oneMKL PARDISO Parameters in Tabular Form

void*

Solver internal data address pointer

Must be initialized with zeros and never be modified later

MKL_INT*

Maximal number of factors in memory

Generally used value is 1

MKL_INT*

The number of matrix (from 1 to maxfct) to solve

[1: maxfct]

Generally used value is 1

MKL_INT*

Matrix type

Real and structurally symmetric

MKL_INT*

Controls the execution of the solver

For iparm[35] > 0, phases 331, 332, and 333 perform a different decomposition. See the phase parameter of pardiso for details.

Analysis

MKL_INT*

Number of equations in the sparse linear system A*X = B

void*

Contains the non-zero elements of the coefficient matrix A

The size of a is the same as that of ja, and the coefficient matrix can be either real or complex. The matrix must be stored in the 3-array variation of compressed sparse row (CSR3) format with increasing values of ja for each row

MKL_INT*

rowIndex array in CSR3 format

ia[i] gives the index of the element in array a that contains the first non-zero element from row i of A. The last element ia(n) is taken to be equal to the number of non-zero elements in A.

Note: iparm[34] indicates whether row/column indexing starts from 1 or 0.

MKL_INT*

columns array in CSR3 format

The column indices for each row of A must be sorted in increasing order. For structurally symmetric matrices zero diagonal elements must be stored in a and ja. Zero diagonal elements should be stored for symmetric matrices, although they are not required. For symmetric matrices, the solver needs only the upper triangular part of the system.

Note: iparm[34] indicates whether row/column indexing starts from 1 or 0.

MKL_INT*

Holds the permutation vector of size n, specifies elements used for computing a partial solution, or specifies differing values of the input matrices for low rank update

You can apply your own fill-in reducing ordering (iparm[4]= 1) or return the permutation from the solver (iparm[4]= 2 ).

Let C = P*A*P^T be the permuted matrix. Row (column) i of C is the perm(i) row (column) of A. The numbering of the array must describe a permutation.

To specify elements for a partial solution, set iparm[4]= 0, iparm[30]> 0, and iparm[35]= 0.

To specify elements for a Schur complement, set iparm[4]= 0, iparm[30]= 0, and iparm[35]> 0.

To specify values that differ in A for low rank update (see Low Rank Update), set iparm[38] = 1. The size of the array must be at least 2*ndiff + 1, where ndiff is the number of values of A that are different. The values of perm should be:

where row_index_m and column_index_m are the row and column indices of the m-th differing non-zero value in matrix A. The row and column index pairs can be in any order, but must use zero-based indexing regardless of the value of iparm[34].

MKL_INT*

Number of right-hand sides that need to be solved for

Generally used value is 1

To obtain better Intel® oneAPI Math Kernel Library PARDISO performance, during the numerical factorization phase you can provide the maximum number of right-hand sides, which can be used further during the solving phase.

MKL_INT*

This array is used to pass various parameters to Intel® oneAPI Math Kernel Library PARDISO and to return some useful information after execution of the solver (see pardiso iparm Parameter for more details)

If iparm[0]=0, Intel® oneAPI Math Kernel Library PARDISO fillsiparm[1] through iparm[63] with default values and uses them.

MKL_INT*

Message level information

Intel® oneAPI Math Kernel Library PARDISO generates no output

void*

Right-hand side vectors

On entry, contains the right-hand side vector/matrix B, which is placed contiguously in memory. The b[i+k*n] element must hold the i-th component of k-th right-hand side vector. Note that b is only accessed in the solution phase.

On output, the array is replaced with the solution if iparm[5]=1.

void*

Solution vectors

On output, if iparm[5]=0, contains solution vector/matrix X which is placed contiguously in memory. The x[i+k*n] element must hold the i-th component of k-th solution vector. Note that x is only accessed in the solution phase.

MKL_INT*

Error indicator

No error