What is difference between these two commands?
especially in regards to there application
MATLAB: Conv vs conv2
digital image processingMATLABsignal processing
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It happens because of finite precision of double() precision datatype: https://en.wikipedia.org/wiki/Double-precision_floating-point_format. Also, because of the fact that MATLAB only prints 16 digits by default, the remaining digits after conversion are not shown (double datatype cannot store more than 16 digits accurately). Try the following
>> fprintf('%0.20f\n', 1+eps)1.00000000000000022204>> fprintf('%0.20f\n', 1+2.5*eps)1.00000000000000044409It looks like this question has gotten enough interest that it deserves a complete answer on how to do it using MATLAB. And since you have done something reasonable...
You simply cannot compute factorial of a number as a double, if n is greater than 18.
factorial(1:20) < flintmaxans = 1×20 logical array 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0Actually, it looks like you might get to 20, if you use uint64. But uint64 overflows beyond that point. So using a double will just fail for the sum of digits of factorial(100).
factorial(100)ans = 9.3326e+157That is WAY past flintmax. Personally, I'd do it elegantly as:
sum(char(factorial(sym(100))) - '0')ans = 648However nothing stops you from doing the multiplication the hard way, using carries.
factdigs = zeros(1,200);factdigs(end) = 1;N = 100;for n = 2:N % multiply. note that you multiply ALL digits of
% the number by n.
factdigs = factdigs * n; % carry op
carry = 1; % a while loop, since there may be multiple carries.
% for example, a multiple carry would occur when you
% multiply the number 6 times 100.
while any(carry) % strip off the units digit
R = rem(factdigs,10); % this divide will always be safe, resulting
% in an exact integer.
carry = (factdigs - R)/10; % The carry is just an add, with a shift.
% if I knew the highest order digit will
% always be zero, I could have used circshift.
factdigs = R + [carry(2:end),0]; endendsum(factdigs)ans = 648This will work as long as I make the vector of digits long enough that factorial(100) does not overflow a 200 digit number. And since we know that factorial(100) is on the order of 9e157, 200 digits is fine.
reshape(factdigs,10,20)'ans = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 3 3 2 6 2 1 5 4 4 3 9 4 4 1 5 2 6 8 1 6 9 9 2 3 8 8 5 6 2 6 6 7 0 0 4 9 0 7 1 5 9 6 8 2 6 4 3 8 1 6 2 1 4 6 8 5 9 2 9 6 3 8 9 5 2 1 7 5 9 9 9 9 3 2 2 9 9 1 5 6 0 8 9 4 1 4 6 3 9 7 6 1 5 6 5 1 8 2 8 6 2 5 3 6 9 7 9 2 0 8 2 7 2 2 3 7 5 8 2 5 1 1 8 5 2 1 0 9 1 6 8 6 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0Of course, the code as I wote it would fail around n = 122.
factorial(122)ans = 9.875e+202That would be fixable merely by preallocating factdigs to be a longer vector. Or, with a little more care in the code, I could have written it to dynamically expand the vector of digits, so factorials of any size would then theoretically work.
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