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The Pardiso.jl package provides an interface for using PARDISO 6.0 and Intel MKL PARDISO from the Julia language. You cannot use Pardiso.jl without either having a valid license for PARDISO or having the MKL library installed. This package is available free of charge and in no way replaces or alters any functionality of the linked libraries.


The package itself is installed with Pkg.add("Pardiso") but you also need to follow the installation instructions below to install a working PARDISO library.


By default Julia, will automatically install a suitable MKL for your platform. If you rather use a self installed MKL follow these instructions:

  • Set the MKLROOT environment variable. See the MKL getting started manual for a thorough guide how to set this variable correctly, typically done by executing something like source /opt/intel/mkl/bin/mklvars.sh intel64 or running "C:\Program Files (x86)\IntelSWTools\compilers_and_libraries\windows\mkl\bin\mklvars.bat" intel64
  • Run Pkg.build("Pardiso")
  • Run Pardiso.show_build_log() to see the build log for additional information.
  • Note that the MKLROOT environment variable must be set whenever using the library.


  • Put the PARDISO library libpardiso600-WIN-X86-64.dll, libpardiso600-GNUXXX-X86-64.so or libpardiso600-MACOS-X86-64.dylib in a folder somewhere and set the environment variable JULIA_PARDISO to that folder. For example, create an entry ENV["JULIA_PARDISO"] = "/Users/Someone/Pardiso" in the .julia/config/startup.jl file and download the Pardiso library to that folder.
  • Perform the platform specific steps below
  • Run Pkg.build("Pardiso")
  • Run Pardiso.show_build_log() to see the build log for additional information.

Note: Weird errors and problems with MKL Pardiso has been observed when Pardiso 6.0 is enabled (likely because some library that is needed by Pardiso 6.0 is problematic with MKL). If you want to use MKL Pardiso it is better ot just disable Paridso 6.0 by not setting the environment variable JULIA_PARDISO (and rerunning build Pardiso).

Linux / macOS specific
  • Make sure that the version of gfortran corresponding to the pardiso library is installed.
  • Make sure OpenMP is installed.
  • Install a (fast) installation of a BLAS and LAPACK (this should preferably be single threaded since PARDISO handles threading itself), using for example OpenBLAS

Basic Usage

This section will explain how to solve equations using Pardiso.jl with the default settings of the library. For more advanced users there is a section further down.

Creating the PardisoSolver

A PardisoSolver is created with PardisoSolver() for solving with PARDISO 6.0 or MKLPardisoSolver() for solving with MKL PARDISO. This object will hold the settings of the solver and will be passed into the solve functions. In the following sections an instance of a PardisoSolver or an MKLPardisoSolver() will be referred to as ps.


Solving equations is done with the solve and solve! functions. They have the following signatures:

  • solve(ps, A, B) solves AX=B and returns X
  • solve!(ps, X, A, B) solves AX=B and stores it in X

The symbols :T or :C can be added as an extra argument to solve the transposed or the conjugate transposed system of equations, respectively.

Here is an example of solving a system of real equations with two right-hand sides:

ps = PardisoSolver()

A = sparse(rand(10, 10))
B = rand(10, 2)
X = zeros(10, 2)
solve!(ps, X, A, B)

which happened to give the result

julia> X
10x2 Array{Float64,2}:
 -0.487361  -0.715372
 -0.644219  -3.38342
  0.465575   4.4838
  1.14448   -0.103854
  2.00892   -7.04965
  0.870507   1.7014
  0.590723  -5.74338
 -0.843841  -0.903796
 -0.279381   7.24754
 -1.17295    8.47922

Schur Complement (6.0 only)

Given a partitioned matrix M = [A B; C D], the Schur complement of A in M is S = D-CA⁻¹B. This can be found with the function schur_complement with the following signatures:

  • schur_complement(ps, M, n) returns Schur complement of submatrix A in M, where n is the size of submatrix D (and therefore also of Schur complement)
  • schur_complement(ps, M, x) returns Schur complement of submatrix A in M, where submatrix D is defined by nonzero rows of SparseVector or SparseMatrix x.

The symbols :T or :C can be added as an extra argument to solve the transposed or the conjugate transposed system of equations, respectively.

Here is an example of finding the Schur complement:

ps = PardisoSolver()
m = 100; n = 5; p = .5; T = Float64
rng = MersenneTwister(1234);
A = I + sprand(rng,T,m,m,p)
A⁻¹ = inv(Matrix(A))
B = sprand(rng,T,m,n,p)
C = sprand(rng,T,n,m,p)
D = sprand(rng,T,n,n,p)
M = [A B; C D]
S = schur_complement(ps,M,n)

which gives

julia> S
5×5 Array{Float64,2}:
  -0.121404    1.49473  -1.25965    7.40326    0.571538
 -19.4928     -7.71151  12.9496    -7.13646  -20.4194  
   9.88029     3.35502  -7.2346     1.70651   13.9759  
  -9.06094    -5.86454   7.44917   -2.54985   -9.17327
 -33.7006    -17.8323   20.2588   -19.5863   -37.6132

We can check the validity by comparing to explicity form:

julia> norm(D - C*A⁻¹*B - S)

At present there seems to be an instability in the Schur complement computation for complex matrices.

Setting the number of threads

The number of threads to use is set in different ways for MKL PARDISO and PARDISO 6.0.


set_nprocs!(ps, i) # Sets the number of threads to use
get_nprocs(ps) # Gets the number of threads being used


The number of threads are set at the creation of the PardisoSolver by looking for the environment variable OMP_NUM_THREADS. This can be done in Julia with for example ENV["OMP_NUM_THREADS"] = 2. Note: OMP_NUM_THREADS must be set before Pardiso is loaded and can not be changed during runtime.

The number of threads used by a PardisoSolver can be retrieved with get_nprocs(ps)

More advanced usage.

This section discusses some more advanced usage of Pardiso.jl.

For terminology in this section please refer to the PARDISO 6.0 manual and the MKL PARDISO section.

After using functionality in this section, calls should no longer be made to the solve functions but instead directly to the function

pardiso(ps, X, A, B)

This will ensure that the properties you set will not be overwritten.

If you want, you can use get_matrix(ps, A, T) to return a matrix that is suitable to use with pardiso depending on the matrix type that ps has set. The parameter T is a symbol representing if you will solve the normal, transposed or conjugated system. These are represented by :N, :T, :C) respectively.

For ease of use, Pardiso.jl provides enums for most options. These are not exported so has to either be explicitly imported or qualified with the module name first. It is possible to both use the enum as an input key to the options or the corresponding integer as given in the manuals.

Setting the matrix type

The matrix type can be explicitly set with set_matrixtype!(ps, key) where the key has the following meaning:

enum integer Matrix type
REAL_SYM 1 real and structurally symmetric
REAL_SYM_POSDEF 2 real and symmetric positive definite
REAL_SYM_INDEF -2 real and symmetric indefinite
COMPLEX_STRUCT_SYM 3 complex and structurally symmetric
COMPLEX_HERM_POSDEF 4 complex and Hermitian positive definite
COMPLEX_HERM_INDEF -4 complex and Hermitian indefinite
COMPLEX_SYM 6 complex and symmetric
REAL_NONSYM 11 real and nonsymmetric
COMPLEX_NONSYM 13 complex and nonsymmetric

The matrix type for a solver can be retrieved with get_matrixtype(ps).

Setting the solver (6.0 only)

PARDISO 6.0 supports direct and iterative solvers. The solver is set with set_solver!(ps, key) where the key has the following meaning:

enum integer Solver
DIRECT_SOLVER 0 sparse direct solver
ITERATIVE_SOLVER 1 multi-recursive iterative solver

Setting the phase

Depending on the phase calls to solve (and pardiso which is mentioned later) does different things. The phase is set with set_phase!(ps, key) where key has the meaning:

enum integer Solver Execution Steps
ANALYSIS 11 Analysis
ANALYSIS_NUM_FACT 12 Analysis, numerical factorization
ANALYSIS_NUM_FACT_SOLVE_REFINE 13 Analysis, numerical factorization, solve, iterative refinement
NUM_FACT 22 Numerical factorization
SELECTED_INVERSION -22 Selected Inversion
NUM_FACT_SOLVE_REFINE 23 Numerical factorization, solve, iterative refinement
SOLVE_ITERATIVE_REFINE 33 Solve, iterative refinement
SOLVE_ITERATIVE_REFINE_ONLY_FORWARD 331 MKL only, like phase=33, but only forward substitution
SOLVE_ITERATIVE_REFINE_ONLY_DIAG 332 MKL only, like phase=33, but only diagonal substitution (if available)
SOLVE_ITERATIVE_REFINE_ONLY_BACKWARD 333 MKL only, like phase=33, but only backward substitution
RELEASE_LU_MNUM 0 Release internal memory for L and U matrix number MNUM
RELEASE_ALL -1 Release all internal memory for all matrices

Setting IPARM and DPARM explicitly

Advanced users likely want to explicitly set and retrieve the IPARM and DPARM (6.0 only) parameters. This can be done with the getters and setters:

get_iparm(ps, i) # Gets IPARM[i]
get_iparms(ps) # Gets IPARM
set_iparm!(ps, i, v) # Sets IPARM[i] = v

# 6.0 only
get_dparm(ps, i) # Gets DPARM[i]
get_dparms(ps) # Gets DPARM
set_dparm!(ps, i, v) # Sets DPARM[i] = v

To set the default values of the IPARM and DPARM call pardisoinit(ps). The default values depend on what solver and matrix type is set.

Setting message level

It is possible for Pardiso to print out timings and statistics when solving. This is done by set_msglvl!(ps, key) where key has the meaning:

enum integer Solver
MESSAGE_LEVEL_OFF 0 no statistics printed
MESSAGE_LEVEL_ON 1 statistics printed

Matrix and vector checkers

PARDISO 6.0 comes with a few matrix and vector checkers to check the consistency and integrity of the input data. These can be called with the functions:

printstats(ps, A, B)
checkmatrix(ps, A)
checkvec(ps, B)

In MKL PARDISO this is instead done by setting IPARM[27] to 1 before calling pardiso.


These are set and retrieved with the functions

set_mnum!(ps, i)

set_maxfct!(ps, i)

set_perm!(ps, perm) # Perm is a Vector{Int}

Schur Complement (6.0 only)

The pardiso(ps,...) syntax can be used to compute the Schur compelement (as described below). The answer can be retrieved with pardisogetschur(ps).

To use the low-level API to compute the Schur complement:

  • use custom IPARMS (set_iparm!(ps,1,1)), set the Schur complement block size to n (set_iparm!(ps,38,n)), and set the phase to analyze & factorize (set_phase!(ps,12)).
  • compute the Schur complement by calling pardiso(ps,X,M,X), where B is a dummy vector with length(X)=size(M,1) that shares element type with M.
  • retrieve with pardisogetschur(ps)

Potential "gotchas"

  • Julia uses CSC sparse matrices while PARDISO expects a CSR matrix. These can be seen as transposes of each other so to solve AX = B the transpose flag (IPARAM[12]) should be set to 1.
  • For symmetric matrices, PARDISO needs to have the diagonal stored in the sparse structure even if the diagonal element happens to be 0. The manual recommends adding an eps to the diagonal when you suspect you might have 0 values diagonal elements that are not stored in the sparse structure.
  • Unless IPARM[1] = 1, all values in IPARM will be ignored and default values are used.
  • When solving a symmetric matrix, Pardiso expects only the upper triangular part. Since Julia has CSC matrices this means you should pass in tril(A) to the pardiso function. Use checkmatrix to see that you managed to get the matrix in a valid format.


If you have suggestions or idea of improving this package, please file an issue or even better, create a PR!

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