?pbtf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?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 = U^T*U for real flavors, A = U^H*U for complex flavors if uplo = 'U', or

A = L*L^T for real flavors, A = L*L^H 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=U^T*U (A=U^H*U), or A= L*L^T (A = L*L^H) 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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?pbtf2