spbtf2 (l) - Linux Manuals
spbtf2: computes the Cholesky factorization of a real symmetric positive definite band matrix A
NAMESPBTF2 - computes the Cholesky factorization of a real symmetric positive definite band matrix A
- SUBROUTINE SPBTF2(
- UPLO, N, KD, AB, LDAB, INFO )
- CHARACTER UPLO
- INTEGER INFO, KD, LDAB, N
- REAL AB( LDAB, * )
PURPOSESPBTF2 computes the Cholesky factorization of a real symmetric positive definite band matrix A. The factorization has the form
where U is an upper triangular matrix, Uaq is the transpose of U, and L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
- UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= aqUaq: Upper triangular
= aqLaq: Lower triangular
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- KD (input) INTEGER
- The number of super-diagonals of the matrix A if UPLO = aqUaq, or the number of sub-diagonals if UPLO = aqLaq. KD >= 0.
- AB (input/output) 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 = aqUaq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = aqLaq, 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 = Uaq*U or A = L*Laq of the band matrix A, in the same storage format as A.
- LDAB (input) INTEGER
- The leading dimension of the array AB. LDAB >= KD+1.
- INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading minor of order k is not positive definite, and the factorization could not be completed.
FURTHER DETAILSThe band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = aqUaq:
On entry: On exit:
On entry: On exit: