p?dttrs

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?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)

Include Files

Description

The p?dttrsroutine 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) =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 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).

dl, d, du

(local)

REAL for psdttrs

DOUBLE PRECISON for pddttrs

COMPLEX for pcdttrs

DOUBLE COMPLEX for pzdttrs.

Pointers to the local arrays of size nb_a 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 matrix A indicating 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 size dlen_. The array descriptor for the distributed matrix A.

If dtype_a = 501 or dtype_a = 502, then dlen_≥ 7;

else if dtype_a = 1, then dlen_≥ 9.

b

(local) Same type as d.

Pointer into the local memory to an array of local size (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 matrix B indicating 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 size dlen_. The array descriptor for the distributed matrix B.

If dtype_b = 502, then dlen_≥ 7;

else if dtype_b = 1, then dlen_≥ 9.

af, work

(local) REAL for psdttrs

DOUBLE PRECISION for pddttrs

COMPLEX for pcdttrs

DOUBLE COMPLEX for pzdttrs.

Arrays of size laf and (lwork), respectively.

The array af contains auxiliary fill-in space. The fill-in space is created in a call to the factorization routine p?dttrf and is stored in af. If a linear system is to be solved using p?dttrs after the factorization routine,af must not be altered.

The array work is a workspace array.

laf

(local) INTEGER. The size 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 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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