Optimize squaring operations

src/AnomalyDetectors/GaussianMLE.php

@@ -254,13 +254,15 @@ public function partial(Dataset $dataset) : void
 
             $oldVariance -= $this->epsilon;
 
+            $delta = $n * ($oldMean - $mean);
+
             $this->means[$column] = (($this->n * $oldMean)
                 + ($n * $mean)) / $weight;
 
             $this->variances[$column] = ($this->n
                 * $oldVariance + ($n * $variance)
                 + ($this->n / ($n * $weight))
-                * ($n * $oldMean - $n * $mean) ** 2)
+                * ($delta * $delta))
                 / $weight;
         }
 
@@ -346,7 +348,10 @@ protected function logLikelihood(array $sample) : float
             $variance = $this->variances[$column];
 
             $pdf = 0.5 * log(TWO_PI * $variance);
-            $pdf += 0.5 * (($value - $mean) ** 2) / $variance;
+
+            $delta = $value - $mean;
+
+            $pdf += 0.5 * ($delta * $delta) / $variance;
 
             $likelihood += $pdf;
         }

src/Classifiers/GaussianNB.php

@@ -273,14 +273,16 @@ public function partial(Dataset $dataset) : void
 
                     [$mean, $variance] = Stats::meanVar($values);
 
+                    $delta = $n * ($oldMean - $mean);
+
                     $means[] = (($n * $mean)
                         + ($oldWeight * $oldMean))
                         / $weight;
 
                     $variances[] = ($oldWeight
                         * $oldVariance + ($n * $variance)
                         + ($oldWeight / ($n * $weight))
-                        * ($n * $oldMean - $n * $mean) ** 2)
+                        * ($delta * $delta))
                         / $weight;
                 }
             } else {
@@ -418,7 +420,8 @@ protected function jointLogLikelihood(array $sample) : array
                 $variance = $variances[$column];
 
                 $pdf = -0.5 * log(TWO_PI * $variance);
-                $pdf -= 0.5 * (($value - $mean) ** 2) / $variance;
+                $delta = $value - $mean;
+                $pdf -= 0.5 * ($delta * $delta) / $variance;
 
                 $likelihood += $pdf;
             }

src/Clusterers/GaussianMixture.php

@@ -355,7 +355,9 @@ public function train(Dataset $dataset) : void
                     $mean = $sigma / $total;
 
                     foreach ($column as $i => $value) {
-                        $ssd += $affinities[$i] * ($value - $mean) ** 2;
+                        $delta = $value - $mean;
+
+                        $ssd += $affinities[$i] * ($delta * $delta);
                     }
 
                     $variance = $ssd / $total;
@@ -505,7 +507,10 @@ protected function jointLogLikelihood(array $sample) : array
                 $variance = $variances[$column];
 
                 $pdf = -0.5 * log(TWO_PI * $variance);
-                $pdf -= 0.5 * (($feature - $mean) ** 2) / $variance;
+
+                $delta = $feature - $mean;
+
+                $pdf -= 0.5 * ($delta * $delta) / $variance;
 
                 $likelihood += $pdf;
             }

src/Helpers/Stats.php

@@ -173,7 +173,8 @@ public static function variance(array $values, ?float $mean = null) : float
         $ssd = 0.0;
 
         foreach ($values as $value) {
-            $ssd += ($value - $mean) ** 2;
+            $delta = $value - $mean;
+            $ssd += $delta * $delta;
         }
 
         return $ssd / count($values);

src/Kernels/Distance/Cosine.php

@@ -54,8 +54,8 @@ public function compute(array $a, array $b) : float
 
             $sigma += $valueA * $valueB;
 
-            $ssA += $valueA ** 2;
-            $ssB += $valueB ** 2;
+            $ssA += $valueA * $valueA;
+            $ssB += $valueB * $valueB;
         }
 
         if ($ssA === 0.0 and $ssB === 0.0) {

src/Kernels/Distance/Euclidean.php

@@ -44,7 +44,9 @@ public function compute(array $a, array $b) : float
         $distance = 0.0;
 
         foreach ($a as $i => $value) {
-            $distance += ($value - $b[$i]) ** 2;
+            $delta = $value - $b[$i];
+
+            $distance += $delta * $delta;
         }
 
         return sqrt($distance);

src/Kernels/Distance/SafeEuclidean.php

@@ -68,7 +68,9 @@ public function compute(array $a, array $b) : float
                 continue;
             }
 
-            $distance += ($valueA - $valueB) ** 2;
+            $delta = $valueA - $valueB;
+
+            $distance += $delta * $delta;
         }
 
         $n = count($a);

src/Kernels/Distance/SparseCosine.php

@@ -48,15 +48,15 @@ public function compute(array $a, array $b) : float
             if ($valueA != 0 and $valueB != 0) {
                 $sigma += $valueA * $valueB;
 
-                $ssA += $valueA ** 2;
-                $ssB += $valueB ** 2;
+                $ssA += $valueA * $valueA;
+                $ssB += $valueB * $valueB;
             } else {
                 if ($valueA != 0) {
-                    $ssA += $valueA ** 2;
+                    $ssA += $valueA * $valueA;
                 }
 
                 if ($valueB != 0) {
-                    $ssB += $valueB ** 2;
+                    $ssB += $valueB * $valueB;
                 }
             }
         }

src/Transformers/ZScaleStandardizer.php

@@ -173,13 +173,15 @@ public function update(Dataset $dataset) : void
 
             [$mean, $variance] = Stats::meanVar($values);
 
+            $delta = $n * ($oldMean - $mean);
+
             $this->means[$column] = (($this->n * $oldMean)
                 + ($n * $mean)) / $weight;
 
             $this->variances[$column] = ($this->n
                 * $oldVariance + ($n * $variance)
                 + ($this->n / ($n * $weight))
-                * ($n * $oldMean - $n * $mean) ** 2)
+                * ($delta * $delta))
                 / $weight;
         }