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import interquartileRange from "./interquartile_range.js";import stddev from "./sample_standard_deviation.js";
const SQRT_2PI = Math.sqrt(2 * Math.PI);
/** * [Well-known kernels](https://en.wikipedia.org/wiki/Kernel_(statistics)#Kernel_functions_in_common_use) * @private */const kernels = {    /**     * The gaussian kernel.     * @private     */    gaussian: function (u) {        return Math.exp(-0.5 * u * u) / SQRT_2PI;    }};
/** * Well known bandwidth selection methods * @private */const bandwidthMethods = {    /**     * The ["normal reference distribution"     * rule-of-thumb](https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/bandwidth.nrd.html),     * a commonly used version of [Silverman's     * rule-of-thumb](https://en.wikipedia.org/wiki/Kernel_density_estimation#A_rule-of-thumb_bandwidth_estimator).     * @private     */    nrd: function (x) {        let s = stddev(x);        const iqr = interquartileRange(x);        if (typeof iqr === "number") {            s = Math.min(s, iqr / 1.34);        }        return 1.06 * s * Math.pow(x.length, -0.2);    }};
/** * [Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) * is a useful tool for, among other things, estimating the shape of the * underlying probability distribution from a sample. * * @name kernelDensityEstimation * @param X sample values * @param kernel The kernel function to use. If a function is provided, it should return non-negative values and integrate to 1. Defaults to 'gaussian'. * @param bandwidthMethod The "bandwidth selection" method to use, or a fixed bandwidth value. Defaults to "nrd", the commonly-used ["normal reference distribution" rule-of-thumb](https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/bandwidth.nrd.html). * @returns {Function} An estimated [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) for the given sample. The returned function runs in `O(X.length)`. */function kernelDensityEstimation(X, kernel, bandwidthMethod) {    let kernelFn;    if (kernel === undefined) {        kernelFn = kernels.gaussian;    } else if (typeof kernel === "string") {        if (!kernels[kernel]) {            throw new Error('Unknown kernel "' + kernel + '"');        }        kernelFn = kernels[kernel];    } else {        kernelFn = kernel;    }
    let bandwidth;    if (typeof bandwidthMethod === "undefined") {        bandwidth = bandwidthMethods.nrd(X);    } else if (typeof bandwidthMethod === "string") {        if (!bandwidthMethods[bandwidthMethod]) {            throw new Error(                'Unknown bandwidth method "' + bandwidthMethod + '"'            );        }        bandwidth = bandwidthMethods[bandwidthMethod](X);    } else {        bandwidth = bandwidthMethod;    }
    return function (x) {        let i = 0;        let sum = 0;        for (i = 0; i < X.length; i++) {            sum += kernelFn((x - X[i]) / bandwidth);        }        return sum / bandwidth / X.length;    };}
export default kernelDensityEstimation;