MATLAB: Simplyfing computations in arrays

syntax matlab for loop mathe

int = zeros(1,length(x));  
for n = 3:length(x)
    y1 = x(2:n) ;
    t1 = n*dt - (2*dt:dt:n*dt) ;
    y2 = x(1:n-1) ;
    t2 = n*dt - (dt:dt:(n-1)*dt) ;
    int(n) = sum (t1.^(k-1)/factorial(k-1).*y1 ...
             + t2.^(k-1)/factorial(k-1).*y2)*dt/2 ;
end

I want to write t1= ((n-2)*dt:dt:0dt) is it okay? and also t2=((n-1)dt:dt:dt).

Is it possible? I sew also some errors…

Best Answer

Is t1= ((n-2)*dt:dt:0dt) intended to go to 0 ? If so then because n-2 is positive so you are going backwards from positive towards 0, you will need

(n-2)*dt: -dt : 0

Related Solutions

MATLAB: SYNTAX MATLAB

Eg.

x=1:20;   %i.e x=1 2 3.... 20
n=5;    % assign value of 5 to n
y1 = x(2:n)   % get second to nth (5th )value in x and put it in y1

Output of above

 y1 =
            2.00          3.00          4.00          5.00
 dt=1; %assign value of 1 to dt.. you can give any value
 t1 = n*dt - (2*dt:dt:n*dt);

frist term n*dt %multiply n (scalar) by dt a scalar

n*dt
ans =
          5.00

second term 2*dt:dt:n*dt % range twice dt to ntimes dt witht a difference of dt for above case 2*1:1:5*1 i.e (2:1:5)

2*dt:dt:n*dt
ans =
          2.00          3.00          4.00          5.00

ti=sub first term (scalar) -second term (array) (5-2, 5-3, 5-4, 5-5)

t1 = n*dt - (2*dt:dt:n*dt)
t1 =
          3.00          2.00          1.00             0

MATLAB: Accelerating code in matlab – for loop

At first I've clean up your code a bit:

if k <= 0
   int = x ;
   return
end
int = zeros(1, length(x));
fk1 = factorial(k - 1);
dt2 = dt / 2;
for n = 3:length(x)
  y1 = x(2:n);
  t1 = ((n-2):-1:0) * dt;
  y2 = x(1:n-1);
  t2 = t1 + dt; 
  int(n) = sum(t1 .^ (k-1) / fk1 .* y1 + t2 .^ (k-1) / fk1 .* y2) * dt2;
end

Now some improvements:

lenx = length(x);
fk1 = factorial(k - 1);
t1Vec = (((lenx - 2):-1:0) * dt) .^ (k-1) * dt / fk1;
int = zeros(1, lenx);
dt2 = dt / 2;
for n = 3:lenx
  y1 = x(2:n);
  t1 = t1vec(lenx-a-n:lenx-b);  % **see comment**
  y2 = x(1:n-1);
  t2 = t1 + dt; 
  int(n) = sum(t1 .* y1 + t2 .^ (k-1) / fk1 .* y2) * dt2;
end

I do not have the time to find the right constantd for a and b. Without access to Matlab I cannot simply try it, but you can. The idea is to avoid the repeated expensive calculation of t1 .^(k-1), when all elements except for one have been processed already. The same works for t2. I leave it up to you to elaborate this.

Best Answer

Related Solutions

MATLAB: SYNTAX MATLAB

MATLAB: Accelerating code in matlab – for loop

Related Question