131 lines
2.9 KiB
Markdown
131 lines
2.9 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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# isUnityProbabilityArray
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> Test if a value is an array of probabilities that sum to one.
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<section class="usage">
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## Usage
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```javascript
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var isUnityProbabilityArray = require( '@stdlib/assert/is-unity-probability-array' );
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```
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#### isUnityProbabilityArray( value )
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Tests if a `value` is an array of probabilities that sum to one.
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```javascript
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var Uint8Array = require( '@stdlib/array/uint8' );
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var bool = isUnityProbabilityArray( [ 0.25, 0.5, 0.25 ] );
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// returns true
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bool = isUnityProbabilityArray( new Uint8Array( [ 0, 1 ] ) );
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// returns true
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bool = isUnityProbabilityArray( [ 3.14, 0.0 ] );
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// returns false
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- Summation of finite-precision floating-point numbers often has numerical error. For example,
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```javascript
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var arr = [ 0.1, 0.2, 0.1, 0.1, 0.2, 0.2, 0.1 ]; // => 1.0
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var sum = 0.0;
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var i;
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for ( i = 0; i < arr.length; i++ ) {
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sum += arr[ i ];
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}
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console.log( sum );
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// => 0.9999999999999999
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```
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To account for numerical error, the function tests if array elements sum to approximately one; specifically,
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```text
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1.0 - sqrt(eps) <= sum(A) <= 1.0 + sqrt(eps)
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```
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where `eps` is [double-precision floating-point][ieee754] epsilon (`~2.22e-16`) and `sqrt(eps) ~ 1.49e-8`. The above comparison ensures equality for approximately half the significand bits.
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</section>
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<!-- /.notes -->
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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 Uint8Array = require( '@stdlib/array/uint8' );
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var isUnityProbabilityArray = require( '@stdlib/assert/is-unity-probability-array' );
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var arr = [ 0.0, 1.0 ];
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var bool = isUnityProbabilityArray( arr );
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// returns true
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arr = [ 0.5, 0.25, 0.25 ];
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bool = isUnityProbabilityArray( arr );
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// returns true
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arr = new Uint8Array( [ 0, 0, 1, 0 ] );
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bool = isUnityProbabilityArray( arr );
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// returns true
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arr = [ 0.4, 0.4, 0.4 ];
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bool = isUnityProbabilityArray( arr );
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// returns false
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arr = [ 3.14, -1.0 ];
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bool = isUnityProbabilityArray( arr );
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// returns false
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bool = isUnityProbabilityArray( [] );
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// returns false
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bool = isUnityProbabilityArray( null );
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// returns false
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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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[ieee754]: https://en.wikipedia.org/wiki/IEEE_floating_point
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</section>
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<!-- /.links -->
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