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# kde2d

> Two-dimensional kernel density estimation.

<section class="usage">

## Usage

```javascript
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][mdn-array] or [typed-arrays][mdn-typed-array] `x` and `y`. When these arguments are supplied, the arrays are coerced into a Matrix-like object.

<!-- eslint-disable array-element-newline -->

```javascript
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][nd-array]. 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`. 

<!-- eslint-disable array-element-newline -->

```javascript
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 lower 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 X. Must be strictly less than `yMax`. Will default to the minimum value of `Y`.
-   **yMax**: A `number` indicating the lower bound of X. 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.

<!-- eslint-disable array-element-newline -->

```javascript
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.

<!-- eslint-disable array-element-newline -->

```javascript
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:

<!-- eslint-disable array-element-newline -->

```javascript
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, ... ]}
    }
*/
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
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, ...]}
}
*/
```

</section>

<!-- /.examples -->

<section class="links">

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays

[nd-array]: https://github.com/stdlib-js/stdlib/blob/develop/lib/node_modules/@stdlib/ndarray/ctor/README.md

</section>

<!-- /.links -->