p?potrs

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?potrs

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

Syntax

call pspotrs(uplo, n, nrhs, a, ia, ja, desca, b, ib, jb, descb, info)

call pdpotrs(uplo, n, nrhs, a, ia, ja, desca, b, ib, jb, descb, info)

call pcpotrs(uplo, n, nrhs, a, ia, ja, desca, b, ib, jb, descb, info)

call pzpotrs(uplo, n, nrhs, a, ia, ja, desca, b, ib, jb, descb, info)

Include Files

Description

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

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

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

This routine uses Cholesky factorization

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

computed by p?potrf.

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).

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 pspotrs

DOUBLE PRECISION for pdpotrs

COMPLEX for pcpotrs

DOUBLE COMPLEX for pzpotrs.

Pointers into the local memory to arrays of local sizes

(lld_a,LOCc(ja+n-1)) and (lld_b,LOCc(jb+nrhs-1)), respectively.

The array a contains the factors L or U from the Cholesky factorization sub(A) = L*L^H or sub(A) = U^H*U, as computed by p?potrf.

On entry, the array b contains the local pieces of the right hand sides sub(B).

ia, ja

(global) INTEGER. The row and column indices in the global matrix A indicating the first row and the first column of the matrix sub(A), respectively.

desca

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

ib, jb

(global) INTEGER. The row and column indices in the global matrix B indicating the first row and the first column of the matrix sub(B), respectively.

descb

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

Output Parameters

b

Overwritten by the local pieces of the solution matrix X.

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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