Question

用matlab求高斯函数积分

a1=0.3826;
b1=452.1;
c1=9.185;
a2=0.5569;
b2=455;
c2=18.23;
a3=-0.03431;
b3=497.9;
c3=11.48;
a4=0.2741;
b4=554.2;
c4=85.93;
f=a1*exp(-((x-b1)/c1).^2)+a2*exp(-((x-b2)/c2).^2)+a3*exp(-((x-b3)/c3).^2)+a4*exp(-((x-b4)/c4).^2);
求f的积分

Answer 1

积分区间呢？

%%%==========
a1=0.3826;
b1=452.1;
c1=9.185;
a2=0.5569;
b2=455;
c2=18.23;
a3=-0.03431;
b3=497.9;
c3=11.48;
a4=0.2741;
b4=554.2;
c4=85.93;
%积分上下限
x0=1;
x1=3;
%高斯积分点以及权系数
gx=[-0.9061799,-0.5384693,0,0.5384693,0.9061799];
gweight=[0.2369269,0.4786287,0.5688889,0.4786287,0.2369269];
intf=0;
for i=1:5
x=(x0+x1)/2+(x1-x0)/2*gx(i);
intf=intf+gweight(i)*(a1*exp(-((x-b1)/c1).^2)+a2*exp(-((x-b2)/c2).^2)+a3*exp(-((x-b3)/c3).^2)+a4*exp(-((x-b4)/c4).^2));
end
intf=intf*(x1-x0)/2;
intf

Answer 2

就是要多峰值的高斯函数吧？下面的这个行不行？
ezplot('0.5*exp(-(x+4)^2)+exp(-(x/2)^2)+0.7*exp(-(x-5)^2)')

Answer 3

x=1：del：n，做成离散函数。积分=int（x）；del越小越精确，n在del确定的基础上覆盖f的范围就行，做个plot（f）看看确保积分的范围足够。