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core.js
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core.js
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/**
* jStat - JavaScript Statistical Library
* Copyright (c) 2011
* This document is licensed as free software under the terms of the
* MIT License: http://www.opensource.org/licenses/mit-license.php */
this.j$ = this.jStat = (function( Math, undefined ) {
// for quick reference
var slice = Array.prototype.slice,
toString = Object.prototype.toString,
// ascending/descending functions for sort
ascNum = function( a, b ) { return a - b; },
descNum = function( a, b ) { return b - a; },
// test if array
isArray = Array.isArray || function( arg ) {
return toString.call( arg ) === "[object Array]";
},
// test if function
isFunction = function( arg ) {
return toString.call( arg ) === "[object Function]";
},
// test if object
isObject = function( arg ) {
return toString.call( arg ) === "[object Object]";
},
// calculate correction for IEEE
calcRdx = function( n, m ) {
var val = n > m ? n : m;
return Math.pow( 10, 15 - ~~( Math.log((( val > 0 ) ? val : -val )) * Math.LOG10E ));
};
// implement bind if browser doesn't natively support it
if ( !Function.prototype.bind ) {
Function.prototype.bind = function( obj ) {
var slice = [].slice,
args = slice.call( arguments, 1 ),
self = this,
nop = function() {},
bound = function() {
return self.apply( this instanceof nop ? this : ( obj || {} ),
args.concat( slice.call( arguments ))
);
};
bound.prototype = this.prototype;
return bound;
};
}
// global function
function jStat() {
return new jStat.fn.init( arguments );
}
// extend jStat prototype
jStat.fn = jStat.prototype = {
constructor : jStat,
init : function( args ) {
// if first argument is an array, must be vector or matrix
if ( isArray( args[0] )) {
if ( isArray( args[0][0] )) {
for ( var i = 0; i < args[0].length; i++ ) {
this[i] = args[0][i];
}
this.length = args[0].length;
} else {
this[0] = args[0];
this.length = 1;
}
// if first argument is number, assume creation of sequence
} else if ( !isNaN( args[0] )) {
this[0] = jStat.seq.apply( null, args );
this.length = 1;
}
return this;
},
// default length
length : 0,
// return clean array
toArray : function() {
return slice.call( this );
},
// only to be used internally
push : [].push,
sort : [].sort,
splice : [].splice
};
jStat.fn.init.prototype = jStat.fn;
// create method for easy extension
jStat.extend = function( obj ) {
var args = slice.call( arguments ),
i = 1, j;
if ( args.length === 1 ) {
for ( i in obj ) {
jStat[i] = obj[i];
}
return this;
}
for ( ; i < args.length; i++ ) {
for ( j in args[i] ) obj[j] = args[i][j];
}
return obj;
};
// extend jStat.fn with methods which don't require arguments and work on columns
(function( funcs ) {
for ( var i = 0; i < funcs.length; i++ ) (function( passfunc ) {
// if a matrix is passed, automatically assume operation should be done on the columns
jStat.fn[ passfunc ] = function( fullbool, func ) {
var arr = [],
i = 0,
tmpthis = this;
if ( isFunction( fullbool )) {
func = fullbool;
fullbool = false;
}
if ( func ) {
setTimeout( function() {
func.call( tmpthis, jStat.fn[ passfunc ].call( tmpthis, fullbool ));
}, 15 );
return this;
}
if ( this.length > 1 ) {
tmpthis = fullbool === true ? this : this.transpose();
for ( ; i < tmpthis.length; i++ )
arr[i] = jStat[ passfunc ]( tmpthis[i] );
arr = fullbool === true ? jStat[ passfunc ]( arr ) : arr;
}
return arr;
};
})( funcs[i] );
})( 'sum min max mean median mode range variance stdev meandev meddev quartiles'.split( ' ' ));
// extend jStat.fn with methods that have no argument
(function( funcs ) {
for ( var i = 0; i < funcs.length; i++ ) (function( passfunc ) {
jStat.fn[ passfunc ] = function( func ) {
var tmpthis = this,
results;
if ( func ) {
setTimeout( function() {
func.call( tmpthis, jStat.fn[ passfunc ].call( tmpthis ));
}, 15 );
return this;
}
results = jStat[ passfunc ]( this );
return isArray( results ) ? jStat( results ) : results;
};
})( funcs[i] );
})( 'transpose clear norm symmetric'.split( ' ' ));
// extend jStat.fn with methods that require one argument
(function( funcs ) {
for ( var i = 0; i < funcs.length; i++ ) (function( passfunc ) {
jStat.fn[ passfunc ] = function( arg, func ) {
var tmpthis = this;
if ( func ) {
setTimeout( function() {
func.call( tmpthis, jStat.fn[ passfunc ].call( tmpthis, arg ));
}, 15 );
return this;
}
return jStat( jStat[ passfunc ]( this, arg ));
};
})( funcs[i] );
})( 'add divide multiply subtract dot pow abs angle'.split( ' ' ));
// extend jStat.fn
jStat.extend( jStat.fn, {
// Returns the number of rows in the matrix
rows: function() {
return this.length || 1;
},
// Returns the number of columns in the matrix
cols: function() {
return this[0].length || 1;
},
// Returns the dimensions of the object { rows: i, cols: j }
dimensions : function() {
return {
rows : this.rows(),
cols : this.cols()
};
},
// Returns a specified row as a vector
row: function( index ) {
return jStat( this[index] );
},
// Returns the specified column as a vector
col: function( index ) {
var column = [],
i = 0;
for ( ; i < this.length; i++ ) {
column[i] = [ this[i][index] ];
}
return jStat( column );
},
// Returns the diagonal of the matrix
diag : function() {
var row = 0,
nrow = this.rows(),
res = [];
for( ; row < nrow; row++ ) {
res[row] = [ this[row][row] ];
}
return jStat( res );
},
// Returns the anti-diagonal of the matrix
antidiag : function() {
var nrow = this.rows() - 1,
res = [],
i = 0;
for( ; nrow >= 0; nrow--, i++ ) {
res[i] = [ this[i][nrow] ];
}
return jStat( res );
},
// map a function to a matrix or vector
map : function( func ) {
return jStat( jStat.map( this, func ));
},
// destructively alter an object
alter : function( func ) {
jStat.alter( this, func );
return this;
}
});
// static methods //
jStat.extend({
// transpose a matrix or array
transpose : function( arr ) {
arr = isArray( arr[0] ) ? arr : [ arr ];
var rows = arr.length,
cols = arr[0].length,
obj = [],
i = 0, j;
for ( ; i < cols; i++ ) {
obj[i] = [];
for ( j = 0; j < rows; j++ ) {
obj[i][j] = arr[j][i];
}
}
return obj;
},
// map a function to a matrix or vector
map : function( arr, func, toAlter ) {
var len = arr.length,
res = toAlter ? arr : [],
i = 0;
for ( ; i < len; i++ )
if ( isArray( arr[i] )) res[i] = jStat.map( arr[i], func, toAlter );
else res[i] = func( arr[i], i, arr );
return res;
},
// destructively alter an array
alter : function( arr, func ) {
return jStat.map( arr, func, true );
},
// generate a rows x cols matrix according to the supplied function
create: function ( rows, cols, func ) {
var res = [], i, j;
for( i = 0; i < rows; i++ ) {
res[i] = [];
for( j = 0; j < cols; j++ ) {
res[i][j] = func( i, j );
}
}
return res;
},
// generate a rows x cols matrix of zeros
zeros : function( rows, cols ) {
return jStat.create( rows, cols, function() { return 0; });
},
// generate a rows x cols matrix of ones
ones: function( rows, cols ) {
return jStat.create( rows, cols, function() { return 1; });
},
// generate a rows x cols matrix of uniformly random numbers
rand: function( rows, cols ) {
return jStat.create( rows, cols, function() { return Math.random(); });
},
// generate an identity matrix of size row x cols
identity : function( rows, cols ) {
return jStat.create( rows, cols, function( i, j ) { return ( i === j ) ? 1 : 0; });
},
// generate sequence
seq : function( min, max, length, func ) {
var arr = [],
hival = calcRdx( min, max ),
step = ( max * hival - min * hival ) / (( length - 1 ) * hival ),
current = min,
cnt = 0;
for ( ; current <= max; cnt++, current = ( min * hival + step * hival * cnt ) / hival ) {
arr.push(( func ? func( current ) : current ));
}
return arr;
},
// add a vector or scalar to the vector
add : function( arr, arg ) {
return isNaN( arg ) ?
jStat.map( arr, function( value, row, col ) { return value + arg[row][col]; })
: jStat.map( arr, function ( value ) { return value + arg; });
},
// TODO: Implement matrix division
// matrix division
divide : function( arr, arg ) {
return isNaN( arg ) ?
false
: jStat.map(arr, function ( value ) { return value / arg; });
},
// matrix multiplication
multiply : function( arr, arg ) {
var row, col, nrescols, sum,
nrow = arr.length,
ncol = arr[0].length,
res = jStat.zeros( nrow, nrescols = ( isNaN( arg )) ? arg[0].length : ncol ),
rescols = 0;
if( isNaN( arg )) {
for( ; rescols < nrescols; rescols++ ) {
for( row = 0; row < nrow; row++ ) {
sum = 0;
for( col = 0; col < ncol; col++ ) {
sum += arr[row][col] * arg[col][rescols];
}
res[row][rescols] = sum;
}
}
return ( nrow === 1 && rescols === 1 ) ? res[0][0] : res;
}
return jStat.map( arr, function( value ) { return value * arg; });
},
// subtract a vector or scalar from the vector
subtract : function( arr, arg ) {
return isNaN( arg ) ?
jStat.map( arr, function( value, row, col ) { return value - arg[row][col]; })
: jStat.map( arr, function( value ) { return value - arg; });
},
// Returns the dot product of two matricies
dot : function( arr, arg ) {
arr = isArray( arr[0] ) ? arr : [ arr ];
arg = isArray( arg[0] ) ? arg : [ arg ];
// convert column to row vector
var left = ( arr[0].length === 1 && arr.length !== 1 ) ? jStat.transpose( arr ) : arr,
right = ( arg[0].length === 1 && arg.length !== 1 ) ? jStat.transpose( arg ) : arg,
res = [],
row = 0,
nrow = left.length,
ncol = left[0].length,
sum, col;
for( ; row < nrow; row++ ) {
res[row] = [];
sum = 0;
for( col = 0; col < ncol; col++ ) {
sum += left[row][col] * right[row][col];
}
res[row] = sum;
}
return ( res.length === 1 ) ? res[0] : res;
},
// raise every element by a scalar or vector
pow : function( arr, arg ) {
return jStat.map( arr, function( value ) { return Math.pow( value, arg ); });
},
// generate the absolute values of the vector
abs : function( arr ) {
return jStat.map( arr, function( value ) { return Math.abs( value ); });
},
// set all values to zero
clear : function( arr ) {
return jStat.alter( arr, function() { return 0; });
},
// BUG: Does not work for matrices
// computes the norm of the vector
norm : function( arr ) {
arr = isArray( arr[0] ) ? arr : [arr];
if( arr.length > 1 && arr[0].length > 1 ) {
// matrix norm
} else {
// vector norm
return Math.sqrt( jStat.dot( arr, arr ));
}
},
// BUG: Does not work for matrices
// computes the angle between two vectors
angle : function( arr, arg ) {
return Math.acos( jStat.dot( arr, arg ) / ( jStat.norm( arr ) * jStat.norm( arg )));
},
// Tests whether a matrix is symmetric
symmetric : function( arr ) {
var issymmetric = true,
row = 0,
size = arr.length, col;
if( arr.length !== arr[0].length ) return false;
for ( ; row < size; row++ ) {
for ( col = 0; col < size; col++ ) {
if ( arr[col][row] !== arr[row][col] ) return false;
}
}
return true;
},
// array/vector specific functions //
// sum of an array
sum : function( arr ) {
var sum = 0,
i = arr.length;
while( --i >= 0 ) sum += arr[i];
return sum;
},
// minimum value of an array
min : function( arr ) {
return Math.min.apply( null, arr );
},
// maximum value of an array
max : function( arr ) {
return Math.max.apply( null, arr );
},
// mean value of an array
mean : function( arr ) {
return jStat.sum( arr ) / arr.length;
},
// median of an array
median : function( arr ) {
var arrlen = arr.length,
_arr = arr.slice().sort( ascNum );
// check if array is even or odd, then return the appropriate
return !( arrlen & 1 ) ? ( _arr[ ( arrlen / 2 ) - 1 ] + _arr[ ( arrlen / 2 ) ] ) / 2 : _arr[ ( arrlen / 2 ) | 0 ];
},
// mode of an array
mode : function( arr ) {
var arrLen = arr.length,
_arr = arr.slice().sort( ascNum ),
count = 1,
maxCount = 0,
numMaxCount = 0,
i = 0,
maxNum;
for ( ; i < arrLen; i++ ) {
if ( _arr[ i ] === _arr[ i + 1 ] ) {
count++;
} else {
if ( count > maxCount ) {
maxNum = _arr[i];
maxCount = count;
count = 1;
numMaxCount = 0;
} else {
// are there multiple max counts
if ( count === maxCount ) {
numMaxCount++;
// count is less than max count, so reset values
} else {
count = 1;
}
}
}
}
return ( numMaxCount === 0 ) ? maxNum : false;
},
// range of an array
range : function( arr ) {
var _arr = arr.slice().sort( ascNum );
return _arr[ _arr.length - 1 ] - _arr[0];
},
// variance of an array
variance : function( arr ) {
var mean = jStat.mean( arr ),
stSum = 0,
i = arr.length - 1;
for( ; i >= 0; i-- ) {
stSum += Math.pow(( arr[i] - mean ), 2 );
}
return stSum / ( arr.length - 1 );
},
// standard deviation of an array
stdev : function( arr ) {
return Math.sqrt( jStat.variance( arr ));
},
// mean deviation (mean absolute deviation) of an array
meandev : function( arr ) {
var devSum = 0,
mean = jStat.mean( arr ),
i = arr.length - 1;
for ( ; i >= 0; i-- ) {
devSum += Math.abs( arr[i] - mean );
}
return devSum / arr.length;
},
// median deviation (median absolute deviation) of an array
meddev : function( arr ) {
var devSum = 0,
median = jStat.median( arr ),
i = arr.length - 1;
for ( ; i >= 0; i-- ) {
devSum += Math.abs( arr[i] - median );
}
return devSum / arr.length;
},
// quartiles of an array
quartiles : function( arr ) {
var arrlen = arr.length,
_arr = arr.slice().sort( ascNum );
return [
_arr[ Math.round(( arrlen ) / 4 ) - 1 ],
_arr[ Math.round(( arrlen ) / 2 ) - 1 ],
_arr[ Math.round(( arrlen ) * 3 / 4 ) - 1 ]
];
},
// covariance of two arrays
covariance : function( arr1, arr2 ) {
var u = jStat.mean( arr1 ),
v = jStat.mean( arr2 ),
sq_dev = [],
arr1Len = arr1.length,
i = 0;
for ( ; i < arr1Len; i++ ) {
sq_dev[i] = ( arr1[i] - u ) * ( arr2[i] - v );
}
return jStat.sum( sq_dev ) / arr1Len;
},
// correlation coefficient of two arrays
corrcoeff : function( arr1, arr2 ) {
return jStat.covariance( arr1, arr2 ) / jStat.stdev( arr1 ) / jStat.stdev( arr2 );
}
});
// exposing jStat
return jStat;
})( Math );