matlab多重积分.doc

精品tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.2,1),toctic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.1,1),tocf1 =10.213463739161501Elapsed time is 0.056856 seconds.f1 =19.868526412761902Elapsed time is 0.245491 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.01,1),tocf1 =61.334993990451785Elapsed time is 1.103514 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.001,1),tocf1 = 1.063674743047246e+002Elapsed time is 2.785133 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.0001,1),tocf1 = 1.517765989598245e+002Elapsed time is 5.657963 seconds.精度设为1e-10，重新算了下：耗时明显增加tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.2,1,1e-10),tocf1 =10.213463738922437Elapsed time is 0.251798 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.1,1,1e-10),tocf1 =19.868526415332266Elapsed time is 0.888888 seconds.（NB，第一次算出这样的时间，哈哈 :P ） tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.01,1,1e-10),tocf1 =61.334993966628041Elapsed time is 4.295050 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.001,1,1e-10),tocf1 = 1.063674742766796e+002Elapsed time is 10.851554 seconds. tic;f1 = quadl(y) 2*y.*exp(-y.2).*arrayfun(y)quadl(x) exp(-x.2)./(y.2+x.2),-1,1),y).2,0.0001,1,1e-10),tocf1 = 1.517765989315576e+002Elapsed time is 22.210441 seconds.用matlab进行三重积分：tic;quadl(x) arrayfun(xx) quad2d(y,z) xx.*y.*z,xx,2*xx,(y) xx*y,(y) 2*xx*y),x),1,2),toctic;quad2d(x,y) arrayfun(xx,yy) quadl(z) xx.*yy.*z,xx*yy,2*xx*yy),x,y),1,2,(x)x,(x)2*x),toctic;quadl(x) arrayfun(xx) quadl(y) arrayfun(yy) quadl(z) xx.*yy.*z,xx*yy,2*xx*yy),y),xx,2*xx),x),1,2),toctic;triplequad(x,y,z) x.*y.*z.*(z=x.*y&y=x),1,2,1,4,1,16),tocans =179.2969Elapsed time is 0.037453 seconds.ans =179.2969Elapsed time is 0.223533 seconds.ans =17