spbtrf (l) - Linux Man Pages
spbtrf: computes the Cholesky factorization of a real symmetric positive definite band matrix A
NAMESPBTRF - computes the Cholesky factorization of a real symmetric positive definite band matrix A
- SUBROUTINE SPBTRF(
- UPLO, N, KD, AB, LDAB, INFO )
- CHARACTER UPLO
- INTEGER INFO, KD, LDAB, N
- REAL AB( LDAB, * )
PURPOSESPBTRF 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 and L is lower triangular.
- UPLO (input) CHARACTER*1
= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
- N (input) INTEGER
- The order of the matrix A. N >= 0.
- KD (input) INTEGER
- The number of superdiagonals of the matrix A if UPLO = aqUaq, or the number of subdiagonals 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 = U**T*U or A = L*L**T 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 = -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.
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:
Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989