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feat(math): add math/base/special/heavisidef
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‎lib/node_modules/@stdlib/math/base/special/heavisidef/README.md‎

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<!--
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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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# Heaviside Function
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> Evaluate the [Heaviside function][heaviside-function] for a single-precision floating-point numeric value.
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<section class="intro">
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The [Heaviside function][heaviside-function] is defined as
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<!-- <equation class="equation" label="eq:heaviside_function" align="center" raw="H(x) = \begin{cases} 1 & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}" alt="Heaviside function."> -->
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```math
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H(x) = \begin{cases} 1 & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} 1 &amp; \textrm{if}\ x \gt 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function.svg" alt="Heaviside function.">
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<br>
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</div> -->
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<!-- </equation> -->
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and is discontinuous at `0`. Depending on the context, the [Heaviside function][heaviside-function] may be defined as a continuous function. To define the [Heaviside function][heaviside-function] such that the function has rotational symmetry,
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<!-- <equation class="equation" label="eq:heaviside_function_half_maximum" align="center" raw="H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ \frac{1}{2} & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}" alt="Heaviside function half-maximum."> -->
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```math
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H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ \frac{1}{2} & \textrm{if}\ x = 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \gt 0 \\ \frac{1}{2} &amp; \textrm{if}\ x = 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function_half_maximum">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_half_maximum.svg" alt="Heaviside function half-maximum.">
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<br>
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</div> -->
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<!-- </equation> -->
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To define the [Heaviside function][heaviside-function] as a left-continuous function,
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<!-- <equation class="equation" label="eq:heaviside_function_left_continuous" align="center" raw="H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases}" alt="Heaviside function left-continuous."> -->
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```math
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H(x) = \begin{cases} x & \textrm{if}\ x \gt 0 \\ 0 & \textrm{if}\ x \leq 0\end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \gt 0 \\ 0 &amp; \textrm{if}\ x \leq 0\end{cases}" data-equation="eq:heaviside_function_left_continuous">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_left_continuous.svg" alt="Heaviside function left-continuous.">
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<br>
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</div> -->
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<!-- </equation> -->
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To define the [Heaviside function][heaviside-function] as a right-continuous function,
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<!-- <equation class="equation" label="eq:heaviside_function_right_continuous" align="center" raw="H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}" alt="Heaviside function right-continuous."> -->
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```math
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H(x) = \begin{cases} x & \textrm{if}\ x \geq 0 \\ 0 & \textrm{if}\ x \lt 0\end{cases}
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```
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<!-- <div class="equation" align="center" data-raw-text="H(x) = \begin{cases} x &amp; \textrm{if}\ x \geq 0 \\ 0 &amp; \textrm{if}\ x \lt 0\end{cases}" data-equation="eq:heaviside_function_right_continuous">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/heaviside/docs/img/equation_heaviside_function_right_continuous.svg" alt="Heaviside function right-continuous.">
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<br>
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</div> -->
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<!-- </equation> -->
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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 heavisidef = require( '@stdlib/math/base/special/heavisidef' );
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```
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#### heavisidef( x\[, continuity] )
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Evaluates the [Heaviside function][heaviside-function] for a single-precision floating-point numeric value.
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```javascript
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var v = heavisidef( 3.14 );
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// returns 1.0
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v = heavisidef( -3.14 );
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// returns 0.0
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v = heavisidef( NaN );
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// returns NaN
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```
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The `continuity` parameter may be one of the following values:
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- `'half-maximum'`: if `x == 0`, the function returns `0.5`.
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- `'left-continuous'`: if `x == 0`, the function returns `0.0`.
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- `'right-continuous'`: if `x == 0`, the function returns `1.0`.
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By default, the function is discontinuous at `0`.
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```javascript
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var v = heavisidef( 0.0 );
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// returns NaN
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```
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To define the [Heaviside function][heaviside-function] as a continuous function, set the `continuity` parameter.
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```javascript
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var v = heavisidef( 0.0, 'half-maximum' );
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// returns 0.5
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v = heavisidef( 0.0, 'left-continuous' );
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// returns 0.0
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v = heavisidef( 0.0, 'right-continuous' );
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// returns 1.0
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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/base/linspace' );
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var heavisidef = require( '@stdlib/math/base/special/heavisidef' );
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var x = linspace( -10.0, 10.0, 101 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( 'H(%d) = %f', x[ i ], heavisidef( x[ i ] ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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* * *
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## See Also
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- <span class="package-name">[`@stdlib/math/base/special/ramp`][@stdlib/math/base/special/ramp]</span><span class="delimiter">: </span><span class="description">evaluate the ramp function.</span>
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[heaviside-function]: https://en.wikipedia.org/wiki/Heaviside_step_function
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<!-- <related-links> -->
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[@stdlib/math/base/special/ramp]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/ramp
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/special/heavisidef/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var randu = require( '@stdlib/random/base/randu' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var heavisidef = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var x;
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var y;
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var i;
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x = randu( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = heavisidef( x[ i % x.length ] );
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if ( y > 1.0 ) {
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b.fail( 'should not return a value greater than 1' );
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}
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}
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b.toc();
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if ( y > 1.0 ) {
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b.fail( 'should not return a value greater than 1' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::left-continuous', function benchmark( b ) {
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var x;
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var y;
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var i;
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x = randu( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = heavisidef( x[ i % x.length ], 'left-continuous' );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::right-continuous', function benchmark( b ) {
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var x;
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var y;
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var i;
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x = randu( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = heavisidef( x[ i % x.length ], 'right-continuous' );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::half-maximum', function benchmark( b ) {
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var x;
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var y;
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var i;
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x = randu( 100, -50.0, 50.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = heavisidef( x[ i % x.length ], 'half-maximum' );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/math/base/special/heavisidef/docs/img/equation_heaviside_function.svg‎

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