Visible to Intel only — GUID: GUID-A58D34C1-2129-4380-9E44-956BD292521D
Visible to Intel only — GUID: GUID-A58D34C1-2129-4380-9E44-956BD292521D
?pbtf2
Computes the Cholesky factorization of a symmetric/ Hermitian positive-definite band matrix (unblocked algorithm).
Syntax
call spbtf2( uplo, n, kd, ab, ldab, info )
call dpbtf2( uplo, n, kd, ab, ldab, info )
call cpbtf2( uplo, n, kd, ab, ldab, info )
call zpbtf2( uplo, n, kd, ab, ldab, info )
Include Files
- mkl.fi
Description
The routine computes the Cholesky factorization of a real symmetric or complex Hermitian positive definite band matrix A.
The factorization has the form
A = UT*U for real flavors, A = UH*U for complex flavors if uplo = 'U', or
A = L*LT for real flavors, A = L*LH for complex flavors if uplo = 'L',
where U is an upper triangular matrix, and L is lower triangular. This is the unblocked version of the algorithm, calling BLAS Level 2 Routines.
Input Parameters
- uplo
-
CHARACTER*1.
Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix A is stored:
= 'U': upper triangular
= 'L': lower triangular
- n
-
INTEGER. The order of the matrix A. n≥ 0.
- kd
-
INTEGER. The number of super-diagonals of the matrix A if uplo = 'U', or the number of sub-diagonals if uplo = 'L'.
kd≥ 0.
- ab
-
REAL for spbtf2
DOUBLE PRECISION for dpbtf2
COMPLEX for cpbtf2
DOUBLE COMPLEX for zpbtf2.
Array, DIMENSION (ldab, n).
On entry, the upper or lower triangle of the symmetric/ Hermitian 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).
- ldab
-
INTEGER. The leading dimension of the array ab. ldab≥kd+1.
Output Parameters
- ab
-
On exit, If info = 0, the triangular factor U or L from the Cholesky factorization A=UT*U (A=UH*U), or A= L*LT (A = L*LH) of the band matrix A, in the same storage format as A.
- info
-
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.