Contents
dpbtf2 - compute the Cholesky factorization of a real sym-
metric positive definite band matrix A
SUBROUTINE DPBTF2(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
INTEGER N, KD, LDAB, INFO
DOUBLE PRECISION AB(LDAB,*)
SUBROUTINE DPBTF2_64(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, KD, LDAB, INFO
DOUBLE PRECISION AB(LDAB,*)
F95 INTERFACE
SUBROUTINE PBTF2(UPLO, [N], KD, AB, [LDAB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDAB, INFO
REAL(8), DIMENSION(:,:) :: AB
SUBROUTINE PBTF2_64(UPLO, [N], KD, AB, [LDAB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, LDAB, INFO
REAL(8), DIMENSION(:,:) :: AB
C INTERFACE
#include <sunperf.h>
void dpbtf2(char uplo, int n, int kd, double *ab, int ldab,
int *info);
void dpbtf2_64(char uplo, long n, long kd, double *ab, long
ldab, long *info);
dpbtf2 computes the Cholesky factorization of a real sym-
metric positive definite band matrix A.
The factorization has the form
A = U' * U , if UPLO = 'U', or
A = L * L', if UPLO = 'L',
where U is an upper triangular matrix, U' is the transpose
of U, and L is lower triangular.
This is the unblocked version of the algorithm, calling
Level 2 BLAS.
UPLO (input)
Specifies whether the upper or lower triangular
part of the symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) The order of the matrix A. N >= 0.
KD (input)
The number of super-diagonals of the matrix A if
UPLO = 'U', or the number of sub-diagonals if UPLO
= 'L'. KD >= 0.
AB (input/output)
On entry, the upper or lower triangle of the sym-
metric 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
kd)<=i<=j; if UPLO = 'L', 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'*U or A =
L*L' of the band matrix A, in the same storage
format as A.
LDAB (input)
The leading dimension of the array AB. LDAB >=
KD+1.
INFO (output)
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an ille-
gal value
> 0: if INFO = k, the leading minor of order k is
not positive definite, and the factorization could
not be completed.
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.