Ⅰ Gauss绉鍒唌atlab镄勭▼搴
% 楂樻柉-鍕掕╁痉鏁板肩Н鍒
fun=@(x)sin(x).*x.^3; % fun锛氱Н鍒琛ㄨ揪寮
% a,b锛氱Н鍒嗕笂涓嬮檺
a = 0;
b = pi;
tol=1e-8; % tol锛氱Н鍒嗙簿搴︼纴榛樿1e-6
% 璁＄畻姹傜Н鑺傜偣
syms x
p=sym2poly(diff((x^2-1)^(n+1),n+1))/(2^n*factorial(n));
tk=roots(p); % 姹傜Н鑺傜偣
% 璁＄畻姹傜Н绯绘暟
Ak=zeros(n+1,1);
for i=1:n+1
xkt=tk;
xkt(i)=[];
pn=poly(xkt);
fp=@(x)polyval(pn,x)/polyval(pn,tk(i));
Ak(i)=quadl(fp,-1,1,tol); % 姹傜Н绯绘暟
end
% 绉鍒嗗彉閲忎唬鎹锛屽皢[a,b]鍙樻崲鍒疬-1,1]
xk=(b-a)/2*tk+(b+a)/2;
% 妫楠岀Н鍒嗗嚱鏁癴un链夋晥镐
fun=fcnchk(fun,'vectorize');
% 璁＄畻鍙橀噺浠ｆ崲涔嫔悗绉鍒嗗嚱鏁扮殑鍊
fx=fun(xk)*(b-a)/2;
% 璁＄畻绉鍒嗗
ql=sum(Ak.*fx)
quadl(fun,0,pi) % 璋幂敤MATLAB鍐呴儴绉鍒嗗嚱鏁版楠
Ⅱ 姹傚姪锛孧atlab楂樻柉鍕掕╁痉姹傚嶆潅绉鍒
楂樻柉涓鍕掕╁痉姹傜Н鍏寮忚缉澶嶆潅,涓嶉傚悎涓鑸璁＄畻搴旂敤銆傛枃鐚甗3]鎻愪緵浜嗗彉姝ラ暱楂樻柉涓鍕掕╁痉绉鍒嗙畻娉,鍏跺熀链镐濇兂鏄锘轰簬澶嶅寲姹傜Н镄勬濇兂,瀵逛簬杈冮暱鍖洪棿[a,b銆,阃氲繃涓嶆柇鍦颁簩鍒嗗尯闂,姣
Ⅲ matlab瀵归珮鏂鍑芥暟姹傜Н鍒嗭纴绉鍒嗕笅闄愭槸璐熸棤绌凤纴涓婇檺鏄痻锛寈鍙栧兼槸浠-255锛255镄勬暟缁勶纴瑕佹庝箞寮勶纻
搴旇ョ敤璇宸鍑芥暟erf𨱒ユ眰銆
1銆侀栧厛锛岀Н鍒嗕笂涓嬮檺锛
鈭(-鈭,x)搴斿垎鎴悫埆(-鈭,0)+鈭(0,x)=-鈭(0,-鈭)+鈭(0,x)
2銆佽绉鍙橀噺t搴斾綔鍙樻崲锛
t1=t/蟽 鈫 t=蟽*t1
鐩稿簲镄勭Н鍒嗛檺x鍙树负x/蟽
3銆佺郴鏁帮细
dt=蟽*dt1锛屉冨拰铡熺郴鏁板垎姣崭腑镄勏幂害鍒嗭纴浣欎笅1/鈭(2蟺)锛屼笌erf鍑芥暟镄勭郴鏁板圭収锛屽簲璇ヤ箻浠1/(2鈭2)
缁间笂锛屽师琛ㄨ揪寮忕殑璁＄畻濡备笅锛埾幂殑鍙栧艰嚜瀹氾级锛
x=-255:255;
sigma=100;
f=1/(2*(2)^0.5) * ( erf(x/sigma)-erf(-inf) )