Java 8矩陣*向量乘法

Question

我想知道在Java 8中使用流來執行以下操作是否有更簡潔的方法：

public static double[] multiply(double[][] matrix, double[] vector) {
    int rows = matrix.length;
    int columns = matrix[0].length;

    double[] result = new double[rows];

    for (int row = 0; row < rows; row++) {
        double sum = 0;
        for (int column = 0; column < columns; column++) {
            sum += matrix[row][column]
                    * vector[column];
        }
        result[row] = sum;
    }
    return result;
}

編輯。 我收到了一個非常好的答案，但是性能比舊的實現慢了大約10倍，所以我在這里添加測試代碼以防有人想要調查它：

@Test
public void profile() {
    long start;
    long stop;
    int tenmillion = 10000000;
    double[] vector = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };

    double[][] matrix = new double[tenmillion][10];

    for (int i = 0; i < tenmillion; i++) {
        matrix[i] = vector.clone();
    }
    start = System.currentTimeMillis();
    multiply(matrix, vector);
    stop = System.currentTimeMillis();
 }

Answer 1

使用Stream的直接方法如下：

public static double[] multiply(double[][] matrix, double[] vector) {
    return Arrays.stream(matrix)
                 .mapToDouble(row -> 
                    IntStream.range(0, row.length)
                             .mapToDouble(col -> row[col] * vector[col])
                             .sum()
                 ).toArray();
}

這將創建矩陣的每一行的Stream<double[]> （ Stream<double[]> ），然后將每一行映射到使用vector數組計算乘積的double值。

我們必須在索引上使用Stream來計算產品，因為遺憾的是沒有內置工具可以將兩個Streot壓縮在一起。

Answer 2

衡量性能的方式對於衡量性能並不是非常可靠，手動編寫微基准通常不是一個好主意。 例如，在編譯代碼時，JVM可能會選擇更改執行順序，並且可能無法將啟動和停止變量分配到您希望分配的位置，從而在測量中產生意外結果。 預熱JVM以及讓JIT編譯器進行所有優化也非常重要。 GC還可以在引入應用程序吞吐量和響應時間的變化方面發揮重要作用。 我強烈建議使用JMH和Caliper等專用工具進行微基准測試。

我還用JVM預熱，隨機數據集和更多迭代次數編寫了一些基准測試代碼。 事實證明，Java 8流提供了更好的結果。

/**
 *
 */
public class MatrixMultiplicationBenchmark {
    private static AtomicLong start = new AtomicLong();
    private static AtomicLong stop = new AtomicLong();
    private static Random random = new Random();

    /**
     * Main method that warms-up each implementation and then runs the benchmark.
     *
     * @param args main class args
     */
    public static void main(String[] args) {
        // Warming up with more iterations and smaller data set
        System.out.println("Warming up...");
        IntStream.range(0, 10_000_000).forEach(i -> run(10, MatrixMultiplicationBenchmark::multiplyWithStreams));
        IntStream.range(0, 10_000_000).forEach(i -> run(10, MatrixMultiplicationBenchmark::multiplyWithForLoops));

        // Running with less iterations and larger data set
        startWatch("Running MatrixMultiplicationBenchmark::multiplyWithForLoops...");
        IntStream.range(0, 10).forEach(i -> run(10_000_000, MatrixMultiplicationBenchmark::multiplyWithForLoops));
        endWatch("MatrixMultiplicationBenchmark::multiplyWithForLoops");

        startWatch("Running MatrixMultiplicationBenchmark::multiplyWithStreams...");
        IntStream.range(0, 10).forEach(i -> run(10_000_000, MatrixMultiplicationBenchmark::multiplyWithStreams));
        endWatch("MatrixMultiplicationBenchmark::multiplyWithStreams");
    }

    /**
     * Creates the random matrix and vector and applies them in the given implementation as BiFunction object.
     *
     * @param multiplyImpl implementation to use.
     */
    public static void run(int size, BiFunction<double[][], double[], double[]> multiplyImpl) {
        // creating random matrix and vector
        double[][] matrix = new double[size][10];
        double[] vector = random.doubles(10, 0.0, 10.0).toArray();
        IntStream.range(0, size).forEach(i -> matrix[i] = random.doubles(10, 0.0, 10.0).toArray());

        // applying matrix and vector to the given implementation. Returned value should not be ignored in test cases.
        double[] result = multiplyImpl.apply(matrix, vector);
    }

    /**
     * Multiplies the given vector and matrix using Java 8 streams.
     *
     * @param matrix the matrix
     * @param vector the vector to multiply
     *
     * @return result after multiplication.
     */
    public static double[] multiplyWithStreams(final double[][] matrix, final double[] vector) {
        final int rows = matrix.length;
        final int columns = matrix[0].length;

        return IntStream.range(0, rows)
                .mapToDouble(row -> IntStream.range(0, columns)
                        .mapToDouble(col -> matrix[row][col] * vector[col])
                        .sum()).toArray();
    }

    /**
     * Multiplies the given vector and matrix using vanilla for loops.
     *
     * @param matrix the matrix
     * @param vector the vector to multiply
     *
     * @return result after multiplication.
     */
    public static double[] multiplyWithForLoops(double[][] matrix, double[] vector) {
        int rows = matrix.length;
        int columns = matrix[0].length;

        double[] result = new double[rows];

        for (int row = 0; row < rows; row++) {
            double sum = 0;
            for (int column = 0; column < columns; column++) {
                sum += matrix[row][column] * vector[column];
            }
            result[row] = sum;
        }
        return result;
    }

    private static void startWatch(String label) {
        System.out.println(label);
        start.set(System.currentTimeMillis());
    }

    private static void endWatch(String label) {
        stop.set(System.currentTimeMillis());
        System.out.println(label + " took " + ((stop.longValue() - start.longValue()) / 1000) + "s");
    }
}

這是輸出

Warming up...
Running MatrixMultiplicationBenchmark::multiplyWithForLoops...
MatrixMultiplicationBenchmark::multiplyWithForLoops took 100s
Running MatrixMultiplicationBenchmark::multiplyWithStreams...
MatrixMultiplicationBenchmark::multiplyWithStreams took 89s