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kde2d

Two-dimensional kernel density estimation.

Installation

npm install @stdlib/stats-kde2d

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var kde2d = require( '@stdlib/stats-kde2d' );

kde2d( x, y[, opts] )

By default, the function computes two-dimensional normal kernel density estimation for data provided in arrays or typed-arrays x and y. When these arguments are supplied, the arrays are coerced into a Matrix-like object.

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 );
/* e.g., returns
    {
        'x': [ ~0.633, ~0.72, ... ],
        'y': [ ~-0.047, ~0.271 ... ],
        'z': ndarray{ <Float64Array>[ ~0.0455, ... ]}
    }
*/

kde2d( arr[, opts] )

The function has the ability to handle ndarrays. Specifically the ndarray must be constructed so that there are two columns present, the first column containing the x values and the second column containing the y values.

Note that for the output the x and y properties refer to the equally spaced gridpoints of X and Y used to calculate z.

var ndarray = require( '@stdlib/ndarray-ctor' );

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 buffer = x.concat( y );
var n = x.length;
var shape = [ n, 2 ];
var strides = [ 1, n ];
var offset = 0;
var order = 'column-major';

var arr = ndarray( 'generic', buffer, shape, strides, offset, order );

var out = kde2d( arr );
/* e.g., returns
    {
        'x': [ ~0.633, ~0.72, ... ],
        'y': [ ~-0.047,~ 0.271, ... ],
        'z': ndarray{ <Float64Array>[0.04547178438418015, ... ]}
    }
*/

The function accepts the following options:

• h: NumberArray of length 2 indicating the X and Y bandwidth values, respectively.
• n: a positive integer indicating the number of partitions to create in the grid. Default: 25.
• xMin: a number indicating the lower bound of X. Must be strictly less than xMax. Will default to the minimum value of X.
• xMax: a number indicating the upper bound of X. Must be strictly greater than xMin. Will default to the maximum value of X.
• yMin: a number indicating the lower bound of Y. Must be strictly less than yMax. Will default to the minimum value of Y.
• yMax: a number indicating the upper bound of Y. Must be strictly greater than yMin. Will default to the maximum value of Y.
• kernel: a string or function indicating the kernel to be used when calculating the estimation. If a string is supplied then it will be matched to a pre-defined kernel function. Otherwise you may supply a function to support custom kernels. Will default to the gaussian kernel.

By default, the bandwidth argument is set by a builtin function. To choose different bandwidth values, set the h option. Note that if you use a custom bandwidth for one axis, you must also use a custom bandwidth for the other axis.

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, {
    'h': [ 0.05, 0.1 ]
});
/* e.g., returns
    {
        'x': [ 0.148, 0.3772, ... ],
        'y': [ -1.1511, -0.253, ... ],
        'z': ndarray{ <Float64Array>[ 6.344e-154, 1.93e-171, ... ]}
    }
*/

By default, we use 25 partitions. To change the number of partitions, set the n option.

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, {
    'n': 15
});
/* e.g., returns
    {
        'x': [ 0.0623, 0.452, ... ],
        'y': [ 0.1378, 1.6266, ... ],
        'z': ndarray{ <Float64Array>[1.211e-7, 5.76e-7, ... ]}
    }
*/

As a default choice, the kde2d function sets the xMin, xMax, yMin and yMax values to be the minimum and maximum of the X and Y arrays or columns of the supplied arguments. We may change the options as follows:

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, {
    'xMin': 0.0,
    'xMax': 2.5,
    'yMin': 0.0,
    'yMax': 6.0
});
/* e.g., returns
    {
        'x': [ 0, 0.1041, ... ],
        'y': [ 0, 0.25, ... ],
        'z': ndarray{ <Float64Array>[ 1.762e-8, 2.94e-8, ... ]}
    }
*/

Examples

var normal = require( '@stdlib/random-base-normal' );
var kde2d = require( '@stdlib/stats-kde2d' );

var randX;
var randY;
var out;
var i;
var x;
var y;
var n;

n = 100;

x = new Array( n );
y = new Array( n );

randX = normal.factory( 3.0, 1.2 );
randY = normal.factory( 10.0, 4.5 );

for ( i = 0; i < n; i++ ) {
    x[ i ] = randX();
    y[ i ] = randY();
}

out = kde2d( x, y );
/* e.g., returns
    {
        'x': [0.022, 0.2614, ...],
        'y': [-4.533, 3.602, ...],
        'z': ndarray { Float64Array [9.8266e-11, 6.45e-9, ...]}
}
*/

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.