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 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', -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, as NaN values are cast to 0.

  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

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License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.