How to write a time efficient user-defined function with local variables?

Questions
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1

I want to write a ‘Gauss’ function in my main program like the way its written in Matlab. In the following example I want to pass the variables (‘aar’ & ‘es’ are matrices and other are scalars) “aar, es, x1value, x2value, x3value, x4value, y1value, y2value, y3value, y4value” like given below. I want the output to store in detjacobs & Invdetjacobs. Kindly suggest me the correct way.

[detjacobs, Invdetjacobs] = Gauss[aar, es, x1value, x2value, x3value, x4value, y1value, y2value, y3value, y4value]


Do[
Do[
r = aar[[i]]; s = es[[j]];

			shape1 = ((1. - r) (1. - s))/4.;
			shape2 = ((1. + r) (1. - s))/4.; 
            shape3 = ((1. + r) (1. + s))/4.; 
            shape4 = ((1. - r) (1. + s))/4.;
                                      dhdr1 = 1./4. (-1. + s); 
                                      dhdr2 = (1. - s)/4.;
                                      dhdr3 = 1./4. (1. + s); 
                                      dhdr4 = -(1. + s)/4.;
                             dhds1 = 1./4. (-1. + r); 
                             dhds2 = 1./4. (-1. - r); 
                             dhds3 = (1. + r)/4.; 
                             dhds4 = (1. - r)/4.;
        
 detjacobs = {{dhdr1 x1value + dhdr2 x2value + dhdr3 x3value + 
  dhdr4 x4value, 
 dhdr1 y1value + dhdr2 y2value + dhdr3 y3value + 
  dhdr4 y4value}, {dhds1 x1value + dhds2 x2value + dhds3 x3value +
   dhds4 x4value, 
 dhds1 y1value + dhds2 y2value + dhds3 y3value + dhds4 y4value}};

Invdetjacobs = 1/detjacobs;

,{j,1,4}];

,{i,1,4}];

d.nb (6.26 KB)

2

Mathematica has at least a few ways to do it.

I assume you already looked in Help and found your answers. And I’m unsure what your Guass function is (what book what equation) (there must be many guass equations).

I do know in the old Mathematica book it could be hard to find the right section in Help (if one looked up Function one got a lesson on that keyword). However in the new Help there are tutorial related guides and suggested other readings: I assume you’ve already found your answer.

Value assignment:

{detjacobs, Invdetjacobs} = Gauss[aar_Integer, es_, x1value_, x2value_, x3value_, x4value_, y1value_, y2value_, y3value_, y4value_] := Block[ {i=1,j=1}, Do[ Do[ r = aar[[i]]; s = es[[j]],imax],jmax] ]

where the last expr evaluated is the return value (Return[value] can be used). I used Block because

 n=fun[x_]:=x+1;

does not include any facility for “local variables” which you may be used to (it actually DOES but that’s a lesson on Context[]).

Delayed assignment (value is evaluated each time variable as a value appears)

{detjacobs, Invdetjacobs} := Gauss …

Now note aar_Integer - it says this function is ignored if Guass is called with something other than. There can be many Guass each matching certain variable types or even certain patterned expressions.

3

Thanks Mr. John. This time I uploaded the notebook file. Kindly look into it. I have so many local variables. Will “Block” and" Return" commands consume more time? Actually, I am trying to write a time-efficient program.So, I thought of using this function in between to minimize time.
In Matlab, there is room to define local variables while maintaining time efficiency. How to doit in mathematica?

4

Take a look at the documentation for Module and Block for defining local variables. If evaluation speed is important, see 10 Tips for Writing Fast Mathematica Code—Wolfram Blog. Hope this helps, Ian