-
template<typename T>
void pbstf(char *uplo, integer *n, integer *kb, T *bb, integer *ldbb, integer *info)# PBSTF computes a split Cholesky factorization of a real symmetric
positive definite band matrix.
Purpose:
PBSTF 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.
- Parameters:
UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangle of A is stored;
= ‘L’: Lower triangle of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
KD – [in]
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.
AB – [inout]
AB is REAL array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric 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 fla_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 – [in]
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal 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.