Contents
dpbstf - compute a split Cholesky factorization of a real
symmetric positive definite band matrix A
SUBROUTINE DPBSTF(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
INTEGER N, KD, LDAB, INFO
DOUBLE PRECISION AB(LDAB,*)
SUBROUTINE DPBSTF_64(UPLO, N, KD, AB, LDAB, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, KD, LDAB, INFO
DOUBLE PRECISION AB(LDAB,*)
F95 INTERFACE
SUBROUTINE PBSTF(UPLO, [N], KD, AB, [LDAB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDAB, INFO
REAL(8), DIMENSION(:,:) :: AB
SUBROUTINE PBSTF_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 dpbstf(char uplo, int n, int kd, double *ab, int ldab,
int *info);
void dpbstf_64(char uplo, long n, long kd, double *ab, long
ldab, long *info);
dpbstf computes a split Cholesky factorization of a real
symmetric positive definite band matrix A.
This routine is designed to be used in conjunction with
SSBGST.
The factorization has the form A = S**T*S where S is a
band matrix of the same bandwidth as A and the following
structure:
S = ( U )
( M L )
where U is upper triangular of order m = (n+kd)/2, and L is
lower triangular of order n-m.
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.
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 factor S from the split
Cholesky factorization A = S**T*S. See Further
Details.
LDAB (input)
The leading dimension of the array AB. LDAB >=
KD+1.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: if INFO = i, the factorization could not be
completed, because the updated element a(i,i) was
negative; the matrix A is not positive definite.
The band storage scheme is illustrated by the following
example, when N = 7, KD = 2:
S = ( s11 s12 s13 )
( s22 s23 s24 )
( s33 s34 )
( s44 )
( s53 s54 s55 )
( s64 s65 s66 )
( s75 s76 s77 )
If UPLO = 'U', the array AB holds:
on entry: on exit:
* * a13 a24 a35 a46 a57 * * s13 s24 s53
s64 s75
* a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54
s65 s76 a11 a22 a33 a44 a55 a66 a77 s11 s22 s33
s44 s55 s66 s77
If UPLO = 'L', the array AB holds:
on entry: on exit:
a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55
s66 s77 a21 a32 a43 a54 a65 a76 * s12 s23 s34
s54 s65 s76 * a31 a42 a53 a64 a64 * * s13
s24 s53 s64 s75 * *
Array elements marked * are not used by the routine.