I am trying to make an iPhone-app that does the Monte Carlo simulation on
equations given by the user. I want the user to be able to input something like:
"2x+(y^2)" and then recieve a result.
Is there a way to parse this string and get usable variables that i can do calculations on (a library u know of perhaps)?
Take a look on compiler tools. although it might be a bit bloated, it is easy to write any "language" in it even if its just for simple mathematical expressions.
Related
I am trying to develop a model in netlogo, in which user can enter the equation for change in some variables. My question is what could be the best way to get equation input and how should i parse it and calculate results. looking for something like "mathml" which could work in netlogo.
A simple solution that doesn't involve MathML or anything of the sort would be to have your users directly enter NetLogo expressions and run those using runresult, which can take a string of NetLogo code and execute it.
Here is a simple example that uses an input box widget (with the type "String (reporter)") to allow the user to enter an arbitrary mathematical expression. The button prints the result of running the expression in the output box:
In a real world application, of course, you would have to be very careful about error handling.
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 often have function such as:
sin(a*w*t + p)
where:
w = natural frequency
t = time
a,p = parameters (which I can vary)
As you can see if you want to vary a,p, you can do so via the standard interface but it's not very convenient. So I thought I'd look for a GUI which has a slider for each parameter. Does such a thing exist?
I've never seen one so I thought I'd quickly write one. However, I'm worried that due to lack of time and knowledge of matlab I will cause problems such as generating too many plot commands when the slider is moved instead of just one. Of course I also have the problem that I want to specify a field where the user can specify the function e.g. by typing sin(a*w*t +p) in a text field and then specify what each variable means which I currently don't know how to do (it looks like a parsing task). Can I do this or should I go with a predefined set of functions?
You can find similar projects in Matlab File Exchange as example.
For instance:
Integral Tool
Function Parameter Slider
I didn't have a look at the code but according to the screenshots, it should help you.
Regarding the function input feature, you can use the function eval (with a few checks on the input if you need reliability). If you want to allow any parametric variable, it may be harder.
Matlab Coder is a recently released MathWorks product. My understanding is that it is a Matlab-to-C compiler with the biggest advantage over previous solutions being that the resulting program does not need to be linked against a Matlab shared library.
Can someone with access to this product confirm the above? What are the dependencies of the translated programs and what kind of performance are we talking about? Also I would really like to see some example outputs, to know if the resulting C programs can be understood and improved without access to the Matlab source.
If done right this could be very powerful, allowing rapid prototyping in Matlab and instantaneous conversion to C when things are getting serious. I kind of whish it doesn't work well so that Python+Numpy+Scipy.weave is still superior ^^.
MATLAB Coder can allocate memory using malloc, so you can generate C code from MATLAB functions that operate on dynamically sized data. You can also choose the option of static allocation with a maximum size for variables.
RE: using BLAS for matrix multiplication – while the generated C code doesn’t automatically include any processor/platform specific optimizations, there is a feature called Target Function Library, which that allows users to write their own implementation of primitive operations (such as matrix multiplication), and include them in the generated code. You can hook up BLAS libraries to MATLAB Coder via that method. There’s also an ability to include optimized processor specific calls for larger functions through custom code integration and conditional compilation that lets you specify one set of code to use for code generation, and another set for simulation (for example, an optimized FIR function for an Texas Instruments DSP and functionally equivalent code for simulation that can execute on your PC written in C or in MATLAB).
Hope this is helpful --
Arvind Ananthan; Product Manager for MATLAB Coder; MathWorks
I am using Matlab Coder with Real Time Workshop (RTW) in order to generate self standind standard C code.
First of all you are asked to use a Matlab subset called "Embedded Matlab" you can find the doc about it on the web
You also have to avoid any dynamic exploitation of variables and you can't obviously generate c code for plots or figures.
The code it generates could be a mess to understand but it works.
you should actually not try to understand it. In a certain way it is as you would try to understand the assembler your compiler generates from a C code you wrote, quite pointless.
another thing you should take care of is to declare persistent big data types (vectors, big arryes, etc.) otherwise they will be allocated into your stack...
good luck!
I have variables which are of double type I want them to be float. Is there a way to force a variable to be float and not double, also, Is there a way to do it in some global way for all functions and sub functions with few lines at the start of the main function? I have many functions and they use many temporary variables and create variables that they return. Going over all of my functions and changing them will be very difficult.
My rational for this request:
I'm writing the MATLAB program in order to simulate an algorithm which I'll then implement in hardware, I want to make sure that using 32bit as the size of my signals will not cause calculation errors.
Using B=single(A) as suggested by #cbz, or defining arrays as SINGLE, such as by calling B=zeros(3,3,'single') creates "floats" in Matlab.
There is no way to globally turn Matlab into a "float" environment. Although most lower-level functions are implemented for single as well (with a few exceptions, for example those mentioned in the help to DOUBLE), many high-level builtin functions will only work with double.
In other words, you'll have to manually define your variables as single, you'll have to periodically check that the variables haven't been quietly converted to double, and in the end, your code might not work if it needs a function that isn't implemented for single yet.
The MATLAB equivalent to 'float' is 'single. You can convert using
B = single(A).
That said, your assumption that this amounts to 32-bit might need revisiting. It's not as simple as that.