# 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)

## Description

The routine p?pttrs 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*LH*PT`, or `sub(A) = P*UH*D*U*PT`

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 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)`.

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 dimension `(desca(nb_))` each.

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

ja

  (global) INTEGER. The index in the global array A that points to 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, dimension (dlen_). The array descriptor for the distributed matrix A.

  If `desca(dtype_) = 501` or `502`, then `dlen_ ≥ 7`;

  else if `desca(dtype_) = 1`, then `dlen_ ≥ 9`.

b

  (local) Same type as d, e.

  Pointer into the local memory to an array of local dimension

  `b(lld_b`, `LOCc(nrhs))`.

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

ib

  (global) INTEGER. The row index in the global array B that points to 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, dimension (dlen_). The array descriptor for the distributed matrix B.

  If `descb(dtype_) = 502`, then `dlen_ ≥ 7`;

  else if `descb(dtype_) = 1`, then `dlen_ ≥ 9`.

af, work

  (local) REAL for pspttrs

  DOUBLE PRECISION for pdpttrs

  COMPLEX for pcpttrs

  DOUBLE COMPLEX for pzpttrs.

  Arrays of dimension (laf) and (lwork), respectively The array af contains auxiliary Fillin space. Fillin is created during the factorization routine p?pttrf and this is stored in af.

  The array work is a workspace array.

laf

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

  Must be `laf ≥ NB+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: Routines for Solving Systems of Linear Equations