p?pttrs

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?pttrs

Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal distributed matrix using the factorization computed by p?pttrf.

Syntax

call pspttrs(n, nrhs, d, e, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pdpttrs(n, nrhs, d, e, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pcpttrs(uplo, n, nrhs, d, e, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pzpttrs(uplo, n, nrhs, d, e, ja, desca, b, ib, descb, af, laf, work, lwork, info)

Include Files

Description

The p?pttrsroutine 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 tridiagonal distributed matrix, and sub(B) denotes the distributed matrix B(ib:ib+n-1, 1:nrhs).

This routine uses the factorization

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

computed by p?pttrf.

Input Parameters

uplo

(global, used in complex flavors only)

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).

d, e

(local)

REAL for pspttrs

DOUBLE PRECISON for pdpttrs

COMPLEX for pcpttrs

DOUBLE COMPLEX for pzpttrs.

Pointers into the local memory to arrays of size nb_a each.

These arrays contain details of the factorization as returned by p?pttrf

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 or dtype_a = 502, then dlen_≥ 7;

else if dtype_a = 1, then dlen_≥ 9.

b

(local) Same type as d, e.

Pointer into the local memory to an array of local size

(lld_b,LOCc(nrhs)).

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

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_. 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) REAL for pspttrs

DOUBLE PRECISION for pdpttrs

COMPLEX for pcpttrs

DOUBLE COMPLEX for pzpttrs.

Arrays of size laf and (lwork), respectively. The array af contains auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?pttrf and is stored in af.

The array work is a workspace array.

laf

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

Must be laf≥nb_a+2.

If laf is not large enough, an error code is 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≥ (10+2*min(100,nrhs))*NPCOL+4*nrhs.

Output Parameters

b

On exit, this array contains the local pieces of the 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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