function times = bench(count)
%BENCH MATLAB Benchmark
% BENCH times six different MATLAB tasks and compares the execution
% speed with the speed of several other computers. The six tasks are:
%
% LU LAPACK. Floating point, regular memory access.
% FFT Fast Fourier Transform. Floating point, irregular memory access.
% ODE Ordinary diff. eqn. Data structures and M-files.
% Sparse Solve sparse system. Mixed integer and floating point.
% 2-D plot(fft(eye)). 2-D line drawing graphics.
% 3-D MathWorks logo. 3-D animated OpenGL graphics.
%
% A final bar chart shows speed, which is inversely proportional to
% time. Here, longer bars are faster machines, shorter bars are slower.
%
% BENCH runs each of the six tasks once.
% BENCH(N) runs each of the six tasks N times.
% BENCH(0) just displays the results from other machines.
% T = BENCH(N) returns an N-by-6 array with the execution times.
%
% The comparison data for other computers is stored in a text file:
% .../toolbox/matlab/demos/bench.dat
% Updated versions of this file are available from <a href="matlab:web('http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=1836&objectType=file#','-browser')">MATLAB Central</a>
% Note the link above opens your system web browser as defined by WEB.
%
% Fluctuations of five or 10 percent in the measured times of repeated
% runs on a single machine are not uncommon. Your own mileage may vary.
%
% This benchmark is intended to compare performance of one particular
% version of MATLAB on different machines. It does not offer direct
% comparisons between different versions of MATLAB. The tasks and
% problem sizes change from version to version.
%
% The LU and FFT tasks involve large matrices and long vectors.
% Machines with less than 64 megabytes of physical memory or without
% optimized Basic Linear Algebra Subprograms may show poor performance.
%
% The 2-D and 3-D tasks measure graphics performance, including software
% or hardware support for OpenGL. The command
% opengl info
% describes the OpenGL support available on a particular machine.
% Copyright 1984-2009 The MathWorks, Inc.
% $Revision: 5.37.4.20.4.1 $ $Date: 2009/02/06 03:18:49 $
if nargin < 1, count = 1; end;
times = zeros(count,6);
fig1 = figure;
set(fig1,'pos','default','menubar','none','numbertitle','off', ...
'name','MATLAB Benchmark')
hax1 = axes('pos',[0 0 1 1],'parent',fig1);
axis(hax1,'off');
%text(.5,.5,'MATLAB Benchmark','horizontal','center','fontsize',18)
text(.5,.6,'MATLAB Benchmark','parent',hax1,'horizontalalignment','center','fontsize',18)
task = text(.50,.42,'','parent',hax1,'horizontalalignment','center','fontsize',18);
drawnow
pause(1);
% Use a private stream to avoid resetting the global stream
stream = RandStream('mt19937ar');
problemsize = zeros(1, 4);
for k = 1:count
% LU, n = 1000.
set(task,'string','LU')
drawnow
lu(0);
n = 1000;
problemsize(1) = n;
reset(stream,0);
A = randn(stream,n,n);
X = A; %#ok Used to preallocate X
clear X
tic
X = lu(A); %#ok Result not used -- strictly for timing
times(k,1) = toc;
clear A
clear X
% FFT, n = 2^20. Do it twice to roughly match LU time.
set(task,'string','FFT')
drawnow
fft(0);
n = 2^20;
problemsize(2) = n;
y = ones(1,n)+i*ones(1,n); %#ok Used to preallocate y
clear y
reset(stream,1);
x = randn(stream,1,n);
tic
y = fft(x); %#ok Result not used -- strictly for timing
clear y
y = fft(x); %#ok Result not used -- strictly for timing
times(k,2) = toc;
clear x
clear y
% ODE. van der Pol equation, mu = 1
set(task,'string','ODE')
drawnow
F = @vdp1;
y0 = [2; 0];
tspan = [0 eps];
[s,y] = ode45(F,tspan,y0); %#ok Used to preallocate s and y
tspan = [0 400];
problemsize(3) = tspan(end);
tic
[s,y] = ode45(F,tspan,y0); %#ok Results not used -- strictly for timing
times(k,3) = toc;
clear s y
% Sparse linear equations
set(task,'string','Sparse')
drawnow
n = 300;
A = delsq(numgrid('L',n));
problemsize(4) = size(A, 1);
b = sum(A)';
tic
x = A\b; %#ok Result not used -- strictly for timing
times(k,4) = toc;
clear A b
% 2-D graphics
set(task,'string','2-D')
drawnow
pause(1)
hh = figure('doublebuffer','on');
aa = axes('parent',hh);
x = (0:1/256:1)';
plot(aa,x,bernstein(x,0))
drawnow
tic
for j = 1:2
for n = [1:12 11:-1:2]
plot(aa,x,bernstein(x,n))
drawnow
end
end
times(k,5) = toc;
close(hh)
% 3-D graphics. Vibrating logo.
% Gouraud lighting allows smooth motion with OpenGL.
set(task,'string','3-D')
drawnow
pause(1)
evalc('logo');
set(logoFig,'color',[.8 .8 .8])
s = findobj(logoFig, 'type','surf', 'tag', 'TheMathWorksLogo');
set(s,'facelighting','gouraud')
L1 = 40*membrane(1,25);
L2 = 10*membrane(2,25);
L3 = 10*membrane(3,25);
mu = sqrt([9.6397238445, 15.19725192, 2*pi^2]);
n = 40;
tic
for j = 0:n
t = 0.5*(1-j/n);
L = cos(mu(1)*t)*L1 + sin(mu(2)*t)*L2 + sin(mu(3)*t)*L3;
set(s,'zdata',L)
drawnow
end
times(k,6) = toc;
pause(1)
close(logoFig)
end % loop on k
% Compare with other machines. Get latest data file, bench.dat, from
% MATLAB Central at the URL given in the M-file help at the beginning of bench.m
if exist('bench.dat','file') ~= 2
warning('MATLAB:bench:noDataFileFound', 'Comparison data in file matlab/demos/bench.dat not available.')
return
end
fp = fopen('bench.dat', 'rt');
% Skip over headings in first six lines.
for k = 1:6
fgetl(fp);
end
% Read the comparison data
specs = {};
T = [];
details = {};
g = fgetl(fp);
m = 0;
desclength = 61;
while length(g) > 1
m = m+1;
specs{m} = g(1:desclength);
T(m,:) = sscanf(g((desclength+1):end),'%f')';
details{m} = fgetl(fp);
g = fgetl(fp);
end
% Close the data file
fclose(fp);
% Determine the best 10 runs (if user asked for at least 10 runs)
if count > 10
warning('MATLAB:bench:display10BestTrials', '%s\n%s\n%s%d%s', ...
'BENCH will only display the 10 best times on the comparison graph and in the table of results', ...
'in the figure window, to prevent the graph and table from being overcrowded.', ...
'However, the output argument of BENCH will contain data from all ', ...
count, ' trials.');
totaltimes = 100./sum(times, 2);
[ignore, timeOrder] = sort(totaltimes); %#ok
selected = timeOrder(1:10);
else
selected = 1:count;
end
% Add the current machine and sort
T = [T; times(selected, :)];
this = [zeros(m,1); ones(length(selected),1)];
TM = ['This machine' repmat(' ', 1, desclength-12)];
for k = m+1:size(T, 1)
specs(k) = {TM};
details{k} = ['It''s your machine running MATLAB ' version];
end
m = size(T, 1);
totals = sum(T, 2);
speeds = 100./totals;
[speeds,k] = sort(speeds);
specs = specs(k);
details = details(k);
T = T(k,:);
this = this(k);
% Horizontal bar chart. Highlight this machine with another color.
clf(fig1)
% Stretch the figure's width slightly to account for longer machine
% descriptions
units1 = get(fig1, 'Units');
set(fig1, 'Units', 'normalized');
pos1 = get(fig1, 'Position');
set(fig1, 'Position', pos1 + [-0.1 -0.1 0.2 0.1]);
set(fig1, 'Units', units1);
hax2 = axes('position',[.4 .1 .5 .8],'parent',fig1);
barh(hax2,speeds.*(1-this),'y')
hold(hax2,'on')
barh(hax2,speeds.*this,'m')
set(hax2,'xlim',[0 max(speeds)+.1],'xtick',0:4:max(speeds))
title(hax2,'Relative Speed')
axis(hax2,[0 max(speeds)+.1 0 m+1])
set(hax2,'ytick',1:m)
set(hax2,'yticklabel',specs,'fontsize',9)
% Display report in second figure
fig2 = figure('pos',get(fig1,'pos')+[50 -150 50 0], 'menubar','none', ...
'numbertitle','off','name','MATLAB Benchmark (times in seconds)');
% Defining layout constants - change to adjust 'look and feel'
% The names of the tests
TestNames = {'LU', 'FFT', 'ODE', 'Sparse', '2-D', '3-D'};
testDatatips = {sprintf('LU of a %d-by-%d matrix', problemsize(1), problemsize(1)), ...
sprintf('FFT of a %d-element vector', problemsize(2)), ...
sprintf('Solution from t=0 to t=%g', problemsize(3)), ...
sprintf('Solving a %d-by-%d sparse linear system', problemsize(4), problemsize(4)), ...
'Bernstein polynomial graph', ...
'Animated L-shaped membrane'};
% Number of test columns
NumTests = size(TestNames, 2);
NumRows = m+1; % Total number of rows - header (1) + number of results (m)
TopMargin = 0.05; % Margin between top of figure and title row
BotMargin = 0.20; % Margin between last test row and bottom of figure
LftMargin = 0.03; % Margin between left side of figure and Computer Name
RgtMargin = 0.03; % Margin between last test column and right side of figure
CNWidth = 0.40; % Width of Computer Name column
MidMargin = 0.03; % Margin between Computer Name column and first test column
HBetween = 0.01; % Distance between two rows of tests
WBetween = 0.015; % Distance between two columns of tests
% Width of each test column
TestWidth = (1-LftMargin-CNWidth-MidMargin-RgtMargin-(NumTests-1)*WBetween)/NumTests;
% Height of each test row
RowHeight = (1-TopMargin-(NumRows-1)*HBetween-BotMargin)/NumRows;
% Beginning of first test column
BeginTestCol = LftMargin+CNWidth+MidMargin;
% Retrieve the background color for the figure
bc = get(fig2,'Color');
YourMachineColor = [0 0 1];
% Create headers
% Computer Name column header
uicontrol(fig2,'Style', 'text', 'Units', 'normalized', ...
'Position', [LftMargin 1-TopMargin-RowHeight CNWidth RowHeight],...
'String', 'Computer Type', 'BackgroundColor', bc, 'Tag', 'Computer_Name','FontWeight','bold');
% Test name column header
for k=1:NumTests
uicontrol(fig2,'Style', 'text', 'Units', 'normalized', ...
'Position', [BeginTestCol+(k-1)*(WBetween+TestWidth) 1-TopMargin-RowHeight TestWidth RowHeight],...
'String', TestNames{k}, 'BackgroundColor', bc, 'Tag', TestNames{k}, 'FontWeight', 'bold', ...
'TooltipString', testDatatips{k});
end
% For each computer
for k=1:NumRows-1
VertPos = 1-TopMargin-k*(RowHeight+HBetween)-RowHeight;
if this(NumRows - k)
thecolor = YourMachineColor;
else
thecolor = [0 0 0];
end
% Computer Name row header
uicontrol(fig2,'Style', 'text', 'Units', 'normalized', ...
'Position', [LftMargin VertPos CNWidth RowHeight],...
'String', specs{NumRows-k}, 'BackgroundColor', bc, 'Tag', specs{NumRows-k},...
'TooltipString', details{NumRows-k}, 'HorizontalAlignment', 'left', ...
'ForegroundColor', thecolor);
% Test results for that computer
for n=1:NumTests
uicontrol(fig2,'Style', 'text', 'Units', 'normalized', ...
'Position', [BeginTestCol+(n-1)*(WBetween+TestWidth) VertPos TestWidth RowHeight],...
'String', sprintf('%.4f',T(NumRows-k, n)), 'BackgroundColor', bc, ...
'Tag', sprintf('Test_%d_%d',NumRows-k,n), 'ForegroundColor', thecolor);
end
end
% Warning text
uicontrol(fig2, 'Style', 'text', 'Units', 'normalized', ...
'Position', [0.01 0.01 0.98 BotMargin-0.02], 'BackgroundColor', bc, 'Tag', 'Disclaimer', ...
'String', sprintf('%s\n%s\n%s','Place the cursor near a computer name for system and version details. Before using', ...
'this data to compare different versions of MATLAB, or to download an updated timing data file,',...
'see the help for the bench function by typing ''help bench'' at the MATLAB prompt.'));
set([fig1 fig2], 'NextPlot', 'new');
% ----------------------------------------------- %
function B = bernstein(x,n)
% BERNSTEIN Generate Bernstein polynomials.
% B = bernstein(x,n) is a length(x)-by-n+1 matrix whose columns
% are the Bernstein polynomials of degree n evaluated at x,
% B_sub_k(x) = nchoosek(n,k)*x.^k.*(1-x).^(n-k), k = 0:n.
x = x(:);
B = zeros(length(x),n+1);
B(:,1) = 1;
for k = 2:n+1
B(:,k) = x.*B(:,k-1);
for j = k-1:-1:2
B(:,j) = x.*B(:,j-1) + (1-x).*B(:,j);
end
B(:,1) = (1-x).*B(:,1);
end
