Python学习笔记——数学建模初体验

             1
            import
             numpy as np

             2
            import
             matplotlib.pyplot as plt

             3
            def
             myfunc(x):

             4
            if 0 > x >= -1:
 5return x+1
 6elif 1 > x  >= 0:
 7return 1
 8elif 2 > x >= 1:
 9return x**2
1011 x = np.linspace(-1, 2, 300)
12 y = np.array([myfunc(t) for t in x])
1314 y1 = myfunc(-1)
15 y2 = myfunc(0.5)
16 y3 = myfunc(1.5)
17print("f(-1) = %.2f f(0.5) = %.2f f(1.5) = %.2f" %(y1, y2, y3))
18plt.figure()
19plt.plot(x, y)  
20 plt.show()

            1
            ‘
            Hello, {0}, 成绩提升了 {1:.1f}%
            ‘.format(‘小明‘, 17.125)
2‘Hello, 小明, 成绩提升了 17.1%‘

             1
            #
            允许状态集合，例num=3
             2
            #
            S={(x,y)|x=0,y=0,1,2,3;x=3,y=0,1,2,3;x=y=1,2} x是此岸的商人数，y是此岸的仆人数
             3
            #
            允许决策集合，例boat_limit=2
             4
            #
            D={(u,v)|1<=u+v<=2,u,v=0,1,2} u是撘载的商人数，v是搭载的仆人数
             5
            def
             cross_river(person, boat):

             6     num = person
 7     boat_limit= boat
 8     temp=[]#允许状态集合 9for i in range(0,num+1):
10if i==0 or i==num:
11for j in range(0,num+1):
12                temp.append((i,j))
13else:
14            temp.append((i,i))
15     S=set(temp)
16     D=[]#允许决策集合17for u in range(0,boat_limit+1):
18for v in range(0,boat_limit+1):
19if u+v>=1 and u+v<=boat_limit :
20                D.append((u,v))
21     start=(num,num)#起始22     end=(0,0)#目标23     queue=[]
24     queue.append((0,start)) #前面的元素如果是0，说明是船在此岸，是1，说明船在对岸25     step_dict={}
26     flag=0
27     finish=[]
28while len(queue)!=0:
29         q_pop=queue.pop(0)
30if q_pop[0]==0:
31for x in D:
32                 temp_s=(q_pop[1][0]-x[0],q_pop[1][1]-x[1])
33if temp_s notin S:
34continue35if (1,temp_s) in step_dict:
36continue37                 queue.append((1,temp_s))
38                 step_dict[(1,temp_s)]=q_pop
39if temp_s==end:
40                     flag=1
41                     finish=(1,temp_s)
42break43else:
44for x in D:
45                 temp_s=(q_pop[1][0]+x[0],q_pop[1][1]+x[1])
46if temp_s notin S:
47continue48if (0,temp_s) in step_dict:
49continue50                queue.append((0,temp_s))
51                 step_dict[(0,temp_s)]=q_pop
52if flag==1:
53break54if flag==1:
55print(‘该问题有解！最短路径：‘)
56         path=[]
57        path.append(finish)
58while path[-1]!=(0,start):
59             path.append(step_dict[path[-1]])
60        path.reverse()
61         real_path=list(map(str,path))
62for i in range(len(real_path)):
63if i!=len(real_path)-1:
64print(real_path[i] + ‘->‘)
65else:
66print(real_path[i])
67else:
68print(‘该问题无解‘)
6970return  None
717273 cross_river(3,2)

             1
            import
             matplotlib.pyplot as plt

             2
            from pylab import mpl
 3import math
 4import numpy as np
 5import matplotlib.pyplot as plt
 6from scipy.optimize import curve_fit
 7 8 t = []
 9 n = 0
10for i in range(1790, 2010, 10):
1112    t.append (i)
13     n = n+1 
1415 y = [3.9, 5.3, 7.2, 9.6, 12.9, 17.1, 23.2, 31.4,
16    38.6, 50.2, 62.9, 76.0,92.0,106.5, 123.2,131.7,
17    150.7, 179.3,204.0, 226.5, 251.4, 281.4]
181920#指数增长21def func(t,r): 
22return y[0]*np.exp(r*t)
2324 t2 = np.array(t)-1790
25 y2 = np.array(y)
26 popt, pcov = curve_fit(func, t2, y2, p0 = [0.02])
27#如果直接这样拟合要给个初值p0，不然会拟合次数达到上限，拟合失败28print(popt)
29 r = popt[0]
3031#阻滞增长32def func2(t, r2, x_m): 
33return x_m/(1+ (((x_m/y[0])-1)*np.exp((-r2)*t)))
34 popt2, pcov2 = curve_fit(func2, t2, y2, p0 = [r, 400])
35#如果直接这样拟合要给个初值p0，不然会拟合结果和实际相差太多36print(popt2)
37 r2 = popt2[0]
38 x_m = popt2[1]
3940#画图41 yvals = func(t2, r)
42 yvals2 = func2(t2,r2, x_m)
43plt.figure()
44 plot1 = plt.plot(t2, y2, ‘s‘,label=‘original values‘)
45 plot2 = plt.plot(t2, yvals, ‘r‘,label=‘exp‘)
46 plot3 = plt.plot(t2, yvals2, ‘g‘,label=‘zuzhi‘)
4748 plt.xlabel(‘t‘)
49 plt.ylabel(‘y‘)
50 plt.legend(loc=4) #指定legend的位置右下角51 plt.title(‘curve_fit‘)
52plt.show() 
5354#预测2010年的人口55 pred = func2(2010-1790, r2, x_m )
56print(pred)