Get row of functions from a matrix of functions - matlab

Question

Before overwhelming you with examples where I try to encapsulate every aspect of my issue I'll try to just state the problem as simply as possible:
If f11 , ... , fnm is n*m real valued funtions that I wish to evaluate m at a time in n steps, through some higher order function b i.e.
v = []
f1 = #(x) [f11(x) f12(x) ... f1m(x)]
v = [v b(f1)]
f2 = #(x) [f21(x) f22(x) ... f2m(x)]
v = [v b(f2)]
How would I solve this through iteration? i.e. something like this:
f = #(x) [f11(x) ... f1m(x) ; ... ; fn1(x) ... fnm(x)];
% now iterate over the rows of f
for i=1:n
v = [v b(f(i,:)) ]
end
Here's an example of what I have (it grew in order to not miss out any details of my actual real-world problem but I have tried to make it as small as possible):
% 4 functions that take a 1x2 real valued vector as argument
% and return a real value
f11 = #(x) x(1) + x(2);
f12 = #(x) x(1) - x(2);
f21 = #(x) x(2) - x(1);
f22 = #(x) x(1) * x(2);
% we'll run function b for 2 steps, then 4 steps
steps = [2 4];
% start value
x = [1 2];
% vector to hold results
v = []
% get the result of passing the 1:st 2 functions to b with steps(1)
f1 = #(x) [f11(x) f12(x)];
v = [v ;b(x, f1, steps(1))]
% update x
x = v(end,:)
% add the result of passing the 2:nd 2 functions to b with steps(2)
f2 = #(x) [f21(x) f22(x)];
v = [v ;b(x, f2, steps(2))];
% update x
x = v(end,:)
Where b is a function defined as follows:
function [ X ] = b( x, f, n )
% #param:
% x = an 1x2 real valued vector
% f = a real valued function returning
% a 1x2 real valued vector
% n = an integer defining the rows of return matrix
%
% #return:
% X = an nx2 real valued matrix defined as below
X = zeros(n,2);
for i=1:n
% apply the functions on x
a = f(x+1);
b = f(x+2);
% update x
x = a+b
% add x to return matrix
X(i,:) = x;
end
end
The above code could be generalized as:
% n*m functions that take a 1xm real valued vector as argument
% and return a real value
f11 = #(x) ... ;
f12 = #(x) ... ;
.
.
.
fnm = #(x) ... ;
% we'll run function b for a1 steps, then a2 steps, ... , then an steps
steps = [a1 a2 ... an];
% start value
x = [1 2 ... m];
% vector to hold results
v = []
% get the result of passing the 1:st m functions to b with steps(1)
f1 = #(x) [f11(x) ... f1m(x)];
v = [v ;b(x, f1, steps(1))]
% update x
x = v(end,:)
% add the result of passing the 2:nd m functions to b with steps(2)
f2 = #(x) [f21(x) ... f2m(x)];
v = [v ;b(x, f2, steps(2))];
% update x
x = v(end,:)
.
.
.
% add the result of passing the n:ed m functions to b with steps(n)
fn = #(x) [fn1(x) ... fnm(x)];
v = [v ;b(x, fn, steps(n))];
% update x
x = v(end,:)
Where b is any function that returns an steps(i) x m matrix.
I wonder if both the small concrete example and the general example should be solvable through a general iteration, something like this:
% let f hold all the functions as a matrix
f = #(x) [f11(x) ... f1m(x) ; ... ; fn1(x) ... fnm(x)];
% now iterate over the rows of f
for i=1:n
v = [v ; b(x, f(i,:), steps(i)) ]
end

Answer 1

So the trick is in defining your functions as a cell matrix and then using some vectorization to solve the problem. This is the code that I came up with:
%First define your functions in a cell matrix
fn_mat = {#(x) x(1) + x(2), #(x) x(1) - x(2); ...
#(x) x(2) - x(1), #(x) x(1) * x(2)};
%Store the sixe of this matrix in two variables
[n, m] = size(fn_mat);
%Number of steps
steps = [2, 4];
% start value
x = [1 2];
% vector to hold results
v = [];
%This will run the required code for n iterations
for ii = 1:n
%This is the tricky part. What I have done is used arrayfun to run over
%all the functions in the row defined by ii and pass x as an argument
%each time. The rest is same as before
fn = #(x) arrayfun(#(a, b) fn_mat{ii, a}(b{:}), 1:m, repmat({x}, 1, m));
v = [v; b(x, fn, steps(ii))];
x = v(ii, :);
end
For the current values, the output is:
v =
12 -2
26 28
-28 -13
30 610
1160 38525
74730 89497060
The for loop is general enough to accommodate any size of fn_mat.