matlab parallel-processing

# 其他 - 用于分叉的MATLAB并行池

Problem Statement: I'm having a non-linear system (Rossler equation) & I have to plot its Bifurcation diagram, I tried to do it normally using for loop but its computation time was too much and my computer got hanged several times, so I got an advice to parallel pool my code in order to come out of this problem. I tried to learn how to parallel pool using MATLAB on the net but still I'm not able to resolve my Issues as there are still some problems since there are 2 parfor loops in my code I'm having problems with Indexing and in assignment of the global parameter (Please note: This code is written for normal execution without using parallel pooling).

I'm attaching my code below here, please excuse if I've mentioned a lot many lines of codes.

``````clc;
a = 0.2; b = 0.2; global c;
crange = 1:0.05:90; % Range for parameter c
k = 0; tspan = 0:0.1:500; % Time interval for solving Rossler system
xmax = []; % A matrix for storing the sorted value of x1

for c = crange
f = @(t,x) [-x(2)-x(3); x(1)+a*x(2); b+x(3)*(x(1)-c)];
x0 = [1 1 0]; % initial condition for Rossler system
k = k + 1;
[t,x] = ode45(f,tspan,x0); % call ode() to solve Rossler system
count = find(t>100); % find all the t values which is >10
x = x(count,:);
j = 1;
n = length(x(:,1)); % find the length of vector x1(x in our problem)

for i=2 : n-1
% check for the min value in 1st column of sol matrix
if (x(i-1,1)+eps) < x(i,1) && x(i,1) > (x(i+1,1)+eps)
xmax(k,j)=x(i,1); % Sorting the values of x1 in increasing order
j=j+1;
end
end

% generating bifurcation map by plotting j-1 element of kth row each time
if j>1
plot(c,xmax(k,1:j-1),'k.','MarkerSize',1);
end

hold on;
index(k)=j-1;
end
xlabel('Bifuracation parameter c');
ylabel('x max');
title('Bifurcation diagram for c');
``````

akhil krishnan

92 Edric 2020-01-31 17:08

This can be made compatible with `parfor` by taking a few relatively simple steps. Firstly, `parfor` workers cannot produce on-screen graphics, so we need to change things to emit a result. In your case, this is not totally trivial since your primary result `xmax` is being assigned-to in a not-completely-uniform manner - you're assigning different numbers of elements on different loop iterations. Not only that, it appears not to be possible to predict up-front how many columns `xmax` needs.

Secondly, you need to make some minor changes to the loop iteration to be compatible with `parfor`, which requires consecutive integer loop iterates.

``````clc;
a = 0.2; b = 0.2;
crange = 1:0.05:90; % Range for parameter c
tspan = 0:0.1:500; % Time interval for solving Rossler system

% PARFOR loop outputs: a cell array of result rows ...
xmax_cell = cell(numel(crange), 1);
% ... and a track of the largest result row
maxNumCols = 0;

parfor k = 1:numel(crange)
c = crange(k);
f = @(t,x) [-x(2)-x(3); x(1)+a*x(2); b+x(3)*(x(1)-c)];
x0 = [1 1 0]; % initial condition for Rossler system
[t,x] = ode45(f,tspan,x0); % call ode() to solve Rossler system
count = find(t>100); % find all the t values which is >10
x = x(count,:);
j = 1;
n = length(x(:,1)); % find the length of vector x1(x in our problem)
this_xmax = [];
for i=2 : n-1
% check for the min value in 1st column of sol matrix
if (x(i-1,1)+eps) < x(i,1) && x(i,1) > (x(i+1,1)+eps)
this_xmax(j) = x(i,1);
j=j+1;
end
end

% Keep track of what's the maximum number of columns
maxNumCols = max(maxNumCols, numel(this_xmax));
% Store this row into the output cell array.
xmax_cell{k} = this_xmax;
end

% Fix up xmax - push each row into the resulting matrix.
xmax = NaN(numel(crange), maxNumCols);
for idx = 1:numel(crange)
this_max = xmax_cell{idx};
xmax(idx, 1:numel(this_max)) = this_max;
end

% Plot
plot(crange, xmax', 'k.', 'MarkerSize', 1)
xlabel('Bifuracation parameter c');
ylabel('x max');
title('Bifurcation diagram for c');
``````