121 lines
2.8 KiB
Markdown
121 lines
2.8 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# erfcinv
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> [Inverse complementary error function][erfcinv].
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<section class="intro">
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The [inverse complementary error function][erfcinv] is defined as
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<!-- <equation class="equation" label="eq:inverse_complementary_error_function" align="center" raw="\operatorname{erfc}^{-1}(1-z) = \operatorname{erf}^{-1}(z)" alt="Inverse complementary error function."> -->
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<div class="equation" align="center" data-raw-text="\operatorname{erfc}^{-1}(1-z) = \operatorname{erf}^{-1}(z)" data-equation="eq:inverse_complementary_error_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/erfcinv/docs/img/equation_inverse_complementary_error_function.svg" alt="Inverse complementary error function.">
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<br>
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</div>
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<!-- </equation> -->
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where `erf^{-1}(z)` is the [inverse error function][@stdlib/math/base/special/erfinv].
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var erfcinv = require( '@stdlib/math/base/special/erfcinv' );
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```
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#### erfcinv( x )
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Evaluates the [inverse complementary error function][erfcinv].
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```javascript
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var y = erfcinv( 0.5 );
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// returns ~0.4769
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y = erfcinv( 0.8 );
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// returns ~0.1791
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y = erfcinv( 0.0 );
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// returns Infinity
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y = erfcinv( 2.0 );
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// returns -Infinity
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```
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The domain of `x` is restricted to `[0,2]`. If `x` is outside this interval, the function returns `NaN`.
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```javascript
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var y = erfcinv( -3.14 );
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// returns NaN
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```
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If provided `NaN`, the function returns `NaN`.
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```javascript
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var y = erfcinv( NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var linspace = require( '@stdlib/array/linspace' );
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var erfcinv = require( '@stdlib/math/base/special/erfcinv' );
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var x = linspace( 0.0, 2.0, 100 );
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var y;
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var i;
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for ( i = 0; i < x.length; i++ ) {
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y = erfcinv( x[ i ] );
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console.log( 'x: %d, erfcinv(x): %d', x[ i ], y );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[erfcinv]: https://en.wikipedia.org/wiki/Error_function#Inverse_functions
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[@stdlib/math/base/special/erfinv]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/erfinv
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</section>
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<!-- /.links -->
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