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TWEET # Untitled a guest Nov 19th, 2019 88 Never
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1. def maxTime():
2.     def heatmap(ix,iy,iz,borders):
3.         levels = MaxNLocator(nbins=50).tick_values(iz.min(), iz.max())
4.         # pick the desired colormap, sensible levels, and define a normalization
5.         # instance which takes data values and translates those into levels.
6.         cmap = plt.get_cmap('Greys')
7.         norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)
8.
9.         fig, (ax0, ax1) = plt.subplots(nrows=2)
10.
11.         im = ax0.pcolormesh(ix,iy, iz, cmap=cmap, norm=norm)
12.         fig.colorbar(im, ax=ax0)
13.         ax0.set_title('pcolormesh with levels')
14.
15.
16.         # contours are *point* based plots, so convert our bound into point
17.         # centers
18.         cf = ax1.contourf(ix[:-1, :-1] + 0.01/2.,
19.                           iy[:-1, :-1] + 0.01/2., iz, levels = borders,
20.                           cmap=cmap)
21.         fig.colorbar(cf, ax=ax1)
22.         ax1.set_title('contourf with levels')
23.
24.         # adjust spacing between subplots so `ax1` title and `ax0` tick labels
25.         # don't overlap
26.         fig.tight_layout()
27.         plt.show()
28.
29.
30.     x = np.arange(0.1, 1, 0.1)
31.     y = np.arange(0.1, 1, 0.1)
32.
33.     t = sp.Symbol('t', positive=True)
34.     p = sp.symbols('p')
35.     Ki = sp.symbols('Ki', real = True)
36.     Kp = sp.symbols('Kp', real=True)
37.     a = sp.symbols('a', real=True)
38.     b = sp.symbols('b', real=True)
39.     c = sp.symbols('c', real=True)
40.     expression = (p*Kp+Ki)*a/(p*(b*c*p+a*a)+(p*Kp+Ki)*a)
41.
42.     orig1 = sp.inverse_laplace_transform(expression, p, t)
43.     orig2 = sp.inverse_laplace_transform(expression/p, p, t)
44.     x, y = np.meshgrid(x, y)
45.     tp = np.empty([9,9])
46.     mp = np.empty([9,9])
47.     for i in range(9):
48.         for j in range(9):
49.             tp[i][j] = nsolve(simplify(orig1.subs([(Ki,x[i][j]),(Kp,y[i][j]),(a,0.03),(b,2.44),(c,0.00003)])),t,(0,1))
50.             print(orig2.subs([(Ki,x[i][j]),(Kp,y[i][j]),(a,0.03),(b,2.44),(c,0.00003),(t,tp[i][j])]))
51.
52.     tp = tp[:-1, :-1]
53.     heatmap(x,y,tp,[0,15,500])
54.
55.
56.
57.
58. maxTime()
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