p?pbsv

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?pbsv

Solves a symmetric/Hermitian positive definite banded system of linear equations.

Syntax

void pspbsv (char *uplo , MKL_INT *n , MKL_INT *bw , MKL_INT *nrhs , float *a , MKL_INT *ja , MKL_INT *desca , float *b , MKL_INT *ib , MKL_INT *descb , float *work , MKL_INT *lwork , MKL_INT *info );

void pdpbsv (char *uplo , MKL_INT *n , MKL_INT *bw , MKL_INT *nrhs , double *a , MKL_INT *ja , MKL_INT *desca , double *b , MKL_INT *ib , MKL_INT *descb , double *work , MKL_INT *lwork , MKL_INT *info );

void pcpbsv (char *uplo , MKL_INT *n , MKL_INT *bw , MKL_INT *nrhs , MKL_Complex8 *a , MKL_INT *ja , MKL_INT *desca , MKL_Complex8 *b , MKL_INT *ib , MKL_INT *descb , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *info );

void pzpbsv (char *uplo , MKL_INT *n , MKL_INT *bw , MKL_INT *nrhs , MKL_Complex16 *a , MKL_INT *ja , MKL_INT *desca , 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?pbsvfunction solves a system of linear equations

A(1:n, ja:ja+n-1)*X = B(ib:ib+n-1, 1:nrhs),

where A(1:n, ja:ja+n-1) is an n-by-n real/complex banded symmetric positive definite distributed matrix with bandwidth bw.

Cholesky factorization is used to factor a reordering of the matrix into L*L'.

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

uplo

(global) Must be 'U' or 'L'.

Indicates whether the upper or lower triangular of A is stored.

If uplo = 'U', the upper triangular A is stored

If uplo = 'L', the lower triangular of A is stored.

n

(global) The order of the distributed matrix A(n≥ 0).

bw

(global) The number of subdiagonals in L or U. 0 ≤ bw ≤ n-1.

nrhs

(global) The number of right-hand sides; the number of columns in B(nrhs≥ 0).

a

(local).

Pointer into the local memory to an array with leading size lld_a ≥ (bw+1) (stored in desca). On entry, this array contains the local pieces of the distributed matrix sub(A) to be factored.

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.

b

(local)

Pointer into the local memory to an array of local lead size lld_b ≥ nb. On entry, this array contains the local pieces of the right hand sides B(ib:ib+n-1, 1:nrhs).

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.

If 1D type (dtype_b =502), dlen ≥ 7;

If 2D type (dtype_b =1), dlen ≥ 9.

The array descriptor for the distributed matrix B.

Contains information of mapping of B to memory.

work

(local).

Temporary workspace. This space may be overwritten in between calls to functions. work must be the size given in lwork.

lwork

(local or global) Size of user-input workspace work. If lwork is too small, the minimal acceptable size will be returned in work[0] and an error code is returned. lwork ≥ (nb+2*bw)*bw +max((bw*nrhs), bw*bw)

Output Parameters

a

On exit, this array contains information containing details of the factorization. Note that permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.

b

On exit, contains the local piece of the solutions distributed matrix X.

work

On exit, work[0] contains the minimal lwork.

info

(global) If info=0, the execution is successful.

< 0: If the i-th argument is an array and the j-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.

> 0: If info = k ≤ NPROCS, the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed.

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

Parent topic: ScaLAPACK Driver Routines

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