eval() is too slow to numerically evaluate a function with X(t) and Y(t).

Hello,

I have a symbolic vector function, Vfun, that depends of two symbolic variables, X(t) and Y(t).

I want to evaluate Vfun for a series of numerical values for X and Y. Here's what I've tried. It works, but it's quite slow.

%% SETUP
syms X(t) Y(t) % (here the "(t)" isn't very relevant, but, I'll need to be able to use diff(Vfun,t) later on)

Vfun = [2*X + Y ; cos(X)*X^2 + Y^3 ; 3 + sin(Y)]; % (actually generated by an algorithm I can't change)

N = 40000;
Xnum = rand(1,N);
Ynum = rand(1,N);

%% TRYING TO EVALUATE Vfun WITH Xnum AND Ynum

tic

Mresults = zeros(3,N);

for j = 1:N
    X = Xnum(j);
    Y = Ynum(j);
    Mresults(:,j) = subs(Vfun);
end

toc

I suspect the problem lies in the subs() function.

I've tried to use matlabFunction(), but it doesn't work and I don't know how to remove the "(t)"

Any ideas? I doesn't need to be ultra-fast, just something more reasonable.

Thank you in advance

Answer 1

[James Tursa]

Something like this?

syms X(t) Y(t) 
Vfun = [2*X + Y ; cos(X)*X^2 + Y^3 ; 3 + sin(Y)]

Vfun(t) = 

syms x y
vfun = subs(Vfun,[X Y],[x y])

vfun(t) = 

f = str2func(['@(x,y)' vectorize(char(vfun))]) % explicit code with no t

f = function_handle with value:
    @(x,y)[2.*x+y;x.^2.*cos(x)+y.^3;sin(y)+3]

g = matlabFunction(vfun(0)) % using matlabFunction( ) with arbitrary t=0

g = function_handle with value:
    @(x,y)[x.*2.0+y;x.^2.*cos(x)+y.^3;sin(y)+3.0]

N = 40000;
Xnum = rand(1,N);
Ynum = rand(1,N);
fnum = f(Xnum,Ynum);
gnum = g(Xnum,Ynum);
isequal(fnum,gnum)

ans = logical
   1

[Perico Nasdemico]

It works, thank you!