Getting NaN while using the ratio of power and factorial
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With the following piece of code, I get NaN
Is there any way to modify the code to get rid of the issue?
Steven Lord on 13 Jul 2022
m = 500;
d = 200;
The numerator and denominator of your expression (for sufficiently large m) both overflow to inf. Dividing infinity by infinity results in a NaN.
numerator = 2^m*d^m
denominator = factorial(m)
x = numerator / denominator
One potential approach to avoid this is to avoid explicitly computing 2^m, d^m, or factorial(m).
numeratorVector = repmat(2*d, 1, m); % prod(numeratorVector) would effectively give numerator
denominatorVector = 1:m; % prod(denominatorVector) would effectively give denominator
xVector = numeratorVector./denominatorVector;
x2 = prod(xVector)
Let's check symbolically.
numeratorSymbolic = sym(2*d)^m;
vpa(numeratorSymbolic) % Pretty big
denominatorSymbolic = factorial(sym(m));
vpa(denominatorSymbolic) % Also pretty big
x3 = vpa(numeratorSymbolic/denominatorSymbolic) % Big but not quite as big as above
You could be a little more sophisticated / clever if you wanted (preemptively cancelling out factors of 2 in numeratorVector by dividing even values in denominatorVector by 2.) Or you could keep track of x for each value of m then figure out what you need to multiply it by to get x for the next value of m.
Benjamin Thompson on 13 Jul 2022
The factorial function output increases very fast as input increases. See "doc factorial" for details. The output is "inf" for input of 171 or larger.