Step size increment?

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Angela Mehta
Angela Mehta 2020-7-13
评论： Walter Roberson 2020-7-13
Hello! I am new to Matlab and this might be a very simple question but please try and help me out!
So basically, I have both initial value(k0) and w(k0), where w is a function of k. Now we can step to k1 = k0 + dk and we will have to use w(k0) as the initial guess to find w(k1) then, k2 = k1 + dk and w(k2) can be found from w(k1) so on.
I have set k as the following;
k0 = 1/2;
w(k0) = 1.4;
k= linspace(1/2, 2/3, 101);
I would like find w(k).
Thank you very much!
  2 个评论
Image Analyst
Image Analyst 2020-7-13
What is the formula for w(k)? Or how does w(k+1) depend on w(k), the prior element?
Angela Mehta
Angela Mehta 2020-7-13
编辑：Angela Mehta 2020-7-13
I have made a function that's dependent on w and k (myf2(w,k)) and I ran the function under a for loop. Here's part of the code that does that;
Nx= 201;
Ny= 301;
k0 = 1/3;
xa = 0;
xb = 5;,
ya = -3;
yb = 1;
%define x and y
x = linspace(xa, xb, Nx); %real part of w
y = linspace(ya, yb, Ny); % imag part of w
I = sqrt(-1);
for ix = 1:Nx
for iy = 1:Ny
z = x(ix) + I*y(iy);
func = @(z) myf2(z,k0);
funcp = @(z) myf2p(z,k0);
end
end
fprintf("Initial guess:\n");
[xi,yi] = ginput(1);
r0 = xi + I*yi;
r = r0;
maxit = 10; % max no of interations
%Runs Newton method
for it = 1:maxit
tol = 1e-16; %tolerance
r = newton(func, funcp, x0, tol, maxit);
format long
%fprintf("%12.12e \n", r); %12 digits
%disp(['f(x) = ' num2str(func(r))]); % residal
end
fprintf("Root: (%12.12e, %12.12e)\n", real(r), imag(r));
%%%%This is where I want to set w(k0) = real(r)
I hope that answered your question! Thanks a lot!

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Walter Roberson
Walter Roberson 2020-7-13
编辑：Walter Roberson 2020-7-13
k = linspace(1/2, 2/3, 101);
w = zeros(size(k));
w(k(1)) = 1.4;
for idx = 2 : numel(k)
w(idx) = function_to_find_w_k(k(idx), w(idx-1));
end
  2 个评论
Angela Mehta
Angela Mehta 2020-7-13
编辑：Angela Mehta 2020-7-13
Hello! I tried to use this code with my code, posted in the previous comment, I am getting an error when I set
w(k(1)) = real(r);
Error message: "Array indices must be positive integers or logical values."
I don't know the reason for it! Also apologies for setting w(k0)=1.4, I thought it might be easier that way.
Thank you very much!
Walter Roberson
Walter Roberson 2020-7-13
k = linspace(1/2, 2/3, 101);
w = zeros(size(k));
w(1) = 1.4;
for idx = 2 : numel(k)
w(idx) = function_to_find_w_k(k(idx), w(idx-1));
end

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