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version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][coveralls-image]][coveralls-url] [![Dependencies][dependencies-image]][dependencies-url]\n\n> [Inverse complementary error function](https://en.wikipedia.org/wiki/Error_function#Inverse_functions).\n\nThe [inverse complementary error function](https://en.wikipedia.org/wiki/Error_function#Inverse_functions) is defined as\n\n<div class=\"equation\" align=\"center\" data-raw-text=\"\\operatorname{erfc}^{-1}(1-z) = \\operatorname{erf}^{-1}(z)\" data-equation=\"eq:inverse_complementary_error_function\">\n\t<img src=\"https://cdn.rawgit.com/compute-io/erfcinv/6a87397a81cb2298117b6ae6da0289cbd1986de9/docs/img/eqn.svg\" alt=\"Definition of the inverse complementary error function.\">\n\t<br>\n</div>\n\nwhere `erf^{-1}(z)` is the [inverse error function](https://github.com/compute-io/erfinv).\n\n\n## Installation\n\n``` bash\n$ npm install compute-erfcinv\n```\n\nFor use in the browser, use [browserify](https://github.com/substack/node-browserify).\n\n\n## Usage\n\n``` javascript\nvar erfcinv = require( 'compute-erfcinv' );\n```\n\n#### erfcinv( x[, options] )\n\nEvaluates the [inverse complementary error function](https://en.wikipedia.org/wiki/Error_function#Inverse_function). `x` may be either a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix). All numeric values __must__ reside on the interval `[0,2]`.\n\n``` javascript\nvar matrix = require( 'dstructs-matrix' ),\n\tdata,\n\tmat,\n\tout,\n\ti;\n\nout = erfcinv( 0.5 );\n// returns ~0.4769\n\nout = erfcinv( [ 0, 0.5, 1, 1.5, 2 ] );\n// returns [ +infinity, 0.4769, 0, -0.4769, -infinity ]\n\ndata = [ 0, 1, 2 ];\nout = erfcinv( data );\n// returns [ +infinity, 0, -infinity ]\n\ndata = new Int8Array( data );\nout = erfcinv( data );\n// returns Float64Array( [ +infinity, 0, -infinity ] )\n\ndata = new Float64Array( 4 );\nfor ( i = 0; i < 4; i++ ) {\n\tdata[ i ] = i / 2;\n}\nmat = matrix( data, [2,2], 'float64' );\n/*\n\t[ 0  0.5\n\t  1  1.5 ]\n*/\n\nout = erfcinv( mat );\n/*\n\t[ +infinity  0.477\n\t  0         -0.477 ]\n*/\n```\n\nThe function accepts the following `options`:\n\n* \t__accessor__: accessor `function` for accessing `array` values.\n* \t__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`.\n*\t__copy__: `boolean` indicating if the `function` should return a new data structure. Default: `true`.\n*\t__path__: [deepget](https://github.com/kgryte/utils-deep-get)/[deepset](https://github.com/kgryte/utils-deep-set) key path.\n*\t__sep__: [deepget](https://github.com/kgryte/utils-deep-get)/[deepset](https://github.com/kgryte/utils-deep-set) key path separator. Default: `'.'`.\n\nFor non-numeric `arrays`, provide an accessor `function` for accessing `array` values.\n\n``` javascript\nvar data = [\n\t['beep', 0],\n\t['boop', 0.5],\n\t['bip', 1],\n\t['bap', 1.5],\n\t['baz', 2]\n];\n\nfunction getValue( d, i ) {\n\treturn d[ 1 ];\n}\n\nvar out = erfcinv( data, {\n\t'accessor': getValue\n});\n// returns [ +infinity, 0.4769, 0, -0.4769, -infinity ]\n```\n\nTo [deepset](https://github.com/kgryte/utils-deep-set) an object `array`, provide a key path and, optionally, a key path separator.\n\n``` javascript\ndata = [\n\t{'x':[9,1.75]},\n\t{'x':[9,1.25]},\n\t{'x':[9,1.01]},\n\t{'x':[9,1e-5]},\n\t{'x':[9,1e-100]},\n\t{'x':[9,5e-324]}\n];\n\nvar out = erfcinv( data, 'x|1', '|' );\n/*\n\t [\n\t\t{'x':[9,-0.8134198]},\n\t\t{'x':[9,-0.2253121]},\n\t\t{'x':[9,-0.00886250]},\n\t\t{'x':[9,3.12341327]},\n\t\t{'x':[9,15.0655747]},\n\t\t{'x':[9,27.2130740]}\n\t]\n*/\n\nvar bool = ( data === out );\n// returns true\n```\n\nBy default, when provided a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays) or [`matrix`](https://github.com/dstructs/matrix), the output data structure is `float64` in order to preserve precision. To specify a different data type, set the `dtype` option (see [`matrix`](https://github.com/dstructs/matrix) for a list of acceptable data types).\n\n``` javascript\nvar data, out;\n\ndata = new Float64Array( [ 1e-5, 1e-100, 5e-324 ] );\n\nout = erfcinv( data, {\n\t'dtype': 'int32'\n});\n// returns Int32Array( [3,15,27] )\n\n// Works for plain arrays, as well...\nout = erfcinv( [ 1e-5, 1e-100, 5e-324 ] , {\n\t'dtype': 'uint8'\n});\n// returns Uint8Array( [3,15,27] )\n```\n\nBy 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`.\n\n``` javascript\nvar data,\n\tbool,\n\tmat,\n\tout,\n\ti;\n\ndata = [\n\t1.75,\n\t1.25,\n\t1.01,\n\t1e-5,\n\t1e-100,\n\t5e-324\n];\n\nvar out = erfcinv( data, {\n\t'copy': false\n});\n// returns [ 0.813 0.225 -0.009 3.123 15.066 27.213 ]\n\nbool = ( data === out );\n// returns true\n\ndata = new Float64Array( 4 );\nfor ( i = 0; i < 4; i++ ) {\n\tdata[ i ] = i / 2;\n}\nmat = matrix( data, [2,2], 'float64' );\n/*\n\t[ 0  0.5\n\t  1  1.5 ]\n*/\n\nout = erfcinv( mat, {\n\t'copy': false\n});\n/*\n\t[ +infinity  0.477\n\t  0         -0.477 ]\n*/\n\nbool = ( mat === out );\n// returns true\n```\n\n\n## Notes\n\n*\tIf an element is __not__ a numeric value, the evaluated [inverse complementary error function](https://en.wikipedia.org/wiki/Error_function#Inverse_function) is `NaN`.\n\n\t``` javascript\n\tvar data, out;\n\n\tout = erfcinv( null );\n\t// returns NaN\n\n\tout = erfcinv( true );\n\t// returns NaN\n\n\tout = erfcinv( {'a':'b'} );\n\t// returns NaN\n\n\tout = erfcinv( [ true, null, [] ] );\n\t// returns [ NaN, NaN, NaN ]\n\n\tfunction getValue( d, i ) {\n\t\treturn d.x;\n\t}\n\tdata = [\n\t\t{'x':true},\n\t\t{'x':[]},\n\t\t{'x':{}},\n\t\t{'x':null}\n\t];\n\n\tout = erfcinv( data, {\n\t\t'accessor': getValue\n\t});\n\t// returns [ NaN, NaN, NaN, NaN ]\n\n\tout = erfcinv( data, {\n\t\t'path': 'x'\n\t});\n\t/*\n\t\t[\n\t\t\t{'x':NaN},\n\t\t\t{'x':NaN},\n\t\t\t{'x':NaN,\n\t\t\t{'x':NaN}\n\t\t]\n\t*/\n\t```\n\n*\tBe 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`.\n\n\t``` javascript\n\tvar out = erfcinv( [ true, null, [] ], {\n\t\t'dtype': 'int8'\n\t});\n\t// returns Int8Array( [0,0,0] );\n\t```\n\n\n## Examples\n\n``` javascript\nvar matrix = require( 'dstructs-matrix' ),\n\terfcinv = require( 'compute-erfcinv' );\n\nvar data,\n\tmat,\n\tout,\n\ttmp,\n\ti;\n\n// Plain arrays...\ndata = new Array( 100 );\nfor ( i = 0; i < data.length; i++ ) {\n\tdata[ i ] = Math.random() * 2;\n}\nout = erfcinv( data );\n\n// Object arrays (accessors)...\nfunction getValue( d ) {\n\treturn d.x;\n}\nfor ( i = 0; i < data.length; i++ ) {\n\tdata[ i ] = {\n\t\t'x': data[ i ]\n\t};\n}\nout = erfcinv( data, {\n\t'accessor': getValue\n});\n\n// Deep set arrays...\nfor ( i = 0; i < data.length; i++ ) {\n\tdata[ i ] = {\n\t\t'x': [ i, data[ i ].x ]\n\t};\n}\nout = erfcinv( data, {\n\t'path': 'x/1',\n\t'sep': '/'\n});\n\n// Typed arrays...\ndata = new Int32Array( 10 );\nfor ( i = 0; i < data.length; i++ ) {\n\tdata[ i ] = Math.random() * 2;\n}\ntmp = erfcinv( data );\nout = '';\nfor ( i = 0; i < data.length; i++ ) {\n\tout += tmp[ i ];\n\tif ( i < data.length-1 ) {\n\t\tout += ',';\n\t}\n}\n\n// Matrices...\nmat = matrix( data, [5,2], 'int32' );\nout = erfcinv( mat );\n\n// Matrices (custom output data type)...\nout = erfcinv( mat, {\n\t'dtype': 'uint8'\n});\n```\n\nTo run the example code from the top-level application directory,\n\n``` bash\n$ node ./examples/index.js\n```\n\n\n## Tests\n\n### Unit\n\nUnit tests use the [Mocha](http://mochajs.org) test framework with [Chai](http://chaijs.com) assertions. To run the tests, execute the following command in the top-level application directory:\n\n``` bash\n$ make test\n```\n\nAll new feature development should have corresponding unit tests to validate correct functionality.\n\n\n### Test Coverage\n\nThis repository uses [Istanbul](https://github.com/gotwarlost/istanbul) as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:\n\n``` bash\n$ make test-cov\n```\n\nIstanbul creates a `./reports/coverage` directory. To access an HTML version of the report,\n\n``` bash\n$ make view-cov\n```\n\n\n---\n## License\n\n[MIT license](http://opensource.org/licenses/MIT).\n\n\n## Copyright\n\nCopyright &copy; 2014-2015. The [Compute.io](https://github.com/compute-io) Authors.\n\n\n[npm-image]: http://img.shields.io/npm/v/compute-erfcinv.svg\n[npm-url]: https://npmjs.org/package/compute-erfcinv\n\n[travis-image]: http://img.shields.io/travis/compute-io/erfcinv/master.svg\n[travis-url]: https://travis-ci.org/compute-io/erfcinv\n\n[coveralls-image]: https://img.shields.io/coveralls/compute-io/erfcinv/master.svg\n[coveralls-url]: https://coveralls.io/r/compute-io/erfcinv?branch=master\n\n[dependencies-image]: http://img.shields.io/david/compute-io/erfcinv.svg\n[dependencies-url]: https://david-dm.org/compute-io/erfcinv\n\n[dev-dependencies-image]: http://img.shields.io/david/dev/compute-io/erfcinv.svg\n[dev-dependencies-url]: https://david-dm.org/dev/compute-io/erfcinv\n\n[github-issues-image]: http://img.shields.io/github/issues/compute-io/erfcinv.svg\n[github-issues-url]: https://github.com/compute-io/erfcinv/issues\n","maintainers":[{"name":"kgryte","email":"kgryte@gmail.com"},{"name":"planeshifter","email":"pgb@andrew.cmu.edu"}],"time":{"modified":"2022-06-13T20:28:00.453Z","created":"2014-09-20T19:17:08.069Z","0.0.0":"2014-09-20T19:17:08.069Z","1.0.0":"2014-09-20T19:17:32.565Z","2.0.0":"2015-06-19T07:56:03.610Z","3.0.0":"2015-08-01T22:34:18.217Z","3.0.1":"2016-01-30T22:48:36.919Z"},"homepage":"https://github.com/compute-io/erfcinv#readme","keywords":["compute.io","compute","computation","erf","error function","erfc","complementary","error","function","erfcinv","inverse","statistics","stats","mathematics","math","matrix","matrices","array","arrays","typed array","accessor","dstructs","deep","set","get","deepset"],"repository":{"type":"git","url":"git://github.com/compute-io/erfcinv.git"},"contributors":[{"name":"Athan Reines","email":"kgryte@gmail.com"},{"name":"Philipp Burckhardt","email":"pburckhardt@outlook.com"}],"author":{"name":"Athan Reines","email":"kgryte@gmail.com"},"bugs":{"url":"https://github.com/compute-io/erfcinv/issues"},"readmeFilename":"README.md","license":"MIT"}