190 lines
3.9 KiB
Markdown
190 lines
3.9 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2020 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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# Kronecker Delta
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> Evaluate the [Kronecker delta][kronecker-delta] (single-precision).
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<section class="intro">
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The [Kronecker delta][kronecker-delta] is defined as
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<!-- <equation class="equation" label="eq:kronecker_delta" align="center" raw="\delta_{ij} = \begin{cases} 1 & \textrm{if}\ i = j \\ 0 & \textrm{if}\ i \neq j\end{cases}" alt="Kronecker delta."> -->
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<div class="equation" align="center" data-raw-text="\delta_{ij} = \begin{cases} 1 & \textrm{if}\ i = j \\ 0 & \textrm{if}\ i \neq j\end{cases}" data-equation="eq:kronecker_delta">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b245da8d5397f5cf6a71ec8a0147cf47d876eeb7/lib/node_modules/@stdlib/math/base/special/kronecker-deltaf/docs/img/equation_kronecker_delta.svg" alt="Kronecker delta.">
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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 kroneckerDeltaf = require( '@stdlib/math/base/special/kronecker-deltaf' );
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```
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#### kroneckerDeltaf( i, j )
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Evaluates the [Kronecker delta][kronecker-delta] (single-precision).
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```javascript
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var v = kroneckerDeltaf( 3.14, 3.14 );
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// returns 1.0
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v = kroneckerDeltaf( 3.14, 0.0 );
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// returns 0.0
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v = kroneckerDeltaf( NaN, 3.14 );
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// returns NaN
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v = kroneckerDeltaf( 3.14, NaN );
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// returns NaN
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v = kroneckerDeltaf( NaN, 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 kroneckerDeltaf = require( '@stdlib/math/base/special/kronecker-deltaf' );
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var x = linspace( -1.0, 1.0, 101 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( 'kronecker(%d,%d) = %d', x[ i ], 0.0, kroneckerDeltaf( x[ i ], 0.0 ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/math/base/special/kronecker_deltaf.h
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```
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#### stdlib_base_kronecker_deltaf( i, j )
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Evaluates the Kronecker delta (single-precision).
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```c
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float v = stdlib_base_kronecker_deltaf( 3.0f, 3.0f );
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// returns 1.0f
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```
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The function accepts the following arguments:
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- **i**: `[in] float` input value.
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- **j**: `[in] float` input value.
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```c
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float stdlib_base_kronecker_delta( const float i, const float j );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/math/base/special/kronecker_deltaf.h"
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#include <stdio.h>
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int main() {
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float x[] = { 3.0f, 4.0f, 5.0f, 5.0f };
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float y;
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int i;
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for ( i = 0; i < 4; i += 2 ) {
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y = stdlib_base_kronecker_deltaf( x[ i ], x[ i+1 ] );
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printf( "kronecker_delta(%f, %f) = %f\n", x[ i ], x[ i+1 ], y );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<section class="links">
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[kronecker-delta]: https://en.wikipedia.org/wiki/Kronecker_delta
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</section>
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<!-- /.links -->
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