# p?dttrs

Solves a system of linear equations with a diagonally dominant-like tridiagonal distributed matrix using the factorization computed by p?dttrf.

## Syntax

call psdttrs(trans, n, nrhs, dl, d, du, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pddttrs(trans, n, nrhs, dl, d, du, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pcdttrs(trans, n, nrhs, dl, d, du, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pzdttrs(trans, n, nrhs, dl, d, du, ja, desca, b, ib, descb, af, laf, work, lwork, info)

## Description

The routine p?dttrs solves for X one of the systems of equations:

`sub(A)*X = sub(B)`,

`(sub(A))T*X = sub(B)`, or

`(sub(A))H*X = sub(B)`,

where `sub(A) = `(1:n, ja:ja+n-1)`;` is a diagonally dominant-like tridiagonal distributed matrix, and `sub(B)` denotes the distributed matrix `B(ib:ib+n-1, 1:nrhs`).

This routine uses the LU factorization computed by p?dttrf.

## 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 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)`.

dl, d, du

  (local)

  REAL for psdttrs

  DOUBLE PRECISON for pddttrs

  COMPLEX for pcdttrs

  DOUBLE COMPLEX for pzdttrs.

  Pointers to the local arrays of dimension `(desca(nb_))` each.

  On entry, these arrays contain details of the factorization. Globally, dl(1) and du(n) are not referenced; dl 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, 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.

  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 psdttrs

  DOUBLE PRECISION for pddttrs

  COMPLEX for pcdttrs

  DOUBLE COMPLEX for pzdttrs.

  Arrays of dimension (laf) and (lwork), respectively.

  The array af contains auxiliary Fillin space. Fillin is created during the factorization routine p?dttrf and this is stored in af. If a linear system is to be solved using p?dttrsafter the factorization routine, af must not be altered.

  The array work is a workspace array.

laf

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

  Must be `laf ≥ NB*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu)`.

  If laf is not large enough, an error code will be 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*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 ith 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