Java中的矩阵乘法

Question

我创建了一个函数来与一个矩阵相乘，它有两个参数，一个是矩阵，另一个是int n。问题是我不知道应该在我的代码中在哪里使用n，以便它将矩阵本身乘以n 的次数（换句话说，matrix^n）。在当前阶段它只做matrix^2;

public static int[][] lungimeDrumuri(int[][] array, int n) {
    int[][] newArray = new int[array.length][array.length];
    for (int i = 0; i < array.length; i++) {
        for (int j = 0; j < array.length; j++) {
            int sum = 0;
            for (int x = 0; x < array.length; x++) {
                sum += array[i][x] * array[x][j];
            }
            newArray[i][j] = sum;
        }
    }
    return newArray;
}

Answer 1

添加从 1 < k < n 开始的第三个 for 循环。您将需要保持array 保持不变以保持初始矩阵的值，还需要一个矩阵newArray 来保持先前乘法的值和一个临时矩阵tmp 在乘法期间只保存值本身，然后复制到newArray。 请看下面的示例。

完整代码

public static int[][] lungimeDrumuri(int[][] array, int n) {
    int[][] newArray = new int[array.length][array.length];
    // Just holds values during multiplication between two matrices
    int[][] tmp = new int[array.length][array.length];
    
    // Initialize newArray to be equal to array
    for (int i = 0; i < array.length; i++) {
        for (int j = 0; j < array.length; j++) {
            newArray[i][j] = array[i][j];
        }
    }

    // Outer loop that multiplies as many times as you want
    for (int k = 1; k < n; k++) {
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array.length; j++) {
                int sum = 0;
                for (int x = 0; x < array.length; x++) {
                    sum += newArray[i][x] * array[x][j]; // Use newArray here
                }
                tmp[i][j] = sum;
            }
        }
        // Copy the result from multiplication to newArray and restart tmp
        System.arraycopy(tmp, 0, newArray, 0, tmp.length);
        tmp = new int[array.length][array.length];
    }

    return newArray;
}

希望对您有所帮助！

Answer 2

为了清楚起见，您可以创建两种方法：第一种方法是乘方矩阵，第二种方法是调用第一个n 的次数。

public static int[][] lungimeDrumuri(int[][] array, int n) {
    int[][] newArray = array;
    for (int i = 0; i < n; i++) {
        newArray = squareMatrixMultiplication(newArray);
    }
    return newArray;
}

public static int[][] squareMatrixMultiplication(int[][] array) {
    int[][] newArray = new int[array.length][array.length];
    for (int i = 0; i < array.length; i++) {
        for (int j = 0; j < array.length; j++) {
            for (int x = 0; x < array.length; x++) {
                newArray[i][j] += array[i][x] * array[x][j];
            }
        }
    }
    return newArray;
}

Answer 3

初始化newArray等于数组，然后 在矩阵乘法周围添加一个循环并在嵌套循环中使用newArray：将newArray 乘以数组。

public static int[][] lungimeDrumuri(int[][] array, int n) {
    int[][] newArray = new int[array.length][array.length];
    // Add loops to initialize newArray to array
    for (int i = 0; i < array.length; i++) {
        for (int j = 0; j < array.length; j++) {
            newArray[i][j] = array[i][j];
        }
    }
    for (int j = 0; j < n; j++) {   // Add this loop
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array.length; j++) {
                int sum = 0;
                for (int x = 0; x < array.length; x++) {
                    sum += newArray[i][x] * array[x][j];  // Use newArray here
                }
                newArray[i][j] = sum;
            }
        }
    } // and this
    return newArray;
}

Answer 4

public class MyClass {
    public static void main(String args[]) {
        int array[][] = new int[2][2];
        array[0][0] = 1;
        array[0][1] = 2;
        array[1][0] = 3;
        array[1][1] = 4;
        int newArray[][] = new int[2][2];
        //initialize array with these elements
        newArray[0][0] = 1;
        newArray[0][1] = 0;
        newArray[1][0] = 0;
        newArray[1][1] = 1;
        int n = 5;
        for (int i = 0; i < n; i++) {
            newArray = lungimeDrumuri(array, newArray, i);
        }
    }

    public static int[][] lungimeDrumuri(int[][] array, int newArray[][], int n) {
        int newArray1[][] = new int[array.length][array.length];
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array.length; j++) {
                int sum = 0;
                for (int x = 0; x < array.length; x++) {
                    sum += array[i][x] * newArray[x][j];
                }
                newArray1[i][j] = sum;
            }
        }
        return newArray1;
    }
}

希望这篇文章对你有所帮助。