p?getrs

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?getrs

Solves a system of distributed linear equations with a general square matrix, using the LU factorization computed by p?getrf.

Syntax

call psgetrs(trans, n, nrhs, a, ia, ja, desca, ipiv, b, ib, jb, descb, info)

call pdgetrs(trans, n, nrhs, a, ia, ja, desca, ipiv, b, ib, jb, descb, info)

call pcgetrs(trans, n, nrhs, a, ia, ja, desca, ipiv, b, ib, jb, descb, info)

call pzgetrs(trans, n, nrhs, a, ia, ja, desca, ipiv, b, ib, jb, descb, info)

Include Files

Description

The p?getrsroutine solves a system of distributed linear equations with a general n-by-n distributed matrix sub(A) = A(ia:ia+n-1, ja:ja+n-1) using the LU factorization computed by p?getrf.

The system has one of the following forms specified by trans:

sub(A)*X = sub(B) (no transpose),

sub(A)^T*X = sub(B) (transpose),

sub(A)^H*X = sub(B) (conjugate transpose),

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

Before calling this routine,you must call p?getrf to compute the LU factorization of sub(A).

Input Parameters

trans

(global) CHARACTER*1. Must be 'N' or 'T' or 'C'.

Indicates the form of the equations:

If trans = 'N', then sub(A)*X = sub(B) is solved for X.

If trans = 'T', then sub(A)^T*X = sub(B) is solved for X.

If trans = 'C', then sub(A)^H *X = sub(B) is solved for X.

n

(global) INTEGER. The number of linear equations; the order of the 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 psgetrs

DOUBLE PRECISION for pdgetrs

COMPLEX for pcgetrs

DOUBLE COMPLEX for pzgetrs.

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

On entry, the array a contains the local pieces of the factors L and U from the factorization sub(A) = P*L*U; the unit diagonal elements of L are not stored. On entry, the array b contains 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.

ipiv

(local) INTEGER Array of size of LOCr(m_a) + mb_a. Contains the pivoting information: local row i of the matrix was interchanged with the global row ipiv(i).

This array is tied to 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

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

Output Parameters

b

On exit, overwritten by the solution distributed 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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