分享矩阵乘法单线程与多线程的Java实现与效率对比,请教Strassen算法
分享矩阵乘法单线程与多线程的Java实现与效率对比,请教Strassen算法
矩阵乘法的多线程实现:
/** 
* @Title: MultiThreadMatrix.java * @Package matrix * @Description: 多线程计算矩阵乘法 * @author Aloong * @date 2010-10-28 下午09:45:56 * @version V1.0 
*/
package
matrix;
import
java.util.Date;
public
class
MultiThreadMatrix
{ static int[][] matrix1; static int[][] matrix2; static int[][] matrix3; static int m,n,k; static int index; static int threadCount; static long startTime; public static void main(String[] args) throws InterruptedException
{ //矩阵a高度m=100宽度k=80,矩阵b高度k=80宽度n=50 ==> 矩阵c高度m=100宽度n=50 m = 1024; n = 1024; k = 1024; matrix1 = new int[m][k]; matrix2 = new int[k][n]; matrix3 = new int[m][n]; //随机初始化矩阵a,b fillRandom(matrix1); fillRandom(matrix2); startTime = new Date().getTime(); //输出a,b// printMatrix(matrix1);// printMatrix(matrix2); //创建线程,数量 <= 4 for(int i=0; i<4; i++) { if(index < m) { Thread t = new Thread(new MyThread()); t.start();
}else { break; } } //等待结束后输出 while(threadCount!=0) { Thread.sleep(20); } // printMatrix(matrix3); long finishTime = new Date().getTime(); System.out.println("计算完成,用时"+(finishTime-startTime)+"毫秒"); } static void printMatrix(int[][] x) { for (int i=0; i<x.length; i++) { for(int j=0; j<x[i].length; j++) { System.out.print(x[i][j]+" "); } System.out.println(""); } System.out.println(""); } static void fillRandom(int[][] x) { for (int i=0; i<x.length; i++) { for(int j=0; j<x[i].length; j++) { //每个元素设置为0到99的随机自然数 x[i][j] = (int) (Math.random() * 100); } } } synchronized static int getTask() { if(index < m) { return index++; } return -1; }}
class
MyThread
implements
Runnable
{ int task; @Override public void run() { MultiThreadMatrix.threadCount++; while( (task = MultiThreadMatrix.getTask()) != -1 ) { System.out.println("进程: "+Thread.currentThread().getName()+"\t开始计算第 "+(task+1)+"行"); for(int i=0; i<MultiThreadMatrix.n; i++) { for(int j=0; j<MultiThreadMatrix.k; j++) { MultiThreadMatrix.matrix3[task][i] += MultiThreadMatrix.matrix1[task][j] * MultiThreadMatrix.matrix2[j][i]; } } } MultiThreadMatrix.threadCount--; }}
单线程:
/** * @Title: SingleThreadMatrix.java * @Package matrix * @Description: 单线程计算矩阵乘法 * @author Aloong * @date 2010-10-28 下午11:33:18 * @version V1.0 */
package
matrix;
import
java.util.Date;
public
class
SingleThreadMatrix
{ static int[][] matrix1; static int[][] matrix2; static int[][] matrix3; static int m,n,k; static long startTime; public static void main(String[] args) { m = 1024; n = 1024; k = 1024; matrix1 = new int[m][k]; matrix2 = new int[k][n]; matrix3 = new int[m][n]; fillRandom(matrix1); fillRandom(matrix2); startTime = new Date().getTime(); //输出a,b// printMatrix(matrix1);// printMatrix(matrix2); for(int task=0; task<m; task++) { System.out.println("进程: "+Thread.currentThread().getName()+"\t开始计算第 "+(task+1)+"行"); for(int i=0; i<n; i++) { for(int j=0; j<k; j++) { matrix3[task][i] += matrix1[task][j] * matrix2[j][i]; } } } // printMatrix(matrix3); long finishTime = new Date().getTime(); System.out.println("计算完成,用时"+(finishTime-startTime)+"毫秒"); } static void fillRandom(int[][] x) { for (int i=0; i<x.length; i++) { for(int j=0; j<x[i].length; j++) { //每个元素设置为0到99的随机自然数 x[i][j] = (int) (Math.random() * 100); } } }}
修改m,n,k的值可以修改相乘矩阵的阶数.
结果对比,计算1024阶矩阵的时候多线程用时约4.8秒,单线程用时16秒,
单线程占用内存21M,多线程占用16M.
本机是4核CPU,单线程的时候只有25%的CPU占用,使用4个子线程可以达到接近100%的CPU使用率.
另外请教一个问题,是矩阵乘法的Strassen算法
下面这个是来自网上的一段代码,在我自己的电脑上,只要超过12阶就会内存溢出
不解是什么原因,设置jvm的内存不管多大也会崩溃在12阶
请高手帮忙解答....
package
matrix;
import
java.io.
*
;
import
java.util.
*
;
class
Matrix
//
定义矩阵结构
{ public int[][] m = new int[32][32];}
public
class
StrassenMatrix2
{ public int IfIsEven(int n)//判断输入矩阵阶数是否为2^k { int a = 0, temp = n; while (temp % 2 == 0) { if (temp % 2 == 0) temp /= 2; else a = 1; } if (temp == 1) a = 0; return a; } public void Divide(Matrix d, Matrix d11, Matrix d12, Matrix d21, Matrix d22, int n)//分解矩阵 { int i, j; for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) { d11.m[i][j] = d.m[i][j]; d12.m[i][j] = d.m[i][j + n]; d21.m[i][j] = d.m[i + n][j]; d22.m[i][j] = d.m[i + n][j + n]; } } public Matrix Merge(Matrix a11, Matrix a12, Matrix a21, Matrix a22, int n)//合并矩阵 { int i, j; Matrix a = new Matrix(); for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) { a.m[i][j] = a11.m[i][j]; a.m[i][j + n] = a12.m[i][j]; a.m[i + n][j] = a21.m[i][j]; a.m[i + n][j + n] = a22.m[i][j]; } return a; } public Matrix TwoMatrixMultiply(Matrix x, Matrix y) //阶数为2的矩阵乘法 { int m1, m2, m3, m4, m5, m6, m7; Matrix z = new Matrix(); m1 = (y.m[1][2] - y.m[2][2]) * x.m[1][1]; m2 = y.m[2][2] * (x.m[1][1] + x.m[1][2]); m3 = (x.m[2][1] + x.m[2][2]) * y.m[1][1]; m4 = x.m[2][2] * (y.m[2][1] - y.m[1][1]); m5 = (x.m[1][1] + x.m[2][2]) * (y.m[1][1] + y.m[2][2]); m6 = (x.m[1][2] - x.m[2][2]) * (y.m[2][1] + y.m[2][2]); m7 = (x.m[1][1] - x.m[2][1]) * (y.m[1][1] + y.m[1][2]); z.m[1][1] = m5 + m4 - m2 + m6; z.m[1][2] = m1 + m2; z.m[2][1] = m3 + m4; z.m[2][2] = m5 + m1 - m3 - m7; return z; } public Matrix MatrixPlus(Matrix f, Matrix g, int n) //矩阵加法 { int i, j; Matrix h = new Matrix(); for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) h.m[i][j] = f.m[i][j] + g.m[i][j]; return h; } public Matrix MatrixMinus(Matrix f, Matrix g, int n) //矩阵减法方法 { int i, j; Matrix h = new Matrix(); for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) h.m[i][j] = f.m[i][j] - g.m[i][j]; return h; } public Matrix MatrixMultiply(Matrix a, Matrix b, int n) //矩阵乘法方法 { int k; Matrix a11, a12, a21, a22; a11 = new Matrix(); a12 = new Matrix(); a21 = new Matrix(); a22 = new Matrix(); Matrix b11, b12, b21, b22; b11 = new Matrix(); b12 = new Matrix(); b21 = new Matrix(); b22 = new Matrix(); Matrix c11, c12, c21, c22, c; c11 = new Matrix(); c12 = new Matrix(); c21 = new Matrix(); c22 = new Matrix(); c = new Matrix(); Matrix m1, m2, m3, m4, m5, m6, m7; k = n; if (k == 2) { c = TwoMatrixMultiply(a, b); return c; } else { k = n / 2; Divide(a, a11, a12, a21, a22, k); //拆分A、B、C矩阵 Divide(b, b11, b12, b21, b22, k); Divide(c, c11, c12, c21, c22, k); m1 = MatrixMultiply(a11, MatrixMinus(b12, b22, k), k); m2 = MatrixMultiply(MatrixPlus(a11, a12, k), b22, k); m3 = MatrixMultiply(MatrixPlus(a21, a22, k), b11, k); m4 = MatrixMultiply(a22, MatrixMinus(b21, b11, k), k); m5 = MatrixMultiply(MatrixPlus(a11, a22, k), MatrixPlus(b11, b22, k), k); m6 = MatrixMultiply(MatrixMinus(a12, a22, k), MatrixPlus(b21, b22, k), k); m7 = MatrixMultiply(MatrixMinus(a11, a21, k), MatrixPlus(b11, b12, k), k); c11 = MatrixPlus(MatrixMinus(MatrixPlus(m5, m4, k), m2, k), m6, k); c12 = MatrixPlus(m1, m2, k); c21 = MatrixPlus(m3, m4, k); c22 = MatrixMinus(MatrixMinus(MatrixPlus(m5, m1, k), m3, k), m7, k); c = Merge(c11, c12, c21, c22, k); //合并C矩阵 return c; } } public Matrix GetMatrix(Matrix X, int n) { int i, j; X = new Matrix(); for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) X.m[i][j] = (int) (Math.random() * 10); for (i = 1; i <= n; i++) { for (j = 1; j <= n; j++) System.out.print(X.m[i][j] + " "); System.out.println(); } return X; } public Matrix UsualMatrixMultiply(Matrix A, Matrix B, Matrix C, int n) { int i, j, t, k; for (i = 1; i <= n; i++) for (j = 1; j <= n; j++) { for (k = 1, t = 0; k <= n; k++) t += A.m[i][k] * B.m[k][j]; C.m[i][j] = t; } return C; } public static void main(String[] args) throws IOException { StrassenMatrix2 instance = new StrassenMatrix2(); int i, j, n;// Matrix A, B, C, D; Matrix A, B, C; A = new Matrix(); B = new Matrix(); C = new Matrix();// D = new matrix(); Scanner in = new Scanner(System.in); System.out.print("输入矩阵的阶数: "); n = in.nextInt(); if (instance.IfIsEven(n) == 0) { System.out.println("矩阵A:"); A = instance.GetMatrix(A, n); System.out.println("矩阵B:"); B = instance.GetMatrix(B, n); if (n == 1) C.m[1][1] = A.m[1][1] * B.m[1][1]; //矩阵阶数为1时的特殊处理 else { long startTime = new Date().getTime(); C = instance.MatrixMultiply(A, B, n); long finishTime = new Date().getTime(); System.out.println("计算完成,用时"+(finishTime-startTime)+"毫秒"); } System.out.println("Strassen矩阵C为:"); for (i = 1; i <= n; i++) { for (j = 1; j <= n; j++) System.out.print(C.m[i][j] + " "); System.out.println(); } /* D = instance.UsualMatrixMultiply(A, B, D, n); System.out.println("普通乘法矩阵D为:"); for (i = 1; i <= n; i++) { for (j = 1; j <= n; j++) System.out.print(D.m[i][j] + " "); System.out.println(); }*/ } else System.out.println("输入的阶数不是2的N次方"); }}