Obtaining a scalar value from a vector output

Hi, with the given files, if you run test-modified.m and then enzymeLeastSquares.m, you obtain the necessary inputs for running

enzymeGeneral.m

So when running finally enzymeGeneral.m, it outputs F and G.

However, the output from enzymeGeneral.m should be the scalar value of the objective F and the corresponding 2x1 gradient G.

The first I get by doing

F=norm((1/2)*(sum(y0_all)).^2)

which gives the scalar value of F. However, the correspondikng 2x1 gradient G is not returned. What is the right command? Do anyone have a link to a MATLAB page that shows the relevant command?

Thanks

Answer 1

[Voss]

% take a look at what enzymeGeneral.m is
type enzymeGeneral.m

function [result,grad_all] = enzymeGeneral(k)
N = 4; % number of experiments
result = zeros(2*N,1); % pre-allocate result arrays
grad_all = zeros(2*N,2);
dt=0.01;
T=1;
%k=[5;1];
y0_all = [2 1 1 4; 1 1 0 1];
y1_all = [1.0 0.5 0.3 2.4; 2.1 1.6 0.9 2.7];
for ii = 1:N
    y0 = y0_all(:,ii);
    y1 = y1_all(:,ii);
    [SP,grad]=enzyme(y0,k,dt,T);
    result((ii-1)*2+[1 2]) = y1-SP;
    grad_all((ii-1)*2+[1 2],:) = -grad;
end
F = (1/2)*(sum(y0_all)).^2
G =  (sum(y0_all)).*(y1_all).*(y0_all)

If you want enzymeGeneral to return the F and G it calculates, change its first line to:

function [F,G] = enzymeGeneral(k)

But then, result and grad_all are calculated for no reason and the input k is unused, so I'm not sure if that's what you want.

Anyway, here's the relevant documentation:

https://www.mathworks.com/help/matlab/ref/function.html

[Sergio]

@Voss

F and G are only the names of the vector scalar product and 2x1 gradient and k is generated in test-modified. So this can be ignored.

[Voss]

What outputs should enzymeGeneral have?

If the only outputs are F and G, then you only need y0_all and y1_all; there is no need to calculate result and grad_all because they are not used in the calculation of F and G. If you are not calculating result and grad_all, then you don't need k (or anything else besides y0_all and y1_all).

[Sergio]

@Voss . That is correct. I just had those other inputs since I used the same structure from before.

The problem is that the sum/gradient command I use in :

G =  sum((y1_all).*gradient((y1_all)))

and it should have refelcted this:

where r_i(k) is y1_all

which is supposed to give a 2x1 matrix, gives a 1 x 5 vector.

[Voss]

G =  sum(y1_all.*gradient(y1_all), 2)
%                                  ^ sum over the 2nd dimension

[Sergio]

Ah, thanks that solved the problem!

[Voss]

You're welcome!