Add Box-Cox transformation with special consideration for small x values (#223)

* created readme for boxcox1p
* created package.json
* initial implementation of boxcox1p function
* added benchmarking ofboxcox1p
* added tests and fixtures for tests
* added repl docs
* added boxcox1p simple examples
* fixed typo in jsdoc
* applied suggestions to README
* applied suggestions to repl.txt
* applied suggestions to boxcox1p implementation
* updated package.json
* updated tests

Author: justin1dennison

lib/node_modules/@stdlib/math/base/special/boxcox1p/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.
+
+-->
+
+# boxcox1p
+
+> Compute a one-parameter [Box-Cox transformation][box-cox-transformation] of `1+x`.
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+A one-parameter [Box-Cox transformation][box-cox-transformation] is defined as 
+
+<!-- <equation class="equation" label="eq:boxcox_transformation_one_parameter" align="center" raw="y^{\lambda} = \begin{cases}\frac{(y + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(y + 1) & \textrm{if}\ \lambda = 0 \end{cases}" alt="One-Parameter Box-Cox Transformation"> -->
+
+<div class="equation" align="center" data-raw-text="y^{\lambda} = \begin{cases}\frac{(y + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(y + 1) & \textrm{if}\ \lambda = 0 \end{cases}" data-equation="eq:boxcox_transformation_one_parameter">
+    <img src="" alt="One-Parameter Box-Cox Transformation" />
+    <br>
+</div>
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var boxcox1p = require( '@stdlib/math/base/special/boxcox1p' );
+```
+
+#### boxcox1p( x, lambda )
+
+Compute a one-parameter [Box-Cox transformation][box-cox-transformation].
+
+```javascript
+var v = boxcox1p( 1.0, 2.5 );
+// returns ~1.8627
+
+v = boxcox1p( 4.0, 2.5 );
+// returns ~21.9607
+
+v = boxcox1p( 10.0, 2.5 );
+// returns ~160.1246
+
+v = boxcox1p( 2.0, 0.0 );
+// returns ~1.0986
+
+v = boxcox1p( -1.0, 2.5 );
+// returns -0.4
+
+v = boxcox1p( 0.0, -1.0 );
+// returns 0.0
+
+v = boxcox1p( -1.0, -1.0 );
+// returns -Infinity
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var incrspace = require( '@stdlib/math/utils/incrspace' );
+var boxcox1p = require( '@stdlib/math/base/special/boxcox1p' );
+
+var x = incrspace( -1.0, 10.0, 1.0 );
+var l = incrspace( -0.5, 5.0, 0.5 );
+var b;
+var i;
+var j;
+
+for ( i = 0; i < x.length; i++ ) {
+    for ( j = 0; j < l.length; j++ ) {
+        b = boxcox1p( x[ i ], l[ j ] );
+        console.log( 'boxcox1p(%d, %d) = %d', x[ i ], l[ j ], b );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[box-cox-transformation]: https://en.wikipedia.org/wiki/Power_transform#Box-Cox_transformation
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/base/special/boxcox1p/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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var boxcox1p = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var x;
+	var y;
+	var r;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		x = ( randu()*10.0 ) + 1.0;
+		y = ( randu()*10.0 ) + 1.0;
+		r = boxcox1p( x, y );
+		if ( isnan( r ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( r ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/math/base/special/boxcox1p/benchmark/python/benchmark.py

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+#!/usr/bin/env python
+#
+# @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.
+
+"""Benchmark scipy.special.boxcox1p."""
+
+from __future__ import print_function
+import timeit
+
+NAME = "boxcox1p"
+REPEATS = 3
+ITERATIONS = 1000000
+
+
+def print_version():
+    """Print the TAP version."""
+    print("TAP version 13")
+
+
+def print_summary(total, passing):
+    """Print the benchmark summary.
+
+    # Arguments
+
+    * `total`: total number of tests
+    * `passing`: number of passing tests
+
+    """
+    print("#")
+    print("1.." + str(total))
+    print("# total " + str(total))
+    print("# pass " + str(passing))
+    print("#")
+    print("# ok")
+
+
+def print_results(elapsed):
+    """Print benchmark results.
+
+    # Arguments
+
+    * `elapsed`: elapsed time (in seconds)
+
+    # Examples
+
+    ```python
+    python> print_results(0.2543188374)
+    ```
+    """
+    rate = ITERATIONS / elapsed
+
+    print(" ---")
+    print(" iterations: " + str(ITERATIONS))
+    print(" elapsed: " + str(elapsed))
+    print(" rate: " + str(rate))
+    print(" ...")
+
+
+def benchmark():
+    """Run the benchmark and print benchmark results."""
+    setup = "from scipy.special import boxcox1p; from random import random;"
+    stmt = "boxcox1p((100.0 * random()) - 50.0, (100.0 * random()) - 50.0)"
+
+    t = timeit.Timer(stmt, setup=setup)
+
+    print_version()
+
+    for i in range(REPEATS):
+        print("# python::scipy::special::" + NAME)
+        elapsed = t.timeit(number=ITERATIONS)
+        print_results(elapsed)
+        print("ok " + str(i+1) + " benchmark finished")
+
+    print_summary(REPEATS, REPEATS)
+
+
+def main():
+    """Run the benchmark."""
+    benchmark()
+
+
+if __name__ == "__main__":
+    main()

lib/node_modules/@stdlib/math/base/special/boxcox1p/docs/repl.txt

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+
+{{alias}}( x, lambda )
+    Computes a one-parameter Box-Cox transformation of 1+x.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    lambda: number
+       Power parameter.
+
+    Returns
+    -------
+    b: number
+        Function value.
+
+    Examples
+    --------
+    > var v =  {{alias}}( 1.0, 2.5 )
+    ~1.8627
+    > v = {{alias}}( 4.0, 2.5 )
+    ~21.9607
+    > v = {{alias}}( 10.0, 2.5 )
+    ~160.1246
+    > v = {{alias}}( 2.0, 0.0 )
+    ~1.0986
+    > v = {{alias}}( -1.0, 2.5 )
+    -0.4
+    > v = {{alias}}( 0.0, -1.0 )
+    0.0
+    > v = {{alias}}( -1.0, -1.0 )
+    -Infinity
+
+    See Also
+    --------

lib/node_modules/@stdlib/math/base/special/boxcox1p/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 incrspace = require( '@stdlib/math/utils/incrspace' );
+var boxcox1p = require( './../lib' );
+
+var x = incrspace( -1.0, 10.0, 1.0 );
+var l = incrspace( -0.5, 5.0, 0.5 );
+var b;
+var i;
+var j;
+
+for ( i = 0; i < x.length; i++ ) {
+	for ( j = 0; j < l.length; j++ ) {
+		b = boxcox1p( x[ i ], l[ j ] );
+		console.log( 'boxcox1p(%d, %d) = %d', x[ i ], l[ j ], b );
+	}
+}