p?gbtrf

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?gbtrf

Computes the LU factorization of a general n-by-n banded distributed matrix.

Syntax

call psgbtrf(n, bwl, bwu, a, ja, desca, ipiv, af, laf, work, lwork, info)

call pdgbtrf(n, bwl, bwu, a, ja, desca, ipiv, af, laf, work, lwork, info)

call pcgbtrf(n, bwl, bwu, a, ja, desca, ipiv, af, laf, work, lwork, info)

call pzgbtrf(n, bwl, bwu, a, ja, desca, ipiv, af, laf, work, lwork, info)

Include Files

Description

The p?gbtrf routine computes the LU factorization of a general n-by-n real/complex banded distributed matrix A(1:n, ja:ja+n-1) using partial pivoting with row interchanges.

The resulting factorization is not the same factorization as returned from the LAPACK routine ?gbtrf. 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*L*U*Q

where P and Q are permutation matrices, and L and U are banded lower and upper triangular matrices, respectively. The matrix Q represents reordering of columns for the sake of parallelism, while P represents reordering of rows for numerical stability using classic partial pivoting.

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

n

(global) INTEGER. The number of rows and columns in the distributed submatrix A(1:n, ja:ja+n-1); n≥ 0.

bwl

(global) INTEGER. The number of sub-diagonals within the band of A

( 0 ≤ bwl ≤ n-1 ).

bwu

(global) INTEGER. The number of super-diagonals within the band of A

( 0 ≤ bwu ≤ n-1 ).

a

(local)

REAL for psgbtrf

DOUBLE PRECISION for pdgbtrf

COMPLEX for pcgbtrf

DOUBLE COMPLEX for pzgbtrf.

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

lld_a≥ 2*bwl + 2*bwu +1.

Contains the local pieces of the n-by-n distributed banded 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_a+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu).

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 (lwork≥ 1). If lwork is too small, the minimal acceptable size will be returned in work(1) and an error code is returned.

Output Parameters

a

On exit, this array contains details of the factorization. Note that additional permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.

ipiv

(local) INTEGER array.

The size of ipiv must be ≥nb_a.

Contains pivot indices for local factorizations. Note that you should not alter the contents of this array between factorization and solve.

af

(local)

REAL for psgbtrf

DOUBLE PRECISION for pdgbtrf

COMPLEX for pcgbtrf

DOUBLE COMPLEX for pzgbtrf.

Array of size laf.

Auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?gbtrf and is stored in af.

Note that if a linear system is to be solved using p?gbtrs after the factorization routine,af must not be altered after the factorization.

work(1)

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

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 nonsingular, 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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