# 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)

## Description

The routine p?potrs 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) = UH*U`, or `sub(A) = L*LH`

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 submatrix sub(A) `(n≥0)`.

nrhs

  (global) INTEGER. The number of right hand sides; the number of columns of the distributed submatrix 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 dimension

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

  The array a contains the factors L or U from the Cholesky factorization sub(A) = L*LH or sub(A) = UH*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 array A indicating the first row and the first column of the submatrix sub(A), respectively.

desca

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

ib, jb

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

descb

  (global and local) INTEGER array, dimension (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: Routines for Solving Systems of Linear Equations