p?gesv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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p?gesv

Computes the solution to the system of linear equations with a square distributed matrix and multiple right-hand sides.

Syntax

void psgesv (MKL_INT *n , MKL_INT *nrhs , float *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , float *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pdgesv (MKL_INT *n , MKL_INT *nrhs , double *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , double *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pcgesv (MKL_INT *n , MKL_INT *nrhs , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex8 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

void pzgesv (MKL_INT *n , MKL_INT *nrhs , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex16 *b , MKL_INT *ib , MKL_INT *jb , MKL_INT *descb , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

The p?gesvfunction computes the solution to a real or complex system of linear equations sub(A)*X = sub(B), where sub(A) = A(ia:ia+n-1, ja:ja+n-1) is an n-by-n distributed matrix and X and sub(B) = B(ib:ib+n-1, jb:jb+nrhs-1) 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, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. L and U are stored in sub(A). The factored form of sub(A) is then used to solve the system of equations sub(A)*X = sub(B).

Input Parameters

n

(global) The number of rows and columns to be operated on, that is, the order of the distributed submatrix sub(A) (n≥ 0).

nrhs

(global) The number of right hand sides, that is, the number of columns of the distributed submatrices B and X(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(jb+nrhs-1), respectively.

On entry, the array a contains the local pieces of the n-by-n distributed matrix sub(A) to be factored.

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

ia, ja

(global) The row and column indices in the global matrix A indicating the first row and the first column of sub(A), respectively.

desca

(global and local) array of size dlen_. The array descriptor for the distributed matrix A.

ib, jb

(global) The row and column indices in the global matrix B indicating the first row and the first column of sub(B), respectively.

descb

(global and local) array of size dlen_. The array descriptor for the distributed matrix B.

Output Parameters

a

Overwritten by the factors L and U from the factorization sub(A) = P*L*U; the unit diagonal elements of L are not stored .

b

Overwritten by the solution distributed matrix X.

ipiv

(local) Array of size LOCr(m_a)+mb_a. This array contains the pivoting information. The (local) row i of the matrix was interchanged with the (global) row ipiv[i - 1].

This array is tied to the distributed matrix A.

info

(global) 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.

info> 0:

If info = k, U(ia+k-1,ja+k-1) is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.

Parent topic: ScaLAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?gesv

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also