MATLAB: Symbolic variables – how to force Matlab to substitute it with real value

MATLABsymbolic

Hello,
I have a slight problem with my work and I was hoping maybe someone knows some easy solution I do not (I'm not a pro with Matlab:))
I am calculating symbolic variables (gradient, to be precise) through function and returning it to my main program. The equation has variables: z1, z2 and theta, which are all numeric values inside my main program. But I have no idea how to make Matlab substitute symbolic with real values. I tried to just copy the symbolic equation I got into the program, but it is really complicated and long and it slows my Matlab to the point it don't want to work properly (is it possible? I was over 25 000 characters long).
Is there any command, function, whatever, to just substitute symbolic with real values? It would be like life saver:).

Best Answer

There are two ways:
1. The subs function will work in all version of the MATLAB Symbolic Math Toolbox;
2. From R2012a onward, you can define symbolic functions. They operate essentially the same way as other MATLAB functions.
Example:
syms t x
y1 = sin(x*t)
y2(x,t) = cos(x*t)
a = 1;
b = [0:0.5:1.5];
y1_out = subs(y1,{x,t},{a,b})
y2_out = y2(a,b)
y1_out =
[ 0, sin(1/2), sin(1), sin(3/2)]
y2_out =
[ 1, cos(1/2), cos(1), cos(3/2)]
Use the vpa function to get floating-point numbers instead of the symbolic expressions:
q1 = vpa(y1_out)
q2 = vpa(y2_out)
q1 =
[ 0, 0.47942553860420300027328793521557, 0.8414709848078965066525023216303, 0.99749498660405443094172337114149]
q2 =
[ 1.0, 0.87758256189037271611628158260383, 0.54030230586813971740093660744298, 0.070737201667702910088189851434269]
See the Symbolic Math Toolbox documentation to learn all the details.
EDIT —
3. If you want to get an executable function from your expression that you can execute in core MATLAB (outside the Symbolic Math Toolbox), use the matlabFunction function:
yfcn = matlabFunction([y1; y2])
yfcn = @(x,t)[sin(t.*x);cos(t.*x)]                          % Manually Edit To Put It All On One Line
q3 = yfcn(a,b)
q3 =
            0      0.47943      0.84147      0.99749
            1      0.87758       0.5403     0.070737
Still waking up, or I’d have included that earlier.
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