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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 = [ V11(t, x, y), V12(t, x, y), V13(t, x, y)] [ V21(t, x, y), V22(t, x, y), V23(t, x, y)] ans = V12(t, x, y)
Array valued symbolic function (not indexable)
V(t,x,y) = V, V(3,1,2)
V(t, x, y) = [ V11(t, x, y), V12(t, x, y), V13(t, x, y)] [ V21(t, x, y), V22(t, x, y), V23(t, x, y)] ans = [ V11(3, 1, 2), V12(3, 1, 2), V13(3, 1, 2)] [ V21(3, 1, 2), V22(3, 1, 2), V23(3, 1, 2)]
Convert back into an array of symbolic functions
V = V(t,x,y), V(1,3), dV = diff(V,x,y)
V = [ V11(t, x, y), V12(t, x, y), V13(t, x, y)] [ V21(t, x, y), V22(t, x, y), V23(t, x, y)] ans = V13(t, x, y) dV = [ diff(V11(t, x, y), x, y), diff(V12(t, x, y), x, y), diff(V13(t, x, y), x, y)] [ diff(V21(t, x, y), x, y), diff(V22(t, x, y), x, y), diff(V23(t, x, y), x, y)]
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) = [ V11(t, x, y), V12(t, x, y), V13(t, x, y)] [ V21(t, x, y), V22(t, x, y), V23(t, x, y)] ans = [ V11(1, x, 2), V12(1, x, 2), V13(1, x, 2)] [ V21(1, x, 2), V22(1, x, 2), V23(1, x, 2)]
Substritute a concrete function into $V$ and $\frac{\partial^2 V}{\partial x \partial y}$
V12(t,x,y) = sin(x) * exp(-y)
V = subs(V), dV = subs(dV)
V12(t, x, y) = exp(-y)*sin(x) V(t, y, z) = [ V11(t, x, y), exp(-y)*sin(x), V13(t, x, y)] [ V21(t, x, y), V22(t, x, y), V23(t, x, y)] dV = [ diff(V11(t, x, y), x, y), -exp(-y)*cos(x), diff(V13(t, x, y), x, y)] [ diff(V21(t, x, y), x, y), diff(V22(t, x, y), x, y), diff(V23(t, x, y), x, y)]