Error with l2 normalization on a vector [Java] -

i'm trying use l2 normalization on double vector java.

double[] vector = {0.00423823948, 0.00000000000823285934, 0.0000342523505342, 0.000040240234023423, 0, 0}; 

now if use l2 normalization

for(double : vector){     squarevectorsum += * i; }  normalizationfactor = math.sqrt(squarevectorsum); // system.out.println(squarevectorsum+" "+normalizationfactor); for(int = 0; < vector.length; i++){     double normalizedfeature = vector[i] / normalizationfactor;     vector_result[i] = normalizedfeature; } 

my normalized vector this

normalized vector (l2 normalization) 0.9999222784309146 1.9423676996312713e-9 0.008081112110203743 0.009493825603572155 0.0 0.0 

now if if make squared sum of normalized-vector components should sum is equal one, instead squared sum

for(double : vector_result){     sum += i*i; } squared sum of normalized-vector 1.0000000000000004 

why sum not equal one? there problems in code? or it's because numbers small , there approximation doubles?

as indicated above, common issue, 1 you're going have deal if you're going use floating point binary arithmetic. problem crops when want compare 2 floating point binary numbers equality. since operations applied arrive @ values may not identical, neither binary representations.

there @ least couple strategies can consider deal situation. first involves comparing absolute difference between 2 floating point numbers, x , y rather strict equality , comparing them small value ϵ>0. like

if (math.abs(y-x) < epsilon) {     // assume x == y } else {     // assume x != y } 

this works when possible values of x , y have relatively tight bounding on exponents. when not case, value of x , y may such difference dominates ϵ choose (if exponent large) or ϵ dominates difference (such when possible exponents of x , y small). around this, instead of comparing absolute difference, instead compare ratio of x , y 1.0 , see whether ratio has absolute difference 1.0 more ϵ. like:

if (math.abs(x/y-1.0) < epsilon) {     // assume x == y } else {     // assume x != y } 

you need add check ensure y!=0 avoid division zero, that's general idea.

other options include using fixed point library java or rational number library java. have no recommendations that, though.