p?dbsv

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?dbsv

Solves a general band system of linear equations.

Syntax

call psdbsv(n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, work, lwork, info)

call pddbsv(n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, work, lwork, info)

call pcdbsv(n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, work, lwork, info)

call pzdbsv(n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, work, lwork, info)

Include Files

Description

The p?dbsvroutine solves the following system of linear equations:

A(1:n, ja:ja+n-1)* X = B(ib:ib+n-1, 1:nrhs),

where A(1:n, ja:ja+n-1) is an n-by-n real/complex banded diagonally dominant-like distributed matrix with bandwidth bwl, bwu.

Gaussian elimination without pivoting is used to factor a reordering of the matrix into LU.

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 order of the distributed submatrix A, (n≥ 0).

bwl

(global) INTEGER. Number of subdiagonals. 0 ≤ bwl ≤ n-1.

bwu

(global) INTEGER. Number of subdiagonals. 0 ≤ bwu ≤ n-1.

nrhs

(global) INTEGER. The number of right-hand sides; the number of columns of the distributed submatrix B, (nrhs ≥ 0).

a

(local). REAL for psdbsv

DOUBLE PRECISION for pddbsv

COMPLEX for pcdbsv

DOUBLE COMPLEX for pzdbsv.

Pointer into the local memory to an array with leading size lld_a ≥ (bwl+bwu+1) (stored in desca). On entry, this array contains the local pieces of the distributed matrix.

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.

If 1d type (dtype_a=501 or 502), dlen ≥ 7;

If 2d type (dtype_a=1), dlen ≥ 9.

The array descriptor for the distributed matrix A.

Contains information of mapping of A to memory.

b

(local)

REAL for psdbsv

DOUBLE PRECISON for pddbsv

COMPLEX for pcdbsv

DOUBLE COMPLEX for pzdbsv.

Pointer into the local memory to an array of local lead size lld_b ≥ nb. On entry, this array contains the local pieces of the right hand sides B(ib:ib+n-1, 1:nrhs).

ib

(global) INTEGER. The row index in the global matrix B indicating the first row of the matrix to be operated on (which may be either all of b or a submatrix of B).

descb

(global and local) INTEGER array of size dlen.

If 1d type (dtype_b =502), dlen ≥ 7;

If 2d type (dtype_b =1), dlen ≥ 9.

The array descriptor for the distributed matrix B.

Contains information of mapping of B to memory.

work

(local).

REAL for psdbsv

DOUBLE PRECISON for pddbsv

COMPLEX for pcdbsv

DOUBLE COMPLEX for pzdbsv.

Temporary workspace. This space may be overwritten in between calls to routines. work must be the size given in lwork.

lwork

(local or global) INTEGER. Size of user-input workspace work. If lwork is too small, the minimal acceptable size will be returned in work(1) and an error code is returned.

lwork ≥ nb(bwl+bwu)+6max(bwl,bwu)*max(bwl,bwu)+max((max(bwl,bwu)nrhs), max(bwl,bwu)*max(bwl,bwu))

Output Parameters

a

On exit, this array contains information containing details of the factorization.

Note that permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.

b

On exit, this contains the local piece of the solutions distributed matrix X.

work

On exit, work(1) contains the minimal lwork.

info

(local) INTEGER. If info=0, the execution is successful.

< 0: If the i-th argument is an array and the j-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.

> 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 positive definite, and the factorization was not completed.

Parent topic: ScaLAPACK Driver Routines

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p?dbsv

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