Arrays are Empty? WHY?

Trying to do a math homework to make 1st order forward backward difference, 1 order forward difference, 2nd order forwad differnece, and 2nd order central difference.

Given x interval [-10,1-], distance between points h = 0.38. Was given formulas for SOFD,SOBD, and CD.

My Question, when I run the code my arrays are not being filled in the for loop.

L = -10; U = 10; h = 0.38; 
x =L:h:U; 
f= sech(x) ;
dfdt =(-sech(x).*tanh(x));
df2dt2 = sech(x).*(tanh(x).^2).*(sech(x).^3);
%f= function
%dfdt = 1st derivative
%df2dt2 = second derivative 
%U = upper bound
%L = lower bound
% n = number of elements
% h = subinterval size 
%CD= Centered Difference 
%SOFD = Second order forward difference
%SOCD = Second Order Central Difference 
%%
%Part A --> x = -10 to 10, h = 0.38 

% array between upper and lower bounds via h different between points  
n = length(x); 
%prellocating for speed
x1p = zeros(1,n);
x2p = zeros(1,n);
x1m = zeros(1,n);
x2m = zeros(1,n);
f1p = zeros(1,n);
f2p = zeros(1,n);
f1m = zeros(1,n);
f2m = zeros(1,n);
CD= zeros(1,n);
SOFD = zeros(1,n);
SOBD= zeros(1,n);
eCD = zeros(1,n);
eSOFD = zeros(1,n);
eSOBD= zeros(1,n);

% for loop to solve all points for the give interval 
for i = 1:n
% points of x with +1, +1, -2 and +2 
    x1p(i) = x(i) + x(i);
    x2p(i) = x(i) + 2*x(i); 
    x1m(i) = x(i) - x(i);
    x2m(i) = x(i) - 2*x(i);
% function of above x values based on +1, +1, -2 and +2 
   f1p(i) = f(x1p(i)); %f(x+1)
   f2p(i) = f(x2p(i)); %f(x+2)
   f1m(i) = f(x1m(i)); %f(x-1)
   f2m(i) = f(x2m(i)); %f(x-2)
%Centered Difference
   CD(i) = (f1p(i) - f1m(i))/ (2*x(i));  
% Second Order Forward Difference  
   SOFD(i) = (-f2p(i) + 4*f1p(i) -3*f(x(i)))/(2*x(i)); 
% Second Order Backward Difference 
   SOBD(i) = (3*f(x(i)) - 4*f1m(i) + f2m(i))/(2*x(i));

% Calculating Error
   if i ~=n
       eCD(i) = abs((eCD(i-1)-eCD(i))/eCD(i-1))*100;
       eSOFD(i) = abs((eSOFD(i-1)-eSOFD(i))/eSOFD(i-1))*100;
       eSOBD(i) = abs((eSOBD(i-1)-eSOBD(i))/eSOBD(i-1))*100;
   
   else, break, 
   end
end % end for loop 
%%
%plotting
disp(eCD)
disp(eSOFD)
disp(eSOBD)
hold on
loglog(x,eSOFD,'r.-')
legend('Error SOFD') 

Answer 1

[Walter Roberson]

I suspect you want f = @sech rather than f = sech(x) . You appear to be using f as a function inside your loop.

Your for loop at the end has

if i ~= n
else
    break
end

but on the first iteration, i = 1 and that is not n, so the else break is going to happen, causing the for loop to exit.

Answer 2

[Guillaume]

My Question, when I run the code my arrays are not being filled in the for loop.

More to the point, when you run the code you get an error, something you haven't mentioned. So basically, your code doesn't run and it's no wonder nothing gets filled.

The error is Array indices must be positive integers or logical values and indeed xp1(i) is not a valid index into the vector f, since xp1 is not made of integers.

It's not clear what you're trying to do with the expressions

   f1p(i) = f(x1p(i)); %f(x+1)
   f2p(i) = f(x2p(i)); %f(x+2)
   f1m(i) = f(x1m(i)); %f(x-1)
   f2m(i) = f(x2m(i)); %f(x-2)

but none of them are valid.

By the way, x(i) + x(i), most people write that as 2*x(i), x(i) + 2*x(i) as 3*x(i) and of course x(i) - x(i) as 0 and x(i) - 2*x(i) as -x(i).

Answer 3

[Alexa Shumaker]

clear 
clc
L = -10; U = 10; h = 0.38; 
x =L:h:U; 
f= sech(x) ;
dfdt =(-sech(x).*tanh(x));
df2dt2 = sech(x).*(tanh(x).^2).*(sech(x).^3);
%f= function
%dfdt = 1st derivative
%df2dt2 = second derivative 
%U = upper bound
%L = lower bound
% n = number of elements
% h = subinterval size 
%CD= Centered Difference 
%SOFD = Second order forward difference
%SOCD = Second Order Central Difference 
%%
%Part A --> x = -10 to 10, h = 0.38 

% array between upper and lower bounds via h different between points  
n = length(x); 
%prellocating for speed
x1p = zeros(1,n);
x2p = zeros(1,n);
x1m = zeros(1,n);
x2m = zeros(1,n);
f1p = zeros(1,n);
f2p = zeros(1,n);
f1m = zeros(1,n);
f2m = zeros(1,n);
CD= zeros(1,n);
FOFD = zeros(1,n);
FOBD = zeros(1,n); 
SOFD = zeros(1,n);
SOBD = zeros(1,n);
eCD = zeros(1,n);
eFOFD = zeros(1,n);
eFOBD= zeros(1,n);
eSOFD = zeros(1,n);
eSOBD= zeros(1,n);

% for loop to solve all points for the give interval 
for i = 1:n
% points of x with +1, +1, -2 and +2 
    x1p(i) = x(i);
    x2p(i) = 2*x(i); 
    x1m(i) = -x(i);
    x2m(i) =  -2*x(i);
% function of above x values based on +1, +1, -2 and +2 
   f1p(i) = sech(x1p(i)); %f(x+1)
   f2p(i) = sech(x1p(i)); %f(x+2)
   f1m(i) = sech(x1m(i)); %f(x-1)
   f2m(i) = sech(x2m(i)); %f(x-2)
%Centered Difference
   CD(i) = (f1p(i) - f1m(i))/ (2*h);  
%First Order Forward Difference
   FOFD(i) = (f1p(i) - sec(x(i)))/(h); 
%First Order Backward Difference
   FOBD(i) = (sec(x(i))-f1m(i))/(h); 
% Second Order Forward Difference  
   SOFD(i) = (-f2p(i) + 4*f1p(i) -3*sec(x(i)))/(2*h); 
% Second Order Backward Difference 
   SOBD(i) = (3*sec(x(i)) - 4*f1m(i) + f2m(i))/(2*h);

% Calculating Error
   if i<= n 
       if i == 1; break
       else 
       eCD(i) = abs((CD(i)-CD(i-1))/CD(i))*100; 
       eFOFD(i) = abs((FOFD(i)-FOFD(i))/FOFD(i))*100;
       eFOBD(i) = abs((FOBD(i)-FOBD(i-1))/FOBD(i))*100;
       eSOFD(i) = abs((SOFD(i)-SOFD(i))/SOFD(i))*100;
       eSOBD(i) = abs((SOBD(i)-SOBD(i-1))/SOBD(i))*100;
       end 
   else, break, 
   end
end % end for loop 
%%
%plotting

hold on
first =(-sech(0)*tanh(0));
second = sech(0)*(tanh(0)^2)*(sech(0)^3);
loglog(x,(eSOFD),'--m', x,(eSOBD), 'g',x,(eCD), 'b', 0, first, 'rs',0, second,'bs')
legend('Error SOFD', 'Error SOBD', 'Error CD','df/dt,x = 0','df2/dt2, x=0');
%plot(x,eSOFD),'r.-')
%plot(x,eSOBD), 'g')
%plot(x,eCD), 'b')

%title('Comparisions')
%xlabel('X Axis')
%ylabel('Y Axis') 
%Part c 
%first = (-sech(0).*tanh(0));
%second =sech(0).*(tanh(0).^2).*(sech(0).^3);

%plot(x0,first, 'ro')
%plot(x0, second,'bo')
%legend('df/dt,x = 0','df2/dt2, x=0')

So I updated the code. It still doesn't fill in the arrays. I know the for loop finishes since my plot shows up but only the 1st position of array is filled the rest become zero, why is that?

[Stephen23]

"So I updated the code."

Yes, but you need to understand Walter Roberson's answer, which explains why your loop never passes the first iteration. You are still making the same mistake here (combined with badly aligned code, which makes the code much harder to understand):

if i<= n 
    if i == 1; break
    else 
        ... your code
    end 
else, break,
end

"I know the for loop finishes since my plot shows up but only the 1st position of array is filled the rest become zero, why is that? "

Read Walter Roberson's answer, it explains why your break concept is buggy.

Solution: get rid of those pointless nested IF and ELSE calls and get rid of all of the counter-productive break calls that you are doing in your code, and replace them with one simple:

if i > 1
    ... your code ... NO BREAK!
end

It worked when I tried it.