURPOSEcpbtrf computes the Cholesky factorization of a complex Hermitian posi‐
tive 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.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
A (input/output)
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 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 >= KD+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 posi‐
tive 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 = '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
6 Mar 2009 cpbtrf(3P)
