Not Enough Input Arguments: Newtons Method/Jacobian Matrix

Hey all, I am getting a "not enough input arguments" in the following code in the "gradfun" line, which is the jacobian matrix of the three functions listed in the vector "fun". Can anyone help with this?

tol = 10^-9;
x0 = [-1 1 1];
x = x0(1);
y = x0(2);
z = x0(3);
fun = @(x,y,z) [x^2-y-sin(z)+1, x+1+sin(10*y)-y, (1-x)*z-y];
gradfun = @(x,y,z) [2*x, -1, -cos(z); 1, 10*cos(10*y)-1, 0;-z,-1,1-x]; 
newton(fun,gradfun,x0,tol)

The newton function, which i from a textbook of mine, is as follows:

function [root,numits] = newton(fun,gradfun,x0,tol)
% Solve fun(x)=0 using Newton's method given the function and its gradient
% gradfun starting from the initial guess x0.
x0 = x0(:); % this will force x0 to be a column vector
xold = x0+1; % this needs to be ~= x0 so that we enter the while loop
xnew = x0;
numits = 0;
n = length(x0);
%data_x=[xnew(1)];
%data_y=[xnew(2)];
while norm(xnew-xold)>tol  
    gradfxk = gradfun(xnew);
    fxk = fun(xnew);
    fxk = fxk(:); % this will force fxk to be a column vector
    
    [a,b]=size(fxk);
    if a~=n || b~=1
        error('function has wrong dimension, expecting %d x 1, but got %d x %d',n, a, b)
    end
    [a,b]=size(gradfxk);
    if a~=n || b~=n
        error('gradient has wrong dimension, expecting %d x %d, but got %d x %d',n, n, a, b)
    end
    
    xold = xnew;
    xnew = xold - (gradfxk)^{-1} * fxk, but implement as a linear solve
    xnew = xold - gradfxk \ fxk;
    numits = numits+1;
    
    plot(xnew(1), xnew(2),'-o','MarkerEdgeColor','black');
    %xlim([-5 5])
    %ylim([-80 10])
    pause(0.1)
    if (numits>=100)
        root = xnew;
        fprintf('current step:\n')
        disp(xnew)
        error('no convergence after %d iterations', numits);
    end
end
root = xnew;
root
end

[Jan]

Please post a copy of the complete message instead of paraphrasing some parts of it. Which line is "in the "gradfun" line"?

Please use the tools to format code. This improves the readability of the code.

Answer 1

[Jan]

You define gradfun with 3 inputs:

gradfun = @(x,y,z) ...

In the code you call it with 1 input:

gradfxk = gradfun(xnew);

The same happens in the next line with fun():

fxk = fun(xnew);

Either call them as

gradfxk = gradfun(xnew(1), xnew(2), xnew(3));
fxk     = fun(xnew(1), xnew(2), xnew(3));

Or define the functions as:

fun     = @(x) [x(1)^2-x(2)-sin(x(3))+1, x(1)+1+sin(10*x(2))-x(2), (1-x(1))*x(3)-x(2)];
gradfun = @(x) [2*x(1), -1, -cos(x(3)); 1, 10*cos(10*x(2))-1, 0;-x(3),-1,1-x(1)];