compute-digamma v0.0.0
digamma
Computes the digamma function.
The digamma function ψ
is the logarithmic derivative of the gamma function, i.e.
Installation
$ npm install compute-digamma
For use in the browser, use browserify.
Usage
var digamma = require( 'compute-digamma' );
digamma( x, options )
Evaluates the digamma function (element-wise). x
may be either a number
, an array
, a typed array
, or a matrix
.
var matrix = require( 'dstructs-matrix' ),
data,
mat,
out,
i;
out = digamma( -1 );
// returns NaN
out = digamma( [ -2.5, -1, 0, 1, 10 ] );
// returns [ ~1.103, NaN, NaN, ~-0.577, ~2.252 ]
data = [ 0, 1, 2 ];
out = digamma( data );
// returns [ NaN, ~-0.5772, ~0.423 ]
data = new Int8Array( data );
out = digamma( data );
// returns Float64Array( [NaN,~-0.577,~0.423] )
data = new Float64Array( 6 );
for ( i = 0; i < 6; i++ ) {
data[ i ] = i / 2;
}
mat = matrix( data, [3,2], 'float64' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/
out = digamma( mat );
/*
[ NaN ~-1.964
~-0.577 ~0.036
~0.423 ~0.703 ]
*/
The function accepts the following options
:
__accessor__: accessor `function` for accessing `array` values.
__dtype__: output [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays) or [`matrix`](https://github.com/dstructs/matrix) data type. Default: `float64`.
- copy:
boolean
indicating if thefunction
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', -2.5],
['boop', -1],
['bip', 0],
['bap', 1],
['baz', 10]
];
function getValue( d, i ) {
return d[ 1 ];
}
var out = digamma( data, {
'accessor': getValue
});
// returns [ ~1.103, NaN, NaN, ~-0.577, ~2.252 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var data = [
{'x':[0,-2.5]},
{'x':[1,-1]},
{'x':[2,0]},
{'x':[3,1]},
{'x':[4,10]}
];
var out = digamma( data, {
'path': 'x|1',
'sep': '|'
});
/*
[
{'x':[0,~1.103]},
{'x':[1,NaN]},
{'x':[2,NaN]},
{'x':[3,~-0.577]},
{'x':[4,~2.252]}
]
*/
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 = digamma( data, {
'dtype': 'int32'
});
// returns Int32Array( [0,0,0] )
// Works for plain arrays, as well...
out = digamma( [0, 1, 2], {
'dtype': 'uint8'
});
// returns Uint8Array( [0,0,0] )
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 = [ -2.5, -1, 0, 1, 10 ];
var out = digamma( data, {
'copy': false
});
// returns [ ~1.103, NaN, NaN, ~-0.577,~ 2.252 ]
bool = ( data === out );
// returns true
data = new Float64Array( 6 );
for ( i = 0; i < 6; i++ ) {
data[ i ] = i / 2;
}
mat = matrix( data, [3,2], 'float64' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/
out = digamma( mat, {
'copy': false
});
/*
[ NaN ~-1.964
~-0.577 ~0.036
~0.423 ~0.703 ]
*/
bool = ( mat === out );
// returns true
Implementation
The function has been adapted from the implementation found in the Boost C++ library. See the Boost documentation about implementation details. Only the necessary parts for 17 significant digits were translated, as JavaScript floating-point numbers cannot the high-precision versions.
Notes
If an element is not a numeric value, the evaluated error function is
NaN
.var data, out; out = digamma( null ); // returns NaN out = digamma( true ); // returns NaN out = digamma( {'a':'b'} ); // returns NaN out = digamma( [ true, null, [] ] ); // returns [ NaN, NaN, NaN ] function getValue( d, i ) { return d.x; } data = [ {'x':true}, {'x':[]}, {'x':{}}, {'x':null} ]; out = digamma( data, { 'accessor': getValue }); // returns [ NaN, NaN, NaN, NaN ] out = digamma( data, { '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, asNaN
values are cast to0
.var out = digamma( [ true, null, [] ], { 'dtype': 'int8' }); // returns Int8Array( [0,0,0] );
Examples
var matrix = require( 'dstructs-matrix' ),
digamma = require( 'compute-digamma' );
var data,
mat,
out,
tmp,
i;
// Plain arrays...
data = new Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = Math.random()*20 - 10;
}
out = digamma( data );
// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = digamma( data, {
'accessor': getValue
});
// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = digamma( data, {
'path': 'x/1',
'sep': '/'
});
// Typed arrays...
data = new Int32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = Math.random() * 100;
}
tmp = digamma( data );
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 = digamma( mat );
// Matrices (custom output data type)...
out = digamma( mat, {
'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
Copyright
Copyright © 2015. The Compute.io Authors.
8 years ago