ode_sweep_parfor, a MATLAB code which repeatedly solves an ordinary differential equation (ODE) which depends on parameters B and K, notes the maximum value P achieved by each solution, and makes a plot of P(B,K). The parfor() command is used to perform these computations in parallel.
Consider the parameterized second order differential equation:
m x'' + b x' + k x = 0
which represents the behavior of a spring mass system with a
mass of m, a spring constant of k and a damping
coefficient b.
We now suppose that we are interested in properties of the solution x(t) over the time interval from 0 to 25 seconds, as we vary the physical properties b and k. In particular, we would like to know the maximum value of x(t) over the time interval for each choice of the physical parameters.
To answer this question, we must solve the ODE for each choice of the parameters. Each solution is an independent computation, and one way to carry out the computations in parallel is to use MATLAB's parfor statement.
The basic function has the form:
function peakVals = ode_fun ( bVals, kVals )where
Depending on the situation, the function could be executed in parallel:
The computer code and data files described and made available on this web page are distributed under the MIT license
ode_sweep_parfor is available in a MATLAB version.
collatz_parfor, a MATLAB program which seeks the maximum Collatz sequence between 1 and N, running in parallel using the parfor() command.
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, 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.
MATRIX_ASSEMBLE_PARFOR, a MATLAB program which demonstrates the parfor parallel programming feature by assembling the Hilbert matrix in a parallel loop.
MD_PARFOR, a MATLAB program which carries out a molecular dynamics simulation, running in parallel using MATLAB's "PARFOR" feature.
ODE_SWEEP_SERIAL, a MATLAB program which computes a grid of solutions to a parameterized system of ordinary differential equations (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.