I run a Matlab code with an iteration loop, and during each iteration it sample random numbers and uses the function intlinprog. My issue is that, due to the large amount of data I provide to the intlinprog function and to the stochastic values I assign to part of its variables, some of the iterations take a really long time.
My code is more or less like this:
rounds = 1E3;
Total_PF = zeros(rounds,4893);
for i=1:rounds
i
cT = zeros (4894,1);
cT(4894,1) = 1;
xint = linspace(1,4893,4893);
xint = xint';
AT = rand(4,4894);
beT = ones(4,1);
lb = zeros(4894,1);
ub = ones (4894,1);
ub(4894,1) = Inf;
[x] = intlinprog(cT,xint,AT,beT,[],[],lb,ub);
Total_PF(i,:)= (x(1:length(x)-1)');
end
Now in the minimal working example I provided, all the iterations are quite fast, but in my real code, sometimes intlinprog takes really long time ( I mean hours) to do a single iteration.
Therefore, I was wondering: is there a way to break the intlinprog while the intlinprog line is being executed? I was thinking that it may be done by modifying the matlab function but first of all I do not know if I am allowed to do it, secondly I am afraid that may be very dangerous.
This is very difficult to do effectively.
You could try using a timer object to watch the value. However, since you are using inherent Matlab functions and not executing external functions, you could set a time limit value and utilize tic and toc in a while loop while you execute the intlinprog and checking the value of toc against your time limit and break your code if toc exceeds the limit.
Related
I wanted to bootstrap with matlab using the built in command "bootstrp". What I noticed was that the procedure makes N+1 iterations when I am only asking for N iterations. Why is that? When I build a manual loop to do the bootstrapping, so that it really just runs N times, then it is faster. Here is a minimal example of the problem:
clear all
global iterationcounter
tic
iterationcounter=0;
data=unifrnd(0,1,1,1000); %draw vector of 1000 random numbers
bootstat = bootstrp(100,#testmean,data); %evaluate function for 100 bootstrap samples
toc
which uses the function
function [ m ] = testmean( data )
global iterationcounter
m=mean(data);
iterationcounter=iterationcounter+1
end
The function should evaluate 100 samples, yet when I run the script, it will evaluate the function 101 times:
...
iterationcounter =
101
Elapsed time is 0.102291 seconds.
So why should one use this build-in Matlab function that appears to waste time?
bootstrp makes a call to bootfun (the function argument) for sanity checks (from the source code, in MATLAB 2015b, bootstrp.m, l.167 ff) :
% Sanity check bootfun call and determine dimension and type of result
try
% Get result of bootfun on actual data, force to a row.
bootstat = feval(bootfun,bootargs{:});
bootstat = bootstat(:)';
catch ME
m = message('stats:bootstrp:BadBootFun');
MEboot = MException(m.Identifier,'%s',getString(m));
ME = addCause(ME,MEboot);
rethrow(ME);
end
I would think that in a realistic application, N>>100, so the extra overhead is (much) less than a percent of he total runtime (not taking into account speed gains from possible parallelisation), so that should not matter that much?
I have to iterate a process where I have an initial guess for the Mach number (M0). This initial guess will give me another guess for the Mach number by using two equations (Mn). Eventually, i want to iterate this process untill the error between M0 and Mn is small. I have the following piece of code and it actually works well with a while loop.
However, I am afraid that the while loop will take many iterations and computational time for certain inputs since this will be part of a bigger code which most likely will give unfeasible inputs for the while loop.
Therefore my question is the following. How can I iterate this process within Matlab without consulting a while loop? The code that I am implementing now is the following:
%% Input
gamma = 1.4;
theta = atan(0.315);
cpi = -0.732;
%% Loop
M0 = 0.2; %initial guess
Err = 100;
iterations = 0;
while Err > 0.5E-3
B = (1-(M0^2)*(1-M0*cpi))^0.5;
Mn = (((gamma+1)/2) * ((B+((1-cpi)^0.5)*sec(theta)-1)^2/(B^2 + (tan(theta))^2)) - ((gamma-1)/2) )^-0.5;
Err = abs(M0 - Mn);
M0 = Mn;
iterations=iterations+1;
end
disp(iterations) disp(Mn)
Many thanks
Since M0 is calculated in each iteration and you have trigonometric functions, you cannot use another way than iteration structures (i.e. while).
If you had a specific increase or decrease at M0, then you could initialize a vector of M0 and do vector calculations for B and Err.
But, with sec and tan this is not possible.
Another wat would be to use the parallel processing. But, since you change the M0 at each iteration then you cannot use the parfor loop.
As for a for loop, in MATLAB you need an array for for "command" argument (e.g. 1:10 or 1:length(x) or i = A, where A = 1:10 or A = [1:10;11:20]). Since you evaluate a condition and depending on the result of the evaluation you judge if you continue the execution or not, it seems that the while loop (or do while in another language) is the only way to go.
I think you need to clarify the issue. If it the issue you want to solve is that some inputs take a long time to calculate, it is not the while loop that takes the time, it is the execution of the code multiple times that causes it. Any method that loops through will be restricted by the time the block of code takes to execute multiplied by the number of iterations required to converge.
You can introduce something to stop at a certain number of iterationtions, conceptually:
While ((err > tolerance) && (numIterations < limit))
If you want an answer which does not require iterating over the code, this is akin to finding a closed form solution, and I suspect this does not exist.
Edit to add: by not exist I mean in a practical form which can be implemented in a more efficient way then iterating to a solution.
Is there a way to rewrite my code to make it faster?
for i = 2:length(ECG)
u(i) = max([a*abs(ECG(i)) b*u(i-1)]);
end;
My problem is the length of ECG.
You should pre-allocate u like this
>> u = zeros(size(ECG));
or possibly like this
>> u = NaN(size(ECG));
or maybe even like this
>> u = -Inf(size(ECG));
depending on what behaviour you want.
When you pre-allocate a vector, MATLAB knows how big the vector is going to be and reserves an appropriately sized block of memory.
If you don't pre-allocate, then MATLAB has no way of knowing how large the final vector is going to be. Initially it will allocate a short block of memory. If you run out of space in that block, then it has to find a bigger block of memory somewhere, and copy all the old values into the new memory block. This happens every time you run out of space in the allocated block (which may not be every time you grow the array, because the MATLAB runtime is probably smart enough to ask for a bit more memory than it needs, but it is still more than necessary). All this unnecessary reallocating and copying is what takes a long time.
There are several several ways to optimize this for loop, but, surprisingly memory pre-allocation is not the part that saves the most time. By far. You're using max to find the largest element of a 1-by-2 vector. On each iteration you build this vector. However, all you're doing is comparing two scalars. Using the two argument form of max and passing it two scalar is MUCH faster: 75+ times faster on my machine for large ECG vectors!
% Set the parameters and create a vector with million elements
a = 2;
b = 3;
n = 1e6;
ECG = randn(1,n);
ECG2 = a*abs(ECG); % This can be done outside the loop if you have the memory
u(1,n) = 0; % Fast zero allocation
for i = 2:length(ECG)
u(i) = max(ECG2(i),b*u(i-1)); % Compare two scalars
end
For the single input form of max (not including creation of random ECG data):
Elapsed time is 1.314308 seconds.
For my code above:
Elapsed time is 0.017174 seconds.
FYI, the code above assumes u(1) = 0. If that's not true, then u(1) should be set to it's value after preallocation.
I'm going to write a program in MATLAB that takes a function, sets the value D from 10 to 100 (the for loop), integrates the function with Simpson's rule (the while loop) and then displays it. Now, this works fine for the first 7-8 values, but then it takes longer time and eventually I run out of memory, and I don't understand the reason for this. This is the code so far:
global D;
s=200;
tolerance = 9*10^(-5);
for D=10:1:100
r = Simpson(#f,0,D,s);
error = 1;
while(error>tolerance)
s = 2*s;
error = (1/15)*(Simpson(#f,0,D,s)-r);
r = Simpson(#f,0,D,s);
end
clear error;
disp(r)
end
mtrw's comment probably already answers the question in part: s should be reinitialized inside the for loop. The posted code results in s increasing irreversibly every time the error was too large, so for larger values of D the largest s so far will be used.
Additionally, since the code re-evaluates the entire integration instead of reusing the previous integration from [0, D-1] you waste lots of resources unless you want to explicitly show the error tolerance of your Simpson function - s will have to increase a lot for large D to maintain the same low error (since you integrate over a larger range you have to sum up more points).
Finally, your implementation of Simpson could of course do funny stuff as well, which no one can tell without seeing it...
I have a program which I copied from a textbook, and which times the difference in program execution runtime when calculating the same thing with uninitialized, initialized array and vectors.
However, although the program runs somewhat as expected, if running several times every once in a while it will give out a crazy result. See below for program and an example of crazy result.
clear all; clc;
% Purpose:
% This program calculates the time required to calculate the squares of
% all integers from 1 to 10000 in three different ways:
% 1. using a for loop with an uninitialized output array
% 2. Using a for loop with a pre-allocated output array
% 3. Using vectors
% PERFORM CALCULATION WITH AN UNINITIALIZED ARRAY
% (done only once because it is so slow)
maxcount = 1;
tic;
for jj = 1:maxcount
clear square
for ii = 1:10000
square(ii) = ii^2;
end
end
average1 = (toc)/maxcount;
% PERFORM CALCULATION WITH A PRE-ALLOCATED ARRAY
% (averaged over 10 loops)
maxcount = 10;
tic;
for jj = 1:maxcount
clear square
square = zeros(1,10000);
for ii = 1:10000
square(ii) = ii^2;
end
end
average2 = (toc)/maxcount;
% PERFORM CALCULATION WITH VECTORS
% (averaged over 100 executions)
maxcount = 100;
tic;
for jj = 1:maxcount
clear square
ii = 1:10000;
square = ii.^2;
end
average3 = (toc)/maxcount;
% Display results
fprintf('Loop / uninitialized array = %8.6f\n', average1)
fprintf('Loop / initialized array = %8.6f\n', average2)
fprintf('Vectorized = %8.6f\n', average3)
Result - normal:
Loop / uninitialized array = 0.195286
Loop / initialized array = 0.000339
Vectorized = 0.000079
Result - crazy:
Loop / uninitialized array = 0.203350
Loop / initialized array = 973258065.680879
Vectorized = 0.000102
Why is this happening ?
(sometimes the crazy number is on vectorized, sometimes on loop initialized)
Where did MATLAB "find" that number?
That is indeed crazy. Don't know what could cause it, and was unable to reproduce on my own Matlab R2010a copy over several runs, invoked by name or via F5.
Here's an idea for debugging it.
When using tic/toc inside a script or function, use the "tstart = tic" form that captures the output. This makes it safe to use nested tic/toc calls (e.g. inside called functions), and lets you hold on to multiple start and elapsed times and examine them programmatically.
t0 = tic;
% ... do some work ...
te = toc(t0); % "te" for "time elapsed"
You can use different "t0_label" suffixes for each of the tic and toc returns, or store them in a vector, so you preserve them until the end of your script.
t0_uninit = tic;
% ... do the uninitialized-array test ...
te_uninit = toc(t0_uninit);
t0_prealloc = tic;
% ... test the preallocated array ...
te_prealloc = toc(t0_prealloc);
Have the script break in to the debugger when it finds one of the large values.
if any([te_uninit te_prealloc te_vector] > 5)
keyboard
end
Then you can examine the workspace and the return values from tic, which might provide some clues.
EDIT: You could also try testing tic() on its own to see if there's something odd with your system clock, or whatever tic/toc is calling. tic()'s return value looks like a native timestamp of some sort. Try calling it many times in a row and comparing the subsequent values. If it ever goes backwards, that would be surprising.
function test_tic
t0 = tic;
for i = 1:1000000
t1 = tic;
if t1 <= t0
fprintf('tic went backwards: %s to %s\n', num2str(t0), num2str(t1));
end
t0 = t1;
end
On Matlab R2010b (prerelease), which has int64 math, you can reproduce a similar ridiculous toc result by jiggering the reference tic value to be "in the future". Looks like an int rollover effect, as suggested by gary comtois.
>> t0 = tic; toc(t0+999999)
Elapsed time is 6148914691.236258 seconds.
This suggests that if there were some jitter in the timer that toc were using, you might get rollover if it occurs while you're timing very short operations. (I assume toc() internally does something like tic() to get a value to compare the input to.) Increasing the number of iterations could make the effect go away because a small amount of clock jitter would be less significant as part of longer tic/toc periods. Would also explain why you don't see this in your non-preallocated test, which takes longer.
UPDATE: I was able to reproduce this behavior. I was working on some unrelated code and found that on one particular desktop with a CPU model we haven't used before, a Core 2 Q8400 2.66GHz quad core, tic was giving inaccurate results. Looks like a system-dependent bug in tic/toc.
On this particular machine, tic/toc will regularly report bizarrely high values like yours.
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
elapsed: 6934787980.471930500
elapsed: 6934787980.471931500
elapsed: 6934787980.471899000
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
>> for i = 1:50000; t0 = tic; te = toc(t0); if te > 1; fprintf('elapsed: %.9f\n', te); end; end
elapsed: 6934787980.471928600
elapsed: 6934787980.471913300
>>
It goes past that. On this machine, tic/toc will regularly under-report elapsed time for operations, especially for low CPU usage tasks.
>> t0 = tic; c0 = clock; pause(4); toc(t0); fprintf('Wall time is %.6f seconds.\n', etime(clock, c0));
Elapsed time is 0.183467 seconds.
Wall time is 4.000000 seconds.
So it looks like this is a bug in tic/toc that is related to particular CPU models (or something else specific to the system configuration). I've reported the bug to MathWorks.
This means that tic/toc is probably giving you inaccurate results even when it doesn't produce those insanely large numbers. As a workaround, on this machine, use etime() instead, and time only longer chunks of work to compensate for etime's lower resolution. You could wrap it in your own tick/tock functions that use the for i=1:50000 test to detect when tic is broken on the current machine, use tic/toc normally, and have them warn and fall back to using etime() on broken-tic systems.
UPDATE 2012-03-28: I've seen this in the wild for a while now, and it's highly likely due to an interaction with the CPU's high resolution performance timer and speed scaling, and (on Windows) QueryPerformanceCounter, as described here: http://support.microsoft.com/kb/895980/. It is not a bug in tic/toc, the issue is in the OS features that tic/toc is calling. Setting a boot parameter can work around it.
Here's my theory about what might be happening, based on these two pieces of data I found:
There is a function maxNumCompThreads which controls the maximum number of computational threads used by MATLAB to perform tasks. Quoting the documentation:
By default, MATLAB makes use of the
multithreading capabilities of the
computer on which it is running.
Which leads me to think that perhaps multiple copies of your script are running at the same time.
This newsgroup thread discusses a bug in an older version of MATLAB (R14) "in the way that MATLAB accelerates M-code with global structure variables", which it appears the TIC/TOC functions may use. The solution there was to disable the accelerator using the undocumented FEATURE function:
feature accel off
Putting these two things together, I'm wondering if the multiple versions of your script that are running in the workspace may be simultaneously resetting global variables used by the TIC/TOC functions and screwing one another up. Maybe this isn't a problem when converting your script to a function as Amro did since this would separate the workspaces that the two programs are running in (i.e. they wouldn't both be running in the main workspace).
This could also explain the exceedingly large numbers you get. As gary and Andrew have pointed out, these numbers appear to be due to an integer roll-over effect (i.e. an integer overflow) whereby the starting time (from TIC) is larger than the ending time (from TOC). This would result in a huge number that is still positive because TIC/TOC are internally using unsigned 64-bit integers as time measures. Consider the following possible scenario with two scripts running at the same time on different threads:
The first thread calls TIC, initializing a global variable to a starting time measure (i.e. the current time).
The first thread then calls TOC, and the immediate action the TOC function is likely to make is to get the current time measure.
The second thread calls TIC, resetting the global starting time measure to the current time, which is later than the time just measured by the TOC function for the first thread.
The TOC function for the first thread accesses the global starting time measure to get the difference between it and the measure it previously took. This difference would result in a negative number, except that the time measures are unsigned integers. This results in integer overflow, giving a huge positive number for the time difference.
So, how might you avoid this problem? Changing your scripts to functions like Amro did is probably the best choice, as that seems to circumvent the problem and keeps the workspace from becoming cluttered. An alternative work-around you could try is to set the maximum number of computational threads to one:
maxNumCompThreads(1);
This should keep multiple copies of your script from running at the same time in the main workspace.
There are at least two possible error sources. Can you try to differentiate between 'tic/toc' and 'fprintf' by just looking at the computed values without formatting them.
I don't understand the braces around 'toc' but they shouldn't do any harm.
Here is a hypothesis which is testable. Matlab's tic()/toc() have to be using some high-resolution timer. On Windows, because their return value looks like clock cycles, I think they're using the Win32 QueryPerformanceCounter() call, or maybe something else hitting the CPU's RDTSC time stamp counter. These apparently have glitches on some multiprocessor systems, mentioned in the linked articles. Perhaps your machine is one of those, getting different results if the Matlab process is moved from core to core by the process scheduler.
http://msdn.microsoft.com/en-us/library/ms644904(VS.85).aspx
http://www.virtualdub.org/blog/pivot/entry.php?id=106
This would be hardware and system configuration dependent, which would explain why other posters haven't been able to reproduce it.
Try using Windows Task Manager to set the affinity on your Matlab.exe process to a single CPU. (On the Processes tab, right-click MATLAB.exe, "Set affinity...", un-check all but CPU 0.) If the crazy timing goes away while affinity is set, looks like you found the cause.
Regardless, the workaround looks like to just increase maxcount so you're timing longer pieces of work, and the noise you're apparently getting in tic()/toc() is small compared to the measured value. (You don't want to have to muck around with CPU affinity; Matlab is supposed to be easy to run.) If there's a problem in there that's causing int overflow, the other small positive numbers are a bit suspect too. Besides, hi-res timing in a high level language like Matlab is a bit problematic. Timing workloads down to a couple hundred microseconds subjects them to noise from other transient conditions in your machine's state.