How do I extract one point from a piecewise function?

I have two piecewise functions M_xy and M_xz, which are both 1x1 syms. These function have been plotted, so I know they're structured correctly. I need to know their values at a specific point (i.e. x = 3.75) so I can alter those numbers by taking the root mean square ( sqrt( (M_xz(3.75))^2 + (M_xy(3.75))^2 ). How can I do this? I'm struggling to find any explanations online anywhere.

Answer 1

[Paul]

Hi Allie,

If M_xy and M_xz are sym objects, like so

syms t
M_xy = piecewise(t < 0, 0, t > 0, t);
M_xz = piecewise(t < 0, 0, t > 0, 2*t);

then use subs to evaluate each and operate on the results

r = sqrt( subs(M_xy,t,3.75)^2 + subs(M_xz,t,3.75)^2 )

r = 

Or if using symfun objects, then

M_xy(t) = piecewise(t < 0, 0, t > 0, t);
M_xz(t) = piecewise(t < 0, 0, t > 0, 2*t);

r = sqrt(M_xy(3.75)^2 + M_xz(3.75)^2)

r = 

Answer 2

[John D'Errico]

You can define a piecewise function as a symbolic function. For example...

syms t
M_xy(t) = piecewise(t < 0, 0, t > 0, t); % Note the change to M_xy, making it a function.
M_xz(t) = piecewise(t < 0, 0, t > 0, 2*t);

r = sqrt(M_xy(3.75)^2 + M_xz(3.75)^2)

r = 

That is, you can now evaluate these things directly as functions of t. If you wanted to define r itself as a function of t, you could have done this

r(t) = sqrt(M_xy(t)^2 + M_xz(t)^2);

And now r is itself a function you can evaluate.

r(3.75)

ans = 

(Which is the same number as before. Strangely, it did not decide to simplify that result.) Anyway, you can even use r in a vectorized form.

r(1:.5:4)

ans = 

And of course, we can turn these into doubles, or you can use vpa.

double(r(3.75))

ans = 8.3853