[Java] Java实现矩阵乘法以及优化的方法实例

c[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1] + a[1][3] * b[3][1] + a[1][4] * b[4][1]

public int[][] multiply(int[][] mat1, int[][] mat2){
  int m = mat1.length, n = mat2[0].length;
  int[][] mat = new int[m][n];
  for(int i = 0; i < m; i++){
    for(int j = 0; j < n; j++){
      for(int k = 0; k < mat1[0].length; k++){
        mat[i][j] += mat1[i][k] * mat2[k][j];
      }
    }
  }
  return mat;
}

c11 = a11 * b11 + a12 * b21
c12 = a11 * b12 + a12 * b22
c21 = a21 * b11 + a22 * b21
c22 = a21 * b12 + a22 * b22

public class matrix {
  private final matrix[] _matrixarray;
  private final int n;
  private int element;
  public matrix(int n) {
    this.n = n;
    if (n != 1) {
      this._matrixarray = new matrix[4];
      for (int i = 0; i < 4; i++) {
        this._matrixarray[i] = new matrix(n / 2);
      }
    } else {
      this._matrixarray = null; 
    }
  }
  private matrix(int n, boolean needinit) {
    this.n = n;
    if (n != 1) {
      this._matrixarray = new matrix[4];
    } else {
      this._matrixarray = null; 
    }
  }
  public void set(int i, int j, int a) {
    if (n == 1) {
      element = a;
    } else {
      int size = n / 2;
      this._matrixarray[(i / size) * 2 + (j / size)].set(i % size, j % size, a);
    }
  }
  public matrix multi(matrix m) {
    matrix result = null;
    if (n == 1) {
      result = new matrix(1);
      result.set(0, 0, (element * m.element));
    } else {
      result = new matrix(n, false);
      result._matrixarray[0] = p5(m).add(p4(m)).minus(p2(m)).add(p6(m));
      result._matrixarray[1] = p1(m).add(p2(m));
      result._matrixarray[2] = p3(m).add(p4(m));
      result._matrixarray[3] = p5(m).add(p1(m)).minus(p3(m)).minus(p7(m));
    }
    return result;
  }
  public matrix add(matrix m) {
    matrix result = null;
    if (n == 1) {
      result = new matrix(1);
      result.set(0, 0, (element + m.element));
    } else {
      result = new matrix(n, false);
      result._matrixarray[0] = this._matrixarray[0].add(m._matrixarray[0]);
      result._matrixarray[1] = this._matrixarray[1].add(m._matrixarray[1]);
      result._matrixarray[2] = this._matrixarray[2].add(m._matrixarray[2]);
      result._matrixarray[3] = this._matrixarray[3].add(m._matrixarray[3]);;
    }
    return result;
  }
  public matrix minus(matrix m) {
    matrix result = null;
    if (n == 1) {
      result = new matrix(1);
      result.set(0, 0, (element - m.element));
    } else {
      result = new matrix(n, false);
      result._matrixarray[0] = this._matrixarray[0].minus(m._matrixarray[0]);
      result._matrixarray[1] = this._matrixarray[1].minus(m._matrixarray[1]);
      result._matrixarray[2] = this._matrixarray[2].minus(m._matrixarray[2]);
      result._matrixarray[3] = this._matrixarray[3].minus(m._matrixarray[3]);;
    }
    return result;
  }
  protected matrix p1(matrix m) {
    return _matrixarray[0].multi(m._matrixarray[1]).minus(_matrixarray[0].multi(m._matrixarray[3]));
  }
  protected matrix p2(matrix m) {
    return _matrixarray[0].multi(m._matrixarray[3]).add(_matrixarray[1].multi(m._matrixarray[3]));
  }
  protected matrix p3(matrix m) {
    return _matrixarray[2].multi(m._matrixarray[0]).add(_matrixarray[3].multi(m._matrixarray[0]));
  }
  protected matrix p4(matrix m) {
    return _matrixarray[3].multi(m._matrixarray[2]).minus(_matrixarray[3].multi(m._matrixarray[0]));
  }
  protected matrix p5(matrix m) {
    return (_matrixarray[0].add(_matrixarray[3])).multi(m._matrixarray[0].add(m._matrixarray[3]));
  }
  protected matrix p6(matrix m) {
    return (_matrixarray[1].minus(_matrixarray[3])).multi(m._matrixarray[2].add(m._matrixarray[3]));
  }
  protected matrix p7(matrix m) {
    return (_matrixarray[0].minus(_matrixarray[2])).multi(m._matrixarray[0].add(m._matrixarray[1]));
  }
  public int get(int i, int j) {
    if (n == 1) {
      return element;
    } else {
      int size = n / 2;
      return this._matrixarray[(i / size) * 2 + (j / size)].get(i % size, j % size);
    }
  }
  public void display() {
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        system.out.print(get(i, j));
        system.out.print(" ");
      }
      system.out.println();
    }
  }
  
  public static void main(string[] args) {
    matrix m = new matrix(2);
    matrix n = new matrix(2);
    m.set(0, 0, 1);
    m.set(0, 1, 3);
    m.set(1, 0, 5);
    m.set(1, 1, 7);
    n.set(0, 0, 8);
    n.set(0, 1, 4);
    n.set(1, 0, 6);
    n.set(1, 1, 2);
    matrix res = m.multi(n);
    res.display();
  }
}