如何使用python完成数学建模常见算法！

#我们使用最小二乘法拟合一个三次函数，选取了5个参数

import numpy as np

import matplotlib.pyplot as plt

SAMPLE_NUM = 100

M = 5

x = np.arange(0, SAMPLE_NUM).reshape(SAMPLE_NUM, 1) / (SAMPLE_NUM - 1) * 10

y = 2*x**3+3*x**2+x+1

plt.plot(x, y, 'bo')

X = x

for i in range(2, M + 1):

   X = np.column_stack((X, pow(x, i)))

X = np.insert(X, 0, [1], 1)

W=np.linalg.inv((X.T.dot(X))).dot(X.T).dot(y)

y_estimate = X.dot(W)

plt.plot(x, y_estimate, 'r')

plt.show()

import numpy as np

from scipy import interpolate

import pylab as pl

x=np.linspace(0,10,11)

y=2*x**3+3*x**2+x+1

xInset=np.linspace(0,10,101)

pl.plot(x,y,"ro")

for kind in["nearest","zero","slinear","quadratic","cubic"]:

   f=interpolate.interp1d(x,y,kind=kind)

   y_estimate=f(xInset)

   pl.plot(xInset,y_estimate,label=str(kind))

pl.legend(loc="lower right")

pl.show()

import numpy as np

from scipy.optimize import minimize

def func(x):

return(2*x[0]*x[1]+2*x[0]-x[0]**2+2*x[1]**2+np.sin(x[0]))

cons=({"type":"eq","fun":lambda x:np.array([x[0]**3-x[1]]),"jac":lambda x:np.array([3*(x[0]**2),-1.0])},{"type":"ineq","fun":lambda x:np.array([x[1]-1]),"jac":lambda x:np.array([0,1])})#定义函数的多个约束条件

res=minimize(func,[-1.0,1.0],constraints=cons,method="SLSQP",options={"disp":True})

print(res)

classDisNode:

def __init__(self,node,dis):

       self.node=node

       self.dis=dis

def __lt__(self, other):

return self.dis<other.dis

classDisPath:

def __init__(self,end):

       self.end=end

       self.path=[self.end]

       self.dis=0

def __str__(self):

       nodes=self.path.copy()

return"->".join(list(map(str,nodes)))+" "+str(self.dis)

classHeap:

def __init__(self):

       self.size=0

       self.maxsize=10000

       self.elements=[0]*(self.maxsize+1)

def isEmpty(self):

return self.size==0

def insert(self,value):

if self.isEmpty():

           self.elements[1]=value

else:

           index=self.size+1

while(index!=1and value<self.elements[index//2]):

               self.elements[index]=self.elements[index//2]

               index=index//2

           self.elements[index]=value

       self.size+=1

def pop(self):

       deleteElement=self.elements[1]

       self.elements[1]=self.elements[self.size]

       self.size-=1

       temp=self.elements[1]

       parent,child=1,2

while(child<=self.size):

if child<self.size and self.elements[child]>self.elements[child+1]:

               child+=1

if temp<self.elements[child]:

break

else:

               self.elements[parent]=self.elements[child]

               parent=child

               child*=2

       self.elements[parent]=temp

return deleteElement

defDijkstraWithHeap(nodes,start,GetNeighbors):

   dis=defaultdict(int)

   paths=defaultdict(DisPath)

   heap=Heap()

   visit=set()

for node in nodes:

       dis[node]=sys.maxsize

       paths[node]=DisPath(node)

   dis[start]=0

   heap.insert(DisNode(start,0))

while(not heap.isEmpty()):

       now=heap.pop().node

if now in visit:

continue

       visit.add(now)

       paths[now].dis=dis[now]

for edge inGetNeighbors(now):

           end=edge.End

if dis[now]+edge.value<dis[end]:

               dis[end]=dis[now]+edge.value

               paths[end].path=paths[now].path+[end]

               heap.insert(DisNode(end,dis[end]))

return paths