p?porfs

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?porfs

Improves the computed solution to a system of linear equations with symmetric/Hermitian positive definite distributed matrix and provides error bounds and backward error estimates for the solution.

Syntax

call psporfs(uplo, n, nrhs, a, ia, ja, desca, af, iaf, jaf, descaf, b, ib, jb, descb, x, ix, jx, descx, ferr, berr, work, lwork, iwork, liwork, info)

call pdporfs(uplo, n, nrhs, a, ia, ja, desca, af, iaf, jaf, descaf, b, ib, jb, descb, x, ix, jx, descx, ferr, berr, work, lwork, iwork, liwork, info)

call pcporfs(uplo, n, nrhs, a, ia, ja, desca, af, iaf, jaf, descaf, b, ib, jb, descb, x, ix, jx, descx, ferr, berr, work, lwork, rwork, lrwork, info)

call pzporfs(uplo, n, nrhs, a, ia, ja, desca, af, iaf, jaf, descaf, b, ib, jb, descb, x, ix, jx, descx, ferr, berr, work, lwork, rwork, lrwork, info)

Include Files

Description

The p?porfsroutine improves the computed solution to the system of linear equations

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

where sub(A) = A(ia:ia+n-1, ja:ja+n-1) is a real symmetric or complex Hermitian positive definite distributed matrix and

sub(B) = B(ib:ib+n-1, jb:jb+nrhs-1),

sub(X) = X(ix:ix+n-1, jx:jx+nrhs-1)

are right-hand side and solution submatrices, respectively. This routine also provides error bounds and backward error estimates for the solution.

Input Parameters

uplo

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

Specifies whether the upper or lower triangular part of the symmetric/Hermitian matrix sub(A) is stored.

If uplo = 'U', sub(A) is upper triangular. If uplo = 'L', sub(A) is lower triangular.

n

(global) INTEGER. The order of the distributed matrix sub(A) (n≥0).

nrhs

(global) INTEGER. The number of right-hand sides, i.e., the number of columns of the matrices sub(B) and sub(X) (nrhs≥0).

a, af, b, x

(local)

REAL for psporfs

DOUBLE PRECISION for pdporfs

COMPLEX for pcporfs

DOUBLE COMPLEX for pzporfs.

Pointers into the local memory to arrays of local sizes

a(lld_a, LOCc(ja+n-1)), af(lld_af,LOCc(jaf+n-1)), b(lld_b,LOCc(jb+nrhs-1)), and x(lld_x,LOCc(jx+nrhs-1)), respectively.

The array a contains the local pieces of the n-by-n symmetric/Hermitian distributed matrix sub(A).

If uplo = 'U', the leading n-by-n upper triangular part of sub(A) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of sub(A) contains the lower triangular part of the distributed matrix, and its strictly upper triangular part is not referenced.

The array af 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 distributed matrix of right hand sides sub(B).

On entry, the array x contains the local pieces of the solution vectors sub(X).

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.

iaf, jaf

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

descaf

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

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

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

ix, jx

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

descx

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

work

(local)

REAL for psporfs

DOUBLE PRECISION for pdporfs

COMPLEX for pcporfs

DOUBLE COMPLEX for pzporfs.

The array work of size lwork is a workspace array.

lwork

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

For real flavors:

lwork must be at least

lwork≥ 3*LOCr(n+mod(ia-1,mb_a))

For complex flavors:

lwork must be at least

lwork≥ 2*LOCr(n+mod(ia-1,mb_a))

NOTE:

mod(x,y) is the integer remainder of x/y.

iwork

(local) INTEGER. Workspace array of size liwork. Used in real flavors only.

liwork

(local or global) INTEGER. The size of the array iwork; used in real flavors only. Must be at least

liwork≥LOCr(n+mod(ib-1,mb_b)).

rwork

(local) REAL for pcporfs

DOUBLE PRECISION for pzporfs

Workspace array of size lrwork. Used in complex flavors only.

lrwork

(local or global) INTEGER. The size of the array rwork; used in complex flavors only. Must be at least lrwork≥LOCr(n+mod(ib-1,mb_b))).

Output Parameters

x

On exit, contains the improved solution vectors.

ferr, berr

REAL for single precision flavors.

DOUBLE PRECISION for double precision flavors.

Arrays of size LOCc(jb+nrhs-1) each.

The array ferr contains the estimated forward error bound for each solution vector of sub(X).

If XTRUE is the true solution corresponding to sub(X), ferr is an estimated upper bound for the magnitude of the largest element in (sub(X) - XTRUE) divided by the magnitude of the largest element in sub(X). The estimate is as reliable as the estimate for rcond, and is almost always a slight overestimate of the true error.

This array is tied to the distributed matrix X.

The array berr contains the component-wise relative backward error of each solution vector (that is, the smallest relative change in any entry of sub(A) or sub(B) that makes sub(X) an exact solution). This array is tied to the distributed matrix X.

work(1)

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

iwork(1)

On exit, iwork(1) contains the minimum value of liwork required for optimum performance (for real flavors).

rwork(1)

On exit, rwork(1) contains the minimum value of lrwork required for optimum performance (for complex flavors).

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.

Parent topic: Refining the Solution and Estimating Its Error: ScaLAPACK Computational Routines

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