Converting anonymous function to a matrix

I have a function of the form:

,

which I want to evaluate. I could do this old school with a double loop but that would take time, so I thought I would try and use an anonymous function. So I did the following:

f_1=@(x,y) (erf(x+y)-erf(x-y));
f_2=@(x,y) (exp(x*y+2*x));
f=@(x,y) (f_1*f_2);

Now when I do individual values, like f_1(1,1), it works as it should. However when I compute say f(1,1) I get the following error:

Undefined operator '*' for input arguments of type 'function_handle'.

Error in @(x,y)(f_1*f_2)

When I do the function in one fell swoop:

f=@(x,y) (exp(x*y+2*x)*(erf(x+y)-erf(x-y)));

It works unsurpringly.

Now, I also want to be able to do say

x=linspace(-2,2,10);y==linspace(-2,2,10);

and get a nice matrix out of it, but when I then do:

a=f(x,y);

I don't get the nice matrix I wanted. So there are two questions I want to ask:

1. How can I build up anonymous functions from other anonymous functions
2. How can I get a matrix from inputting two vectors?

Answer 1

[Stephen23]

"How can I build up anonymous functions from other anonymous functions"

Just call the functions, exactly like you would any other type of function:

f_1 = @(x,y) erf(x+y)-erf(x-y);
f_2 = @(x,y) exp(x*y+2*x);
f   = @(x,y) f_1(x,y)*f_2(x,y); % you need to call them!

"How can I get a matrix from inputting two vectors?"

That depends on which version of MATLAB you are using and what operations your code contains.

Method one: vectorize: If you are using a version >=R2016b then make sure that you vectorize the operations, e.g. using element-wise array operations instead of matrix operations:

f_2 = @(x,y) exp(x.*y+2*x);
%                 ^^ array operation!

and then call the function with one row vector and one column vector. For earlier versions you will instead need to use bsxfun for any operation that involves different sized arrays.

https://www.mathworks.com/help/matlab/matlab_prog/vectorization.html

Method two: arrayfun: Otherwise you can generate the required matrices using ndgrid and use a loop or arrayfun:

>> f_1=@(x,y) (erf(x+y)-erf(x-y));
>> f_2=@(x,y) (exp(x*y+2*x));
>> f  =@(x,y) (f_1(x,y)*f_2(x,y));
>> x = linspace(-2,2,10);
>> y = linspace(-2,2,10);
>> [xM,yM] = ndgrid(x,y);
>> zM = arrayfun(f,xM,yM)
zM =
           -1     -0.21775    -0.035275   -0.0041123  -0.00029302   0.00012046   0.00028574   0.00041426   0.00043219   0.00033546
      -1.4703     -0.50089     -0.13285    -0.026021   -0.0029847     0.001495    0.0032701    0.0041888    0.0039625    0.0029184
      -1.7913     -0.89723     -0.37183     -0.11768    -0.020722     0.012646     0.026748     0.031478     0.028291     0.021036
      -1.9405      -1.3307     -0.80635     -0.38671    -0.098104     0.072947      0.15898      0.18328      0.16723      0.13483
      -1.9864      -1.7473      -1.4215      -0.9381     -0.31685      0.28705      0.69754      0.86751      0.87523      0.81663
      -1.9864      -2.1289      -2.1102      -1.6967     -0.69822       0.7707       2.2819       3.4577       4.2503       4.8318
      -1.9405      -2.4068      -2.6378      -2.2881      -1.0498       1.4119       5.5656       11.605       19.151       27.927
      -1.7913       -2.409      -2.6804      -2.2777      -1.0768       1.7645       10.021       31.662       76.402       152.53
      -1.4703      -1.9964      -2.1104      -1.6475     -0.75323       1.5038        13.11       66.931       252.36       740.79
           -1      -1.2883      -1.2349     -0.85177     -0.35909      0.87347       12.259       105.15       649.09         2981

[Matthew Hunt]

I also want to be able to integrate over q to obtain a vector in k. Would I use method 2 in that case?