p?gbsv
p?gbsv
Computes the solution to the system of linear equations with a general banded distributed matrix and multiple right-hand sides.
Syntax
void
psgbsv
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
float
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
float
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgbsv
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
double
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
double
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgbsv
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
MKL_Complex8
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex8
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzgbsv
(
MKL_INT
*n
,
MKL_INT
*bwl
,
MKL_INT
*bwu
,
MKL_INT
*nrhs
,
MKL_Complex16
*a
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex16
*b
,
MKL_INT
*ib
,
MKL_INT
*descb
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
- mkl_scalapack.h
Description
The
p?gbsv
function
computes the solution to a real or complex system of linear equations sub(
, A
)*X
= sub(B
)where
sub(
is an A
) = A
(1:n
, ja:ja+n-1
)n
-by-n
real/complex general banded distributed matrix with bwl
subdiagonals and bwu
superdiagonals, and X
and sub(
are B
)= B
(ib:ib+n-1
, 1:rhs
)n
-by-nrhs
distributed matrices.The
LU
decomposition with partial pivoting and row interchanges is used to factor sub(A
) as sub(
, where A
) = P
*L
*U
*Q
P
and Q
are permutation matrices, and L
and U
are banded lower and upper triangular matrices, respectively. The matrix Q
represents reordering of columns for the sake of parallelism, while P
represents reordering of rows for numerical stability using classic partial pivoting.Optimization Notice
|
|---|
Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.
Notice revision #20110804
|
This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.
Input Parameters
- n
- (global) The number of rows and columns to be operated on, that is, the order of the distributed matrix sub(A)(.n≥0)
- bwl
- (global) The number of subdiagonals within the band ofA(0≤bwl≤n-1).
- bwu
- (global) The number of superdiagonals within the band ofA(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)Pointers into the local memory to arrays of local sizeanda:lld_a*LOCc(ja+n-1).b:lld_b*LOCc(nrhs)On entry, the arrayacontains the local pieces of the global arrayA.On entry, the arraybcontains the right hand side distributed matrix sub(B).
- ja
- (global) The index in the global matrixAindicating the start of the matrix to be operated on (which may be either all ofAor a submatrix ofA).
- desca
- (global and local) array of sizedlen_. The array descriptor for the distributed matrixA.Ifdesca[dtype_- 1]= 501, then;dlen_≥7else ifdesca[dtype_- 1]= 1, then.dlen_≥9
- ib
- (global) The row index in the global matrixBindicating the first row of the matrix to be operated on (which may be either all ofBor a submatrix ofB).
- descb
- (global and local) array of sizedlen_. The array descriptor for the distributed matrixB.Ifdescb[dtype_-1]= 502, then;dlen_≥7else ifdescb[dtype_-1]= 1, then.dlen_≥9
- work
- (local)Workspace array of sizelwork.
- lwork
- (local or global) The size of the arraywork, must be at leastlwork≥(NB+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) ++ max(.nrhs*(NB+2*bwl+4*bwu), 1)
Output Parameters
- a
- On exit, contains details of the factorization. Note that the resulting factorization is not the same factorization as returned from LAPACK. Additional permutations are performed on the matrix for the sake of parallelism.
- b
- On exit, this array contains the local pieces of the solution distributed matrixX.
- ipiv
- (local) array.The size ofipivmust be at leastdesca[. This array contains pivot indices for local factorizations. You should not alter the contents between factorization and solve.NB- 1]
- work[0]
- On exit,work[0]contains the minimum value oflworkrequired for optimum performance.
- info
- If, the execution is successful.info=0:info< 0If theith argument is an array and thej-th entry had an illegal value, then; if theinfo= -(i*100+j)ith argument is a scalar and had an illegal value, then.info=-i:info>0If, the submatrix stored on processorinfo=k≤NPROCSinfoand factored locally was not nonsingular, and the factorization was not completed. If, the submatrix stored on processorinfo=k>NPROCSrepresenting interactions with other processors was not nonsingular, and the factorization was not completed.info-NPROCS