Symbolic variables - how to force Matlab to substitute it with real value

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:).

Answer 1

[Star Strider]

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.

[Magdalena Mikolajczyk]

Thank you! The subs function did the trick for me, I knew I was missing something:)

[Star Strider]

My pleasure!