I wrote a very simple matlab code which is;
b=4.7;
s=0;
while s <b
s=s+0.1
end
I expect s to be 4.7 but matlab gives 4.8. I am very suprised about this because calculatioun of 0.1 47 times should not give such error. It is a very simple math. Also, if I change b to 4.6 code works fine. I looked the s with format long and matlab gives s = 7.9999999999999. There is a very small error thats why code gives s = 4.8. What is the solution to this problem ? Should I be suspicious about matlab for simple calculations.
I also think your problem is mainly about floating point errors.
Whenever I need it, I use following workaround:
b=4.7;
s=0;
dev = 1e-15; % Maximum deviation (example)
while b-s > dev
s=s+0.1
end
It runs the loop only 47 times and ends it when s = 4.7
It was already indicated that the problem is due to floating point numbers. What you should realize, is that this is not because matlab does something strange, but that other languages that use floating point numbers will encounter exactly the same problem as some numbers simply cannot be stored exactly in this binary format. Here is a simple illustration, that can easily be reproduced in many programming languages:
0.3+0.3+0.3==0.9
This should return true, but unfortunately it returns false.
If you want to be reasonably safe that you do not run into this kind of problem, you should allow for a sufficiently large tolerance. However, you will also want this to be as small as possible to prevent different kinds of problems.
Here is a solution that automatically tries to allow a sensible tolerance:
b=4.7;
s=0;
tol = 100*eps(b);
while s <b-tol
s=s+0.1
end
Note that I would (in general) avoid using a while loop if I already know how often it needs to run. The following code is quite simple and less prone to errors:
for s=0:0.1:4.7
s
end
Related
So, I've recently started using Matlab's built-in profiler on a regular basis, and I've noticed that while its usually great at showing which lines are taking up the most time, sometimes it'll tell me a large chunk of time is being used on the end statement of a for loop.
Now, seeing as such a line is just used for denoting the end of the loop, I can't imagine how it could use anything other than a trivial amount of processing.
I've seen a specific version of this question asked on matlab central, but a consensus didn't seem to be reached.
EDIT: Here's a minimal example of this problem:
for i =1:1000
x = 1;
x = [x 1];
% clear x;
end
Even if you uncomment the clear, the end line still takes up a lot of computation (about 20%), and the clear actually increases the absolute amount of computation performed by the end line.
When I've seen this in my code, it's been the deallocation of large temporaries created in the loop. Each new variable created in the loop is deallocated at the end.
I am writing a matlab code where i calculate the max-min.
I am using matlab's "fminimax" to solve the following problem:
ki=G(i,:);
ki(i)=0;
fs(i)=-((G(i,i)*pt(i)+sum(ki.*pt)+C1)-(C2*(sum(ki.*pt)+C1)));
G: is a system matrix. pt: is the optimization variable.
When the actual system matrix is used, the "fminimax" stops after one iteration and returns the initial value of "pt", no matter what the initial value for "pt", i.e. no solution is found. (the initial value is defined as X0 in the documentation). The system has the following parameters: G is in the order of e-11, pt is in the order of e-1, and c1 is in the order of e-14.
when i try a randomly generated test matrix and different parameters, the "fminimax" finds a solution for the problem, and everything works fine. G in order of e-2, pt in order of e-2, c1 is in the order of e-7.
I tried to scale the actual system: "fminimax" lasted more than one iteration, however, it still returned the initial value of pt, i.e. it couldn't find a solution.
I tried to change the tolerance of the "fminmax", using "options" [StepTolerance, OptimalityTolerance, ConstraintTolerance, and functiontolerance]. There were no impact at all. still no solution.
I thought that the problem might be that the precision of "fminimax" is not that high, or it is not suitable to solve the problem. i think it is also slow.
i downloaded CPLX, and i wanted to transform the max-min problem into linear programing, using a method i found in a book. However, when i tried my code on a simple minimax it didn't give the same solution.
I thought of using CVX for example, but the problem is not convex.
What might be the problem?
P.S. the system matrix, G, has different realizations, i tried some of them. However, the "fminimax" responds in the same way for all of them, i.e. it wasn't able to find an adequate solution.
I am not convinced that the optimization solvers are broken. If the problem is nonconvex, then there can be multiple local minimizers. Given the information you have provided, we have no way of knowing whether you started at an initial condition.
The first place you need to start is by getting more information from the optimization exit condition... Did it finish because it hit the iteration limit? (I hope not since it isn't doing many iterations)... Did it finish because a tolerance was hit (e.g. the function did not change by more than xxxx)? Or perhaps it could not find a feasible solution? (I don't know if you have any constraints that need to be met).
More than likely, I wold guess that you are starting at a local minimizer without realizing it. So you need to determine whether you are indeed at a local minimizer by looking at the jacobian of the function evaluated at your initial guess. Either calculate it analytically or use a finite step approximation....
so I have the following Integral that i need to do numerically:
Int[Exp(0.5*(aCosx + bSinx + cCos2x + dSin2x))] x=0..2Pi
The problem is that the output at any given value of x can be extremely large, e^2000, so larger than I can deal with in double precision.
I havn't had much luck googling for the following, how do you deal with large numbers in fortran, not high precision, i dont care if i know it to beyond double precision, and at the end i'll just be taking the log, but i just need to be able to handle the large numbers untill i can take the log..
Are there integration packes that have the ability to handle arbitrarily large numbers? Mathematica clearly can.. so there must be something like this out there.
Cheers
This is probably an extended comment rather than an answer but here goes anyway ...
As you've already observed Fortran isn't equipped, out of the box, with the facility for handling such large numbers as e^2000. I think you have 3 options.
Use mathematics to reduce your problem to one which does (or a number of related ones which do) fall within the numerical range that your Fortran compiler can compute.
Use Mathematica or one of the other computer algebra systems (eg Maple, SAGE, Maxima). All (I think) of these can be integrated into a Fortran program (with varying degrees of difficulty and integration).
Use a library for high-precision (often called either arbitray-precision or multiple-precision too) arithmetic. Your favourite search engine will turn up a number of these for you, some written in Fortran (and therefore easy to integrate), some written in C/C++ or other languages (and therefore slightly harder to integrate). You might start your search at Lawrence Berkeley or the GNU bignum library.
(Yes I know that I wrote that you have 3 options, but your question suggests that you aren't ready to consider this yet) You could write your own high-/arbitrary-/multiple-precision functions. Fortran provides everything you need to construct such a library, there is a lot of work already done in the field to learn from, and it might be something of interest to you.
In practice it generally makes sense to apply as much mathematics as possible to a problem before resorting to a computer, that process can not only assist in solving the problem but guide your selection or construction of a program to solve what's left of the problem.
I agree with High Peformance Mark that the best option here numerically is to use analytics to scale or simplify the result first.
I will mention that if you do want to brute force it, gfortran (as of 4.6, with the libquadmath library) has support for quadruple precision reals, which you can use by selecting the appropriate kind. As long as your answers (and the intermediate results!) don't get too much bigger than what you're describing, that may work, but it will generally be much slower than double precision.
This requires looking deeper at the problem you are trying to solve and the behavior of the underlying mathematics. To add to the good advice already provided by Mark and Jonathan, consider expanding the exponential and trig functions into Taylor series and truncating to the desired level of precision.
Also, take a step back and ask why you are trying to accomplish by calculating this value. As an example, I recently had to debug why I was getting outlandish results from a property correlation which was calculating vapor pressure of a fluid to see if condensation was occurring. I spent a long time trying to understand what was wrong with the temperature being fed into the correlation until I realized the case causing the error was a simulation of vapor detonation. The problem was not in the numerics but in the logic of checking for condensation during a literal explosion; physically, a condensation check made no sense. The real problem was the code was asking an unnecessary question; it already had the answer.
I highly recommend Forman Acton's Numerical Methods That (Usually) Work and Real Computing Made Real. Both focus on problems like this and suggest techniques to tame ill-mannered computations.
I have a problem with ode45. I've defined a function and trying to solve it by ode, but when i run it, it takes so long. I tried to display the "t" input in my function and it showed time step was 10^-8 ! [I do not get any error from ode45]
So i put a breakpoint at the end of my function, and after I Step once, it goes to sym.m file and calls Function delet(h)
function dxr=Dynfun(t,x)
...
dxr=[A;B]
after Step it goes to
function delete(h)
if builtin('numel',h)==1 && inmem('-isloaded','mupadmex') && builtin('numel',h.s)==1 && ~isa(h.s,'maplesym')
mupadmex(h.s,1);
end
end
and that's what makes it too long, because it goes in a loop in there.
what's the problem?! Thanks
Sounds like it's a "stiff" problem to me. I would recommend using a solver that is designed for stiff problems. I would also recommend trying a fixed step solver at a small step size ~ 0.001 and see what the output looks like. If you are breaking in sym.m, sounds like you've some some symbolic logic going on in there. Is there a way you could take your symbolic expression and convert it to a matlab script?
As indicated by macduff, your problem could be stiff. Try ode15s (which is designed for stiff problems) and see if the stepsize still decreases to unacceptably low values.
If that is indeed the case, then your problem might contain a singularity for the initial values you give it. If your problem has dimensions lower than 3, you can define a small event function to get insight into the values at each step, and plot them to see if there is indeed something problematic going on.
Then -- do you really need symbolic math? The philosophy behind that is that it's easier to read for humans, which makes it terrible to deal with for computers :) If you can transform it into something non-symbolic, please do -- this will noticeably increase performance.
Also, more a word of advice, delete is also Matlab builtin function. It is generally a bad idea to name your functions after Matlab buitins -- it's confusing, and can cause a lot of overhead while Matlab is deciding which one to use.
Although many of you will have a decent idea of what I'm aiming at, just from reading the title -- allow me a simple introduction still.
I have a Fortran program - it consists of a program, some internal subroutines, 7 modules with its own procedures, and ... uhmm, that's it.
Without going into much detail, for I don't think it's necessary at this point, what would be the easiest way to use MATLAB's plotting features (mainly plot(x,y) with some customizations) as an interactive part of my program ? For now I'm using some of my own custom plotting routines (based on HPGL and Calcomp's routines), but just as part of an exercise on my part, I'd like to see where this could go and how would it work (is it even possible what I'm suggesting?). Also, how much effort would it take on my part ?
I know this subject has been rather extensively described in many "tutorials" on the net, but for some reason I have trouble finding the really simple yet illustrative introductory ones. So if anyone can post an example or two, simple ones, I'd be really grateful. Or just take me by the hand and guide me through one working example.
platform: IVF 11.something :) on Win XP SP2, Matlab 2008b
The easiest way would be to have your Fortran program write to file, and have your Matlab program read those files for the information you want to plot. I do most of my number-crunching on Linux, so I'm not entirely sure how Windows handles one process writing a file and another reading it at the same time.
That's a bit of a kludge though, so you might want to think about using Matlab to call the Fortran program (or parts of it) and get data directly for plotting. In this case you'll want to investigate Creating Fortran MEX Files in the Matlab documentation. This is relatively straightforward to do and would serve your needs if you were happy to use Matlab to drive the process and Fortran to act as a compute service. I'd look in the examples distributed with Matlab for simple Fortran MEX files.
Finally, you could call Matlab from your Fortran program, search the documentation for Calling the Matlab Engine. It's a little more difficult for me to see how this might fit your needs, and it's not something I'm terribly familiar with.
If you post again with more detail I may be able to provide more specific tips, but you should probably start rolling your sleeves up and diving in to MEX files.
Continuing the discussion of DISLIN as a solution, with an answer that won't fit into a comment...
#M. S. B. - hello. I apologize for writing in your answer, but these comments are much too short, and answering a question in the form of an answer with an answer is ... anyway ...
There is the Quick Plot feature of DISLIN -- routine QPLOT needs only three arguments to plot a curve: X array, Y array and number N. See Chapter 16 of the manual. Plus only several additional calls to select output device and label the axes. I haven't used this, so I don't know how good the auto-scaling is.
Yes, I know of Quickplot, and it's related routines, but it is too fixed for my needs (cannot change anything), and yes, it's autoscaling is somewhat quircky. Also, too big margins inside the graf.
Or if you want to use the power of GRAF to setup your graph box, there is subroutine GAXPAR to automatically generate recommended values. -2 as the first argument to LABDIG automatically determines the number of digits in tick-mark labels.
Have you tried the routines?
Sorry, I cannot find the GAXPAR routine you're reffering to in dislin's index. Are you sure it is called exactly like that ?
Reply by M.S.B.: Yes, I am sure about the spelling of GAXPAR. It is the last routine in Chapter 4 of the DISLIN 9.5 PDF manual. Perhaps it is a new routine? Also there is another path to automatic scaling: SETSCL -- see Chapter 6.
So far, what I've been doing (apart from some "duck tape" solutions) is
use dislin; implicit none
real, dimension(5) :: &
x = [.5, 2., 3., 4., 5.], &
y = [10., 22., 34., 43., 15.]
real :: xa, xe, xor, xstp, &
ya, ye, yor, ystp
call setpag('da4p'); call metafl('xwin');
call disini(); call winkey('return');
call setscl(x,size(x),'x');
call setscl(y,size(y),'y')
call axslen(1680,2376) !(8/10)*2100 and 2970, respectively
call setgrf('name','name','line','line')
call incmrk(1); call hsymbl(3);
call graf(xa, xe, xor, xstp, ya, ye, yor, ystp); call curve(x,y,size(x))
call disfin()
end
which will put the extreme values right on the axis. Do you know perhaps how could I go to have one "major tick margin" on the outside, as to put some area between the curve and the axis (while still keeping setscl's effects) ?
Even if you don't like the built-in auto-scaling, if you are already using DISLIN, rolling your own auto-scaling will be easier than calling Fortran from MATLAB. You can use the Fortran intrinsic functions minval and maxval to find the smallest and largest values in the data, than write a subroutine to round outwards to "nice" round values. Similarly, a subroutine to decide on the tick-mark spacing.
This is actually not so easy to accomplish (and ideas to prove me wrong will be gladly appreciated). Or should I say, it is easy if you know the rough range in which your values will lie. But if you don't, and you don't know
whether your values will lie in the range of 13-34 or in the 1330-3440, then ...
... if I'm on the wrong track completely here, please, explain if you ment something different. My english is somewhat lacking, so I can only hope the above is understandable.
Inside a subroutine to determine round graph start/end values, you could scale the actual min/max values to always be between 1 and 10, then have a table to pick nice round values, then unscale back to the correct range.
--
Dump Matlab because its proprietary, expensive, bloated/slow and codes are not easy to parallelize.
What you should do is use something on the lines of DISLIN, PLplot, GINO, gnuplotfortran etc.