Substituting values in a symbolic expression, it doesn't throw the expected values

Hello MATLAB Community,

I've got this symbolic matrix made by the symbolic vector q values :

q = sym('q',[6 1],'real');

% J generation process here. The solution, is present in the .txt file as J (too heavy to just post it)

J = [ ... ]

Until here, everything is alright. However I'm having trouble when I try to substitute values in it, getting wrong answers.

q_des = [0.088026003561672   0.667678035326211   0.121424602485228   0.000000000000068   0.781693688983434   0.088026003561606]';
J1 = [ ... ] % Matrix present in the .txt file as J1

The output is:

J1 =

  -0.049283892702272  -0.051798667044203  -0.333398260713620  -0.004025626985947  -0.064748333805210                   0
   0.558431958260024  -0.004571443147132  -0.029423753180835   0.045614066538309  -0.005714303933907                   0
                   0  -0.490602492044063  -0.267703341011117   0.000000000000002  -0.000000000000002                   0
                 NaN                 NaN                 NaN                 NaN                 NaN                 NaN
   0.000000595347956                   0                   0  -0.000000422426208   0.000000000931323  -0.000000595347956
  -0.000000000000004   0.000000000000006   0.000000000000006  -0.000000000000005   0.000000000000006   0.000000000000004
                 NaN                 NaN                 NaN                 NaN                 NaN                 NaN
                 

This is weird, because from my knowledge of the physical system this matrix is modelling, these values can't be correct. Trying out with the function subs():

J2 = double(subs(J,q,q_des));

And the result is:

J2 =

  -0.049283892702272  -0.051798667044203  -0.333398260713620  -0.004025626985947  -0.064748333805210                   0
   0.558431958260024  -0.004571443147132  -0.029423753180835   0.045614066538309  -0.005714303933907                   0
                   0  -0.490602492044063  -0.267703341011117   0.000000000000002  -0.000000000000002                   0
  -0.000000000000012  -0.498064106193923  -0.498064106193923  -0.030966361430369  -0.498064106193925  -0.000000000000012
  -0.500000000000000   0.000000000000012   0.000000000000012   0.354860691160197  -0.000000000000012   0.500000000000000
  -0.000000000000004   0.000000000000006   0.000000000000006  -0.000000000000005   0.000000000000006   0.000000000000004
   0.000000000000005  -0.043956184107000  -0.043956184107000   0.350877434910071  -0.043956184106976   0.000000000000005

Which makes much more sense. The final 4 rows of equations in J seem to be the problematic ones. But why? What is the internal explanation of this anomaly, and more important, how can I get the proper result without using subs(), which is extremely slow? I need it to implement it in a Simulink Function, with plenty of iterations.

Thank you for your time,

• JOSE

[Walter Roberson]

The denominator in row 4 comes out as 0 to within the precision available with double precision.

When you use subs() then higher precision is available and non-zero denominator can be found.

[Jose Antonio Aliaga]

And is there any way of achieving this higher precision without subs()?

[Walter Roberson]

Yes, you can use https://www.mathworks.com/matlabcentral/fileexchange/36534-hpf-a-big-decimal-class

[Jose Antonio Aliaga]

Hello, thank you for the library. I've tried it, but for numerous iterations in a Simulink model, it's even slower than subs(). I guess I'm just stuck here.

[Walter Roberson]

You could experiment. Instead of using subs, define q_des as a vector of symbolic numbers by using sym() around the expression. In particular you might want the sym(expression,'d') form.