help with MuPAD generate::MATLAB command?

Hello all,

I've been using MuPAD since yesterday so I have zero experience with it, apologies in advance if im asking a fairly "stupid" question.

What Im trying to do is make a function from an equation in a MuPAD notepad. I defined the equations in the notepad like so:

   L := (n,x) -> besselI(n,x);
   bn := (n,k,r_s,r_e,r_i,r_o,r) -> piecewise(
                [r <= r_e, 0],
                [r_e < r and r <r_s, L(n,k*r_e)],
                [r > r_s, (L(n,k*r_e)*F(n,k,r_s,r_i,r_o))/(k*r_s)]);

and there are more equations that follow similar structure.

My final equation (which works just fine in the MuPAD environment) is:

V := (r,theta,z,r_s,r_e,r_i,r_o) -> (1/(2*PI^2))*numeric::int(cos(k*z)*sum_n(k,r_s,r_e,r_i,r_o,r,theta), k=0..infinity);

which is the one im trying to convert to an .m file with this command:

fprint(Unquoted, Text, "test.m", generate::MATLAB(V)):

to which command I get the warning message:

Warning: Translating MuPAD procedures ("V") is not implemented. [DOM_PROC::CF]

and nothing happens.

I then tried another way suggested from the documentation. In the command prompt I write:

nb = mupad('equation_system.mn');
t =matlabFunction(nb.getVar('V'))

to which I get:

Warning: Translating MuPAD procedures ("V") is not implemented. [DOM_PROC::CF] 
Error using mupadmex
Error in MuPAD command: The operand is invalid. [_index]

Evaluating: locgen

 Error in sym/matlabFunction>mup2mat (line 316)
 res = mupadmex('symobj::generateMATLAB',r.s,0);

 Error in sym/matlabFunction>mup2matcell (line 304)
    r = mup2mat(c{1});

 Error in sym/matlabFunction (line 123)
    body = mup2matcell(funs);

Can someone suggest what else I can try? Is there a limitation to the type of functions you can use to convert between MuPAD and Matlab?

Thank you for your time,

Andreas.

---------------------------------------------------------------------------

(edit to include the mupad code):

reset();
L := (n,x) -> besselI(n,x);
K := (n,x) -> besselK(n,x);
L_p := (n,x) -> besselI(n+1,x)+n*besselI(n,x)/x;
K_p := (n,x) -> n*besselK(n,x)/x - besselK(n+1,x);
eps := (r_i,r_o) -> r_i/r_o;
F := (n,k,r_s,r_i,r_o) -> 1/(eps(r_i,r_o)*K_p(n,k*r_s)*L(n,k*r_s)-K(n,k*r_s)*L_p(n,k*r_s));
an := (n,k,r_s,r_e,r_i,r_o,r) -> piecewise(
              [r <= r_e, K(n,k*r_e)+(1-eps(r_i,r_o))*L(n,k*r_e)*K(n,k*r_s)*K_p(n,k*r_s)*F(n,k,r_s,r_i,r_o)],
              [r_e < r and r <r_s, (1-eps(r_i,r_o))*L(n,k*r_e)*K(n,k*r_s)*K_p(n,k*r_s)*F(n,k,r_s,r_i,r_o)],
              [r > r_s, 0]);
 bn := (n,k,r_s,r_e,r_i,r_o,r) -> piecewise(
              [r <= r_e, 0],
              [r_e < r and r <r_s, L(n,k*r_e)],
              [r > r_s, (L(n,k*r_e)*F(n,k,r_s,r_i,r_o))/(k*r_s)]);
 gam := (n) -> piecewise([n = 0, 1], [Otherwise, 2]);

   psi_n := (n,k,r_s,r_e,r_i,r_o,r) -> an(n,k,r_s,r_e,r_i,r_o,r)*L(n,k*r) + bn(n,k,r_s,r_e,r_i,r_o,r)*K(n,k*r);
   sum_n := (k,r_s,r_e,r_i,r_o,r,phi) -> numeric::sum(gam(n)*cos(n*phi)*psi_n(n,k,r_s,r_e,r_i,r_o,r), n =0..infinity);
   V := (r,phi,z,r_s,r_e,r_i,r_o) -> (1/(2*PI^2))*numeric::int(cos(k*z)*sum_n(k,r_s,r_e,r_i,r_o,r,phi), k=0..infinity);

Answer 1

[Walter Roberson]

Try

generate::MATLAB(op(V))

and

generate::MATLAB(V(r,theta,z,r_s,r_e,r_i,r_o))

Your difficulty stems from the fact that you need to pass an expression in to generate::MATLAB, but procedures (and some other objects) evaluate to their own name instead of evaluating to their definition when they are named in isolation.

What is sum_n ? Is that one of your own procedures?

I am not sure that numeric::int can get converted to MATLAB by the generate function; I do not have the toolbox to test that with.

[Andreas]

Thank you Walter for your answer. This is the result that comes out:

fprint(Unquoted, Text, "test.m", generate::MATLAB(op(V)))
Error: Code generation failed due to an unexpected object of type 'DOM_NIL'. [generate::CFany]

and

fprint(Unquoted, Text, "test.m", generate::MATLAB(V(r,phi,z,r_s,r_e,r_i,r_o)))
Warning: Function "slot" is not verified to be a valid MATLAB function.
Warning: Function "slot" is not verified to be a valid MATLAB function.
Warning: Function "_range" is not verified to be a valid MATLAB function.
Warning: Function "_range" is not verified to be a valid MATLAB function.

This is sum_n :

sum_n := (k,r_s,r_e,r_i,r_o,r,phi) -> numeric::sum(gam(n)*cos(n*phi)*psi_n(n,k,r_s,r_e,r_i,r_o,r), n =0..infinity);

both gam(n) and psi_n(..) are piecewise functions but without any sums or integrals within them.

[Walter Roberson]

Would it be practical to show us the complete value for V(r,phi,z,r_s,r_e,r_i,r_o) including the definition for any routines it calls?

[Andreas]

I will edit my original question to include the entire mupad code

[Walter Roberson]

Bleh. Those piecewise's are creating a mess. I wonder if rewriting them as if/else would help?

The infinite numeric summation is a bit problematic to generate as MATLAB code, as MATLAB does not provide any infinite numeric summation routine.

Last time I looked around, it appeared that numeric integration could not be code generated, so you may have to generate the integral() call yourself.

There is a division by 0 when k = 0, as k*r_e becomes 0, and BesselI(n,0) can blow up, especially when n = 0 as well. Have you done an analysis to ensure that a limit exists for that combination? 0*BesselI(0,0) is potentially 0 at the limit, but you would need to prove that, and you would need to adjust the code so that it did not end up propagating NaN from the 0/0 (as 0 * NaN is NaN)

[Andreas]

Thank you for your reply! I tried before to write it in an .m file and I found these problems of NaN's and Inf's appearing. That is why I tried to solve it in MuPAD. Cases that fail to compute in Matlab, MuPAD works them out, so that is why I wanted to convert that code back into Matlab so I can integrate it with the rest of my project.

Answer 2

[Andreas]

Following up from my initial question I tried a different approach which also yields an error. I rewrote the equation definitions using:

   L := besselI(n,k*r);

I removed the '(parameter_1,parameter_2,...) ->' from the definitions.

This then generated a .m file when used the generate::MATLAB command but the file was broken and not working.

When I used the command prompt I got the following:

Warning: Function "slot" is not verified to be a valid MATLAB function. 
Warning: Function "slot" is not verified to be a valid MATLAB function. 
Warning: Function "_range" is not verified to be a valid MATLAB function. 
Warning: Function "_range" is not verified to be a valid MATLAB function. 
Error using symengine>makeFhandle (line 109)
Error: Illegal use of reserved keyword "if".

Error in symengine (line 60)

Error in sym/matlabFunction (line 125)
  g = symengine('makeFhandle',varnames,body);

Again not sure how to proceed..any help will be greatly appreciated