Central Difference For Loop

Hello, I am trying to use the central difference for the function sin(2*pi*x), centered around x=0.313. I know what value should be, that is my "act" variable. If someone can help me why my for loop is messed-up, it'll be much appreciated.

CODE:

clc, clear, close all

syms x

% Actual Value 

f = sin(2*pi*x); 
df = diff(f,x);
x = 0.313;
true_value = 2*pi*cos(2*pi*x)

% Central Difference 
for i=1:3
      x = 0.313;
    for h = [0.01 0.1 0.25]
        df_dx(i) = (sin(2*pi*(x+h))-sin(2*pi*(x-h)))/2*h
    end
end

act = (sin(2*pi*0.314)-sin(2*pi*0.312))/0.02

Answer 1

[KALYAN ACHARJYA]

-If someone can help me why my for loop is messed-up-

clc, clear, close all
syms x
% Actual Value 
f=sin(2*pi*x); 
df=diff(f,x);
x=0.313;
true_value=2*pi*cos(2*pi*x);
h=[0.01 0.1 0.25];
df_dx=zeros(1, length(h));
% Central Difference 
for i=1:3
    df_dx(i)=(sin(2*pi*(x+h(i)))-sin(2*pi*(x-h(i))))/2*h(i);
end
act=(sin(2*pi*0.314)-sin(2*pi*0.312))/0.02; 

Output:

df_dx=
   -0.0002   -0.0227   -0.0964

Without for loop

clc, clear, close all
syms x
% Actual Value 
f=sin(2*pi*x); 
df=diff(f,x);
x=0.313;
true_value=2*pi*cos(2*pi*x);
h=[0.01 0.1 0.25];
% Central Difference 
df_dx=(sin(2*pi.*(x+h))-sin(2*pi.*(x-h)))./(2*h);
act=(sin(2*pi*0.314)-sin(2*pi*0.312))/0.02;

Command Window:

>> df_dx
df_dx =
   -0.0002   -0.0227   -0.0964

[madhan ravi]

Why do you need a loop?

[KALYAN ACHARJYA]

@Madhan sir, I have added the answer without loop also.

[madhan ravi]

pre-allocation is essential for a loop, h(1:3) is the same as h

[KALYAN ACHARJYA]

Yes edited, truly thanks sir.

[madhan ravi]

The proper usage is

 ./(2*h) % use parantheses
%^---- element wise operation

[KALYAN ACHARJYA]

yeah..Thanks

[madhan ravi]

What and why is preallocation necessary?

[madhan ravi]

./ is not corrected yet , please by any chance don't delete this answer so that it's pretty clear how many possible mistakes can be made in this problem.

[KALYAN ACHARJYA]

Yes, got it sir, but for small number of iterations, there may be negligible difference.right?

>> matlab_ans_march_19
Without Pre-allocation
Elapsed time is 0.003340 seconds.

%%

>> matlab_ans_march_19
With Pre-allocation
Elapsed time is 0.002957 seconds.

Yes, prefer to use for better coding performance (always).