%quad_exam.m
%求歸一化高斯函數(shù)的在區(qū)間[-1 1]上的定積分,并求得到積分過程的中間結(jié)點(diǎn)
y=@(x)1/sqrt(pi)*exp(-x.^2);               %歸一化高斯函數(shù)
quad(y,-1,1,2e-6,1)                        %求定積分，并顯示中間迭代過程
fplot(y,[-1 1],'b');                       %畫出函數(shù)
hold on;
%跟蹤數(shù)據(jù)（運(yùn)行完上面程序后，可以在命令行中復(fù)制這些數(shù)據(jù)）
trace = [ 9    -1.0000000000    5.43160000e-001     0.1804679399;
      11    -1.0000000000    2.71580000e-001     0.0728222057;
      13    -0.7284200000    2.71580000e-001     0.1076454255;
      15    -0.4568400000    9.13680000e-001     0.4817487615;
      17    -0.4568400000    4.56840000e-001     0.2408826755;
      19    -0.4568400000    2.28420000e-001     0.1142172651;
      21    -0.2284200000    2.28420000e-001     0.1266655031;
      23     0.0000000000    4.56840000e-001     0.2408826755;
      25     0.0000000000    2.28420000e-001     0.1266655031;
      27     0.2284200000    2.28420000e-001     0.1142172651;
      29     0.4568400000    5.43160000e-001     0.1804679399;
      31     0.4568400000    2.71580000e-001     0.1076454255;
      33     0.7284200000    2.71580000e-001     0.0728222057];
x1 = trace(:,2);                          %積分過程的中間結(jié)點(diǎn)
y1 = y(x1);                               %中間結(jié)點(diǎn)的函數(shù)值
plot(x1,y1,'ro');                         %畫圖
xlabel('x');
ylabel('y');
legend('高斯函數(shù)','求積分過程的中間節(jié)點(diǎn)');