Linear transformation function handle

Question

Assume I have the legendre polynomials in cell Array P as function handles. Now I use the linear transformation x = 2/3*t-1. Now I want to get a cell array Q which has the transformation function handle. So P = [1, @(x) x, 1/2*(3*x^2-1),...] to Q = [1,@(t) 2/3*t-1,...]

Thanks!

Answer 1

Assuming you have the Symbolic Toolbox, you can do it this way:

1. Convert your cell array of anonymous functions to a cell array of strings
2. Do the change of variable using subs. This produces symbolic objects as output.
3. Convert from symbolic objects to anonymous functions using matlabFunction:

Code:

P = {@(x) 1, @(x) x, @(x) 1/2*(3*x^2-1)};        %// data 
f = cellfun(@func2str, P, 'uniformoutput', 0);   %// step 1
Q = arrayfun(@(k) matlabFunction(subs(f{k}(5:end), 'x', '2/3*t-1')), 1:numel(P),...
    'uniformoutput', 0);                         %// steps 2 and 3.
    %// Note that the "(5:end)" part is used for removing the initial "@(x)"
    %// from the string obtained from the function

Result in this example:

Q{1} =
    @()1.0
Q{2} =
    @(t)t.*(2.0./3.0)-1.0
Q{3} =
    @(t)(t.*(2.0./3.0)-1.0).^2.*(3.0./2.0)-1.0./2.0