Intel® oneMKL PARDISO Parameters in Tabular Form

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 4/28/2026

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Intel® oneMKL PARDISO Parameters in Tabular Form

The following table lists all parameters of Intel® oneAPI Math Kernel Library (oneMKL) PARDISO and gives their brief descriptions.

Parameter	Type	Description	Values
`pt(64)` in/out	`INTEGER` on 32-bit architectures, `INTEGER*8` on 64-bit architectures `TYPE(MKL_PARDISO_HANDLE) , INTENT(INOUT)`	Solver internal data address pointer	0 Must be initialized with zeros and never be modified later
`maxfct` in	`INTEGER` `INTEGER , INTENT(IN)`	Maximal number of factors in memory	`\(>0\)` Generally used value is 1
`mnum` in	`INTEGER` `INTEGER , INTENT(IN)`	The number of matrix (from 1 to `maxfct` ) to solve	[1: `maxfct` ] Generally used value is 1
`mtype` in	`INTEGER` `INTEGER , INTENT(IN)`	Matrix type	1 - Real and structurally symmetric 2 - Real and symmetric positive definite -2 - Real and symmetric indefinite 3 - Complex and structurally symmetric 4 - Complex and Hermitian positive definite -4 - Complex and Hermitian indefinite 6 - Complex and symmetric matrix 11 - Real and nonsymmetric matrix 13 - Complex and nonsymmetric matrix
`phase` in	`INTEGER` `INTEGER , INTENT(IN)`	Controls the execution of the solver For iparm(36) > 0, phases 331, 332, and 333 perform a different decomposition. See the `phase` parameter of pardiso for details.	11 - Analysis 12 - Analysis, numerical factorization 13 - Analysis, numerical factorization, solve 22 - Numerical factorization 23 - Numerical factorization, solve 33 - Solve, iterative refinement 331 - `phase` =33, but only forward substitution 332 - `phase` =33, but only diagonal substitution 333 - `phase` =33, but only backward substitution 0 - Release internal memory for L and U of the matrix number `mnum` -1 - Release all internal memory for all matrices
`n` in	`INTEGER` `INTEGER , INTENT(IN)`	Number of equations in the sparse linear system `A` * `X` = `B`	`\(>0\)`
`a(*)` in	`PARDISO_DATA_TYPE`¹ `PARDISO_DATA_TYPE, INTENT(IN)`¹	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
`ia(n + 1)` in	`INTEGER` `INTEGER , INTENT(IN)`	`rowIndex` array in CSR3 format	`\(\ge 0\)` `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+1)` (for one-based indexing) or `ia(n)` (for zero-based indexing) is taken to be equal to the number of non-zero elements in `A` , plus one . Note: iparm(35) indicates whether row/column indexing starts from 1 or 0.
`ja(*)` in	`INTEGER` `INTEGER , INTENT(IN)`	`columns` array in CSR3 format	`\(\ge 0\)` 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(35) indicates whether row/column indexing starts from 1 or 0.
`perm(n)` in/out	`INTEGER` `INTEGER , INTENT(INOUT)`	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	`\(\ge 0\)` You can apply your own fill-in reducing ordering ( iparm(5) = 1) or return the permutation from the solver ( iparm(5) = 2 ). Let `C = PAP^{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(5) = 0, iparm(31) > 0, and iparm(36) = 0. To specify elements for a Schur complement, set iparm(5) = 0, iparm(31) = 0, and iparm(36) > 0. To specify values that differ in `A` for low rank update (see Low Rank Update ), set iparm(39) = 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: `perm = {ndiff, row_index1, column_index1, row_index2, column_index2, ...., row_index_ndiff,column_index_ndiff}` 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(35) . NOTE: Unless you have specified low rank update, iparm(35) indicates whether row/column indexing starts from 1 or 0.
`nrhs` in	`INTEGER` `INTEGER , INTENT(IN)`	Number of right-hand sides that need to be solved for	`\(\ge 0\)` Generally used value is 1 To obtain better Intel® oneMKL 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.
`iparm(64)` in/out	`INTEGER` `INTEGER , INTENT(INOUT)`	This array is used to pass various parameters to Intel® oneMKL PARDISO and to return some useful information after execution of the solver (see pardiso iparm Parameter for more details)	* If iparm(1) `=0` , PARDISO fills iparm(2) through iparm(64) with default values and uses them.
`msglvl` in	`INTEGER` `INTEGER , INTENT(IN)`	Message level information	0 - Intel® oneMKL PARDISO generates no output 1 - Intel® oneMKL PARDISO prints statistical information
`b(nnrhs)` in/out*	`PARDISO_DATA_TYPE`¹ `PARDISO_DATA_TYPE, INTENT(INOUT)`¹	Right-hand side vectors	* On entry, contains the right-hand side vector/matrix `B` , which is placed contiguously in memory. The `b(i+(k-1)×nrhs)` 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(6) =1.
`x(nnrhs)` out*	`PARDISO_DATA_TYPE`¹ `PARDISO_DATA_TYPE, INTENT(OUT)`¹	Solution vectors	* On output, if iparm(6) =0, contains solution vector/matrix `X` which is placed contiguously in memory. The `x(i+(k-1)×nrhs)` element must hold the `i` -th component of `k` -th solution vector. Note that `x` is only accessed in the solution phase.
`error` out	`INTEGER` `INTEGER , INTENT(OUT)`	Error indicator	0 - No error -1 - Input inconsistent -2 - Not enough memory -3 - Reordering problem -4 - Zero pivot, numerical factorization or iterative refinement problem -5 - Unclassified (internal) error -6 - Reordering failed (matrix types 11 and 13 only) -7 - Diagonal matrix is singular -8 - 32-bit integer overflow problem -9 - Not enough memory for OOC -10 - Problems with opening OOC temporary files -11 - Read/write problems with the OOC data file

Parameter

Type

Description

Values

pt(64)

in/out

INTEGER on 32-bit architectures, INTEGER*8 on 64-bit architectures

TYPE(MKL_PARDISO_HANDLE) , INTENT(INOUT)

Solver internal data address pointer

Must be initialized with zeros and never be modified later

maxfct

INTEGER

INTEGER , INTENT(IN)

Maximal number of factors in memory

\(>0\)

Generally used value is 1

mnum

INTEGER

INTEGER , INTENT(IN)

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

[1: maxfct ]

Generally used value is 1

mtype

INTEGER

INTEGER , INTENT(IN)

Matrix type

1 - Real and structurally symmetric
2 - Real and symmetric positive definite
-2 - Real and symmetric indefinite
3 - Complex and structurally symmetric
4 - Complex and Hermitian positive definite
-4 - Complex and Hermitian indefinite
6 - Complex and symmetric matrix
11 - Real and nonsymmetric matrix
13 - Complex and nonsymmetric matrix

phase

INTEGER

INTEGER , INTENT(IN)

Controls the execution of the solver

For iparm(36) > 0, phases 331, 332, and 333 perform a different decomposition. See the phase parameter of pardiso for details.

11 - Analysis
12 - Analysis, numerical factorization
13 - Analysis, numerical factorization, solve
22 - Numerical factorization
23 - Numerical factorization, solve
33 - Solve, iterative refinement
331 - phase =33, but only forward substitution
332 - phase =33, but only diagonal substitution
333 - phase =33, but only backward substitution
0 - Release internal memory for L and U of the matrix number mnum
-1 - Release all internal memory for all matrices

n

INTEGER

INTEGER , INTENT(IN)

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

\(>0\)

a(*)

PARDISO_DATA_TYPE¹

PARDISO_DATA_TYPE, INTENT(IN)¹

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

ia(n + 1)

INTEGER

INTEGER , INTENT(IN)

rowIndex array in CSR3 format

\(\ge 0\)

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+1) (for one-based indexing) or ia(n) (for zero-based indexing) is taken to be equal to the number of non-zero elements in A , plus one .

Note: iparm(35) indicates whether row/column indexing starts from 1 or 0.

ja(*)

INTEGER

INTEGER , INTENT(IN)

columns array in CSR3 format

\(\ge 0\)

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(35) indicates whether row/column indexing starts from 1 or 0.

perm(n)

in/out

INTEGER

INTEGER , INTENT(INOUT)

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

\(\ge 0\)

You can apply your own fill-in reducing ordering ( iparm(5) = 1) or return the permutation from the solver ( iparm(5) = 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(5) = 0, iparm(31) > 0, and iparm(36) = 0.

To specify elements for a Schur complement, set iparm(5) = 0, iparm(31) = 0, and iparm(36) > 0.

To specify values that differ in A for low rank update (see Low Rank Update ), set iparm(39) = 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:

perm = {ndiff, row_index1, column_index1, row_index2, column_index2, ...., row_index_ndiff,column_index_ndiff}

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(35) .

NOTE:

Unless you have specified low rank update, iparm(35) indicates whether row/column indexing starts from 1 or 0.

nrhs

INTEGER

INTEGER , INTENT(IN)

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

\(\ge 0\)

Generally used value is 1

To obtain better Intel® oneMKL 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.

iparm(64)

in/out

INTEGER

INTEGER , INTENT(INOUT)

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

If iparm(1) =0 , PARDISO fills iparm(2) through iparm(64) with default values and uses them.

msglvl

INTEGER

INTEGER , INTENT(IN)

Message level information

0 - Intel® oneMKL PARDISO generates no output
1 - Intel® oneMKL PARDISO prints statistical information

b(n*nrhs)

in/out

PARDISO_DATA_TYPE¹

PARDISO_DATA_TYPE, INTENT(INOUT)¹

Right-hand side vectors

On entry, contains the right-hand side vector/matrix B , which is placed contiguously in memory. The b(i+(k-1)×nrhs) 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(6) =1.

x(n*nrhs)

out

PARDISO_DATA_TYPE¹

PARDISO_DATA_TYPE, INTENT(OUT)¹

Solution vectors

On output, if iparm(6) =0, contains solution vector/matrix X which is placed contiguously in memory. The x(i+(k-1)×nrhs) element must hold the i -th component of k -th solution vector. Note that x is only accessed in the solution phase.

error

out

INTEGER

INTEGER , INTENT(OUT)

Error indicator

0 - No error
-1 - Input inconsistent
-2 - Not enough memory
-3 - Reordering problem
-4 - Zero pivot, numerical factorization or iterative refinement problem
-5 - Unclassified (internal) error
-6 - Reordering failed (matrix types 11 and 13 only)
-7 - Diagonal matrix is singular
-8 - 32-bit integer overflow problem
-9 - Not enough memory for OOC
-10 - Problems with opening OOC temporary files
-11 - Read/write problems with the OOC data file

[1]: See description of PARDISO_DATA_TYPE in PARDISO_DATA_TYPE .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Intel® oneMKL PARDISO Parameters in Tabular Form