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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 ndarray = require( '@stdlib/ndarray/array' );
var linspace = require( '@stdlib/array/base/linspace' );
var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
var isNumericArray = require( '@stdlib/assert/is-numeric-array' );
var isMatrixLike = require( '@stdlib/assert/is-matrix-like' );
var format = require( '@stdlib/string/format' );
var pickBandwidth = require( './pick_bandwidth.js' );
var validate = require( './validate.js' );
var ndarrayLike = require( './ndarray_like.js' );
var min = require( './min.js' );
var max = require( './max.js' );
var gaussian = require( './gaussian.js' );
// MAIN //
/**
* Computes two-dimensional kernel density estimates.
*
* @param {NumericArray} x - array of x values
* @param {NumericArray} y - array of y values
* @param {Options} [options] - function options
* @param {NumericArray} [options.h] - array of length two containing the bandwidth values for x and y
* @param {number} [options.n=25] - number of partitions on the x- and y-axes
* @param {number} [options.xMin] - lower limit of x
* @param {number} [options.xMax] - upper limit of x
* @param {number} [options.yMin] - lower limit of y
* @param {number} [options.yMax] - upper limit of y
* @param {(string|Function)} [options.kernel='gaussian'] - a string or function to specifying the used kernel function
* @throws {TypeError} first argument must be an array or matrix-like
* @throws {TypeError} second argument must be an array
* @throws {Error} first and second arguments must have the same length
* @throws {RangeError} `xMin` must be less than `xMax`
* @throws {RangeError} `yMin` must be less than `yMax`
* @throws {TypeError} options argument must be an object
* @throws {TypeError} must provide valid options
* @returns {Object} object containing the density estimates (`z`) along grid points (`x` and `y` values)
*
* @example
* var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571, 1.7881, 2.019, 2.25, 2.481, 2.7119 ];
* var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454, 4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];
* var out = kde2d( x, y );
*/
function kde2d() {
var kernelFunction;
var maxArgs;
var zScoreX;
var zScoreY;
var gridX;
var gridY;
var xMin;
var xMax;
var yMin;
var yMax;
var xVal; // For gridspace loop
var yVal; // For gridspace loop
var subX;
var subY;
var opts;
var arr;
var err;
var ans;
var out;
var gx;
var gy;
var hX;
var hY;
var ix;
var iy;
var x;
var y;
var i;
var n;
var z;
opts = {};
if ( isMatrixLike( arguments[0] ) ) {
// Case of ndarray, opts
arr = arguments[ 0 ];
maxArgs = 1;
} else {
x = arguments[ 0 ];
y = arguments[ 1 ];
if ( !isNumericArray( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a numeric array. Value: `%s`.', x ) );
}
if ( !isNumericArray( y ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a numeric array. Value: `%s`.', y ) );
}
if ( x.length !== y.length ) {
throw new RangeError( 'invalid arguments. First and second arguments must be arrays having the same length.' );
}
arr = ndarrayLike( x, y );
maxArgs = 2;
}
if ( arguments.length > maxArgs ) {
err = validate( opts, arguments[ maxArgs ] );
if ( err ) {
throw err;
}
}
if ( opts.h ) {
hX = opts.h[0];
hY = opts.h[1];
} else {
hX = pickBandwidth( arr, 0 );
hY = pickBandwidth( arr, 1 );
}
n = opts.n || 25;
xMin = opts.xMin || min( arr, 0, arr.shape[0] );
xMax = opts.xMax || max( arr, 0, arr.shape[0] );
yMin = opts.yMin || min( arr, 1, arr.shape[0] );
yMax = opts.yMax || max( arr, 1, arr.shape[0] );
if ( xMin >= xMax ) {
throw new RangeError( format( 'invalid option. Lower bound `%s` must be strictly less than the upper bound `%s`.', 'xMin', 'xMax' ) );
}
if ( yMin >= yMax ) {
throw new RangeError( format( 'invalid option. Lower bound `%s` must be strictly less than the upper bound `%s`.', 'yMin', 'yMax' ) );
}
kernelFunction = opts.kernel || gaussian;
// Create the `ndarray` to hold the density values:
z = ndarray({
'shape': [ n, n ]
} );
// Make the grid:
gridX = linspace( xMin, xMax, n );
gridY = linspace( yMin, yMax, n );
// Loop through x and y indices:
for ( ix = 0; ix < gridX.length; ix++ ) {
gx = gridX[ ix ];
for ( iy = 0; iy < gridY.length; iy++ ) {
gy = gridY[ iy ];
ans = 0.0;
for ( i = 0; i < arr.shape[ 0 ]; i++ ) {
xVal = arr.get( i, 0 );
yVal = arr.get( i, 1 );
zScoreX = ( (xVal - gx) / hX );
zScoreY = ( (yVal - gy) / hY );
subX = ( 1.0 / hX ) * kernelFunction( zScoreX );
subY = ( 1.0 / hY ) * kernelFunction( zScoreY );
ans += ( subX * subY );
}
z.set( ix, iy, ans / arr.shape[0] );
}
}
out = {};
setReadOnly( out, 'x', gridX );
setReadOnly( out, 'y', gridY );
setReadOnly( out, 'z', z );
return out;
}
// EXPORTS //
module.exports = kde2d;
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