p?dbtrs

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?dbtrs

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

Syntax

call psdbtrs(trans, n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pddbtrs(trans, n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pcdbtrs(trans, n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

call pzdbtrs(trans, n, bwl, bwu, nrhs, a, ja, desca, b, ib, descb, af, laf, work, lwork, info)

Include Files

Description

The p?dbtrsroutine 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 banded 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?dbtrf.

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).

bwl

(global) INTEGER. The number of subdiagonals within the band of A

( 0 ≤ bwl ≤ n-1 ).

bwu

(global) INTEGER. The number of superdiagonals within the band of A

( 0 ≤ bwu ≤ n-1 ).

nrhs

(global) INTEGER. The number of right hand sides; the number of columns of the distributed matrix sub(B) (nrhs≥ 0).

a, b

(local)

REAL for psdbtrs

DOUBLE PRECISON for pddbtrs

COMPLEX for pcdbtrs

DOUBLE COMPLEX for pzdbtrs.

Pointers into the local memory to arrays of local sizes (lld_a,LOCc(ja+n-1)) and (lld_b,LOCc(nrhs)), respectively.

On entry, the array a contains details of the LU factorization of the band matrix A, as computed by p?dbtrf.

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

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, then dlen_≥ 7;

else if dtype_a = 1, then dlen_≥ 9.

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 psdbtrs

DOUBLE PRECISION for pddbtrs

COMPLEX for pcdbtrs

DOUBLE COMPLEX for pzdbtrs.

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?dbtrf and is stored in af.

The array work is a workspace array.

laf

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

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

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≥ (max(bwl,bwu))².

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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