Symbolic differentiation using str2sym takes too long.

My problem is to symbolically differentiate a series of functions (string expressions) as a loop operation. The previous method was using diff(sym(funstr), sym(varstr)) works about 2-times faster than the current one diff(str2sym(funstr),sym(varstr) - see examples below. Howecer, it sounds like the former can't be used in a future version. Unfoutunately, I have differentiate a few thousands functions one by one to build a Jacobian at the end, but I don't want to wait forever. Any solutions here?

tic

for k=1:1000

warning off

x=diff(sym('d/x+a*x+b+c+exp(x)+log(x)+y+z'),sym('x'));

warning on

end

toc

Elapsed time is 11.391776 seconds.

tic

for k=1:1000

x=diff(str2sym('d/x+a*x+b+c+exp(x)+log(x)+y+z'),str2sym('x'));

end

toc

Elapsed time is 27.391766 seconds.

Answer 1

[Steven Lord]

Don't redefine the variables each iteration through the loop. Define them as symbolic once and use them in the loop.

tic
syms a b c d x y z
for k = 1:1000
    xd = diff(d/x+a*x+b+c+exp(x)+log(x)+y+z, x);
end
toc

[Tae Hoon Yang]

The operation suggested was also slow. The symbolic differentiation was much faster with MATLAB 2012b, but it looks like there is a problem. If you use jacobian instead of diff, it works somewhat faster. At the end, I had to build a cell-string array for the functions and variables, respectively, and use jacobian(str2sym(function cell array), str2sym(varialbe cell array)) to get the partial derivative expressions to be modified a posteriori. I am wondering what makes the symbolic differentiation so slow compared to the previous version like MATLAB 2012b version.