compute-erfcinv

erfcinv
===
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> Inverse complementary error function.

The inverse complementary error function is defined as

where erf^{-1}(z) is the inverse error function.

Installation

`` bash
$ npm install compute-erfcinv
`

For use in the browser, use browserify.

Usage

` javascript
var erfcinv = require( 'compute-erfcinv' );
`

#### erfcinv( x[, options] )

Evaluates the inverse complementary error function. x may be either a number, an array, a typed array, or a matrix. All numeric values __must__ reside on the interval [0,2].

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

out = erfcinv( 0.5 );
// returns ~0.4769

out = erfcinv( [ 0, 0.5, 1, 1.5, 2 ] );
// returns [ +infinity, 0.4769, 0, -0.4769, -infinity ]

data = [ 0, 1, 2 ];
out = erfcinv( data );
// returns [ +infinity, 0, -infinity ]

data = new Int8Array( data );
out = erfcinv( data );
// returns Float64Array( [ +infinity, 0, -infinity ] )

data = new Float64Array( 4 );
for ( i = 0; i < 4; i++ ) {
data[ i ] = i / 2;
}
mat = matrix( data, [2,2], 'float64' );
/*
[ 0 0.5
1 1.5 ]
*/

out = erfcinv( mat );
/*
[ +infinity 0.477
0 -0.477 ]
*/
`

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.

` javascript
var data = [
['beep', 0],
['boop', 0.5],
['bip', 1],
['bap', 1.5],
['baz', 2]
];

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

var out = erfcinv( data, {
'accessor': getValue
});
// returns [ +infinity, 0.4769, 0, -0.4769, -infinity ]
`

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

` javascript
data = [
{'x':[9,1.75]},
{'x':[9,1.25]},
{'x':[9,1.01]},
{'x':[9,1e-5]},
{'x':[9,1e-100]},
{'x':[9,5e-324]}
];

var out = erfcinv( data, 'x|1', '|' );
/*
[
{'x':[9,-0.8134198]},
{'x':[9,-0.2253121]},
{'x':[9,-0.00886250]},
{'x':[9,3.12341327]},
{'x':[9,15.0655747]},
{'x':[9,27.2130740]}
]
*/

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).

` javascript
var data, out;

data = new Float64Array( [ 1e-5, 1e-100, 5e-324 ] );

out = erfcinv( data, {
'dtype': 'int32'
});
// returns Int32Array( [3,15,27] )

// Works for plain arrays, as well...
out = erfcinv( [ 1e-5, 1e-100, 5e-324 ] , {
'dtype': 'uint8'
});
// returns Uint8Array( [3,15,27] )
`

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.

` javascript
var data,
bool,
mat,
out,
i;

data = [
1.75,
1.25,
1.01,
1e-5,
1e-100,
5e-324
];

var out = erfcinv( data, {
'copy': false
});
// returns [ 0.813 0.225 -0.009 3.123 15.066 27.213 ]

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

data = new Float64Array( 4 );
for ( i = 0; i < 4; i++ ) {
data[ i ] = i / 2;
}
mat = matrix( data, [2,2], 'float64' );
/*
[ 0 0.5
1 1.5 ]
*/

out = erfcinv( mat, {
'copy': false
});
/*
[ +infinity 0.477
0 -0.477 ]
*/

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

Notes

* If an element is __not__ a numeric value, the evaluated inverse complementary error function is NaN.

` javascript
var data, out;

out = erfcinv( null );
// returns NaN

out = erfcinv( true );
// returns NaN

out = erfcinv( {'a':'b'} );
// returns NaN

out = erfcinv( [ true, null, [] ] );
// returns [ NaN, NaN, NaN ]

function getValue( d, i ) {
return d.x;
}
data = [
{'x':true},
{'x':[]},
{'x':{}},
{'x':null}
];

out = erfcinv( data, {
'accessor': getValue
});
// returns [ NaN, NaN, NaN, NaN ]

out = erfcinv( 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.

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

Examples

` javascript
var matrix = require( 'dstructs-matrix' ),
erfcinv = require( 'compute-erfcinv' );

var data,
mat,
out,
tmp,
i;

// Plain arrays...
data = new Array( 100 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = Math.random() * 2;
}
out = erfcinv( data );

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

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

// Typed arrays...
data = new Int32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = Math.random() * 2;
}
tmp = erfcinv( 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 = erfcinv( mat );

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

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

` bash
$ node ./examples/index.js
`

Tests

$3

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

` bash
$ make test
`

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

$3

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:

` bash
$ make test-cov
`

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

` bash
$ make view-cov
``

---

License

MIT license.

Copyright

Copyright © 2014-2015. The Compute.io Authors.

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[npm-url]: https://npmjs.org/package/compute-erfcinv

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[dependencies-url]: https://david-dm.org/compute-io/erfcinv

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[dev-dependencies-url]: https://david-dm.org/dev/compute-io/erfcinv

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[github-issues-url]: https://github.com/compute-io/erfcinv/issues