binomcoef

Computes the binomial coefficient.

The binomial coefficient of two non-negative integers n and k is defined as

It can be generalized for any two real numbers n and k as follows

Installation

$ npm install compute-binomcoef

For use in the browser, use browserify.

Usage

var binomcoef = require( 'compute-binomcoef' );

binomcoef( n, k[, options] )

Computes the Binomial function (element-wise). n may be either a number, an array, a typed array, or a matrix. k has to be either an array or matrix of equal dimensions as n or a single number. Correspondingly, the function returns either an array with the same length as the input array(s), a matrix with the same dimensions as the input matrix/matrices or a single number.

var matrix = require( 'dstructs-matrix' ),
	data,
	mat,
	out,
	i;

out = binomcoef( 8, 2 );
// returns 28

out = binomcoef( 0, 0 );
// returns 1

out = binomcoef( -4, 2 );
// returns 10

out = binomcoef( 2, -1 );
// returns 0

out = binomcoef( 3, 1.5 );
// returns ~3.395

data = [ 0, 1, 2, 3, 4 ];
out = binomcoef( data, 2 );
// returns [ 0, 0, 1, 3, 6 ]

out = binomcoef( 6, data );
// returns [ 1, 6, 15, 20, 15 ]

data = new Int8Array( data );
out = binomcoef( data, 2 );
// returns Float64Array( [ 0, 0, 1, 3, 6 ] )

data = new Float64Array( 6 );
for ( i = 0; i < 6; i++ ) {
	data[ i ] = i;
}
mat = matrix( data, [3,2], 'float64' );
/*
	[ 0  1
	  2  3
	  4  5 ]
*/

out = binomcoef( mat, 3 );
/*
	[ 0  0
	  0  1
	  4 10 ]
*/

The function accepts the following options:

• accessor: accessor function for accessing array values.
• dtype: output typed array or matrix data type. Default: float64.
• copy: boolean indicating if the function should return a new data structure. Default: true.
• path: deepget/deepset key path.
• sep: deepget/deepset key path separator. Default: '.'.

For non-numeric arrays, provide an accessor function for accessing array values.

var data = [
	['beep', 5 ],
	['boop', 10 ],
	['bip', 15 ],
	['bap', 20 ],
	['baz', 25 ]
];

function getValue( d, i ) {
	return d[ 1 ];
}

var out = binomcoef( data, 2, {
	'accessor': getValue
});
// returns [ 10, 45, 105, 190, 300 ]

When computing the binomial coefficient for values of two object arrays, provide an accessor function which accepts 3 arguments.

var data = [
	['beep', 1],
	['boop', 2],
	['bip', 3],
	['bap', 4],
	['baz', 5]
];

var y = [
	{'x': 1},
	{'x': 2},
	{'x': 3},
	{'x': 4},
	{'x': 5}
];

function getValue( d, i, j ) {
	if ( j === 0 ) {
		return d[ 1 ];
	}
	return d.x;
}

var out = beta( data, y, {
	'accessor': getValue
});
// returns [ 1, 1, 1, 1, 1 ]

Note: j corresponds to the input array index, where j=0 is the index for the first input array and j=1 is the index for the second input array.

To deepset an object array, provide a key path and, optionally, a key path separator.

var data = [
	{'x':[0,0]},
	{'x':[1,1]},
	{'x':[2,2]},
	{'x':[3,3]},
	{'x':[4,4]}
];

var out = binomcoef( data, 'x|1', '|' );
/*
	[
		{'x':[0,0]},
		{'x':[1,0]},
		{'x':[2,1]},
		{'x':[3,3]},
		{'x':[4,6]}
	]
*/

var bool = ( data === out );
// returns true

By default, when provided a typed array or matrix, the output data structure is float64 in order to preserve precision. To specify a different data type, set the dtype option (see matrix for a list of acceptable data types).

var data, out;

data = new Int8Array( [0, 1, 2] );

out = binomcoef( data, 1, {
	'dtype': 'int32'
});
// returns Int32Array( [0,1,2] )

// Works for plain arrays, as well...
out = binomcoef( [0, 1, 2], 1, {
	'dtype': 'uint8'
});
// returns Uint8Array( [0,1,2] )

By default, the function returns a new data structure. To mutate the input data structure (e.g., when input values can be discarded or when optimizing memory usage), set the copy option to false.

var data,
	bool,
	mat,
	out,
	i;

var data = [ 0, 1, 2, 3, 4 ];

var out = binomcoef( data, 2, {
	'copy': false
});
// returns [ 0, 0, 1, 3, 6 ]

bool = ( data === out );
// returns true

data = new Float64Array( 6 );
for ( i = 0; i < 6; i++ ) {
	data[ i ] = i;
}
mat = matrix( data, [3,2], 'float64' );
/*
	[ 0  1
	  2  3
	  4  5 ]
*/

out = binomcoef( mat, 3, {
	'copy': false
});
/*
	[ 0  0
	  0  1
	  4 10 ]
*/

bool = ( mat === out );
// returns true

Notes

• If an element is not a numeric value, the evaluated error function is NaN.

  var data, out;
  
  out = binomcoef( null, 1 );
  // returns NaN
  
  out = binomcoef( true, 1 );
  // returns NaN
  
  out = binomcoef( {'a':'b'}, 1 );
  // returns NaN
  
  out = binomcoef( [ true, null, [] ], 1 );
  // returns [ NaN, NaN, NaN ]
  
  function getValue( d, i ) {
  	return d.x;
  }
  data = [
  	{'x':true},
  	{'x':[]},
  	{'x':{}},
  	{'x':null}
  ];
  
  out = binomcoef( data, 1, {
  	'accessor': getValue
  });
  // returns [ NaN, NaN, NaN, NaN ]
  
  out = binomcoef( data, 1, {
  	'path': 'x'
  });
  /*
  	[
  		{'x':NaN},
  		{'x':NaN},
  		{'x':NaN,
  		{'x':NaN}
  	]
  */

• Be careful when providing a data structure which contains non-numeric elements and specifying an integer output data type, as NaN values are cast to 0.

  var out = binomcoef( [ true, null, [] ], 1 {
  	'dtype': 'int8'
  });
  // returns Int8Array( [0,0,0] );

• When calling the function with a numeric value as the first argument and a matrix or array as the second argument, only the dtype option is applicable.

  	// Valid:
  	var out = binomcoef( 2, [ 1, 2, 3 ], {
  		'dtype': 'int8'
  	});
  	// returns Int8Array( [2, 1, 0] )
  
  	// Not valid:
  	var out = binomcoef( 2, [ 1, 2, 3 ], {
  		'copy': false
  	});
  	// throws an error

Implementation

Instead of evaluating the factorial form, which is inefficient and prone to overflow for large inputs arguments, this module computes the following multiplicative representation of the binomial coefficient for integer arguments

For non-integer inputs, the function computes - ln( n + 1 ) - ln( Beta( n - k + 1, k + 1 ) ) and returns the power this value to base e.

Examples

var matrix = require( 'dstructs-matrix' ),
	 binomcoef = require( 'compute-binomcoef' );

var data,
	mat,
	out,
	tmp,
	i;

// ----
// Plain arrays...
data = new Array( 10 );
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = Math.round( Math.random()*20 );
}
out = binomcoef( data, 3 );

// Object arrays (accessors)...
function getValue( d ) {
	return d.x;
}
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = {
		'x': data[ i ]
	};
}
out = binomcoef( data, 3, {
	'accessor': getValue
});

// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = {
		'x': [ i, data[ i ].x ]
	};
}
out = binomcoef( data, 3, {
	'path': 'x/1',
	'sep': '/'
});

// Typed arrays...
data = new Int32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
	data[ i ] = Math.round( Math.random()*20 );
}
tmp = binomcoef( data, 3 );
out = '';
for ( i = 0; i < data.length; i++ ) {
	out += tmp[ i ];
	if ( i < data.length-1 ) {
		out += ',';
	}
}

// Matrices...
mat = matrix( data, [5,2], 'int32' );
out = binomcoef( mat, 3 );

// Matrices (custom output data type)...
out = binomcoef( mat, 3, {
	'dtype': 'uint8'
});

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

---

License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.