p?pbtrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?pbtrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite banded distributed matrix.

Syntax

call pspbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)

call pdpbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)

call pcpbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)

call pzpbtrf(uplo, n, bw, a, ja, desca, af, laf, work, lwork, info)

Include Files

Description

The p?pbtrfroutine computes the Cholesky factorization of an n-by-n real symmetric or complex Hermitian positive-definite banded distributed matrix A(1:n, ja:ja+n-1).

The resulting factorization is not the same factorization as returned from LAPACK. Additional permutations are performed on the matrix for the sake of parallelism.

The factorization has the form:

A(1:n, ja:ja+n-1) = P*U^H*U*P^T, if uplo='U', or

A(1:n, ja:ja+n-1) = P*L*L^H*P^T, if uplo='L',

where P is a permutation matrix and U and L are banded upper and lower triangular matrices, respectively.

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

Input Parameters

uplo

(global) CHARACTER*1. Must be 'U' or 'L'.

If uplo = 'U', upper triangle of A(1:n, ja:ja+n-1) is stored;

If uplo = 'L', lower triangle of A(1:n, ja:ja+n-1) is stored.

n

(global) INTEGER. The order of the distributed submatrix A(1:n, ja:ja+n-1).

(n≥0).

bw

(global) INTEGER.

The number of superdiagonals of the distributed matrix if uplo = 'U', or the number of subdiagonals if uplo = 'L' (bw≥0).

a

(local)

REAL for pspbtrf

DOUBLE PRECISON for pdpbtrf

COMPLEX for pcpbtrf

DOUBLE COMPLEX for pzpbtrf.

Pointer into the local memory to an array of size (lld_a,LOCc(ja+n-1)).

On entry, this array contains the local pieces of the upper or lower triangle of the symmetric/Hermitian band distributed matrix A(1:n, ja:ja+n-1) to be factored.

ja

(global) INTEGER. The index in the global matrix A indicating the start of the matrix to be operated on (which may be either all of A or a submatrix of A).

desca

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix A.

If dtype_a = 501, then dlen_≥ 7;

else if dtype_a = 1, then dlen_≥ 9.

laf

(local) INTEGER. The size of the array af.

Must be laf≥ (NB+2*bw)*bw.

If laf is not large enough, an error code will be returned and the minimum acceptable size will be returned in af(1).

work

(local) Same type as a. Workspace array of size lwork.

lwork

(local or global) INTEGER. The size of the work array, must be lwork≥bw².

Output Parameters

a

On exit, if info=0, contains the permuted triangular factor U or L from the Cholesky factorization of the band matrix A(1:n, ja:ja+n-1), as specified by uplo.

af

(local)

REAL for pspbtrf

DOUBLE PRECISON for pdpbtrf

COMPLEX for pcpbtrf

DOUBLE COMPLEX for pzpbtrf.

Array of size laf. Auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?pbtrf and stored in af. Note that if a linear system is to be solved using p?pbtrs after the factorization routine,af must not be altered.

work(1)

On exit, work(1) contains the minimum value of lwork required for optimum performance.

info

(global) INTEGER.

If info=0, the execution is successful.

info < 0:

If the i-th argument is an array and the j-th entry had an illegal value, then info = -(i*100+j); if the i-th argument is a scalar and had an illegal value, then info = -i.

info>0:

If info = k ≤ NPROCS, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.

If info = k > NPROCS, the submatrix stored on processor info-NPROCS representing interactions with other processors was not nonsingular, and the factorization was not completed.

Parent topic: Matrix Factorization: ScaLAPACK Computational Routines

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