Major confusion for loops - precision not acquired

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DM on 6 Feb 2015
Commented: Star Strider on 6 Feb 2015
I have a loop that sums the values of function called pdfomegat
omegat= -1.9999:0.01:+1.9999;
sum1=0;
for j=1:length(omegat)
func(j)=pdfomegat(j)*0.01;
sum1=sum1+func(j);
end
c1=sum1;
My second loop is slightly different loop and is as follows
sum2=0;
syms t
for j=1:length(omegat)
func2(j)=t*pdfomegat(j)*0.01;
sum2=sum2+func(j);
end
c2=sum2;
I know for fact that c1 is 1 .. However notice that in the second loop I change nothing but multiply by symbolic character t. Howver I get that
c2=0.99999464659732599597363744692302*t.
Why isn't c2=t?
Is there anyway I can fix it, I can't use the round function because it symbolic.. Any thoughts?

A Jenkins on 6 Feb 2015
Play around with vpa() and digits() and make sure to read the help files on Precision Control.
A Jenkins on 6 Feb 2015
>> syms t
>> c2=0.99999464659732599597363744692302*t;
>> cf=vpa(c2,8)
cf =
0.99999465*t
>> cf=vpa(c2,4)
cf =
1.0*t

John D'Errico on 6 Feb 2015
Edited: John D'Errico on 6 Feb 2015
No. You cannot make a double precision number more precise than it is. There are simple many numbers that are not exactly representable using a double. For example, 0.1 is not so, since doubles are stored in binary form.
Anyway, my very good bet is that c1 is NOT 1, but that it was displayed in the command window as 1, using format short. So I think what you know for a fact is actually completely false. As well, it is entirely possible that you were using a single precision format to store pdfomegat, since c1 was so inaccurately NOT equal to 1.
However, you can do many things to improve your work. For example, in this line, rather than multiplying by 0.01, divide by 100, an integer. You do this because 0.01 is not stored exactly as a double, but 100 is.
As for the code itself, write it more efficiently. Learn to use vectors, and simple tools like sum.
Your first loop does nothing more than multiply the vector pdfomegat by 0.01, and then sum it.
omegat= -1.9999:0.01:+1.9999;
func1 = pdfomegat/100;
c1 = sum(func1);
You can also totally replace that second loop simply as
syms t
func2 = t*func1;
c2 = t*c1;
As for making the sums themselves more accurate, you could convert the vector pdfomegat into a symbolic form (or my own HPF) but since they were originally stored as doubles, you simply won't gain much at all there, unless you create those numbers in a form that allows you to store them more accurately in the first place.
John D'Errico on 6 Feb 2015
Any rounding that you do AFTER the fact merely hides the numerical issues. It solves no problem. Instead, you need to show more clearly what you are doing, and do that computation more accurately.

Star Strider on 6 Feb 2015
It’s not straightforward, but you can round the coefficient:
syms t
c2=0.99999464659732599597363744692302*t; % Original Expression
cf = double(vpa(coeffs(c2))) % Get Coefficient
cf = fix(cf * 1E+8)/1E+8 % Round To 8 Digits
Star Strider on 6 Feb 2015
I would suggest that ‘keeping everything simple’ is not appropriate. We Answer the Questions posted, so if you do not state your actual problem, you will likely not get an Answer that will solve it.
I have no idea what ‘func1’ and ‘g’ are, so I can go no further. You might use the numden function to separate the numerator and denominator, then use coeffs or whatever function is appropriate. Consider also matlabFunction or similar functions if you want to use your function in other applications.