Deep symbolic tricks

File: deep_symbolic_tricks.m

Author: Peter Polcz <ppolcz@gmail.com>

Created on 2017. November 08.

Declare some symbolic scalar valued function

syms t x y z real
n = 2;
m = 3;
V = sym(zeros(2,3));
for i = 1:n
    for j = 1:m
        V(i,j) = str2sym(sprintf('V%d%d(t,x,y)',i,j));
    end
end

Array of symbolic scalar valued functions (indexable):

V, V(1,2)

V =

ans =

Array valued symbolic function (not indexable)

V(t,x,y) = V, V(3,1,2)

V(t, x, y) = 

ans = 

Convert back into an array of symbolic functions

V = V(t,x,y), V(1,3), dV = diff(V,x,y)

V =

ans =

dV = 

Array valued symbolic function (not indexable), but the argument is other than previously

V(t,y,z) = V, V(1,2,3)

V(t, y, z) = 

ans = 

Substritute a concrete function into V and

V12(t,x,y) = sin(x) * exp(-y)

V12(t, x, y) =

V = subs(V), dV = subs(dV)

V(t, y, z) = 

dV = 