Java 8矩阵*向量乘法

Question

我想知道在 Java 8 中是否有更简洁的方法使用流来执行以下操作：

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;
}

正在进行编辑。我收到了一个很好的答案，但是性能比旧实现慢了大约 10 倍，所以我在这里添加测试代码以防有人想调查它：

@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();
}

这为矩阵 (Stream<double[]>) 的每一行创建一个 Stream，然后将每一行映射到使用 vector 数组计算乘积的双精度值。

我们必须在索引上使用 Stream 来计算乘积，因为不幸的是没有 built-in 将两个 Stream 压缩在一起的工具。

Answer 2

您衡量性能的方式不是很可靠，手动编写 micro-benchmarks 通常不是一个好主意。例如，在编译代码时，JVM 可能会选择更改执行顺序，并且开始和停止变量可能不会在您期望的位置进行分配，因此会在您的测量中产生意想不到的结果。让 JIT 编译器进行所有优化对 warm-up JVM 也很重要。 GC 还可以在引入应用程序的吞吐量和响应时间变化方面发挥非常重要的作用。我强烈建议为 micro-benchmarking 使用专门的工具，例如 JMH 和 Caliper。

我还编写了一些带有 JVM 预热、随机数据集和更高迭代次数的基准测试代码。事实证明，Java 8 个流提供了更好的结果。

/**
 *
 */
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");
    }
}

这是输出

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

Java 8矩阵*向量乘法

Java 8 matrix * vector multiplication

java

matrix

multiplication

java-8

java-stream