p?pbtrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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p?pbtrs

Solves a system of linear equations with a Cholesky-factored symmetric/Hermitian positive-definite band matrix.

Syntax

call pspbtrs(uplo, n, bw, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pdpbtrs(uplo, n, bw, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pcpbtrs(uplo, n, bw, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pzpbtrs(uplo, n, bw, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

Include Files

Description

The p?pbtrsroutine solves for X a system of distributed linear equations in the form:

sub(A)*X = sub(B) ,

where sub(A) = A(1:n, ja:ja+n-1) is an n-by-n real symmetric or complex Hermitian positive definite distributed band matrix, and sub(B) denotes the distributed matrix B(ib:ib+n-1, 1:nrhs).

This routine uses Cholesky factorization

sub(A) = P*U^H*U*P^T, or sub(A) = P*L*L^H*P^T

computed by p?pbtrf.

Input Parameters

uplo

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

If uplo = 'U', upper triangle of sub(A) is stored;

If uplo = 'L', lower triangle of sub(A) is stored.

n

(global) INTEGER. The order of the distributed matrix sub(A) (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).

nrhs

(global) INTEGER. The number of right hand sides; the number of columns of the distributed matrix sub(B) (nrhs≥0).

a, b

(local)

REAL for pspbtrs

DOUBLE PRECISION for pdpbtrs

COMPLEX for pcpbtrs

DOUBLE COMPLEX for pzpbtrs.

Pointers into the local memory to arrays of local sizes (lld_a,LOCc(ja+n-1)) and (lld_b,LOCc(nrhs-1)), respectively.

The array a contains the permuted triangular factor U or L from the Cholesky factorization sub(A) = P*U^H*U*P^T, or sub(A) = P*L*L^H*P^T of the band matrix A, as returned by p?pbtrf.

On entry, the array b contains the local pieces of the n-by-nrhs right hand side distributed matrix sub(B).

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.

ib

(global) INTEGER. The row index in the global matrix B indicating the first row of the matrix sub(B).

descb

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

If dtype_b = 502, then dlen_≥ 7;

else if dtype_b = 1, then dlen_≥ 9.

af, work

(local) Arrays, same type as a.

The array af is of size laf. It contains auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?dbtrf and is stored in af.

The array work is a workspace array of size lwork.

laf

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

Must be laf≥nrhs*bw.

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

lwork

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

Output Parameters

b

On exit, if info=0, this array contains the local pieces of the n-by-nrhs solution distributed matrix X.

work(1)

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

info

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.

Parent topic: Solving Systems of Linear Equations: ScaLAPACK Computational Routines

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