Update MatrixMultiplicationVerifier.java

Author: Menil-dev

src/main/java/com/thealgorithms/randomized/MatrixMultiplicationVerifier.java

@@ -22,9 +22,143 @@ private MatrixMultiplicationVerifier() {
     static int[] multiply(int[][] matrix, int[] vector) {
         int n = vector.length;
         int[] result = new int[n];
-        for (int i = 0; i < n; i++)
-            for (int j = 0; j < n; j++)
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
                 result[i] += matrix[i][j] * vector[j];
+            }
+        }
+        return result;
+    }
+
+    /*
+        Actual function that performs verification function
+        @params, all three input matrices of int type, number of iterations
+    */
+    public static boolean verify(int[][] matrixA, int[][] matrixB, int[][] matrixC, int iterations) {
+        if (matrixA.length == 0 || matrixB.length == 0 || matrixC.length == 0
+                || matrixA[0].length == 0 || matrixB[0].length == 0 || matrixC[0].length == 0) {
+            return matrixA.length == matrixB[0].length
+                    && matrixB.length == matrixC.length
+                    && matrixC[0].length == matrixA[0].length;
+        }
+
+        if (iterations <= 0) {
+            throw new IllegalArgumentException("Number of iterations must be positive");
+        }
+
+        int n = matrixA.length;
+        if (iterations > 2 * n) {
+            throw new IllegalArgumentException("Number of iterations should not exceed 2 * n where n is the matrix size");
+        }
+
+        Random rand = new Random();
+        for (int t = 0; t < iterations; t++) {
+            int[] r = new int[n];
+            for (int i = 0; i < n; i++) {
+                r[i] = rand.nextInt(2);
+            }
+
+            int[] matrixBtimesR = multiply(matrixB, r);
+            int[] matrixAtimesBtimesR = multiply(matrixA, matrixBtimesR);
+            int[] matrixCtimesR = multiply(matrixC, r);
+
+            for (int i = 0; i < n; i++) {
+                if (matrixAtimesBtimesR[i] != matrixCtimesR[i]) {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    /*
+        It multiplies input matrix of double type with randomized vector.
+        @params matrix which is being multiplied currently with random vector.
+        @params random vector generated for every iteration.
+
+        This basically calculates dot product for every row, which is used to verify whether the product of matrices is valid or not.
+    */
+    static double[] multiply(double[][] matrix, double[] vector) {
+        int n = vector.length;
+        double[] result = new double[n];
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                result[i] += matrix[i][j] * vector[j];
+            }
+        }
+        return result;
+    }
+
+    /*
+        Actual function that performs the verification.
+        @params, all three input matrices of double type, number of iterations
+    */
+    public static boolean verify(double[][] matrixA, double[][] matrixB, double[][] matrixC, int iterations) {
+        if (matrixA.length == 0 || matrixB.length == 0 || matrixC.length == 0
+                || matrixA[0].length == 0 || matrixB[0].length == 0 || matrixC[0].length == 0) {
+            return matrixA.length == matrixB[0].length
+                    && matrixB.length == matrixC.length
+                    && matrixC[0].length == matrixA[0].length;
+        }
+
+        if (iterations <= 0) {
+            throw new IllegalArgumentException("Number of iterations must be positive");
+        }
+
+        int m = matrixA.length;
+        if (iterations > 2 * m) {
+            throw new IllegalArgumentException("Number of iterations should not exceed 2 times m where m is the matrix size");
+        }
+
+        Random rand = new Random();
+        for (int t = 0; t < iterations; t++) {
+            double[] randomizedVector = new double[m];
+            for (int i = 0; i < m; i++) {
+                randomizedVector[i] = rand.nextInt(2);
+            }
+
+            double[] matrixBtimesR = multiply(matrixB, randomizedVector);
+            double[] matrixAtimesBtimesR = multiply(matrixA, matrixBtimesR);
+            double[] matrixCtimesR = multiply(matrixC, randomizedVector);
+
+            for (int i = 0; i < m; i++) {
+                if (Math.abs(matrixAtimesBtimesR[i] - matrixCtimesR[i]) > 1e-9) {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+}
+import java.util.Random;
+
+/*
+   This class implements the Randomized Matrix Multiplication Verification.
+   It generates a random vector and performs verification using Freivalds' Algorithm.
+   @author Menil-dev
+ */
+public final class MatrixMultiplicationVerifier {
+
+    private MatrixMultiplicationVerifier() {
+        throw new UnsupportedOperationException("Utility class");
+    }
+
+    /*
+        It multiplies input matrix with randomized vector.
+        @params matrix which is being multiplied currently with random vector
+        @params random vector generated for every iteration.
+
+        This basically calculates dot product for every row, which is used to verify whether the product of matrices is valid or not.
+        @returns matrix of calculated dot product.
+    */
+    static int[] multiply(int[][] matrix, int[] vector) {
+        int n = vector.length;
+        int[] result = new int[n];
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                result[i] += matrix[i][j] * vector[j];
+            }
+        }
         return result;
     }
 
@@ -79,9 +213,11 @@ public static boolean verify(int[][] matrixA, int[][] matrixB, int[][] matrixC,
     static double[] multiply(double[][] matrix, double[] vector) {
         int n = vector.length;
         double[] result = new double[n];
-        for (int i = 0; i < n; i++)
-            for (int j = 0; j < n; j++)
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
                 result[i] += matrix[i][j] * vector[j];
+            }
+        }
         return result;
     }