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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Topology |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @license OMS License 2.0 |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Math\Topology; |
| 16 | |
| 17 | /** |
| 18 | * Kernels. |
| 19 | * |
| 20 | * @package phpOMS\Math\Topology |
| 21 | * @license OMS License 2.0 |
| 22 | * @link https://jingga.app |
| 23 | * @since 1.0.0 |
| 24 | */ |
| 25 | final class Kernels2D |
| 26 | { |
| 27 | /** |
| 28 | * Constructor |
| 29 | * |
| 30 | * @since 1.0.0 |
| 31 | * @codeCoverageIgnore |
| 32 | */ |
| 33 | private function __construct() |
| 34 | { |
| 35 | } |
| 36 | |
| 37 | /** |
| 38 | * Uniform kernel. |
| 39 | * |
| 40 | * @param float $distance Distance |
| 41 | * @param float $bandwidth Bandwidth |
| 42 | * |
| 43 | * @return float |
| 44 | * |
| 45 | * @since 1.0.0 |
| 46 | */ |
| 47 | public static function uniformKernel(float $distance, float $bandwidth) : float |
| 48 | { |
| 49 | return \abs($distance) <= $bandwidth / 2 |
| 50 | ? 1 / $bandwidth |
| 51 | : 0.0; |
| 52 | } |
| 53 | |
| 54 | /** |
| 55 | * Triangular kernel. |
| 56 | * |
| 57 | * @param float $distance Distance |
| 58 | * @param float $bandwidth Bandwidth |
| 59 | * |
| 60 | * @return float |
| 61 | * |
| 62 | * @since 1.0.0 |
| 63 | */ |
| 64 | public static function triangularKernel(float $distance, float $bandwidth) : float |
| 65 | { |
| 66 | return \abs($distance) <= $bandwidth / 2 |
| 67 | ? 1 - \abs($distance) / ($bandwidth / 2) |
| 68 | : 0.0; |
| 69 | } |
| 70 | |
| 71 | /** |
| 72 | * Epanechnikov kernel. |
| 73 | * |
| 74 | * @param float $distance Distance |
| 75 | * @param float $bandwidth Bandwidth |
| 76 | * |
| 77 | * @return float |
| 78 | * |
| 79 | * @since 1.0.0 |
| 80 | */ |
| 81 | public static function epanechnikovKernel(float $distance, float $bandwidth) : float |
| 82 | { |
| 83 | if (\abs($distance) <= $bandwidth) { |
| 84 | $u = \abs($distance) / $bandwidth; |
| 85 | |
| 86 | return 0.75 * (1 - $u * $u) / $bandwidth; |
| 87 | } else { |
| 88 | return 0.0; |
| 89 | } |
| 90 | } |
| 91 | |
| 92 | /** |
| 93 | * Quartic kernel. |
| 94 | * |
| 95 | * @param float $distance Distance |
| 96 | * @param float $bandwidth Bandwidth |
| 97 | * |
| 98 | * @return float |
| 99 | * |
| 100 | * @since 1.0.0 |
| 101 | */ |
| 102 | public static function quarticKernel(float $distance, float $bandwidth) : float |
| 103 | { |
| 104 | if (\abs($distance) <= $bandwidth) { |
| 105 | $u = \abs($distance) / $bandwidth; |
| 106 | |
| 107 | return (15 / 16) * (1 - $u * $u) * (1 - $u * $u) / $bandwidth; |
| 108 | } else { |
| 109 | return 0.0; |
| 110 | } |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | * Triweight kernel. |
| 115 | * |
| 116 | * @param float $distance Distance |
| 117 | * @param float $bandwidth Bandwidth |
| 118 | * |
| 119 | * @return float |
| 120 | * |
| 121 | * @since 1.0.0 |
| 122 | */ |
| 123 | public static function triweightKernel(float $distance, float $bandwidth) : float |
| 124 | { |
| 125 | if (\abs($distance) <= $bandwidth) { |
| 126 | $u = \abs($distance) / $bandwidth; |
| 127 | |
| 128 | return (35 / 32) * (1 - $u * $u) * (1 - $u * $u) * (1 - $u * $u) / $bandwidth; |
| 129 | } else { |
| 130 | return 0.0; |
| 131 | } |
| 132 | } |
| 133 | |
| 134 | /** |
| 135 | * Tricube kernel. |
| 136 | * |
| 137 | * @param float $distance Distance |
| 138 | * @param float $bandwidth Bandwidth |
| 139 | * |
| 140 | * @return float |
| 141 | * |
| 142 | * @since 1.0.0 |
| 143 | */ |
| 144 | public static function tricubeKernel(float $distance, float $bandwidth) : float |
| 145 | { |
| 146 | if (\abs($distance) <= $bandwidth) { |
| 147 | $u = \abs($distance) / $bandwidth; |
| 148 | |
| 149 | return (70 / 81) * (1 - $u * $u * $u) * (1 - $u * $u * $u) * (1 - $u * $u * $u) / $bandwidth; |
| 150 | } else { |
| 151 | return 0.0; |
| 152 | } |
| 153 | } |
| 154 | |
| 155 | /** |
| 156 | * Gaussian kernel. |
| 157 | * |
| 158 | * @param float $distance Distance |
| 159 | * @param float $bandwidth Bandwidth |
| 160 | * |
| 161 | * @return float |
| 162 | * |
| 163 | * @since 1.0.0 |
| 164 | */ |
| 165 | public static function gaussianKernel(float $distance, float $bandwidth) : float |
| 166 | { |
| 167 | return \exp(-($distance * $distance) / (2 * $bandwidth * $bandwidth)) / ($bandwidth * \sqrt(2 * \M_PI)); |
| 168 | } |
| 169 | |
| 170 | /** |
| 171 | * Cosine kernel. |
| 172 | * |
| 173 | * @param float $distance Distance |
| 174 | * @param float $bandwidth Bandwidth |
| 175 | * |
| 176 | * @return float |
| 177 | * |
| 178 | * @since 1.0.0 |
| 179 | */ |
| 180 | public static function cosineKernel(float $distance, float $bandwidth) : float |
| 181 | { |
| 182 | return \abs($distance) <= $bandwidth |
| 183 | ? (\M_PI / 4) * \cos(\M_PI * $distance / (2 * $bandwidth)) / $bandwidth |
| 184 | : 0.0; |
| 185 | } |
| 186 | |
| 187 | /** |
| 188 | * Logistic kernel. |
| 189 | * |
| 190 | * @param float $distance Distance |
| 191 | * @param float $bandwidth Bandwidth |
| 192 | * |
| 193 | * @return float |
| 194 | * |
| 195 | * @since 1.0.0 |
| 196 | */ |
| 197 | public static function logisticKernel(float $distance, float $bandwidth) : float |
| 198 | { |
| 199 | return 1 / (\exp($distance / $bandwidth) + 2 + \exp(-$distance / $bandwidth)); |
| 200 | } |
| 201 | } |