tepechin_kirill_lab_6/README.md

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+## Лабораторная работа №6, Тепечин Кирилл
+
+### Код
+
+#### Обычный код
+````java
+private static BigDecimal findDeterminantGauss(double[][] matrix) {
+        int n = matrix.length;
+        BigDecimal det = BigDecimal.ONE;
+
+        for (int i = 0; i < n; i++) {
+            int maxRow = i;
+            for (int j = i + 1; j < n; j++) {
+                if (Math.abs(matrix[j][i]) > Math.abs(matrix[maxRow][i])) {
+                    maxRow = j;
+                }
+            }
+
+            if (maxRow != i) {
+                double[] temp = matrix[i];
+                matrix[i] = matrix[maxRow];
+                matrix[maxRow] = temp;
+
+                det = det.multiply(BigDecimal.valueOf(-1));
+            }
+
+            for (int j = i + 1; j < n; j++) {
+                double factor = matrix[j][i] / matrix[i][i];
+                for (int k = i; k < n; k++) {
+                    matrix[j][k] -= factor * matrix[i][k];
+                }
+            }
+        }
+
+        for (int i = 0; i < n; i++) {
+            det = det.multiply(BigDecimal.valueOf(matrix[i][i]));
+        }
+
+        return det;
+
+    }
+````
+
+#### Параллельный код
+````java
+private static BigDecimal findDeterminantGaussParallel(double[][] matrix, int threadsCount) {
+        int n = matrix.length;
+        final BigDecimal[] det = {BigDecimal.ONE};
+
+        ExecutorService executor = Executors.newFixedThreadPool(threadsCount);
+
+        for (int i = 0; i < n; i++) {
+            final int rowIdx = i;
+
+            int maxRow = rowIdx;
+            for (int j = rowIdx + 1; j < n; j++) {
+                if (Math.abs(matrix[j][rowIdx]) > Math.abs(matrix[maxRow][rowIdx])) {
+                    maxRow = j;
+                }
+            }
+
+            if (maxRow != rowIdx) {
+                double[] temp = matrix[rowIdx];
+                matrix[rowIdx] = matrix[maxRow];
+                matrix[maxRow] = temp;
+                det[0] = det[0].multiply(BigDecimal.valueOf(-1));
+            }
+            executor.execute(() -> {
+                for (int j = rowIdx + 1; j < n; j++) {
+                    double factor = matrix[j][rowIdx] / matrix[rowIdx][rowIdx];
+                    for (int k = rowIdx; k < n; k++) {
+                        matrix[j][k] -= factor * matrix[rowIdx][k];
+                    }
+                }
+            });
+            det[0] = det[0].multiply(BigDecimal.valueOf(matrix[rowIdx][rowIdx]));
+        }
+
+        executor.shutdown();
+
+        try {
+            executor.awaitTermination(1, TimeUnit.DAYS);
+        } catch (InterruptedException e) {
+            e.printStackTrace();
+        }
+
+        return det[0];
+
+    }
+````
+
+### Тесты
+
+Тесты проводились на 16 потоках
+
+![result](result.png)
+
+### Выводы
+
+* На матрицах от 100 до 500 последовательное вычисление быстрее.
+
+* Параллельное вычисление работает быстрее на матрицах от 1000 n.
+
+### Ссылка на видео
+
+https://youtu.be/ZK1qSvbUNTk

tepechin_kirill_lab_6/src/MatrixDeterminant.java

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+import java.math.BigDecimal;
+import java.text.DecimalFormat;
+import java.util.Arrays;
+import java.util.concurrent.ExecutorService;
+import java.util.concurrent.Executors;
+import java.util.concurrent.TimeUnit;
+import java.util.concurrent.atomic.AtomicLong;
+
+public class MatrixDeterminant {
+
+    public static double[][] generateMatrix(int n) {
+        double[][] matrix = new double[n][n];
+
+        for (int i = 0; i < n; i++) {
+            for (int j = 0; j < n; j++) {
+                matrix[i][j] = Math.round((Math.random() * 5));
+            }
+        }
+
+        return matrix;
+    }
+
+
+    private static BigDecimal findDeterminantGauss(double[][] matrix) {
+        int n = matrix.length;
+        BigDecimal det = BigDecimal.ONE;
+
+        for (int i = 0; i < n; i++) {
+            int maxRow = i;
+            for (int j = i + 1; j < n; j++) {
+                if (Math.abs(matrix[j][i]) > Math.abs(matrix[maxRow][i])) {
+                    maxRow = j;
+                }
+            }
+
+            if (maxRow != i) {
+                double[] temp = matrix[i];
+                matrix[i] = matrix[maxRow];
+                matrix[maxRow] = temp;
+
+                det = det.multiply(BigDecimal.valueOf(-1));
+            }
+
+            for (int j = i + 1; j < n; j++) {
+                double factor = matrix[j][i] / matrix[i][i];
+                for (int k = i; k < n; k++) {
+                    matrix[j][k] -= factor * matrix[i][k];
+                }
+            }
+        }
+
+        for (int i = 0; i < n; i++) {
+            det = det.multiply(BigDecimal.valueOf(matrix[i][i]));
+        }
+
+        return det;
+
+    }
+
+    private static BigDecimal findDeterminantGaussParallel(double[][] matrix, int threadsCount) {
+        int n = matrix.length;
+        final BigDecimal[] det = {BigDecimal.ONE};
+
+        ExecutorService executor = Executors.newFixedThreadPool(threadsCount);
+
+        for (int i = 0; i < n; i++) {
+            final int rowIdx = i;
+
+            int maxRow = rowIdx;
+            for (int j = rowIdx + 1; j < n; j++) {
+                if (Math.abs(matrix[j][rowIdx]) > Math.abs(matrix[maxRow][rowIdx])) {
+                    maxRow = j;
+                }
+            }
+
+            if (maxRow != rowIdx) {
+                double[] temp = matrix[rowIdx];
+                matrix[rowIdx] = matrix[maxRow];
+                matrix[maxRow] = temp;
+                det[0] = det[0].multiply(BigDecimal.valueOf(-1));
+            }
+            executor.execute(() -> {
+                for (int j = rowIdx + 1; j < n; j++) {
+                    double factor = matrix[j][rowIdx] / matrix[rowIdx][rowIdx];
+                    for (int k = rowIdx; k < n; k++) {
+                        matrix[j][k] -= factor * matrix[rowIdx][k];
+                    }
+                }
+            });
+            det[0] = det[0].multiply(BigDecimal.valueOf(matrix[rowIdx][rowIdx]));
+        }
+
+        executor.shutdown();
+
+        try {
+            executor.awaitTermination(1, TimeUnit.DAYS);
+        } catch (InterruptedException e) {
+            e.printStackTrace();
+        }
+
+        return det[0];
+
+    }
+    public static void main(String[] args) {
+        run(100);
+        run(300);
+        run(500);
+        run(1000);
+        run(3000);
+    }
+
+    public static void run(int n) {
+        System.out.println("N = " + n);
+        double[][] matrix = generateMatrix(n);
+        double[][] matrixClone = Arrays.copyOf(matrix, n);
+
+        long time = System.currentTimeMillis();
+        BigDecimal determinantGauss = findDeterminantGauss(matrix);
+        System.out.println("Time gauss sync: " + (System.currentTimeMillis() - time));
+
+        time = System.currentTimeMillis();
+        BigDecimal determinantGaussAsync = findDeterminantGaussParallel(matrixClone, Runtime.getRuntime().availableProcessors());
+        System.out.println("Time gauss async: " + (System.currentTimeMillis() - time));
+
+
+        if (n < 101) {
+            System.out.println("Determinant (gauss sync): " + new DecimalFormat("#0.##").format(determinantGauss));
+            System.out.println("Determinant (gauss async): " + new DecimalFormat("#0.##").format(determinantGaussAsync));
+        }
+
+        System.out.println();
+
+    }
+
+
+}
+
+