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.

`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{ [ ~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.

`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{ [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.

`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{ [ 6.344e-154, 1.93e-171, ... ]}
}
*/
`

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

`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{ [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:

`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{ [ 1.762e-8, 2.94e-8, ... ]}
}
*/
`