Sigmoid Activation function implementation with simplified batch calculation

Author: crapxxi

src/main/java/com/thealgorithms/maths/SigmoidActivation.java

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+package com.thealgorithms.maths;
+
+/**
+ * Implementation of the Sigmoid Activation function.
+ * Sigmoid function is used as an activation function in machine learning and neural networks
+ * for modeling binary classification problems, smoothing outputs, and introducing non-linearity
+ * into models.
+ *
+ * @author <a href="https://github.com/crapxxi">Alikhan Turugeldiyev</a>
+ */
+
+public class SigmoidActivation {
+    /**
+     * @summary Maps any real-valued number into a value between 0 and 1
+     * @param x In machine learning, x could be a weighted sum of inputs in a neural network neuron or a raw score in logistic regression.
+     * @return The output (range) of the sigmoid function is always strictly between 0 and 1.
+     */
+    public static double activate(double x) {
+        // If the number x is NaN then, returning NaN to saving from unexpected output.
+        if(Double.isNaN(x)) return Double.NaN;
+        // Saving from unnecessary and heavy calculations.
+        // lim x->-inf sigmoid(x) will return number very close to 0
+        if(x < -745) return 0.0;
+        // lim x->inf sigmoid(x) will return number very close to 1
+        if(x > 745) return 1.0;
+        // sigmoid function's formula
+        return 1.0 / ( 1 + Math.exp((-1) * x));
+    }
+
+    public static double[][] activate(double[][] x) {
+        // apply calculation to every value in batch.
+        double[][] activatedNumbers = new double[x.length][x[0].length];
+        for(int i = 0; i < x.length; i++) {
+            for (int j = 0; j < x[0].length; j++) activatedNumbers[i][j] = activate(x[i][j]);
+        }
+        return activatedNumbers;
+    }
+
+    /**
+     * @summary Calculates gradients for mapped values. By the chain rule, you can calculate error.
+     * @param y Activated by sigmoid function value.
+     * @return The output is a gradient of the activated value.
+     */
+    public static double grad(double y) {
+        // sigmoid function derivative is reducing to this value.
+        // sigmoid'(x) = sigmoid(x) * (1-sigmoid(x))
+        return y * (1 - y);
+    }
+
+    public static double[][] grad(double[][] y) {
+        // apply calculation to every value in batch.
+        double[][] grads = new double[y.length][y[0].length];
+        for(int i = 0; i < y.length; i++) {
+            for (int j = 0; j < y[0].length; j++) grads[i][j] = grad(y[i][j]);
+        }
+        return grads;
+    }
+
+}

src/test/java/com/thealgorithms/maths/SigmoidActivationTest.java

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+package com.thealgorithms.maths;
+
+import org.junit.jupiter.api.Test;
+
+import java.util.Arrays;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+public class SigmoidActivationTest {
+
+    @Test
+    public void calculationTest() {
+        assertEquals(0.5,SigmoidActivation.activate(0), 0.01,"1 case correct" );
+        assertEquals(0.73,SigmoidActivation.activate(1),0.01,"2 case correct");
+        assertEquals(0.26,SigmoidActivation.activate(-1),0.01, "3 case correct");
+        assertEquals(0.88,SigmoidActivation.activate(2),0.01,"4 case correct");
+        assertEquals(0.11,SigmoidActivation.activate(-2),0.01,"5 case correct");
+
+        double[][] xBatch = new double[4][3];
+        double[][] expectedX = new double[4][3];
+
+        for(int i = 0; i < 4; i++) {
+            for(int j = 0; j < 3; j++) xBatch[i][j] = 0;
+        }
+
+        for(int i = 0; i < 4; i++) {
+            for(int j = 0; j < 3; j++) expectedX[i][j] = 0.5;
+        }
+
+        assertTrue(Arrays.deepEquals(expectedX, SigmoidActivation.activate(xBatch)), "batch case correct");
+
+        assertEquals(0.25, SigmoidActivation.grad(0.5), 0.01, "grad calculation correct");
+
+        double[][] yBatch = new double[4][3];
+        for(int i = 0; i < 4; i++) {
+            for(int j = 0; j < 3; j++) yBatch[i][j] = 0.5;
+        }
+
+        double[][] expectedY = new double[4][3];
+        for(int i = 0; i < 4; i++) {
+            for(int j = 0; j < 3; j++) expectedY[i][j] = 0.25;
+        }
+        assertTrue(Arrays.deepEquals(expectedY, SigmoidActivation.grad(yBatch)), "grad batch case correct");
+    }
+
+    @Test
+    public void willReturnNaN() {
+        double x = Double.NaN;
+
+        assertTrue(Double.isNaN(SigmoidActivation.activate(x)), "returned NaN");
+    }
+
+    @Test
+    public void extremumNumbersOnActivate() {
+        double x = 777;
+
+        assertEquals(1.0, SigmoidActivation.activate(x), 0.01, "big number case correct");
+        assertEquals(0.0, SigmoidActivation.activate((-1) * x), 0.01, "small number case correct");
+    }
+}