315 lines
7.3 KiB
JavaScript
315 lines
7.3 KiB
JavaScript
/**
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* Simple Javascript eXtension - 1.0, Mathematics Module
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* (c) 2011 - 2015 Steve L. Nyemba, steve@the-phi.com
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* License GPL version 3.0
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*
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* dependencies:
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* utils.js implementation of design patterns and utilities
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*
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* This file contains an enhancement of utilities integrated into the jx.math.* built-in package of javascript
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* Because we implement math and numerical functions it is to be understood that most of the functions will have common preconditions
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* i.e lxi.constructor == Array && isNumber(lxi) unless specified otherwise
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* jx.math.max
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* jx.math.min
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* jx.math.sum
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* jx.math.prod
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* jx.math.freq
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* jx.math.avg
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* jx.math.mean computes the mean/average of a list of observations (arthmetic mean included too)
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* jx.math.sd computes the standard deviation of a list of observations
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* jx.math.var computes the variance of a list of observations
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* jx.math.diff computes the absolute difference of values in an array
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* jx.math.fibonacci comptutes the fibonacci value of a given number
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* jx.math.factorial computes the factorial of a given number
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*/
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if(!jx){
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var jx = {} ;
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}
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jx.math = {}
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jx.math.sqrt = Math.sqrt;
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jx.math.PHI = (1+jx.math.sqrt(5))/2 ;//1.61803399 ;
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/**
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* @param lxi list of observatins xi
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*/
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jx.math.max = function(lxi){
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sortNumber= function(a,b) {
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return a - b;
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}
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index = lxi.length -1 ;
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max = jx.utils.cast(lxi,Number).sort(sortNumber)[index] ; // perhaps need to cast
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return max ;
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}
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/**
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* finds the minimum of a list of observation lxi (vector of values)
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* @param lxi list/vector of values/observations
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*/
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jx.math.min = function(lxi){
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sortNumber = function(a,b){
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return a- b;
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}
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min = jx.utils.cast(lxi,Number).sort(sortNumber)[0] ;
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return min ;
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}
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/**
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* @pre : values.constructor == Array
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* @param lxi list of observed values to be summed
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*/
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jx.math.sum = function(lxi){
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return eval(lxi.join('+'));
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} ;
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/**
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* This function will compute the frequency of a vector i.e providing relative values
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*/
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jx.math.freq = function(lxi){
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var N = jx.math.sum(lxi) ;
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return jx.utils.patterns.visitor(lxi,function(xi){
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return xi/N ;
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});
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}
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/**
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* This function will perform the product of a vector
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* @pre lxi.constructor == Array && isNumber(lxi)
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*/
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jx.math.prod = function(lxi){
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return eval(lxi.join('*')) ;
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}
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/**
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* @pre : lni != null && lxi.length == lni.length
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* @param lxi list of observed values
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* @param lni list of the number of times observations of index i have been made
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*/
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jx.math.avg = function(lxi,lni){
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N = lxi.length ;
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if(lni == null){
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return jx.math.sum(lxi)/N ;
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}else{
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values = []
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for(var i=0; i < lxi.length; i++){
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values[i] = Number(lxi[i])*Number(lni[i]) ;
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}
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return Number(jx.math.sum(values)/N) ;
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}
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};
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/**
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* This function will repete a value a given number of times
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* @pre times > 0
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*/
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jx.math.rep = function(value,times){
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var lvalues = []
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for(var i=0; i < times; i++){
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lvalues.push(value) ;
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}
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return lvalues;
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}
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jx.math.mean = jx.math.avg ;
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/**
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* This function will compute the mode of a given vector
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* The mode is by definition the most frequent item in the vector
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*/
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jx.math.mode = function(x) {
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var N = x.length ;
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map = {}
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var max =0;
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var value = 0;
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for(var i in x){
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id = x[i] ;
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if(map[id] == null){
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map[id] = 0 ;
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}
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map[id] = map[id] + 1 ;
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if(map[id] > max){
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value = id ;
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max = map[id] ;
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}
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}
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var value = jx.utils.patterns.visitor(jx.utils.keys(map),function(id){
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if(map[id] == max){
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return Number(id) ;
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}else{
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return null;
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}
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})
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return value.length == 1?value[0]:value ;
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}
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jx.math.pow = Math.pow
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jx.math.sd = function(lxi,lni){
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N = lxi.length ;
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mean = jx.math.mean(lxi,lni) ;
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sqr = [] ;
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for(var i=0; i < lxi.length ;i++){
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sqr[i] = jx.math.pow((Number(lxi[i])-mean),2 ) ;
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}
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total = jx.math.sum(sqr);
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return jx.math.sqrt(total/(N-1)) ;
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} ;
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/**
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* This function computes the correlation between two vectors
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* @pre x1.length == x2.length
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*/
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jx.math.cor = function(x1,x2){
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return jx.math.cov(x1,x2) / (jx.math.sd(x1)*jx.math.sd(x2))
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}
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/**
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* This function will compute the covariance of 2 vectors
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* @pre x1.length == x2.length
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*/
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jx.math.cov = function(x1,x2){
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var u1 = jx.math.mean(x1) ;
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var u2 = jx.math.mean(x2) ;
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var N = x1.length ;
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var value = 0
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for(var i in x1){
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value += (x1[i] - u1) * (x2[i] - u2)
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}
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return value / (N - 1)
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}
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/**
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* Computes the factorial of a given value
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*/
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jx.math.factorial = function(value){
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r =value;
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for(var i =value-1; i > 0; i--){
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r *= i ;
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}
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return r;
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} ;
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/**
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* Computes the fibonacci value of a given number using the golden ratio
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*/
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jx.math.fibonacci = function(value){
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r = (jx.math.pow(jx.math.PHI,value)/jx.math.sqrt(5)) + 0.5 ;
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return jx.math.floor(r) ;
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} ;
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/**
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* computes the absolute difference of values in a list of observations
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*/
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jx.math.diff = function(lxi){
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var r = [] ;
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var x,y;
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for(var i=0; i < lxi.length-1; i++){
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x = lxi[i] ;
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y = lxi[i+1] ;
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r.push(y-x)
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}
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return r ;
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};
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/**
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* This section implements a few handlers based on sets
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*/
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jx.math.sets = {} ;
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/**
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* This function will perform a unique operation of values/objects
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* @param list list/vector of values or objects
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* @param equals operator to be used, only provide this for complex objects
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*/
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jx.math.sets.unique = jx.utils.unique ;
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/**
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* This function will perform the union of 2 sets (objects, or values)
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* @param list1 list/vector of values or objects
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* @param list2 list/vector of values or objects
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* @param equals operator to be used to evaluate equality (use this for complex objects)
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*/
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jx.math.sets.union = function(list1,list2,equals){
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runion = [] ;
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runion = list1.concat(list2) ;
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runion = jx.math.sets.unique(runion,equals)
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return runion;
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}
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/**
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* This function will normalize values within a vector
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* By definition normalization is (x - u) / sd (assuming population parameters are known)
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*/
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jx.math.normalize = function(lvalues){
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mean = jx.math.mean(lvalues) ;
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sd = jx.math.sd(lvalues) ;
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return jx.utils.patterns.visitor(lvalues,function(x){
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return ((x - mean) / sd)
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})
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}
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/**
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* This function will scale a feature vector over it's range
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*/
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jx.math.scale = function(lvalues,percent){
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max = jx.math.max(lvalues) ;
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min = jx.math.min(lvalues) ;
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return jx.utils.patterns.visitor(lvalues,function(x){
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var value = (x - min ) / max ;
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if(percent == true){
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return (100*value).toFixed(2)
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}else{
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return value ;
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}
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})
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}
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/**
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* This is a lightweight map reduce infrastructure
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*/
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jx.mr = {} ;
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/**
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* This function will perform a map on a given id in rec, then will call emit with the
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*/
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jx.mr.map = null
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/**
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* @param keys
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* @param values array of values that were mapped
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*/
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jx.mr.reduce = null;
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jx.mr.mapreduce = function(data,fn_map,fn_reduce){
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if (fn_map == null){
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throw new "Map function is not defined"
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}
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map = {} ;
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emit = function(id,values){
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if(map[id] == null){
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map[id] = []
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}
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map[id].push(values);
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}
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if(data.constructor != Array){
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for (id in data){
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//rec = data[id] ;
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rec = {}
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rec['__id'] = id;
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rec['data'] = data[id] ;
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fn_map(rec,emit)
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}
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}else{
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for (var i=0; i < data.length; i++){
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rec = data[i];
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fn_map(rec,emit);
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//if(i == 2)break;
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}
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}
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if(fn_reduce != null){
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keys = jx.utils.keys(map) ;
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m = {}
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for(var i=0; i < keys.length; i++){
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id = keys[i] ;
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values = map[id] ;
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value = fn_reduce(id,values) ;
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id = keys[i] ;
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m[id] = value;
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}
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map = m
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}
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return map ;
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}
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