Add pkg to incrementally compute a moving correlation coefficient

lib/node_modules/@stdlib/stats/incr/mpcorr/README.md

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+<!--
+
+@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.
+
+-->
+
+# incrmpcorr
+
+> Compute a moving [sample Pearson product-moment correlation coefficient][pearson-correlation] incrementally.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
+```
+
+#### incrmpcorr( window\[, mx, my] )
+
+Returns an accumulator `function` which incrementally computes a moving [sample Pearson product-moment correlation coefficient][pearson-correlation]. The `window` parameter defines the number of values over which to compute the moving [sample Pearson product-moment correlation coefficient][pearson-correlation].
+
+```javascript
+var accumulator = incrmpcorr( 3 );
+```
+
+If means are already known, provide `mx` and `my` arguments.
+
+```javascript
+var accumulator = incrmpcorr( 3, 5.0, -3.14 );
+```
+
+#### accumulator( \[x, y] )
+
+If provided input values `x` and `y`, the accumulator function returns an updated [sample Pearson product-moment correlation coefficient][pearson-correlation]. If not provided input values `x` and `y`, the accumulator function returns the current [sample Pearson product-moment correlation coefficient][pearson-correlation].
+
+```javascript
+var accumulator = incrmpcorr( 3 );
+
+var r = accumulator();
+// returns null
+
+// Fill the window...
+r = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
+// returns 0.0
+
+r = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
+// returns ~-1.0
+
+r = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
+// returns ~-0.925
+
+// Window begins sliding...
+r = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
+// returns ~-0.863
+
+r = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
+// returns ~-0.803
+
+r = accumulator();
+// returns ~-0.803
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `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.
+-   The first `W-1` returned [sample correlation coefficients][pearson-correlation] will have less statistical support than subsequent [sample correlation coefficients][pearson-correlation], as `W` (x,y) pairs are needed to fill the window buffer. Until the window is full, the returned [sample correlation coefficient][pearson-correlation] equals the [sample correlation coefficient][pearson-correlation] of all provided values.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
+
+var accumulator;
+var x;
+var y;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrmpcorr( 5 );
+
+// For each simulated datum, update the moving sample correlation coefficient...
+for ( i = 0; i < 100; i++ ) {
+    x = randu() * 100.0;
+    y = randu() * 100.0;
+    accumulator( x, y );
+}
+console.log( accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="links">
+
+[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/mpcorr/benchmark/benchmark.js

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+/**
+* @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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrmpcorr = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrmpcorr( (i%5)+1 );
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrmpcorr( 5 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu(), randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator,known_means', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrmpcorr( 5, 3.0, -1.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu(), randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/stats/incr/mpcorr/docs/repl.txt

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+
+{{alias}}( window[, mx, my] )
+    Returns an accumulator function which incrementally computes a moving
+    sample Pearson product-moment correlation coefficient.
+
+    The `window` parameter defines the number of values over which to compute
+    the moving sample correlation coefficient.
+
+    If provided values, the accumulator function returns an updated moving
+    sample correlation coefficient. If not provided values, the accumulator
+    function returns the current moving sample correlation coefficient.
+
+    The first `W-1` returned sample correlation coefficients will have less
+    statistical support than subsequent sample correlation coefficients, as `W`
+    values are needed to fill the window buffer. Until the window is full, the
+    returned sample correlation coefficient equals the sample correlation
+    coefficient of all provided values.
+
+    Parameters
+    ----------
+    window: integer
+        Window size.
+
+    mx: number (optional)
+        Known mean.
+
+    my: number (optional)
+        Known mean.
+
+    Returns
+    -------
+    acc: Function
+        Accumulator function.
+
+    Examples
+    --------
+    > var accumulator = {{alias}}( 3 );
+    > var r = accumulator()
+    null
+    > r = accumulator( 2.0, 1.0 )
+    0.0
+    > r = accumulator( -5.0, 3.14 )
+    ~-1.0
+    > r = accumulator( 3.0, -1.0 )
+    ~-0.925
+    > r = accumulator( 5.0, -9.5 )
+    ~-0.863
+    > r = accumulator()
+    ~-0.863
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/incr/mpcorr/examples/index.js

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+/**
+* @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.
+*/
+
+'use strict';
+
+var randu = require( '@stdlib/random/base/randu' );
+var incrmpcorr = require( './../lib' );
+
+var accumulator;
+var r;
+var x;
+var y;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrmpcorr( 5 );
+
+// For each simulated datum, update the moving sample correlation coefficient...
+console.log( '\nx\ty\tCorrelation Coefficient\n' );
+for ( i = 0; i < 100; i++ ) {
+	x = randu() * 100.0;
+	y = randu() * 100.0;
+	r = accumulator( x, y );
+	console.log( '%d\t%d\t%d', x.toFixed( 4 ), y.toFixed( 4 ), r.toFixed( 4 ) );
+}

lib/node_modules/@stdlib/stats/incr/mpcorr/lib/index.js

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+/**
+* @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.
+*/
+
+'use strict';
+
+/**
+* Compute a moving sample Pearson product-moment correlation coefficient incrementally.
+*
+* @module @stdlib/stats/incr/mpcorr
+*
+* @example
+* var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
+*
+* var accumulator = incrmpcorr( 3 );
+*
+* var r = accumulator();
+* // returns null
+*
+* r = accumulator( 2.0, 1.0 );
+* // returns 0.0
+*
+* r = accumulator( -5.0, 3.14 );
+* // returns ~-1.0
+*
+* r = accumulator( 3.0, -1.0 );
+* // returns ~-0.925
+*
+* r = accumulator( 5.0, -9.5 );
+* // returns ~-0.863
+*
+* r = accumulator();
+* // returns ~-0.863
+*/
+
+// MODULES //
+
+var incrmpcorr = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = incrmpcorr;