/*
Copyright (c) 2004-2011, The Dojo Foundation All Rights Reserved.
Available via Academic Free License >= 2.1 OR the modified BSD license.
see: http://dojotoolkit.org/license for details
*/
if(!dojo._hasResource["dojox.math._base"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code.
dojo._hasResource["dojox.math._base"] = true;
dojo.provide("dojox.math._base");
dojo.getObject("math", true, dojox);
(function(){
var m = dojox.math;
dojo.mixin(dojox.math, {
toRadians: function(/* Number */n){
// summary:
// Convert the passed number to radians.
return (n*Math.PI)/180; // Number
},
toDegrees: function(/* Number */n){
// summary:
// Convert the passed number to degrees.
return (n*180)/Math.PI; // Number
},
degreesToRadians: function(/* Number */n){
// summary:
// Deprecated. Use dojox.math.toRadians.
return m.toRadians(n); // Number
},
radiansToDegrees: function(/* Number */n){
// summary:
// Deprecated. Use dojox.math.toDegrees.
return m.toDegrees(n); // Number
},
_gamma: function(z){
// summary:
// Compute the gamma function for the passed number.
// Approximately 14 dijits of precision with non-integers.
var answer = 1; // 0!
// gamma(n+1) = n * gamma(n)
while (--z >= 1){
answer *= z;
}
if(z == 0){ return answer; } // normal integer quick return
if(Math.floor(z) == z){ return NaN; } // undefined at nonpositive integers since sin() below will return 0
// assert: z < 1, remember this z is really z-1
if(z == -0.5){ return Math.sqrt(Math.PI); } // popular gamma(1/2)
if(z < -0.5){ // remember this z is really z-1
return Math.PI / (Math.sin(Math.PI * (z + 1)) * this._gamma(-z)); // reflection
}
// assert: -0.5 < z < 1
// Spouge approximation algorithm
var a = 13;
// c[0] = sqrt(2*PI) / exp(a)
// var kfact = 1
// for (var k=1; k < a; k++){
// c[k] = pow(-k + a, k - 0.5) * exp(-k) / kfact
// kfact *= -k // (-1)^(k-1) * (k-1)!
// }
var c = [ // precomputed from the above algorithm
5.6658056015186327e-6,
1.2743717663379679,
-4.9374199093155115,
7.8720267032485961,
-6.6760503749436087,
3.2525298444485167,
-9.1852521441026269e-1,
1.4474022977730785e-1,
-1.1627561382389853e-2,
4.0117980757066622e-4,
-4.2652458386405744e-6,
6.6651913290336086e-9,
-1.5392547381874824e-13
];
var sum = c[0];
for (var k=1; k < a; k++){
sum += c[k] / (z + k);
}
return answer * Math.pow(z + a, z + 0.5) / Math.exp(z) * sum;
},
factorial: function(/* Number */n){
// summary:
// Return the factorial of n
return this._gamma(n+1); // Number
},
permutations: function(/* Number */n, /* Number */k){
// summary:
// TODO
if(n==0 || k==0){
return 1; // Number
}
return this.factorial(n) / this.factorial(n-k);
},
combinations: function(/* Number */n, /* Number */r){
// summary:
// TODO
if(n==0 || r==0){
return 1; // Number
}
return this.factorial(n) / (this.factorial(n-r) * this.factorial(r)); // Number
},
bernstein: function(/* Number */t, /* Number */n, /* Number */ i){
// summary:
// TODO
return this.combinations(n, i) * Math.pow(t, i) * Math.pow(1-t, n-i); // Number
},
gaussian: function(){
// summary:
// Return a random number based on the Gaussian algo.
var k=2;
do{
var i=2*Math.random()-1;
var j=2*Math.random()-1;
k = i*i+j*j;
}while(k>=1);
return i * Math.sqrt((-2*Math.log(k))/k); // Number
},
// create a range of numbers
range: function(/* Number */a, /* Number? */b, /* Number? */step){
// summary:
// Create a range of numbers based on the parameters.
if(arguments.length<2){
b=a,a=0;
}
var range=[], s=step||1, i;
if(s>0){
for(i=a; i<b; i+=s){
range.push(i);
}
}else{
if(s<0){
for(i=a; i>b; i+=s){
range.push(i);
}
}else{
throw new Error("dojox.math.range: step must not be zero.");
}
}
return range; // Array
},
distance: function(/* Array */a, /* Array */b){
// summary:
// Calculate the distance between point A and point B
return Math.sqrt(Math.pow(b[0]-a[0],2)+Math.pow(b[1]-a[1],2)); // Number
},
midpoint: function(/* Array */a, /* Array */b){
// summary:
// Calculate the midpoint between points A and B. A and B may be multidimensional.
if(a.length!=b.length){
console.error("dojox.math.midpoint: Points A and B are not the same dimensionally.", a, b);
}
var m=[];
for(var i=0; i<a.length; i++){
m[i]=(a[i]+b[i])/2;
}
return m; // Array
}
});
})();
}