p?gesv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

p?gesv

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

Syntax

call psgesv ( n , nrhs , a , ia , ja , desca , ipiv , b , ib , jb , descb , info )

call pdgesv ( n , nrhs , a , ia , ja , desca , ipiv , b , ib , jb , descb , info )

call pcgesv ( n , nrhs , a , ia , ja , desca , ipiv , b , ib , jb , descb , info )

call pzgesv ( n , nrhs , a , ia , ja , desca , ipiv , b , ib , jb , descb , info )

Include Files

mkl_scalapack.h

Description

psgesv pdgesv pcgesv pzgesv The p?gesv routine function 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) INTEGER . The number of rows and columns to be operated on, that is, the order of the distributed submatrix sub(A) (n≥ 0) .

nrhs

(global) INTEGER . The number of right hand sides, that is, the number of columns of the distributed submatrices B and X(nrhs≥ 0) .

a , b

(local) REAL for psgesv DOUBLE PRECISION for pdgesv COMPLEX for pcgesv DOUBLE COMPLEX for pzgesv .

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) INTEGER . 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) INTEGER array of size dlen_ . The array descriptor for the distributed matrix A .

ib , jb

(global) INTEGER . 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) INTEGER 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) INTEGER 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 ) [i - 1] .

This array is tied to the distributed matrix A .

info

(global) INTEGER . 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.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?gesv

Syntax

Include Files

Description

Input Parameters

Output Parameters