QUAD_SPMD
SPMD (Single Program/Multiple Data) Quadrature


QUAD_SPMD is a MATLAB program which uses the SPMD (single program, multiple data) command to estimate an integral using quadrature.

The SPMD command allows a programmer to set up parallel computations that require more user control than the simple parfor command. In particular, users familiar with MPI will see many features that are similar to that parallel programming model, including the ability to send and receive messages. (Messages will NOT be exhibited in this simple example, however!)

The algorithm carried out estimates the integral of a function f(x) from 0 to 1 by the trapezoidal rule:

        Integral ( a <= x <= b ) f(x) dx = ( b - a ) / ( 2 * ( n - 1 ) )
          * ( f(x1) + 2*f(x2) + 2*f(x3) + ... + 2*f(xn-2) + 2*f(xn-1) + f(xn) )
      
where xi is the i-th point equally spaced between a and b, with the endpoints included.

It's clear that this calculation can be done in parallel, and in fact, simply by defining appropriate values of ai and bi, we can have parallel process i carry out the trapezoidal rule over [ai,bi] and sum the results to get the answer.

This example demonstrates how MATLAB's SPMD facility can be used to implement this parallel calculation. No attempt is made to compare the timings of the parallel code to a sequential calculation. The point here is simply the mechanics of setting up an SPMD calculation, and showing what you can expect.

Several points are worth mentioning:

The function has the form:

function value = quad_fun ( n )
where

Depending on the situation, the function could be executed in parallel:

Licensing:

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

Languages:

QUAD_SPMD is available in a MATLAB version.

Related Data and Programs:

CELL_DETECTION_TASKS, a MATLAB program which creates modified versions of a sequence of gray-scale TIF files containing images of cells; the process of each file is carried out independently, using the "task" feature of MATLAB's parallel computing toolbox.

CG_DISTRIBUTED, a MATLAB program which implements a version of the NAS CG conjugate gradient benchmark, using distributed memory.

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

CONTRAST_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers increase contrast over separate portions, and the client assembles and displays the results.

CONTRAST2_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; this improves the contrast_spmd program by allowing the workers to share some data; this makes it possible to eliminate artificial "seams" in the processed image.

DIJKSTRA_SPMD, a MATLAB program which uses the SPMD feature to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FACE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature; the client has a 3D box that has been dissected into tetrahedrons. Multiple workers cooperate to construct a list of the triangular faces that lie on the boundaries of the box.

FD2D_HEAT_EXPLICIT_SPMD, a MATLAB program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 2D. A black and white image is used as the "initial condition". MATLAB's SPMD facility is used to carry out the computation in parallel.

FMINCON_PARALLEL, a MATLAB program which demonstrates the use of MATLAB's FMINCON constrained minimization function, taking advantage of MATLAB's Parallel Computing Toolbox for faster execution.

IMAGE_DENOISE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers process portions of it, and the client assembles and displays the results.

LINEAR_SOLVE_DISTRIBUTED, a MATLAB program which solves a linear system A*x=b using MATLAB's spmd facility, so that the matrix A is "distributed" across multiple MATLAB workers.

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

MATRIX_ASSEMBLE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature by having each worker assemble part of the Hilbert matrix, which is then combined into one array by the client program.

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.

PLOT_SPMD, a MATLAB library which demonstrates the SPMD parallel programming feature, by having a number of labs compute parts of a sine plot, which is then displayed by the client process.

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

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

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

QUAD_SERIAL, a MATLAB program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.

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

RANDOM_WALK_2D_AVOID_TASKS, a MATLAB program which computes many self avoiding random walks in 2D by creating a job which defines each walk as a task, and then computes these independently using MATLAB's Parallel Computing Toolbox task computing capability.

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.

SUBSET_SUM_TASKS, a MATLAB program which solves a subset sum problem by exhaustive search, subdividing the search range among separate tasks.

Reference:

The User's Guide for the Parallel Computing Toolbox is available at http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf

Source Code:

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


Last revised on 04 February 2010.