I need help with some octave code

b0bd0d

I'm in a class that deals with using Octave to do some math stuff. The trouble I'm having is related to computing pi using a infinite sum of series to within a tolerance of 1e-5.

pi = 4arctan(1)

and

pi = 4(arctan(1/2) + arctan(1/3))

with arctan being

((-1)^n)*(x^(2*n+1)))/(2*n+1)

so here's my code. The first part works fine. The second part causes all types of problems and gets stuck in a loop.

x=1;
tol = 1e-5;
i=0;		#n
a=0;		#answer
b=0;		#next answer. Need to check for tol

more off;			#display output so you know something's happening
format long;
printf("These are both calculated extremely inefficiently, so please wait a few seconds for results...\n");

	a = (a+(((-1)^i)*(x^(2*i+1)))/(2*i+1));
	b = (a+(((-1)^(i+1))*(x^(2*i+2)))/(2*i+2));
	i++;
	
while abs((4*b)-(4*a)) > tol
	a = (a+(((-1)^i)*(x^(2*i+1)))/(2*i+1));
	b = (a+(((-1)^(i+1))*(x^(2*i+2)))/(2*i+2));
	i++;
endwhile
printf("After %g steps to within %g, 4*tan^-1(1) = %f\n",i,tol,(a*4));


#here we go again...

x1=(1/2);
x2=(1/3);

i=0;

a=0;	#tan^-1(1/2)
b=0;	#tan^-1(1/3)
aplusb = 0;	#a+b. need for tol check with cplusd

#next sums
c=0;	#tan^-1(1/2)
d=0;	#tan^-1(1/3)
cplusd=0;	#c+d


	a = (a+(((-1)^i)*(x1^(2*i+1)))/(2*i+1));
	b = (b+(((-1)^i)*(x2^(2*i+1)))/(2*i+1));
	aplusb = a+b;	
	
	c = (c+(((-1)^(i+1))*(x1^(2*i+2)))/(2*i+2));
	d = (d+(((-1)^(i+1))*(x2^(2*i+2)))/(2*i+2));
	cplusd = c+d;
	
	i++;
	
	
	
#there's a bug here and I don't know why....
while abs((cplusd) - (aplusb)) > tol
	a = (a+(((-1)^i)*(x1^(2*i+1)))/(2*i+1));
	b = (b+(((-1)^i)*(x2^(2*i+1)))/(2*i+1));
	aplusb = a+b;	
	
	c = (c+(((-1)^(i+1))*(x1^(2*i+2)))/(2*i+2));
	d = (d+(((-1)^(i+1))*(x2^(2*i+2)))/(2*i+2));
	cplusd = c+d;
	
	i++;
endwhile

printf("After %g steps to within %g, 4*(tan^-1(1/2) + tan^-1(1/3)) = %f\n",i,tol,(4*aplusb));

Daenris

Well, I think I found the problems. Your incremental answers aren't being calculated from the correct previous answer.

In the first set you have it as

a = a+something
b = a+something

Which correctly calculates the b as the next value beyond a. However, in the second set, you have

a = a+something
b = b+something
c = c+something
d = d+something

So, your c and d aren't being calculated correctly as the next answer.
In the second set, to match the formula of your first set, it should be like

a = a+something
b = b+something
c = a+something
d = b+something

Additionally, I think your formula for the next value is off.
Your arctan formula is:
((-1)^n)*(x^(2*n+1)))/(2*n+1)
So your next n formula should be:
((-1)^(n+1))*(x^(2*(n+1)+1)))/(2*(n+1)+1)

You can't simplify 2*(n+1)+1 to 2*n+2, because the 2*(n+1) would be calculated first, so it would be 2*n+3.

edit: With minor syntax edits, I ran it with my changes through Matlab and it no longer hangs on the second set, and at least provides a sensible result estimating pi.