Define a Dense Matrix in Parallel

MATRIX_ASSEMBLE_PARFOR is a MATLAB library which demonstrates how a dense matrix can be define in parallel with the parfor() command.

The elements of the Hilbert matrix are defined by:

        A(i,j) = 1 / ( i + j )


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


MATRIX_ASSEMBLE_PARFOR is available in a MATLAB version.

Related Data and Programs:

COLLATZ_PARFOR, a MATLAB program which seeks the maximum Collatz sequence between 1 and N, running in parallel using MATLAB's parfor feature.

HEATED_PLATE_PARFOR, a MATLAB program which solves the steady (time independent) heat equation in a 2D rectangular region, using MATLAB's parfor facility to run in parallel.

HELLO_PARFOR, a MATLAB program which prints out "Hello, world!" multiple times, using MATLAB's parfor command for parallel execution.

HIGH_CARD_PARFOR, a MATLAB program which uses the parfor statement to compute in parallel the statistics for a card game in which you are required to guess the location of the highest card.

MATLAB_PARALLEL, MATLAB programs which illustrate "local" parallel programming on a single computer with MATLAB's Parallel Computing Toolbox.

MATLAB_RANDOM_PARALLEL, MATLAB programs which illustrate the use of Matlab's random number generator (RNG) functions when using parallel features such as parfor or spmd.

MD_PARFOR, a MATLAB program which carries out a molecular dynamics simulation, running in parallel using MATLAB's parfor feature.

ODE_SWEEP_PARFOR, a MATLAB program which demonstrates how the PARFOR command can be used to parallelize the computation of a grid of solutions to a parameterized system of ODE's.

PRIME_PARFOR, a MATLAB program which counts the number of primes between 1 and N; running in parallel using MATLAB's "PARFOR" feature.

QUAD_PARFOR, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "PARFOR" feature.

SATISFY_PARFOR, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, running in parallel using MATLAB's "PARFOR" feature.

SPARSE_PARFOR, a MATLAB library which demonstrates how a sparse matrix can be constructed by evaluating individual blocks in parallel with the parfor command, and then assembled (on a single processor) using the sparse() command.


  1. Gaurav Sharma, Jos Martin,
    MATLAB: A Language for Parallel Computing,
    International Journal of Parallel Programming,
    Volume 37, Number 1, pages 3-36, February 2009.
  2. The MathWorks,
    User's Guide for the Parallel Computing Toolbox,

Source Code:

Examples and Tests:

HILBERT_POOL executes the function locally and interactively.

HILBERT_BATCH executes the function locally and noninteractively.

HILBERT_FSU executes the function on the FSU HPC cluster.

You can go up one level to the MATLAB source codes.

Last revised on 23 May 2012.