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declare(strict_types=1); |
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namespace Phpml\Helper\Optimizer; |
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use Closure; |
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/** |
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* Stochastic Gradient Descent optimization method |
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* to find a solution for the equation A.ϴ = y where |
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* A (samples) and y (targets) are known and ϴ is unknown. |
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*/ |
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class StochasticGD extends Optimizer |
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{ |
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/** |
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* A (samples) |
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* |
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* @var array |
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*/ |
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protected $samples = []; |
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/** |
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* y (targets) |
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* |
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* @var array |
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*/ |
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protected $targets = []; |
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/** |
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* Callback function to get the gradient and cost value |
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* for a specific set of theta (ϴ) and a pair of sample & target |
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* |
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* @var \Closure|null |
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*/ |
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protected $gradientCb = null; |
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/** |
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* Maximum number of iterations used to train the model |
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* |
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* @var int |
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*/ |
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protected $maxIterations = 1000; |
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/** |
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* Learning rate is used to control the speed of the optimization.<br> |
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* |
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* Larger values of lr may overshoot the optimum or even cause divergence |
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* while small values slows down the convergence and increases the time |
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* required for the training |
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* |
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* @var float |
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*/ |
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protected $learningRate = 0.001; |
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/** |
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* Minimum amount of change in the weights and error values |
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* between iterations that needs to be obtained to continue the training |
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* |
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* @var float |
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*/ |
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protected $threshold = 1e-4; |
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/** |
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* Enable/Disable early stopping by checking the weight & cost values |
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* to see whether they changed large enough to continue the optimization |
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* |
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* @var bool |
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*/ |
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protected $enableEarlyStop = true; |
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/** |
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* List of values obtained by evaluating the cost function at each iteration |
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* of the algorithm |
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* |
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* @var array |
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*/ |
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protected $costValues = []; |
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/** |
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* Initializes the SGD optimizer for the given number of dimensions |
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*/ |
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public function __construct(int $dimensions) |
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{ |
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// Add one more dimension for the bias |
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parent::__construct($dimensions + 1); |
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$this->dimensions = $dimensions; |
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} |
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/** |
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* Sets minimum value for the change in the theta values |
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* between iterations to continue the iterations.<br> |
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* |
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* If change in the theta is less than given value then the |
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* algorithm will stop training |
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* |
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* @return $this |
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*/ |
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public function setChangeThreshold(float $threshold = 1e-5) |
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{ |
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$this->threshold = $threshold; |
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return $this; |
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} |
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/** |
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* Enable/Disable early stopping by checking at each iteration |
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* whether changes in theta or cost value are not large enough |
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* |
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* @return $this |
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*/ |
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public function setEarlyStop(bool $enable = true) |
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{ |
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$this->enableEarlyStop = $enable; |
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return $this; |
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} |
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/** |
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* @return $this |
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*/ |
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public function setLearningRate(float $learningRate) |
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{ |
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$this->learningRate = $learningRate; |
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return $this; |
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} |
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/** |
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* @return $this |
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*/ |
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public function setMaxIterations(int $maxIterations) |
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{ |
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$this->maxIterations = $maxIterations; |
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return $this; |
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} |
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/** |
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* Optimization procedure finds the unknow variables for the equation A.ϴ = y |
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* for the given samples (A) and targets (y).<br> |
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* |
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* The cost function to minimize and the gradient of the function are to be |
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* handled by the callback function provided as the third parameter of the method. |
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*/ |
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public function runOptimization(array $samples, array $targets, Closure $gradientCb): ?array |
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{ |
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$this->samples = $samples; |
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$this->targets = $targets; |
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$this->gradientCb = $gradientCb; |
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$currIter = 0; |
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$bestTheta = null; |
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$bestScore = 0.0; |
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$this->costValues = []; |
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while ($this->maxIterations > $currIter++) { |
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$theta = $this->theta; |
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// Update the guess |
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$cost = $this->updateTheta(); |
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// Save the best theta in the "pocket" so that |
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// any future set of theta worse than this will be disregarded |
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if ($bestTheta == null || $cost <= $bestScore) { |
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$bestTheta = $theta; |
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$bestScore = $cost; |
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} |
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// Add the cost value for this iteration to the list |
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$this->costValues[] = $cost; |
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// Check for early stop |
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if ($this->enableEarlyStop && $this->earlyStop($theta)) { |
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break; |
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} |
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} |
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$this->clear(); |
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// Solution in the pocket is better than or equal to the last state |
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// so, we use this solution |
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return $this->theta = (array) $bestTheta; |
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} |
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/** |
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* Returns the list of cost values for each iteration executed in |
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* last run of the optimization |
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*/ |
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public function getCostValues(): array |
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{ |
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return $this->costValues; |
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} |
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protected function updateTheta(): float |
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{ |
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$jValue = 0.0; |
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$theta = $this->theta; |
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foreach ($this->samples as $index => $sample) { |
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$target = $this->targets[$index]; |
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$result = ($this->gradientCb)($theta, $sample, $target); |
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[$error, $gradient, $penalty] = array_pad($result, 3, 0); |
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// Update bias |
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$this->theta[0] -= $this->learningRate * $gradient; |
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// Update other values |
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for ($i = 1; $i <= $this->dimensions; ++$i) { |
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$this->theta[$i] -= $this->learningRate * |
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($gradient * $sample[$i - 1] + $penalty * $this->theta[$i]); |
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} |
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// Sum error rate |
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$jValue += $error; |
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} |
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return $jValue / count($this->samples); |
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} |
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/** |
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* Checks if the optimization is not effective enough and can be stopped |
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* in case large enough changes in the solution do not happen |
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*/ |
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protected function earlyStop(array $oldTheta): bool |
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{ |
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// Check for early stop: No change larger than threshold (default 1e-5) |
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$diff = array_map( |
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function ($w1, $w2) { |
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return abs($w1 - $w2) > $this->threshold ? 1 : 0; |
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}, |
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$oldTheta, |
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$this->theta |
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); |
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if (array_sum($diff) == 0) { |
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return true; |
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} |
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// Check if the last two cost values are almost the same |
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$costs = array_slice($this->costValues, -2); |
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if (count($costs) == 2 && abs($costs[1] - $costs[0]) < $this->threshold) { |
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return true; |
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} |
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return false; |
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} |
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/** |
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* Clears the optimizer internal vars after the optimization process. |
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*/ |
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protected function clear(): void |
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{ |
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$this->samples = []; |
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$this->targets = []; |
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$this->gradientCb = null; |
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} |
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} |
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This check marks access to variables or properties that have not been declared yet. While PHP has no explicit notion of declaring a variable, accessing it before a value is assigned to it is most likely a bug.