Uniformly Distribute numbers on for loop?

Hello, I have some trouble with my code. The objective of it is to calculate

y(x) = x^3 - sin(x+pi/2) + cos^2*(2x)

for 100 values of x uniformly distributed between -1 and 3 using both a for loop, and vectorization, and to plot the two outputs.

Here is my code.

rng(0, 'Twister');

a = -1;
b = 3;
r = (b-a).*rand(100,1) + a;
pi = 3.14;

for x = r
      y(x) = (x.^3) - sin*(x + (pi/2)) + cos.^2*(2*x);
end
plot(y(x))

I keep getting an error that says there is not enough input arguments for sin and cos. Can anyone help out?

Answer 1

[OCDER]

Here's the vectorized form:

rng(0, 'Twister');

a = -1;
b =  3;
x = randi([a, b], 100, 1);
y = (x.^3) - sin(x + (pi/2)) + cos(2*x).^2;
plot(x, y)

See comments to understand how to fix your for-loop-version of this:

%r = (b-a).*rand(100,1) + a; this can be replaced with randi
%pi = 3.14; don't override pi, which is Matlab constant for pi

y = zeros(size(r)); %preallocate y to improve speed
for x = r  % In common practice, the for loop counter should be a vector of integers, EX k = 1:numel(r). 
           % Then in your code, you refer to r(k) instead of x.
           % With your current x=r, you'll get ERROR: Index must be a positive integer or logical. 
           % Why? because if x(1) = 0.343, Matlab cannot access the 0.343th element of y in y(x) = ... 
           %Note: y(x) should be y(k) instead, where k is the integer for-loop counter.
    y(x) = (x.^3) - sin*(x + (pi/2)) + cos.^2*(2*x); %cannot do sin*(...) or cos.^2(...)
end
plot(y(x)) %Specify the x and y to plot. 
           %Currently, this will give you Index Error or it'll plot 1 point since x is 1 value.

[Matt Amador]

Okay, I tried recorrecting my code to your corrections, but now i'm getting a plot of a diamond shaped graph with some random lines going through it. I don't know if i'm still doing it wrong, but here's the corrected code:

rng(0, 'Twister');

a = -1;
b = 3;
x = randi([a, b], 100, 1);
y = (x.^3) - sin(x + (pi/2)) + cos(2*x).^2;
plot(x,y)

r = (b-a).*rand(100,1) + a;
y = zeros(size(r));
for x = r
    y(x) = (x.^3) - sin(x + (pi/2)) + cos(2*x).^2;
end

[OCDER]

Sort x to make it plot in order. Right now, it plots randomly since that's what randi is doing.

x = sort(randi([a, b], 100, 1));

Here's what you should have:

rng(0, 'Twister');

a = -1;
b = 3;
%===============================================================
%VECTORIZED VERSION
x = sort(randi([a, b], 100, 1));
y = (x.^3) - sin(x + (pi/2)) + cos(2*x).^2;
plot(x,y)
%===============================================================
%FOR LOOP VERSION
r = sort((b-a).*rand(100,1) + a);  %why not just use randi?
y = zeros(size(r));
for x = 1:numel(r) %x = r  you didn't fix this...
    y(x) = (r(x).^3) - sin(r(x) + (pi/2)) + cos(2*r(x)).^2;
end
plot(r, y)

[Matt Amador]

OH! Now, I see what you meant there! Sorry for not looking at it more closely, but now I understand what I did wrong here. Thank you so much for the help! (:

[OCDER]

You're welcome!