DAS_2024_1/afanasev_dmitry_lab_6/FastDeterminantCalculator.java

import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.concurrent.CountDownLatch;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;

public class FastDeterminantCalculator {

    public static void main(String[] args) {
        int[] sizes = {100, 300, 500};
        int[] threads = {1, 4, 8, 10};

        for (int size : sizes) {
            BigDecimal[][] matrix = generateMatrix(size);
            for (int threadCount : threads) {
                long start = System.currentTimeMillis();
                BigDecimal determinant = calculateDeterminant(matrix, threadCount);
                long end = System.currentTimeMillis();
                System.out.printf("Matrix size: %dx%d, Threads: %d, Time: %d ms\n",
                        size, size, threadCount, (end - start));
            }
        }
    }

    public static BigDecimal[][] generateMatrix(int size) {
        BigDecimal[][] matrix = new BigDecimal[size][size];
        for (int i = 0; i < size; i++) {
            BigDecimal rowSum = BigDecimal.ZERO;
            for (int j = 0; j < size; j++) {
                matrix[i][j] = BigDecimal.valueOf(Math.random() * 10);
                if (i != j) {
                    rowSum = rowSum.add(matrix[i][j]);
                }
            }
            matrix[i][i] = rowSum.add(BigDecimal.valueOf(Math.random() * 10 + 1));
        }
        return matrix;
    }

    public static BigDecimal calculateDeterminant(BigDecimal[][] matrix, int threadCount) {
        int size = matrix.length;
        BigDecimal[][] lu = new BigDecimal[size][size];
        int[] permutations = new int[size];
        ExecutorService executor = Executors.newFixedThreadPool(threadCount);

        if (!luDecomposition(matrix, lu, permutations, executor)) {
            executor.shutdown();
            return BigDecimal.ZERO; // Матрица вырожденная
        }

        executor.shutdown();

        BigDecimal determinant = BigDecimal.ONE;
        for (int i = 0; i < size; i++) {
            determinant = determinant.multiply(lu[i][i]);
            if (permutations[i] != i) {
                determinant = determinant.negate(); // Меняем знак при перестановке
            }
        }
        return determinant;
    }

    public static boolean luDecomposition(BigDecimal[][] matrix, BigDecimal[][] lu, int[] permutations, ExecutorService executor) {
        int size = matrix.length;

        for (int i = 0; i < size; i++) {
            System.arraycopy(matrix[i], 0, lu[i], 0, size);
            permutations[i] = i;
        }

        for (int k = 0; k < size; k++) {
            int pivot = k;
            for (int i = k + 1; i < size; i++) {
                if (lu[i][k].abs().compareTo(lu[pivot][k].abs()) > 0) {
                    pivot = i;
                }
            }

            if (lu[pivot][k].abs().compareTo(BigDecimal.valueOf(1e-10)) < 0) {
                return false;
            }

            if (pivot != k) {
                BigDecimal[] temp = lu[k];
                lu[k] = lu[pivot];
                lu[pivot] = temp;

                int tempPerm = permutations[k];
                permutations[k] = permutations[pivot];
                permutations[pivot] = tempPerm;
            }

            CountDownLatch latch = new CountDownLatch(size - k - 1);
            for (int i = k + 1; i < size; i++) {
                int row = i;
                int finalK = k;
                executor.submit(() -> {
                    MathContext mc = new MathContext(20, RoundingMode.HALF_UP);
                    lu[row][finalK] = lu[row][finalK].divide(lu[finalK][finalK], mc);
                    for (int j = finalK + 1; j < size; j++) {
                        lu[row][j] = lu[row][j].subtract(lu[row][finalK].multiply(lu[finalK][j], mc));
                    }
                    latch.countDown();
                });
            }

            try {
                latch.await();
            } catch (InterruptedException e) {
                e.printStackTrace();
                return false;
            }
        }

        return true;
    }
}