Mini-project Advice and Help

Here is a sketch of what your code should look like:

function main
	global % List parameters you need to communicate to "my_objectives"
           % such as weights, endpoints  (no commas)
	% Set the physical parameter values,
	% and code parameters like the number of morphing steps, 
	% newton tol, etc. 
	% Set your initial guesses at x's, y's and t's:
	% load them into a single vector V with 16 elements.
	V = 
	hold off
	for m=1:n_morphing_steps
		xnplus1 = 
		ynplus1 = 
		V = newton(@my_objectives,V,tol,maxits)
		% plot configuration
		hold on
	end

end

function r=newton(f,x0,tol,maxits)
	% Totally general newton's method.
	% Calls fdjac(f,x) to get jacobian at x.
	% Use backslash operator, not "inv".
end

function fdjac(f,x)
	% exactly as I emailed it to you: no changes needed
end

function F = my_objectives(V)
	global % List parameters you need here such as weights, endpoints
	x = V(1:5);  % or maybe x = [x0;V(1:5);xnplus1]
	y = V(6:10);
	t = V(11:16);
	F = zeros(16,1);
    % set all 16 function values
    F(1) = % ... (or use loops)
	% ...
	F(16) = 
end

BROYDEN does not work: use true newton's method, and use fdjac.m to approximate the jacobian for each newton step.

RULE 1: Develop code piece by piece, and test each piece separately on simple cases where you know what the result should be. DO NOT WRITE CODE ALL AT ONCE FOR THE ACTUAL 16D PROBLEM AND EXPECT IT TO WORK. For example, test your newton code with fdjac on the 2D problem from HW5.

RULE 2: Keep all code specific to the hanging objects problem separate from general code. For example, your newton function should have nothing at all in it that refers to the specific objects-dangling-from-a-string problem we'll be using it to solve.

Your code should have at least 3 functions: the main one that sets the parameters and contains the morphing loop, a function "newton" that implements Newton's method using fdjac for jacobian evaluation, and a function that evaluates the 16 components of our objective function F.