Index issue while using gradient of a function

Hello,

I am attempting to take the gradient of a function and use that as a varaible in matlab function in order to calculate a specific matrix of values.

I currently am taking the gradient by the following code, where fun is the function I need to take the gradient of:

syms x [1 2]
fun = -9*x(1) -10*x(2) + theta*(-log(100-x(1)-x(2))-log(x(1))-log(x(2)) - log(50-x(1)+x(2)));
grad_fun = gradient(fun, x);

x0 = [8 90]'; % change this for different sub-problems in the homework
choice = 1; % 1 = bisection; 2 = Armijo


[alpha, F, X]= steepestdescent(fun,grad_fun,eps,x0,choice,stp_eps);

I then have another script that I am writing a rather long function within that needs to use the grad_fun at various points, I thus have the following:

function [out1, out2, out3] = steepestdescent(fun,grad_fun,eps,x0,choice,stp_eps)
    if choice == 1
        X=[]; D=[]; A=[]; F=[];
        X(:,1)= x0; %initialize state
        D(:,1)= -grad_fun(x0); %initial direction

However, in my debugging process, I keep getting an error when I reach D(:,1) that states

Index exceeds the number of array elements (2).

Error in sym/subsref (line 902)

R_tilde = builtin('subsref',L_tilde,Idx);

Error in steepestdescent (line 7)

D(:,1)= -grad_fun(x0); %initial direction

Error in HW4_3 (line 45)

[alpha, F, X]= steepestdescent(fun,grad_fun,eps,x0,choice,stp_eps);

The last element of the error, where it states Error HW4_3 (line 45) I know is associated with my use of grad_fun in my use of the function at the bottom of the first block of code, but I cant figure out why grad_fun is not returning the proper elements.

The gradient should hopefully take in the function fun, take its gradient, save that symbolic gradeint in a 2x1 matrix, then when the grad_fun function is called, be able to plug in the values for x0 and return a 2x1 matrix of two doubles that can then be stored and used elsewhere in the code.

Let me know if I need to clarify anything, thank you.

Answer 1

[Walter Roberson]

grad_fun is a vector not a function. You cannot use () notation to evaluate it, you have to use subs. Or use matlabFunction to turn it into a function handle (and be sure to use the option 'vars',{x} for that)

[Braden Kerr]

Okay,I see how its a vector and thus cant take an input. Would you recommend using a notation something akin to this then:

grad_fun = @(x) [theta((1/(-x(1)+x(2)+50))-(1/(x(1)+x(2)-100))-(1/x(1)))-9,...
theta((-1/(x(1)+x(2)-100))+(1/(x(1)-x(2)-50))-(1/x(2)))-9]

Where the two elements of that array are the two partial derivities of the original function fun but simply typed out after I found them by hand?

[Braden Kerr]

Wait, I believe I understand how to use the subs function, it would be somethign like this then?

syms x [1 2]
fun = -9*x(1) -10*x(2) + theta*(-log(100-x(1)-x(2))-log(x(1))-log(x(2)) - log(50-x(1)+x(2)));
grad_fun = matlabFunction(gradient(fun, 'vars', {x}));



D(:,1)= -grad_fun(x0); %initial direction

[Walter Roberson]

grad_fun = matlabFunction(gradient(fun), 'vars', {x});

[Braden Kerr]

I still get an indexing error in this line below

D(:,1)= -grad_fun(x0); %initial direction

For reference, here are both parts of the code that involve what im attempting to solve

syms x [1 2]
fun = -9*x(1) -10*x(2) + theta*(-log(100-x(1)-x(2))-log(x(1))-log(x(2)) - log(50-x(1)+x(2)));
grad_fun = matlabFunction(gradient(fun), 'vars', {x});

x0 = [8 90]'; % change this for different sub-problems in the homework
choice = 1; % 1 = bisection; 2 = Armijo


[alpha, F, X]= steepestdescent(fun,grad_fun,eps,x0,choice,stp_eps);

Then the other script now holds

function [out1, out2, out3] = steepestdescent(fun,grad_fun,eps,x0,choice,stp_eps)
    if choice == 1
        X=[]; D=[]; A=[]; F=[];
        X(:,1)= x0; %initialize state
        D(:,1)= -grad_fun(x0); %initial direction
        %And the ret of the function that isnt included here 

[Braden Kerr]

Actually, just figued it out. If anyone reads this thread, the issue is that x0 is a 2x1 matric while the function grad_fun needed a 1x2 matrix. By adjusting the argument of grad_fun(x0) to grad_fun(x0') it worked