When does one need to index for plotting

I refer to this question:

https://se.mathworks.com/matlabcentral/answers/452737-problem-with-plotting-a-semilog-function?s_tid=mlc_ans_email_view#comment_686479

I previously never indexed when I filled with values in a while loop and the values were saved in the vector.

But in that case I needed to do :

    iterations(iter) = iter
    error(iter) = norm(x-x_ref)

to make sure the values were saved in the vector and adapt automatically.

Can someone explain why is that, when manipulating vectors, sometimes you need to iterate with an index and sometimes not?

Answer 1

[Walter Roberson]

You do not need indexing when you have vectorized code. For example,

x = linspace(0, 2*pi, 500);
y = sin(x) .* cos(x.^2);
plot(x, y);

All of the values are produced at the same time.

You do need indexing when you are producing only part of the answer at a time. For example,

x = linspace(0, 2*pi, 500);
y = zeros(size(x));
for K = 1 : numel(x)
    y(K) = sin(x(K)) .* cos(x(K).^2);
end

[am]

Thank you.

So I need indexing in every loop?

[Walter Roberson]

No. Consider

t = linspace(0, 2*pi, 500);
x = zeros(size(t));
for K = 1:2:5
    x = x + sin(2*pi*t*K);
end

This is a loop, but each iteration of the loop produces a full vector of results and so does not need any indexing.

Answer 2

[am]

I am sorry, I don't understand. Does each iteration rewrites x?

[Walter Roberson]

You can click on "Comment on this Answer" to add a comment, instead of creating a new Answer.

[Walter Roberson]

In my example above https://www.mathworks.com/matlabcentral/answers/452966-when-does-one-need-to-index-for-plotting#comment_687140 with x = x + sin(2*pi*t*K) then, Yes, each iteration rewrites the entire vector x. The example shows that it is not itself looping that is the key as to whether you need to index, but rather whether you are working with the whole variable (no indexing) or only part of the variable (indexing needed)

Another example:

x = randn(15, 2);
x(:,1) = sin(x(:,1));
x(:,2) = exp(x(:,2));

No looping, and multiple elements are accessed, but indexing was required because only part of the variable is being affected.

[am]

What is that code doing?

Does the first line calculate the sinus av every first column?

Does the second line calculate the e^2 of the second column?

Is it a matrix 15 x 2 ?

[Walter Roberson]

The first line creates a 15 x 2 matrix of normally distributed random numbers (with mean 0 and standard deviation 1)

The second line calculates the sine of the first column and replaces the first column with those sines. Indexing was needed on the right side of the = in order to fetch only the first column, and indexing was needed on the left side of the = in order to assign to only the first column.

The third line calculates the exponential of the second column and replaces the second column with those exponentials. Indexing was needed on the right side of the = in order to fetch only the second column, and indexing was needed on the left side of the = in order to assign to only the second column.

The end result is 15 x 2.

[am]

Thank you, it's clearer.