MATLAB: computations involving large numbers

问题

How can one perform computations in MATLAB that involve large numbers. As a simple example, an arbitrary precision calculator would show that ((1/120)^132)*(370!)/(260!) is approximately 1.56, but MATLAB is not able to perform such a computation (power(120,-132)*factorial(370)/factorial(260) = NaN).

I have also tried the following, which does not work:

syms a b c d;
a=120; b=-132; c=370; d=260;
f=sym('power(a,b)*gamma(c+1)/gamma(d+1)')
double(f); % produces error that instructs use of `vpa`
vpa(f) % produces (gamma(c + 1.0)*power(a, b))/gamma(d + 1.0)

回答1:

If you just want to calculate the factorial of some large numbers, you can use the Java arbitrary precision tools, like so:

result = java.math.BigDecimal(1);
for ix = 1:300
    result = result.multiply(java.math.BigDecimal(ix));
end
disp(result)
306057512216440636035370461297268629388588804173576999416776741259476533176716867465515291422477573349939147888701726368864263907759003154226842927906974559841225476930271954604008012215776252176854255965356903506788725264321896264299365204576448830388909753943489625436053225980776521270822437639449120128678675368305712293681943649956460498166450227716500185176546469340112226034729724066333258583506870150169794168850353752137554910289126407157154830282284937952636580145235233156936482233436799254594095276820608062232812387383880817049600000000000000000000000000000000000000000000000000000000000000000000000000

The value result in this case is a java object. You can see the available methods here: http://docs.oracle.com/javase/6/docs/api/java/math/BigDecimal.html

I'm still not sure that I would trust this method for (1e6)! though. You'll have to experiment and see.

回答2:

Depending on what you're trying to do, then you may be able to evaluate the expression you're interested in in log-space:

log_factorial = sum(log(1:300));

回答3:

You can use Stirling's approximation to approximate large factorials and simplify your expression before computing it numerically.

回答4:

This will work:
vpa('120^-132*370!/260!')

and the result is
1.5625098001612564605522837520443

来源：https://stackoverflow.com/questions/9337342/matlab-computations-involving-large-numbers