How can I get the middle from two numbers? - java

could someone please tell me if I´m on the right way or if I´m doing it totally wrong?
How could I do it easier? I ´m thankful for any helpful tips
I also get that i & mm cannot be resolved to a variable look at (1)
I also get that double cannot covert to int look at (2)
Edit Update:
I´m trying to do it with a try/catch and was coverting to a string instead of a double. But I´ve noticed that I can´t round it then. Isn´t try/catch a good idea?
/**
* Returns the best guess given a range defined by its lowest and highest possible values.
* The best guess that can be taken is the number exactly in the centre of the range.
* If the centre is between two numbers, the number directly below the centre is returned (the centre is rounded down)
* #param lowestPossible The lowest possible value of the range
* #param highestPossible The highest possible value of the range
* #return The best guess for the given range
*/
public static int getBestNewGuess(int lowestPossilbe, int highestPossible) {
//return -1; // TODO: IMPLEMENT ME (AND DELETE THIS COMMENT AFTERWARDS!!!)
My Code:
double x = (lowestPossilbe + highestPossible);
double y = x /2; //Getting the middle
if (int i = (int)y) { //if double y can be converted to a int then return int y (1)
return y; // (2)
}else if (mm = (int) Math.round(y)) { //if that´s not the case, then round double y and convert it to a int (1)
int m = (int)y;
return m; // return rounded and converted y
}
// if (roundf(y) == y) {
// return y;
// }if else {
//
// }
}

If you are worried about overflow, and if you know that the lower value is less than the upper one, you could subtract the lower from the upper, divide the resulting int by 2, and add back to the lower number. Avoids casting a precise int to an approximate double and back again.
That simple case assumes that both numbers are positive. If the lower number is negative and the upper one positive, you need to add them and divide by 2, since subtracting a large negative number from a large positive one can overflow.

Try this:
return Math.floor((Double.valueOf(lowestPossilbe) + Double.valueOf(highestPossible))/2)

Related

Division in Java to get next upper value

I am dividing two ints x/y,. Say 3/2. Then one would get 1 as result though the actual result is 1.5. Ok this is obvious as it's int division. But I want 1.5 to be rounded off to the next highest int not the immediate lowest. So 2 is desired as result. (One can write simple logic using mod and then division... But am looking for simple Java based API). Any thoughts?
You can, in general, write (x + y - 1) / y to get the rounded-up version of x/y. If it's 3/2, then that becomes (3 + 2 - 1) / 2 = 4 / 2 = 2.
You can use the ceil (ceiling) function:
https://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#ceil(double)
That will essentially round up to the nearest whole number.
If you can change the datatype to double, following is the best solution -
double x = 3;
double y = 2;
Math.ceil(Math.abs(x/y));
This will give you 2.0
import java.lang.Math;
//round Up Math.ceil(double num)
//round Down Math.floor(double num)
public class RoundOff
{
public static void main(String args[])
{ //since ceil() method takes double datatype value as an argument
//either declare at least one of this variable as double
int x=3;
int y=2; //double y =2;
//or at least cast one of this variable as a (double) before taking division
System.out.print(Math.ceil((double)x/y)); //prints 2.0
//System.out.print(Math.ceil(x/y));
}
}

Sigmoid function return NaN in Java

I am trying to create a logistic regression algorithm in java but when I calculate the logarithm of the likelihood it is always returning NaN. My method which calculates the logarithm looks like this :
//Calculate log likelihood on given data
private double getLogLikelihood(double cat, double[] x) {
return cat * Math.log(findProbability(x))
+ (1 - cat) * Math.log(1 - findProbability(x));
}
And the findProbability method is just take an instance from the dataset and returning the sigmoid funcion result which is between 0 and 1.
//Calculate the sum of w * x for each weight and attribute
//call the sigmoid function with that s
public double findProbability(double[] x){
double s = 0;
for(int i = 0; i < this.weights.length; i++){
if(i >= x.length) break;
s += this.weights[i] * x[i];
}
return sigmoid(s);
}
private double sigmoid(double s){
return 1 / (1 + Math.exp(-s));
}
Moreover, my starting weights are :
[-0.2982955509135178, -0.4984900460081106, -1.816880187922516, -2.7325608512266073, 0.12542715714800834, 0.1516078084483485, 0.27631147403449774, 0.1371611094778011, 0.16029832096058613, 0.3117065974657231, 0.04262385176091778, 0.1948263133838624, 0.10788353525185314, 0.770608588466501, 0.2697281907888033, 0.09920694325563077, 0.003224073601703939, 0.021573742410541247, 0.21528348692817675, 0.3275511757298476, -0.1500597314893408, -0.7221692528386277, -2.062544912370121, 1.4315146889363015, 0.2522133355419722, 0.23919315019065995, 0.3200037377021523, 0.059466770771758076, 0.04012493980772944, 0.2553236501265919]
Finally, an instance from my dataset is :[M,17.99,10.38,122.8,1001,0.1184,0.2776,0.3001,0.1471,0.2419,0.07871,1.095,0.9053,8.589,153.4,0.006399,0.04904,0.05373,0.01587,0.03003,0.006193,25.38,17.33,184.6,2019,0.1622,0.6656,0.7119,0.2654,0.4601,0.1189]
I tried to initialize the starting weightss with different random numbers but thats didnt solve the problem.
The arithematic is causing a rounding error leaving you with 1.
double b = 1 + Math.exp(-3522);
b will be equal to 1, because otherwise you will need too many sig figs. You'll have to approximate the value to keep the precision. 1/(1+s) ~= 1 - s; Which means you need to calculate log(1) and log(s).
edit: sorry, I made a mistake, it appears Math.exp(-3522) is evaluated as 0 after rounding. Ill leave this answer because Math.exp(-x) might be too small to add to 1, or it might just be zero.
NaN is a result of dividing by zero or calling Math.log on a non-positive number, so u should try and find where exactly this happens. I suggest debugging or adding code to print the values of which u take the logarithm/dividy by.
EDIT: it seems it is a rounding error: exp(-s) will return a result so small that added with 1 it will still remain 1. This causes the logarithm to return -Inf. I'd suggest u try and find a mathematical way to solve this by trying to perhaps to approximate the log of the exponential.
I found a solution to my problem so I post it here:
I added an overflow check:
private double sigmoid(double s){
if(s>20){
s=20;
}else if(s<-20){
s=-20;
}
double exp = Math.exp(s);
return exp/(1+exp);
}
Also changing 1/(1+Math.exp(s) to exp/(1+exp) proved to be more stable in small disturbances of inputs.

Adding and subtracting exact values to float

Question:
The total amount of floating points is finite, there's about 2^32 of them. With a float, you can go directly to the next or previous one using java.lang.Math.nextAfter. I call that a single leap. My main quesion, composed of sub questions is, how can I navigate on floats using leaps ?
First, how can I move a float to another with multiple leaps at once ?
public static float moveFloat(float value, int leaps) {
for(int i = 0; i < Math.abs(leaps); i++)
value = Math.nextAfter(value, Float.POSITIVE_INFINITY * signum(leaps));
return value;
}
That way should work on theory but is really unoptimized. How can I do it in a single addition ?
I also need to know how much leaps there's between 2 floats. Here's the example implementation for this one:
public static int getLeaps(float value, float destination) {
int leaps = 0;
float direction = signum(destination - value);
while(value * direction < destination * direction) {
value = Math.nextAfter(value, Float.POSITIVE_INFINITY * direction);
leaps++;
}
return leaps;
}
Again, same problem here. This implementation isn't suitable.
Extra:
The thing I call a leap, does it have an actual name ?
Background:
I'm trying to make a simple 2D physics engine in Java and I have trouble with my floating point operations. I learned about relative error float comparison and it helped a bit but it's not magic. What I want is to be exact with my floating points.
I already know a lot of base ten numbers cannot be exactly represented with floating points but execptionally, I don't care. All I want is exact float arithmetic in base 2.
To simplify, in my collision detection and response process, I check if shapes overlap (let's stay in one dimension for this example) and I replace the 2 shapes overlapping using their weight.
See this example:
If the black lines are the float values(and the space between each other leaps) whatever the precision is, I want to place both shapes (colored lines) to be exactly at the brown position. (The brown position is determined by the weights ratio and by rounding. What I call penetration is the overlaping area/distance. If the penetration would of been 5, red would been pushed by 1 and blue by 4).
The problem is, do to that I have to keep the penetration of the collision (in this case the penetration is exactly the ULP of the float, or 1 leap) in a float and I suspect this leads to inexactitude. If the penetration value is bigger than the coordinates of the shapes, it will be less precise so they won't be exactly replaced at the good coordinate.
What I imagine is to keep the penetration of the collision as the amount of leaps I need to get from one to the another and use it afterwards.
This is a simplified version of the current code I have:
public class ReplaceResolver implements CollisionResolver {
#Override
public void resolve(Collision collision) {
float deltaB = collision.weightRatio * collision.penetration; //bodyA's weight over the sum of the 2 (pre calculated)
float deltaA = 1f - deltaB;
//the normal indicates where the shape should be pushed. For now, my engine is only AA so a component of the normal (x or y) is always 0 while the other is 1
if(deltaB > 0)
replace(collision.bodyA, collision.normalB, deltaA);
if(deltaA > 0)
replace(collision.bodyB, collision.normalA, deltaB);
}
private void replace(Body body, Vector2 normal, float delta) {
body.getPosition().x += normal.x * delta; //body.getPosition() is a Vector2
body.getPosition().y += normal.y * delta;
}
}
Obviously, this doesn't work properly and accumulates floating point precision error. The error is well handled by my collision detection which checks for float equality using ULP. However it breaks when crossing 0 because of the ULP going extremely low.
I could simply fix an epsilon for a physic simulation but it would remove the whole point of using floats. The technique I want to use lets the user choose his precision implicitly and theorically should be working with any precision.
Underlying IEEE 754 floating point model has this property: if you re-interpret the bits as Integer, taking the next float after (or before depending on the direction) is just like taking the next (or previous) integer, that is adding or subtracting 1 to the bit pattern re-interpreted as integer.
Stepping n times is adding (or subtracting) n to the bit pattern. It's as simple as that as long as the sign does not change, and you don't overflow to NaN or Inf.
And the number of different floats between two floats is the difference of two integers if the signs agree.
If signs differ, since the float has a sign-magnitude like representation, which does not fit the integer representation, you'll then have to exert a bit of arithmetic.
I want to do the same calculation. So, if "leaps" means as #aka.nice said, the integer difference/span/distance between two float-point values according to the IEEE 754 floating-point "single format" bit layout (IEEE754 Format), I may have found a simple method:
public static native int floatToRawIntBits(float value) and Java_java_lang_Float_floatToRawIntBits can be used for this purpose, which has similar functionality to my test code in c++ (reinterpret a memory (reinterpret_cast)).
#include <stdio.h>
/* https://stackoverflow.com/questions/44008357/adding-and-subtracting-exact-values-to-float */
int main(void) {
float float0 = 1.5f;
float float1 = 1.5000001f;
int intbits_of_float0 = *(int *)&float0;
int intbits_of_float1 = *(int *)&float1;
printf("float %.17g is reinterpreted as an integer %d\n", float0, intbits_of_float0);
printf("float %.17g is reinterpreted as an integer %d\n", float1, intbits_of_float1);
return 0;
}
And, the Java code (online compiler) below is used to calcuate the "leaps":
public class Toy {
public static void main(String args[]) {
int length = 0x82000000;
int x = length >>> 24;
int y = (length >>> 24) & 0xFF;
System.out.println("length = " + length + ", x = " + x + ", y = " + y);
float float0 = 1.5f;
float float1 = 1.5000001f;
float float2 = 1.5000002f;
float float4 = 1.5000004f;
float float5 = 1.5000005f;
// testLeaps(float0, float4);
// testLeaps(0, float5);
// testLeaps(0, -float1);
// testLeaps(-float1, 0);
System.out.println(Math.nextAfter(-float1, Float.POSITIVE_INFINITY));
System.out.println(INT_POWER_MASK & Float.floatToIntBits(-float0));
System.out.println(INT_POWER_MASK & Float.floatToIntBits(float0));
// testLeaps(-float1, -float0);
testLeaps(-float0, 0);
testLeaps(float0, 0);
}
public static void testLeaps(float value, float destination) {
System.out.println("optLeaps(" + value + ", " + destination + ") = " + optLeaps(value, destination));
System.out.println("getLeaps(" + value + ", " + destination + ") = " + getLeaps(value, destination));
}
public static final int INT_POWER_MASK = 0x7f800000 | 0x007fffff; // ~0x80000000
/**
* Retrieves the integer difference between two float-point values according to
* the IEEE 754 floating-point "single format" bit layout.
*
* <pre>
* mask 0x80000000 | 0x7f800000 | 0x007fffff
* sign | exponent | coefficient/significand/mantissa
* +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
* | | | |
* +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
* 31 30 23 22 0
* 0x7fc00000 => NaN
* 0x7f800000 +Infinity
* 0xff800000 -Infinity
* </pre>
*
* Using base (radix) 10, the numerical value of such a float type number is
* `(-1)^sign x coefficient x 10^exponent`, so the coefficient is a key factor
* to calculation of leaps coefficient.
*
* #param value the first operand
* #param destination the second operand
* #return the integer span from {#code value} to {#code destination}
*/
public static int optLeaps(float value, float destination) {
// TODO process possible cases for some special inputs.
int valueBits = Float.floatToIntBits(value); // IEEE 754 floating-point "single format" bit layout
int destinationBits = Float.floatToIntBits(destination); // IEEE 754 floating-point "single format" bit layout
int leaps; // Float.intBitsToFloat();
if ((destinationBits ^ valueBits) >= 0) {
leaps = Math.abs(destinationBits - valueBits);
} else {
leaps = INT_POWER_MASK & destinationBits + INT_POWER_MASK & valueBits;
}
return leaps;
}
public static int getLeaps(float value, float destination) {
int leaps = 0;
float signum = Math.signum(destination - value);
// float direction = Float.POSITIVE_INFINITY * signum;
// while (value * signum < destination * signum) {
// value = Math.nextAfter(value, direction); // Float.POSITIVE_INFINITY * direction
// leaps++;
// }
if (0 == signum) {
return 0;
}
if (0 < signum) {
while (value < destination) {
value = Math.nextAfter(value, Float.POSITIVE_INFINITY);
leaps++;
}
} else {
while (value > destination) {
value = Math.nextAfter(value, Float.NEGATIVE_INFINITY);
leaps++;
}
}
return leaps;
}
// optimiaze to reduce the elapsed time by roughly half
}
To start, I just want to say I don't like hacking into an Objects implementation, and you should using your own (or another library) implementation first, but sometimes you have to get creative.
Lets start with key detail here, what you call the "Leap" (I would call rounding error), So What/Why is there rounding error? Floats (and Doubles) are stored as Integer X Base_Integer^exponent_Integer. (IEEE Standard) So using base 10, If you have 1.2340 X 10^3 (or 1,234.0) your "Leap" will be 0.1 since that is the size of your least significant digit (In storage, the . is implied).
(And I'm out, too much black magic here for me)

Taylor series - calculating sin(x) until 6 digits precision

I must calculate sin(x) with a Taylor's series, until the output has 6 decimal places. The argument is an angle. I didn't implement checking the decimal places, I'm just printing next values (to check if it's working), but after 10-20 iteration it shows infinities/NaN's.
What's wrong in my thinking?
public static void sin(double x){
double sin = 0;
int n=1;
while(1<2){
sin += (Math.pow(-1,n) / factorial(2*n+1)) * Math.pow(x, 2*n+1);
n++;
try {
Thread.sleep(50);
} catch (InterruptedException ex) {
}
// CHECKING THE PRECISION HERE LATER
System.out.println(sin);
}
}
the Equation:
Don't compute each term using factorials and powers! You will rapidly overflow.
Just realize that each next term is -term * x * x / ((n+1)*(n+2)) where n increases by 2 for each term:
double tolerance = 0.0000007; // or whatever limit you want
double sin = 0.;
int n = 1;
double term = x;
while ( Math.abs(term) > tolerance ) {
sin += term;
term *= -( (x/(n+1)) * (x/(n+2)) );
n+= 2;
}
To add on to the answer provided by #Xoce (and #FredK), remember that you are computing the McLaurin series (special case of Taylor about x = 0). While this will converge fairly quickly for values that are within about pi/2 of zero, you may not get convergence of the digits before the factorial explodes for values of x further than that.
My recommendation is to use the actual Taylor series about the closest value of sin(x) for which the exact value is known (i.e., the nearest multiple of pi/2, not just about zero. And definitely do the convergence check!
Problem:
NAN error is normally a really big number, something that can happend if you divide 2 numbers but the divisor is very small, or zero.
Solution
This happens because your factorial number is getting an overflow, and later at some point you are dividing by zero again
if your factorial is taken as argument an int, then change it by , for example, a BIgInterger object.

Unique Computational value for an array

I have been thinking of it but have ran out of idea's. I have 10 arrays each of length 18 and having 18 double values in them. These 18 values are features of an image. Now I have to apply k-means clustering on them.
For implementing k-means clustering I need a unique computational value for each array. Are there any mathematical or statistical or any logic that would help me to create a computational value for each array, which is unique to it based upon values inside it. Thanks in advance.
Here is my array example. Have 10 more
[0.07518284315321135
0.002987851573676068
0.002963866526639678
0.002526139418225552
0.07444872939213325
0.0037219653347541617
0.0036979802877177715
0.0017920256571474585
0.07499695903867931
0.003477831820276616
0.003477831820276616
0.002036159171625004
0.07383539747505984
0.004311312204791184
0.0043352972518275745
0.0011786937400740452
0.07353130134299131
0.004339580295941216]
Did you checked the Arrays.hashcode in Java 7 ?
/**
* Returns a hash code based on the contents of the specified array.
* For any two <tt>double</tt> arrays <tt>a</tt> and <tt>b</tt>
* such that <tt>Arrays.equals(a, b)</tt>, it is also the case that
* <tt>Arrays.hashCode(a) == Arrays.hashCode(b)</tt>.
*
* <p>The value returned by this method is the same value that would be
* obtained by invoking the {#link List#hashCode() <tt>hashCode</tt>}
* method on a {#link List} containing a sequence of {#link Double}
* instances representing the elements of <tt>a</tt> in the same order.
* If <tt>a</tt> is <tt>null</tt>, this method returns 0.
*
* #param a the array whose hash value to compute
* #return a content-based hash code for <tt>a</tt>
* #since 1.5
*/
public static int hashCode(double a[]) {
if (a == null)
return 0;
int result = 1;
for (double element : a) {
long bits = Double.doubleToLongBits(element);
result = 31 * result + (int)(bits ^ (bits >>> 32));
}
return result;
}
I dont understand why #Marco13 mentioned " this is not returning unquie for arrays".
UPDATE
See #Macro13 comment for the reason why it cannot be unquie..
UPDATE
If we draw a graph using your input points, ( 18 elements) has one spike and 3 low values and the pattern goes..
if that is true.. you can find the mean of your Peak ( 1, 4, 8,12,16 ) and find the low Mean from remaining values.
So that you will be having Peak mean and Low mean . and you find the unquie number to represent these two also preserve the values using bijective algorithm described in here
This Alogirthm also provides formulas to reverse i.e take the Peak and Low mean from the unquie value.
To find unique pair < x; y >= x + (y + ( (( x +1 ) /2) * (( x +1 ) /2) ) )
Also refer Exercise 1 in pdf page 2 to reverse x and y.
For finding Mean and find paring value.
public static double mean(double[] array){
double peakMean = 0;
double lowMean = 0;
for (int i = 0; i < array.length; i++) {
if ( (i+1) % 4 == 0 || i == 0){
peakMean = peakMean + array[i];
}else{
lowMean = lowMean + array[i];
}
}
peakMean = peakMean / 5;
lowMean = lowMean / 13;
return bijective(lowMean, peakMean);
}
public static double bijective(double x,double y){
double tmp = ( y + ((x+1)/2));
return x + ( tmp * tmp);
}
for test
public static void main(String[] args) {
double[] arrays = {0.07518284315321135,0.002963866526639678,0.002526139418225552,0.07444872939213325,0.0037219653347541617,0.0036979802877177715,0.0017920256571474585,0.07499695903867931,0.003477831820276616,0.003477831820276616,0.002036159171625004,0.07383539747505984,0.004311312204791184,0.0043352972518275745,0.0011786937400740452,0.07353130134299131,0.004339580295941216};
System.out.println(mean(arrays));
}
You can use this the peak and low values to find the similar images.
You can simply sum the values, using double precision, the result value will unique most of the times. On the other hand, if the value position is relevant, then you can apply a sum using the index as multiplier.
The code could be as simple as:
public static double sum(double[] values) {
double val = 0.0;
for (double d : values) {
val += d;
}
return val;
}
public static double hash_w_order(double[] values) {
double val = 0.0;
for (int i = 0; i < values.length; i++) {
val += values[i] * (i + 1);
}
return val;
}
public static void main(String[] args) {
double[] myvals =
{ 0.07518284315321135, 0.002987851573676068, 0.002963866526639678, 0.002526139418225552, 0.07444872939213325, 0.0037219653347541617, 0.0036979802877177715, 0.0017920256571474585, 0.07499695903867931, 0.003477831820276616,
0.003477831820276616, 0.002036159171625004, 0.07383539747505984, 0.004311312204791184, 0.0043352972518275745, 0.0011786937400740452, 0.07353130134299131, 0.004339580295941216 };
System.out.println("Computed value based on sum: " + sum(myvals));
System.out.println("Computed value based on values and its position: " + hash_w_order(myvals));
}
The output for that code, using your list of values is:
Computed value based on sum: 0.41284176550504803
Computed value based on values and its position: 3.7396448842464496
Well, here's a method that works for any number of doubles.
public BigInteger uniqueID(double[] array) {
final BigInteger twoToTheSixtyFour =
BigInteger.valueOf(Long.MAX_VALUE).add(BigInteger.ONE);
BigInteger count = BigInteger.ZERO;
for (double d : array) {
long bitRepresentation = Double.doubleToRawLongBits(d);
count = count.multiply(twoToTheSixtyFour);
count = count.add(BigInteger.valueOf(bitRepresentation));
}
return count;
}
Explanation
Each double is a 64-bit value, which means there are 2^64 different possible double values. Since a long is easier to work with for this sort of thing, and it's the same number of bits, we can get a 1-to-1 mapping from doubles to longs using Double.doubleToRawLongBits(double).
This is awesome, because now we can treat this like a simple combinations problem. You know how you know that 1234 is a unique number? There's no other number with the same value. This is because we can break it up by its digits like so:
1234 = 1 * 10^3 + 2 * 10^2 + 3 * 10^1 + 4 * 10^0
The powers of 10 would be "basis" elements of the base-10 numbering system, if you know linear algebra. In this way, base-10 numbers are like arrays consisting of only values from 0 to 9 inclusively.
If we want something similar for double arrays, we can discuss the base-(2^64) numbering system. Each double value would be a digit in a base-(2^64) representation of a value. If there are 18 digits, there are (2^64)^18 unique values for a double[] of length 18.
That number is gigantic, so we're going to need to represent it with a BigInteger data-structure instead of a primitive number. How big is that number?
(2^64)^18 = 61172327492847069472032393719205726809135813743440799050195397570919697796091958321786863938157971792315844506873509046544459008355036150650333616890210625686064472971480622053109783197015954399612052812141827922088117778074833698589048132156300022844899841969874763871624802603515651998113045708569927237462546233168834543264678118409417047146496
There are that many unique configurations of 18-length double arrays and this code lets you uniquely describe them.
I'm going to suggest three methods, with different pros and cons which I will outline.
Hash Code
This is the obvious "solution", though it has been correctly pointed out that it will not be unique. However, it will be very unlikely that any two arrays will have the same value.
Weighted Sum
Your elements appear to be bounded; perhaps they range from a minimum of 0 to a maximum of 1. If this is the case, you can multiply the first number by N^0, the second by N^1, the third by N^2 and so on, where N is some large number (ideally the inverse of your precision). This is easily implemented, particularly if you use a matrix package, and very fast. We can make this unique if we choose.
Euclidean Distance from Mean
Subtract the mean of your arrays from each array, square the results, sum the squares. If you have an expected mean, you can use that. Again, not unique, there will be collisions, but you (almost) can't avoid that.
The difficulty of uniqueness
It has already been explained that hashing will not give you a unique solution. A unique number is possible in theory, using the Weighted Sum, but we have to use numbers of a very large size. Let's say your numbers are 64 bits in memory. That means that there are 2^64 possible numbers they can represent (slightly less using floating point). Eighteen such numbers in an array could represent 2^(64*18) different numbers. That's huge. If you use anything less, you will not be able to guarantee uniqueness due to the pigeonhole principle.
Let's look at a trivial example. If you have four letters, a, b, c and d, and you have to number them each uniquely using the numbers 1 to 3, you can't. That's the pigeonhole principle. You have 2^(18*64) possible numbers. You can't number them uniquely with less than 2^(18*64) numbers, and hashing doesn't give you that.
If you use BigDecimal, you can represent (almost) arbitrarily large numbers. If the largest element you can get is 1 and the smallest 0, then you can set N = 1/(precision) and apply the Weighted Sum mentioned above. This will guarantee uniqueness. The precision for doubles in Java is Double.MIN_VALUE. Note that the array of weights needs to be stored in _Big Decimal_s!
That satisfies this part of your question:
create a computational value for each array, which is unique to it
based upon values inside it
However, there is a problem:
1 and 2 suck for K Means
I am assuming from your discussion with Marco 13 that you are performing the clustering on the single values, not the length 18 arrays. As Marco has already mentioned, Hashing sucks for K means. The whole idea is that the smallest change in the data will result in a large change in Hash Values. That means that two images which are similar, produce two very similar arrays, produce two very different "unique" numbers. Similarity is not preserved. The result will be pseudo random!!!
Weighted Sums are better, but still bad. It will basically ignore all the elements except for the last one, unless the last element is the same. Only then will it look at the next to last, and so on. Similarity is not really preserved.
Euclidean distance from the mean (or at least some point) will at least group things together in a sort of sensible way. Direction will be ignored, but at least things that are far from the mean won't be grouped with things that are close. Similarity of one feature is preserved, the other features are lost.
In summary
1 is very easy, but is not unique and doesn't preserve similarity.
2 is easy, can be unique and doesn't preserve similarity.
3 is easy, but is not unique and preserves some similarity.
Implementatio of Weighted Sum. Not really tested.
public class Array2UniqueID {
private final double min;
private final double max;
private final double prec;
private final int length;
/**
* Used to provide a {#code BigInteger} that is unique to the given array.
* <p>
* This uses weighted sum to guarantee that two IDs match if and only if
* every element of the array also matches. Similarity is not preserved.
*
* #param min smallest value an array element can possibly take
* #param max largest value an array element can possibly take
* #param prec smallest difference possible between two array elements
* #param length length of each array
*/
public Array2UniqueID(double min, double max, double prec, int length) {
this.min = min;
this.max = max;
this.prec = prec;
this.length = length;
}
/**
* A convenience constructor which assumes the array consists of doubles of
* full range.
* <p>
* This will result in very large IDs being returned.
*
* #see Array2UniqueID#Array2UniqueID(double, double, double, int)
* #param length
*/
public Array2UniqueID(int length) {
this(-Double.MAX_VALUE, Double.MAX_VALUE, Double.MIN_VALUE, length);
}
public BigDecimal createUniqueID(double[] array) {
// Validate the data
if (array.length != length) {
throw new IllegalArgumentException("Array length must be "
+ length + " but was " + array.length);
}
for (double d : array) {
if (d < min || d > max) {
throw new IllegalArgumentException("Each element of the array"
+ " must be in the range [" + min + ", " + max + "]");
}
}
double range = max - min;
/* maxNums is the maximum number of numbers that could possibly exist
* between max and min.
* The ID will be in the range 0 to maxNums^length.
* maxNums = range / prec + 1
* Stored as a BigDecimal for convenience, but is an integer
*/
BigDecimal maxNums = BigDecimal.valueOf(range)
.divide(BigDecimal.valueOf(prec))
.add(BigDecimal.ONE);
// For convenience
BigDecimal id = BigDecimal.valueOf(0);
// 2^[ (el-1)*length + i ]
for (int i = 0; i < array.length; i++) {
BigDecimal num = BigDecimal.valueOf(array[i])
.divide(BigDecimal.valueOf(prec))
.multiply(maxNums).pow(i);
id = id.add(num);
}
return id;
}
As I understand, you are going to make k-clustering, based on the double values.
Why not just wrap double value in an object, with array and position identifier, so you would know in which cluster it ended up?
Something like:
public class Element {
final public double value;
final public int array;
final public int position;
public Element(double value, int array, int position) {
this.value = value;
this.array = array;
this.position = position;
}
}
If you need to cluster array as a whole,
You can transform original arrays of length 18 to array of length 19 with last or first element being unique id, that you will ignore during clustering, but, to which you could refer after clustering finished. That way this have a small memory footprint - of 8 additional bytes for an array, and easy association with the original value.
If space is absolutely a problem, and you have all values of an array lesser than 1, you can add unique id, greater or equal to 1 to each array, and cluster, based on reminder of division to 1, 0.07518284315321135 stays 0.07518284315321135 for the 1st, and 0.07518284315321135 becomes 1.07518284315321135 for the 2nd, although this increases complexity of computation during clustering.
First of all, let's try to understand what you need mathematically:
Uniquely mapping an array of m real numbers to a single number is in fact a bijection between R^m and R, or at least N.
Since floating points are in fact rational numbers, your problem is to find a bijection between Q^m and N, which can be transformed to N^n to N, because you know your values will always be greater than 0 (just multiply your values by the precision).
Thus you need to map N^m to N. Take a look at the Cantor Pairing Function for some ideas
A guaranteed way to generate a unique result based on the array is to convert it to one big string, and use that for your computational value.
It may be slow, but it will be unique based on the array's values.
Implementation examples:
Best way to convert an ArrayList to a string

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