Developer Reference for Intel® oneAPI Math Kernel Library for C
p?dbtrs
Solves a system of linear equations with a diagonally dominant-like banded distributed matrix using the factorization computed by p?dbtrf .
Syntax
voidpsdbtrs ( char*trans , MKL_INT*n , MKL_INT*bwl , MKL_INT*bwu , MKL_INT*nrhs , float*a , MKL_INT*ja , MKL_INT*desca , float*b , MKL_INT*ib , MKL_INT*descb , float*af , MKL_INT*laf , float*work , MKL_INT*lwork , MKL_INT*info );
voidpddbtrs ( char*trans , MKL_INT*n , MKL_INT*bwl , MKL_INT*bwu , MKL_INT*nrhs , double*a , MKL_INT*ja , MKL_INT*desca , double*b , MKL_INT*ib , MKL_INT*descb , double*af , MKL_INT*laf , double*work , MKL_INT*lwork , MKL_INT*info );
voidpcdbtrs ( char*trans , MKL_INT*n , MKL_INT*bwl , MKL_INT*bwu , MKL_INT*nrhs , MKL_Complex8*a , MKL_INT*ja , MKL_INT*desca , MKL_Complex8*b , MKL_INT*ib , MKL_INT*descb , MKL_Complex8*af , MKL_INT*laf , MKL_Complex8*work , MKL_INT*lwork , MKL_INT*info );
voidpzdbtrs ( char*trans , MKL_INT*n , MKL_INT*bwl , MKL_INT*bwu , MKL_INT*nrhs , MKL_Complex16*a , MKL_INT*ja , MKL_INT*desca , MKL_Complex16*b , MKL_INT*ib , MKL_INT*descb , MKL_Complex16*af , MKL_INT*laf , MKL_Complex16*work , MKL_INT*lwork , MKL_INT*info );
Include Files
mkl_scalapack.h
Description
psdbtrs pddbtrs pcdbtrs pzdbtrs The p?dbtrs routine function solves for X one of the systems of equations:
sub( A )* X = sub( B ),
(sub( A )) :code:`T` * X = sub( B ), or
(sub( A )) :code:`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 function uses the LU factorization computed by p?dbtrf (Computes the LU factorization of a n-by-n diagonally dominant-like banded distributed matrix.) .
Input Parameters
trans
(global) 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 )) :code:`T` * X = sub( B ) is solved for X . If trans = 'C' , then (sub( A )) :code:`H` * X = sub( B ) is solved for X .
n
(global) The order of the distributed matrix sub( A ) (n≥ 0) .
bwl
(global) The number of subdiagonals within the band of A
( 0 ≤ bwl ≤ n-1 ) .
bwu
(global) The number of superdiagonals within the band of A
( 0 ≤ bwu ≤ n-1 ) .
nrhs
(global) 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))lld_a * LOCc ( ja + n -1) and (lld_b,LOCc(nrhs))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) 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) 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) 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) 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 function p?dbtrf and is stored in af .
The array work is a workspace array.
laf
(local) 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 [0] .
lwork
(local or global) 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)[0]
On exit, work(1)[0] contains the minimum value of lwork required for optimum performance.
info
If info=0 , the execution is successful. info < 0 :
If the i -th argument is an array and the j- th entry , indexed j - 1, 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 .