海口网站如何制作,电脑二级网页打不开怎么解决,推广产品的软文,兰州迅豹网络Strassen算法于1969年由德国数学家Strassen提出#xff0c;该方法引入七个中间变量#xff0c;每个中间变量都只需要进行一次乘法运算。而朴素算法却需要进行8次乘法运算。原理Strassen算法的原理如下所示#xff0c;使用sympy验证Strassen算法的正确性import sympy as sA …Strassen算法于1969年由德国数学家Strassen提出该方法引入七个中间变量每个中间变量都只需要进行一次乘法运算。而朴素算法却需要进行8次乘法运算。原理Strassen算法的原理如下所示使用sympy验证Strassen算法的正确性import sympy as sA s.Symbol(A)B s.Symbol(B)C s.Symbol(C)D s.Symbol(D)E s.Symbol(E)F s.Symbol(F)G s.Symbol(G)H s.Symbol(H)p1 A * (F - H)p2 (A B) * Hp3 (C D) * Ep4 D * (G - E)p5 (A D) * (E H)p6 (B - D) * (G H)p7 (A - C) * (E F)print(A * E B * G, (p5 p4 - p2 p6).simplify())print(A * F B * H, (p1 p2).simplify())print(C * E D * G, (p3 p4).simplify())print(C * F D * H, (p1 p5 - p3 - p7).simplify())复杂度分析$$f(N)7\times f(\frac{N}{2})7^2\times f(\frac{N}{4})...7^k\times f(\frac{N}{2^k})$$最终复杂度为$7^{log_2 N}N^{log_2 7}$java矩阵乘法(Strassen算法)代码如下可以看看数据结构的定义时间换空间。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();}}总结到此这篇关于使用java写的矩阵乘法的文章就介绍到这了,更多相关java矩阵乘法(Strassen算法)内容请搜索得牛网以前的文章或继续浏览下面的相关文章希望大家以后多多支持得牛网
