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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Matrix |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @copyright JAMA - https://math.nist.gov/javanumerics/jama/ |
| 10 | * @license OMS License 2.0 |
| 11 | * @version 1.0.0 |
| 12 | * @link https://jingga.app |
| 13 | */ |
| 14 | declare(strict_types=1); |
| 15 | |
| 16 | namespace phpOMS\Math\Matrix; |
| 17 | |
| 18 | use phpOMS\Math\Geometry\Shape\D2\Triangle; |
| 19 | use phpOMS\Math\Matrix\Exception\InvalidDimensionException; |
| 20 | |
| 21 | /** |
| 22 | * QR decomposition |
| 23 | * |
| 24 | * For every matrix A = Q*R |
| 25 | * |
| 26 | * @package phpOMS\Math\Matrix |
| 27 | * @license OMS License 2.0 |
| 28 | * @link https://jingga.app |
| 29 | * @since 1.0.0 |
| 30 | */ |
| 31 | final class QRDecomposition |
| 32 | { |
| 33 | /** |
| 34 | * QR matrix. |
| 35 | * |
| 36 | * @var array[] |
| 37 | * @since 1.0.0 |
| 38 | */ |
| 39 | private array $QR = []; |
| 40 | |
| 41 | /** |
| 42 | * Dimension m |
| 43 | * |
| 44 | * @var int |
| 45 | * @since 1.0.0 |
| 46 | */ |
| 47 | private int $m = 0; |
| 48 | |
| 49 | /** |
| 50 | * Dimension n |
| 51 | * |
| 52 | * @var int |
| 53 | * @since 1.0.0 |
| 54 | */ |
| 55 | private int $n = 0; |
| 56 | |
| 57 | /** |
| 58 | * R diagonal |
| 59 | * |
| 60 | * @var array<int, int|float> |
| 61 | * @since 1.0.0 |
| 62 | */ |
| 63 | private array $Rdiag = []; |
| 64 | |
| 65 | /** |
| 66 | * Constructor. |
| 67 | * |
| 68 | * @param Matrix $M Matrix |
| 69 | * |
| 70 | * @since 1.0.0 |
| 71 | */ |
| 72 | public function __construct(Matrix $M) |
| 73 | { |
| 74 | // Initialize. |
| 75 | $this->QR = $M->toArray(); |
| 76 | $this->m = $M->getM(); |
| 77 | $this->n = $M->getN(); |
| 78 | |
| 79 | // Main loop. |
| 80 | for ($k = 0; $k < $this->n; ++$k) { |
| 81 | // Compute 2-norm of k-th column without under/overflow. |
| 82 | $nrm = 0.0; |
| 83 | for ($i = $k; $i < $this->m; ++$i) { |
| 84 | $nrm = Triangle::getHypot($nrm, $this->QR[$i][$k]); |
| 85 | } |
| 86 | |
| 87 | if ($nrm != 0) { |
| 88 | // Form k-th Householder vector. |
| 89 | if ($this->QR[$k][$k] < 0) { |
| 90 | $nrm = -$nrm; |
| 91 | } |
| 92 | |
| 93 | for ($i = $k; $i < $this->m; ++$i) { |
| 94 | $this->QR[$i][$k] /= $nrm; |
| 95 | } |
| 96 | |
| 97 | $this->QR[$k][$k] += 1.0; |
| 98 | |
| 99 | // Apply transformation to remaining columns. |
| 100 | for ($j = $k + 1; $j < $this->n; ++$j) { |
| 101 | $s = 0.0; |
| 102 | for ($i = $k; $i < $this->m; ++$i) { |
| 103 | $s += $this->QR[$i][$k] * $this->QR[$i][$j]; |
| 104 | } |
| 105 | |
| 106 | $s = -$s / $this->QR[$k][$k]; |
| 107 | for ($i = $k; $i < $this->m; ++$i) { |
| 108 | $this->QR[$i][$j] += $s * $this->QR[$i][$k]; |
| 109 | } |
| 110 | } |
| 111 | } |
| 112 | |
| 113 | $this->Rdiag[$k] = -$nrm; |
| 114 | } |
| 115 | } |
| 116 | |
| 117 | /** |
| 118 | * Matrix has full rank |
| 119 | * |
| 120 | * @return bool |
| 121 | * |
| 122 | * @since 1.0.0 |
| 123 | */ |
| 124 | public function isFullRank() : bool |
| 125 | { |
| 126 | for ($j = 0; $j < $this->n; ++$j) { |
| 127 | if (\abs($this->Rdiag[$j]) < Matrix::EPSILON) { |
| 128 | return false; |
| 129 | } |
| 130 | } |
| 131 | |
| 132 | return true; |
| 133 | } |
| 134 | |
| 135 | /** |
| 136 | * Get R matrix |
| 137 | * |
| 138 | * @return Matrix |
| 139 | * |
| 140 | * @since 1.0.0 |
| 141 | */ |
| 142 | public function getR() : Matrix |
| 143 | { |
| 144 | $R = [[]]; |
| 145 | |
| 146 | for ($i = 0; $i < $this->n; ++$i) { |
| 147 | for ($j = 0; $j < $this->n; ++$j) { |
| 148 | if ($i < $j) { |
| 149 | $R[$i][$j] = $this->QR[$i][$j]; |
| 150 | } elseif ($i === $j) { |
| 151 | $R[$i][$j] = $this->Rdiag[$i]; |
| 152 | } else { |
| 153 | $R[$i][$j] = 0.0; |
| 154 | } |
| 155 | } |
| 156 | } |
| 157 | |
| 158 | $matrix = new Matrix(); |
| 159 | $matrix->setMatrix($R); |
| 160 | |
| 161 | return $matrix; |
| 162 | } |
| 163 | |
| 164 | /** |
| 165 | * Get Q matrix |
| 166 | * |
| 167 | * @return Matrix |
| 168 | * |
| 169 | * @since 1.0.0 |
| 170 | */ |
| 171 | public function getQ() : Matrix |
| 172 | { |
| 173 | $Q = [[]]; |
| 174 | |
| 175 | for ($k = $this->n - 1; $k >= 0; --$k) { |
| 176 | for ($i = 0; $i < $this->m; ++$i) { |
| 177 | $Q[$i][$k] = 0.0; |
| 178 | } |
| 179 | |
| 180 | $Q[$k][$k] = 1.0; |
| 181 | for ($j = $k; $j < $this->n; ++$j) { |
| 182 | if ($this->QR[$k][$k] != 0) { |
| 183 | $s = 0.0; |
| 184 | for ($i = $k; $i < $this->m; ++$i) { |
| 185 | $s += $this->QR[$i][$k] * $Q[$i][$j]; |
| 186 | } |
| 187 | |
| 188 | $s = -$s / $this->QR[$k][$k]; |
| 189 | for ($i = $k; $i < $this->m; ++$i) { |
| 190 | $Q[$i][$j] += $s * $this->QR[$i][$k]; |
| 191 | } |
| 192 | } |
| 193 | } |
| 194 | } |
| 195 | |
| 196 | $matrix = new Matrix(); |
| 197 | $matrix->setMatrix($Q); |
| 198 | |
| 199 | return $matrix; |
| 200 | } |
| 201 | |
| 202 | /** |
| 203 | * Solve Ax = b |
| 204 | * |
| 205 | * @param Matrix $B Matrix |
| 206 | * |
| 207 | * @return Matrix |
| 208 | * |
| 209 | * @throws InvalidDimensionException |
| 210 | * @throws \Exception |
| 211 | * |
| 212 | * @since 1.0.0 |
| 213 | */ |
| 214 | public function solve(Matrix $B) : Matrix |
| 215 | { |
| 216 | if ($B->getM() !== $this->m) { |
| 217 | throw new InvalidDimensionException($B->getM()); |
| 218 | } |
| 219 | |
| 220 | if (!$this->isFullRank()) { |
| 221 | throw new \Exception('Rank'); |
| 222 | } |
| 223 | |
| 224 | $nx = $B->getN(); |
| 225 | $X = $B->toArray(); |
| 226 | |
| 227 | // Compute Y = transpose(Q)*B |
| 228 | for ($k = 0; $k < $this->n; ++$k) { |
| 229 | for ($j = 0; $j < $nx; ++$j) { |
| 230 | $s = 0.0; |
| 231 | for ($i = $k; $i < $this->m; ++$i) { |
| 232 | $s += $this->QR[$i][$k] * $X[$i][$j]; |
| 233 | } |
| 234 | |
| 235 | $s = -$s / $this->QR[$k][$k]; |
| 236 | for ($i = $k; $i < $this->m; ++$i) { |
| 237 | $X[$i][$j] += $s * $this->QR[$i][$k]; |
| 238 | } |
| 239 | } |
| 240 | } |
| 241 | |
| 242 | // Solve R*X = Y; |
| 243 | for ($k = $this->n - 1; $k >= 0; --$k) { |
| 244 | for ($j = 0; $j < $nx; ++$j) { |
| 245 | $X[$k][$j] /= $this->Rdiag[$k]; |
| 246 | } |
| 247 | |
| 248 | for ($i = 0; $i < $k; ++$i) { |
| 249 | for ($j = 0; $j < $nx; ++$j) { |
| 250 | $X[$i][$j] -= $X[$k][$j] * $this->QR[$i][$k]; |
| 251 | } |
| 252 | } |
| 253 | } |
| 254 | |
| 255 | $matrix = new Matrix(); |
| 256 | $matrix->setMatrix($X); |
| 257 | |
| 258 | return $matrix->getSubMatrix(0, $this->n - 1, 0, $nx - 1); |
| 259 | } |
| 260 | } |