p?gbsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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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?gbsvfunction computes the solution to a real or complex system of linear equations

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

where sub(A) = A(1:n, ja:ja+n-1) is an n-by-n real/complex general banded distributed matrix with bwl subdiagonals and bwu superdiagonals, and X and sub(B)= B(ib:ib+n-1, 1:rhs) are n-by-nrhs distributed matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor sub(A) as sub(A) = P*L*U*Q, where 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.

Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

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 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)

Pointers into the local memory to arrays of local size a: lld_a*LOCc(ja+n-1) and b: lld_b*LOCc(nrhs).

On entry, the array a contains the local pieces of the global array A.

On entry, the array b contains 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 desca[dtype_ - 1] = 501, then dlen_≥ 7;

else if desca[dtype_ - 1] = 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 descb[dtype_-1] = 502, then dlen_≥ 7;

else if descb[dtype_-1] = 1, then dlen_≥ 9.

work

(local)

Workspace array of size lwork.

lwork

(local or global) The size of the array work, must be at least lwork≥ (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 matrix X.

ipiv

(local) array.

The size of ipiv must be at least desca[NB - 1]. This array contains pivot indices for local factorizations. You should not alter the contents between factorization and solve.

work[0]

On exit, work[0] contains the minimum value of lwork required for optimum performance.

info

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 ith argument is a scalar and had an illegal value, then info = -i.

info> 0:

If info = k ≤ NPROCS, the submatrix stored on processor info and factored locally was not nonsingular, and the factorization was not completed. If info = k > NPROCS, the submatrix stored on processor info-NPROCS representing interactions with other processors was not nonsingular, and the factorization was not completed.

Parent topic: ScaLAPACK Driver Routines

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