# p?ptsv

Solves a symmetric or Hermitian positive definite tridiagonal system of linear equations.

## Syntax

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

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

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

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

## Description

This routine solves a system of linear equations

`A(1:n, ja:ja+n-1)*X = B(ib:ib+n-1, 1:nrhs)`,

where `A(1:n, ja:ja+n-1)` is an n-by-n real tridiagonal symmetric positive definite distributed matrix.

Cholesky factorization is used to factor a reordering of the matrix into L*L'.

## Input Parameters

n

  (global) INTEGER. The order of matrix A `(n ≥ 0)`.

nrhs

  (global) INTEGER. The number of right-hand sides; the number of columns of the distributed submatrix B `(nrhs ≥ 0)`.

d

  (local)

  REAL for psptsv

  DOUBLE PRECISON for pdptsv

  COMPLEX for pcptsv

  DOUBLE COMPLEX for pzptsv.

  Pointer to local part of global vector storing the main diagonal of the matrix.

e

  (local)

  REAL for psptsv

  DOUBLE PRECISON for pdptsv

  COMPLEX for pcptsv

  DOUBLE COMPLEX for pzptsv.

  Pointer to local part of global vector storing the upper diagonal of the matrix. Globally, `du(n)` is not referenced, and du must be aligned with d.

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 of dimension dlen.

  If `1d type (dtype_a=501 or 502)`, `dlen ≥ 7`;

  If `2d type (dtype_a=1)`, `dlen ≥ 9`.

  The array descriptor for the distributed matrix A.

  Contains information of mapping of A to memory.

b

  (local)

  REAL for psptsv

  DOUBLE PRECISON for pdptsv

  COMPLEX for pcptsv

  DOUBLE COMPLEX for pzptsv.

  Pointer into the local memory to an array of local lead dimension `lld_b ≥ nb`.

  On entry, this array contains the local pieces of the right hand sides `B(ib:ib+n-1, 1:nrhs)`.

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 of dimension dlen.

  If `1d type (dtype_b = 502)`, `dlen ≥ 7`;

  If `2d type (dtype_b = 1)`, `dlen ≥ 9`.

  The array descriptor for the distributed matrix B.

  Contains information of mapping of B to memory.

work

  (local).

  REAL for psptsv

  DOUBLE PRECISON for pdptsv

  COMPLEX for pcptsv

  DOUBLE COMPLEX for pzptsv.

  Temporary workspace. This space may be overwritten in between calls to routines. work must be the size given in lwork.

lwork

  (local or global) INTEGER. Size of user-input workspace work. If lwork is too small, the minimal acceptable size will be returned in `work(1)` and an error code is returned. `lwork > (12*NPCOL+3*nb)+max((10+2*min(100, nrhs))*NPCOL+4*nrhs, 8*NPCOL)`.

## Output Parameters

d

  On exit, this array contains information containing the factors of the matrix. Must be of size greater than or equal to `desca(nb_)`.

e

  On exit, this array contains information containing the factors of the matrix. Must be of size greater than or equal to `desca(nb_)`.

b

  On exit, this contains the local piece of the solutions distributed matrix X.

work

  On exit, `work(1)` contains the minimal lwork.

info

  (local) INTEGER. If `info=0`, the execution is successful.

  `< 0`: If the i-th argument is an array and the j-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`.

  `> 0`: If `info = k ≤ NPROCS`, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.

  If `info = k > NPROCS`, the submatrix stored on processor `info-NPROCS` representing interactions with other processors was not positive definite, and the factorization was not completed.

Parent topic: Driver Routines