How to do numerical computations?
in [Mathematica]
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From: bagarti on 31 Mar 2010 06:27 Hello, Any body please help me, I have written some mathematica code which contains some complicated functions.The functions involve integrations and iterations in the intermediate steps. When I run the code it takes a hell lot of time. I do not know what mathematica is doing inside, actually I have another code in fortran that takes only a few minutes to do all the calculations but there are other problems like it dosent work for some parameter range. Is there a method in which I can ask mathematica to give me only the numerical values just like any executable program does. Thanks. TaB
From: Bill Rowe on 1 Apr 2010 07:00 On 3/31/10 at 5:28 AM, bagarti(a)gmail.com (bagarti) wrote: >I have written some mathematica code which contains some complicated >functions.The functions involve integrations and iterations in the >intermediate steps. When I run the code it takes a hell lot of time. >I do not know what mathematica is doing inside, actually I have >another code in fortran that takes only a few minutes to do all the >calculations but there are other problems like it dosent work for >some parameter range. >Is there a method in which I can ask mathematica to give me only the >numerical values just like any executable program does. The way to get Mathematica to return only numerical values is to use functions that begin with a upper case N. For example, NIntegrate does a numerical integration while Integrate will do a symbolic integration. Note, doing N[Integrate[..]] is not equivalent to doing NIntegrate[...] in general. But I don't know that this helps or making these changes would improve the speed of execution. Improving the execution speed is very much dependent on the details of you code. One thing to be careful about. Coming from a background in a procedural language like Fortran, you probably tend to want to use explicit For loops. While Mathematica supports For, code written using For typically runs much slower than other means of getting exactly the same answer. Compare the results below: In[1]:= Timing[For[sum = n = 0, n < 10^6, n++, sum += n]; sum] Out[1]= {2.99546,499999500000} In[2]:= Timing[Plus @@ Range[10^6 - 1]] Out[2]= {0.275468,499999500000} In[3]:= Timing[Total[Range[10^6 - 1]]] Out[3]= {0.22101,499999500000} In[5]:= Timing[Sum[n, {n, 10^6 - 1}]] Out[5]= {0.250184,499999500000} In[6]:= Timing[Sum[n, {n, k}] /. k -> 10^6 - 1] Out[6]= {0.063701,499999500000} All methods give the same answer but the code with the explicit =46or loop runs more than 10 times slower than the next slowest method of summing a range of values.
From: Nasser M. Abbasi on 1 Apr 2010 07:01 "bagarti" <bagarti(a)gmail.com> wrote in message news:hov834$94q$1(a)smc.vnet.net... > Hello, > Any body please help me, > > I have written some mathematica code which contains some complicated > functions.The functions involve integrations and iterations in the > intermediate steps. When I run the code it takes a hell lot of time. I do > not know what mathematica is doing inside, actually I have another code in > fortran that takes only a few minutes to do all the calculations but there > are other problems like it dosent work for some parameter range. > > Is there a method in which I can ask mathematica to give me only the > numerical values just like any executable program does. > > Thanks. > TaB > Symbolic computation is very useful for the analysis and the investigation of a problem analytically. (funny thing to say, because how else would one do this other by symbolic computation?) But when it comes to solving the problem on a large scale, and for speed, I think you want to switch to numerical computation. This could be as easily as warping N[] around an expression, or having the initial parameters be floating point values instead of rational (i.e. for the values of the variables used, write 1.0/2 or 0.5 instead of 1/2 and write 1.0 instead of 1). There is a cascading effect here, if one variable is floating point, then the calculation of the expression which this variable is in will be done numerically and will be normally faster. Also, try to use functions such as NIntegrate and NSolve and NDSolve instead of the symbolic versions. I wrote a small finite elements program last year in Mathematica, and it was very slow when the number of elements and the stiffness matrix became large, this is because at first I kept everything in symbolic form, so all the terms were in symbolic form until the end when I substitute numerical values for the variables. When I started to make some of the changes above, and to assign a numerical values for the variables early on, the program ran much much faster than before. --Nasser
From: Manfred Plagmann on 1 Apr 2010 07:01 On Mar 31, 11:27 pm, bagarti <baga...(a)gmail.com> wrote: > Hello, > Any body please help me, > > I have written some mathematica code which contains some complicated functions.The functions involve integrations and iterations in the intermediate steps. When I run the code it takes a hell lot of time. I do not know what mathematica is doing inside, actually I have another code in fortran that takes only a few minutes to do all the calculations but there are other problems like it dosent work for some parameter range. > > Is there a method in which I can ask mathematica to give me only the numerical values just like any executable program does. > > Thanks. > TaB Many analytical functions with in Mathematica have numerical counterparts for example Integrate[] has NIntegrate[]. You can use those to get numerical results. If your code is very slow this could have many reasons and without giving an example of what you are doing it will be hard to help you. Keep in mind that Mathematica is interpreted and not compiled Fortran code. I hope this helps. Manfred
From: dr DanW on 1 Apr 2010 07:01
I'm taking a guess that you have a fairly complicated Block[] or Module[] with an integration that involves some parameters. Mathematica is hitting that integration and trying to evaluate it symbolically, which can be time consuming. I think what you want to do is prevent that integration from evaluating until it gets numerical values for the parameters. One way to do this is to create a function out of the integration that requires numerical input. A trivial example is int[a_?NumericQ] := NIntegrate[ Sin[x] , {x, 0, a} ] This way, when you say b = int[c] where c has no value, Mathematica will hold it as int[c] and not attempt a symbolic evaluation. Later, you can say c = 3., and the numerical integration can be evaluated quite quickly. Daniel |