矩阵乘法-java

矩阵乘法公式

//矩阵乘法运算public class MatrixMul {    public static void main(String[] args){        int A[][]={{1,2,3},{4,5,6}};        int B[][]={{1,4},{2,5},{3,6}};        //计算A*B则输出的矩阵就是C[A的行数][B的列数]        int C[][]=new int[A.length][B[0].length];       for(int i=0;i<A.length;i++){           for(int j=0;j<B[0].length;j++){               int t=0;               //计算矩阵行乘类的和               for(int k=0;k<A[0].length;k++){ //这里k可以小于A的列数或者B的行数                   t=A[i][k]*B[k][j]+t;               }               C[i][j]=t;           }       }       for(int i=0;i<C.length;i++){           for(int j=0;j<C[0].length;j++){               System.out.print(C[i][j]+" ");           }           System.out.println();       }    }}

Strassen算法实现
虽然代码很长，但很好理解
参考文章

http://m.mamicode.com/info-detail-673908.html 写的很详细！
http://blog.csdn.net/tanlingyun/article/details/1591414 作者的代码有点问题！

算法的关键

class Matrix {    public int[][] m = new int[32][32];}//Strassen矩阵乘法public class Strassen {    //判断阶数是否是2的n次方    public int judge(int p) {        int mark = 0;        if (p < 1) {  //矩阵的阶数必须大于等于1            return mark;        }        while (p % 2 == 0) {            p /= 2;        }        if (p == 1) {            mark = 1;        }        return mark;    }    //a b 两个矩阵加法     public Matrix addMatrix(Matrix a, Matrix b, int n) /*矩阵加法方法*/ {        Matrix c = new Matrix();        for (int i = 1; i <= n; i++) {            for (int j = 1; j <= n; j++) {                c.m[i][j] = a.m[i][j] + b.m[i][j];            }        }        return c;    }    //a b 两个矩阵减法，就改了个加号和名字    public Matrix subMatrix(Matrix a, Matrix b, int n) /*矩阵加法方法*/ {        Matrix c = new Matrix();        for (int i = 1; i <= n; i++) {            for (int j = 1; j <= n; j++) {                c.m[i][j] = a.m[i][j] - b.m[i][j];            }        }        return c;    }    //2阶矩阵乘法和上一个算法差不多    public Matrix MatrixMultiply(Matrix a, Matrix b) {        Matrix c = new Matrix();        for (int i = 1; i <= 2; i++) {            for (int j = 1; j <= 2; j++) {                int t = 0;                for (int k = 1; k <= 2; k++) {                    t = a.m[i][k] * b.m[k][j] + t;                }                c.m[i][j] = t;            }        }        return c;    }    //分解矩阵x为4块    public void decompose(Matrix x, Matrix x11, Matrix x12, Matrix x21, Matrix x22, int n)/*分解矩阵方法*/ {        int i, j;        for (i = 1; i <= n; i++) {            for (j = 1; j <= n; j++) {                x11.m[i][j] = x.m[i][j];                x12.m[i][j] = x.m[i][j + n];                x21.m[i][j] = x.m[i + n][j];                x22.m[i][j] = x.m[i + n][j + n];            }        }    }    //合并算法    public Matrix merge(Matrix c11, Matrix c12, Matrix c21, Matrix c22, int n)/*合并矩阵方法*/ {        int i, j;        Matrix c = new Matrix();        for (i = 1; i <= n; i++) {            for (j = 1; j <= n; j++) {                c.m[i][j] = c11.m[i][j];                c.m[i][j + n] = c12.m[i][j];                c.m[i + n][j] = c21.m[i][j];                c.m[i + n][j + n] = c22.m[i][j];            }        }        return c;    }    public Matrix strassen(Matrix a, Matrix b, int n) {        int halfsize = n / 2;        Matrix a11, a12, a21, a22, b11, b12, b21, b22, c11, c12, c21, c22, c;        //分解a矩阵        a11 = new Matrix();        a12 = new Matrix();        a21 = new Matrix();        a22 = new Matrix();        //分解b矩阵        b11 = new Matrix();        b12 = new Matrix();        b21 = new Matrix();        b22 = new Matrix();        //分解c矩阵        c11 = new Matrix();        c12 = new Matrix();        c21 = new Matrix();        c22 = new Matrix();        //输出结果c        c = new Matrix();        //7个新矩阵        Matrix m1, m2, m3, m4, m5, m6, m7;        if (n == 2) {            c = MatrixMultiply(a, b);            return c;        } else {            //分解矩阵a b c            decompose(a, a11, a12, a21, a22, halfsize);            decompose(b, b11, b12, b21, b22, halfsize);            decompose(c, c11, c12, c21, c22, halfsize);            //计算超级烦的m1--m7，注意眼睛别看花了            m1 = strassen(addMatrix(a11, a22, halfsize), addMatrix(b11, b22, halfsize), halfsize);            m2 = strassen(addMatrix(a11, a22, halfsize), b11, halfsize);            m3 = strassen(a11, subMatrix(b12, b22, halfsize), halfsize);            m4 = strassen(a22, subMatrix(b21, b11, halfsize), halfsize);            m5 = strassen(addMatrix(a11, a12, halfsize), b22, halfsize);            m6 = strassen(subMatrix(a21, a11, halfsize), addMatrix(b11, b12, halfsize), halfsize);            m7 = strassen(subMatrix(a12, a22, halfsize), addMatrix(b21, b22, halfsize), halfsize);            //计算c11-c22            c11 = addMatrix(subMatrix(addMatrix(m1, m4, halfsize), m5, halfsize), m7, halfsize);            c12 = addMatrix(m3, m5, halfsize);            c21 = addMatrix(m2, m4, halfsize);            c22 = addMatrix(subMatrix(addMatrix(m1, m3, halfsize), m2, halfsize), m6, halfsize);            //合并c11-c22到c中            c = merge(c11, c12, c21, c22, halfsize);            return c;        }    }    public static void main(String args[]) {        Strassen stra = new Strassen();        Scanner scan = new Scanner(System.in);        System.out.println("输入矩阵的阶数：");        int p = scan.nextInt();        if (stra.judge(p) == 1) {            Matrix a = new Matrix();            Matrix b = new Matrix();            Matrix c = new Matrix();            System.out.println("输入矩阵A:");            for (int i = 1; i <= p; i++) {                for (int j = 1; j <= p; j++) {                    a.m[i][j] = scan.nextInt();                }            }            System.out.println("输入矩阵B:");            for (int i = 1; i <= p; i++) {                for (int j = 1; j <= p; j++) {                    b.m[i][j] = scan.nextInt();                }            }            System.out.println("矩阵C:");            //当矩阵阶数为1时,单独处理            if (p == 1) {                c.m[1][1] = a.m[1][1] * b.m[1][1];            } else {                c = stra.strassen(a, b, p);            }            for (int i = 1; i <= p; i++) {                for (int j = 1; j <= p; j++) {                    System.out.print(c.m[i][j] + " ");                }                System.out.println();            }        } else {            System.out.println(p + "不是2的n次方！");        }    }}

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