数学建模python实现基础编程练习3

数学建模python实现基础编程练习3 1.一维三次样条插值

from scipy.interpolate import interp1d
x = np.array([0,2,4,5,6,7,8,9,10.5,11.5,12.5,14,16,17,18,19,20,21,22,23,24])
y = np.array([2,2,0,2,5,8,25,12,5,10,12,7,9,28,22,10,9,11,8,9,3])
xnew = np.linspace(0,24,500)
f1 = interp1d(x,y,'cubic');f = f1(xnew)
plt.plot(xnew,f)
plt.show()
sum = 0
for i in x:
    sum = sum +f1(i)
print(sum)

import numpy as np
from scipy.interpolate import interp1d
from scipy.integrate import quad
a = []
f = lambda x: x+2/np.sqrt(x+1)
x = np.linspace(0,1,1000)
for i in x :
     a.append(f(i))
y = np.array(a)
f1 = interp1d(x,y,'cubic')
plt.subplot(1,1,1)
plt.plot(x,y)
plt.show()
y1 = quad(f,0,1)
y2 = quad(f1,0,1)
print("y1={},y2={}".format(y1[0],y2[0]))

2.用numpy做拟合

x = np.array([1960,1961,1962,1963,1964,1965,1966,11967,1968])
y = np.array([2972,3061,3151,3213,3234,3285,3356,3420,3483])
f = np.polyfit(x,y,1)
f = np.poly1d(f)
a = []
x1 = np.linspace(1960,1968,100)
for i in x1:
    a.append(np.polyval(f,i))
print(f)
plt.subplot(1,2,1)
plt.scatter(x,y)
plt.subplot(1,2,2)
plt.plot(x1,a)
plt.show()

3.利用sympy解微分方程的符号解

from sympy.abc import x
from sympy import diff,dsolve,Function,simplify
y = Function('y')
eq = diff(y(x),x,2) - 2*diff(y(x),x)**2 - 1
con = {y(0):0}
y = dsolve(eq,ics=con)
print(simplify(y[0]))