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template<typename T>
void pbtrf(char *uplo, integer *n, integer *kd, T *ab, integer *ldab, integer *info)# PBTRF computes the Cholesky factorization of a real symmetric
positive definite band matrix A.
Purpose:
PBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A. The factorization has the form A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular.
- 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A, in the same storage format as A.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 leading minor of order i is not positive definite, and the factorization could not be completed.