time-to-botec

README.md (6066B)

---

 <!--
 
 @license Apache-2.0
 
 Copyright (c) 2018 The Stdlib Authors.
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at
 
    http://www.apache.org/licenses/LICENSE-2.0
 
 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 
 -->
 
 # incrmmeanstdev
 
 > Compute a moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation] incrementally.
 
 <section class="intro">
 
 For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as
 
 <!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->
 
 <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@10877053965ff3d0149611583ee50714bb64a8ea/lib/node_modules/@stdlib/stats/incr/mmeanstdev/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 and the [corrected sample standard deviation][standard-deviation] is defined as
 
 <!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}" alt="Equation for the corrected sample standard deviation."> -->
 
 <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8284daf692badf90996becd5080db0dabf438411/lib/node_modules/@stdlib/stats/incr/mmeanstdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var incrmmeanstdev = require( '@stdlib/stats/incr/mmeanstdev' );
 ```
 
 #### incrmmeanstdev( \[out,] window )
 
 Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation]. The `window` parameter defines the number of values over which to compute the moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation].
 
 ```javascript
 var accumulator = incrmmeanstdev( 3 );
 ```
 
 By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.
 
 ```javascript
 var Float64Array = require( '@stdlib/array/float64' );
 
 var accumulator = incrmmeanstdev( new Float64Array( 2 ), 3 );
 ```
 
 #### accumulator( \[x] )
 
 If provided an input value `x`, the accumulator function returns updated accumulated values. If not provided an input value `x`, the accumulator function returns the current accumulated values.
 
 ```javascript
 var accumulator = incrmmeanstdev( 3 );
 
 var out = accumulator();
 // returns null
 
 // Fill the window...
 out = accumulator( 2.0 ); // [2.0]
 // returns [ 2.0, 0.0 ]
 
 out = accumulator( 1.0 ); // [2.0, 1.0]
 // returns [ 1.5, ~0.71 ]
 
 out = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
 // returns [ 2.0, 1.0 ]
 
 // Window begins sliding...
 out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
 // returns [ -1.0, ~5.29 ]
 
 out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
 // returns [ -3.0, ~5.29 ]
 
 out = accumulator();
 // returns [ -3.0, ~5.29 ]
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   Input values are **not** type checked. If provided `NaN`, the accumulated values are `NaN` for **at least** `W-1` future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
 -   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var Float64Array = require( '@stdlib/array/float64' );
 var ArrayBuffer = require( '@stdlib/array/buffer' );
 var incrmmeanstdev = require( '@stdlib/stats/incr/mmeanstdev' );
 
 var offset;
 var acc;
 var buf;
 var out;
 var ms;
 var N;
 var v;
 var i;
 var j;
 
 // Define the number of accumulators:
 N = 5;
 
 // Create an array buffer for storing accumulator output:
 buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element
 
 // Initialize accumulators:
 acc = [];
 for ( i = 0; i < N; i++ ) {
     // Compute the byte offset:
     offset = i * 2 * 8; // stride=2, bytes_per_element=8
 
     // Create a new view for storing accumulated values:
     out = new Float64Array( buf, offset, 2 );
 
     // Initialize an accumulator which will write results to the view:
     acc.push( incrmmeanstdev( out, 5 ) );
 }
 
 // Simulate data and update the moving sample means and standard deviations...
 for ( i = 0; i < 100; i++ ) {
     for ( j = 0; j < N; j++ ) {
         v = randu() * 100.0 * (j+1);
         acc[ j ]( v );
     }
 }
 
 // Print the final results:
 console.log( 'Mean\tStDev' );
 for ( i = 0; i < N; i++ ) {
     ms = acc[ i ]();
     console.log( '%d\t%d', ms[ 0 ].toFixed( 3 ), ms[ 1 ].toFixed( 3 ) );
 }
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
 
 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
 
 </section>
 
 <!-- /.links -->