1424.sagews

@interact
def _(xexp = input_box(default=[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0], label="Хэксп"),\
yexp = input_box(default=[5.1,10.9,21.1,34.9,53.7,73,103,131.2,160,208], label="Yэксп"),\
p = slider(vmin=1, vmax=10,step_size=1,default=2,label="Степень: ")
): 
   html("Полиномиальная аппроксимация по методу наименьших квадратов") 
   n=min(len(xexp),len(yexp))
   xexp=vector(xexp)             #экспериментальные
   yexp=vector(yexp).transpose()
   X=matrix(n,p+1) #матрица эксперимента
   for i in range(0,n):
      for j in range(0,p+1):
        X[i,j]=xexp[i]^(p-j)
   a=((X.transpose()*X)^-1)*X.transpose()*yexp
   x=var('x')
   k=[]
   for j in range(0,p+1):
     k.append(x^(p-j))
   k=vector(k)
   f(x)=(k*a)[0]
   s=0
   for i in range(0,n):
      s=s+(f(xexp[i])-yexp[i][0])^2
      #print xexp[i], yexp[i], f(xexp[i]), (f(xexp[i])-yexp[i][0])^2
   p=[]
   for i in range(0,n):
      p.append((xexp[i],yexp[i][0]))
   show(point(p)+plot(f,(x,min(xexp),max(xexp)), rgbcolor='green'))
   show(f)
   print "Отклонение =",sqrt(s/n).n()