Visual Python, Numpy, Matplotlib
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- しゅんすけ みやくぼ
- 5 years ago
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1 Visual Python, Numpy, Matplotlib 1 / 57
2 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 2 / 57
3 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 3 / 57
4 3 Visual Python: 3D Numpy, Scipy: Matplotlib: ( ) 4 / 57
5 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 5 / 57
6 1 ( ) 2 vector 3D 3 Visual Python 6 / 57
7 1 1 n_steps = 2 dt = ( - ) / n_steps # 3 x = 4 v = 5 t = 6 for i in range(n_steps): 7 alpha = / # 8 x += v * dt # += * 9 v += alpha * dt # += * 10 t += dt., t, x, v, 7 / 57
8 : y = 0 t = 0 10 y = 0, v = 0 : ky + mg (g = 0.98) : t, 1 k = g = m = n_steps = dt = (10.0-0) / n_steps 6 y = v = for i in range(n_steps): 9 alpha = -k * y / m + g 10 y += v * dt 11 v += alpha * dt 8 / 57
9 3D Visual Python vector :, 1 from vpython import * 2 k = g = vector(0.0, -9.8, 0.0) 4 m = n_steps = dt = (10.0-0) / n_steps 7 y = vector(0.0, 0.0, 0.0) 8 v = vector(0.0, 0.0, 0.0) 9 for i in range(n_steps): 10 alpha = -k * y /m + g 11 y += v * dt 12 v += alpha * dt 9 / 57
10 Visual Python pos : (helix) 1 from vpython import * 2 k = g = vector(0.0, -9.8, 0.0) 4 m = n_steps = dt = (10.0-0) / n_steps 7 s = sphere(pos=vector(0.0, 0.0, 0.0)) 8 s.vel = vector(0.0, 0.0, 0.0) 9 scene.autoscale = 0 # 10 scene.autocenter = 0 # 11 for i in range(n_steps): 12 rate(1.0/dt) 13 s.alpha = -k * s.pos /m + g 14 s.pos += s.vel * dt 15 s.vel += s.alpha * dt 10 / 57
11 rate(f) : (pos ) f : 1 f ( 1 ) 1: ( ) 2: 1 scene.autocenter = 0 2 scene.autoscale = 0 11 / 57
12 :, 1, 1 = Visual Python 12 / 57
13 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 13 / 57
14 Numpy Scipy SciPy NumPy (Numerical Python) NumPy SciPy numpy, scipy scipy, numpy,, numpy, scipy scipy 14 / 57
15 speed learning, 15 / 57
16 array : numpy numpy, array array : 1 import numpy as np 2 np.array( ) : 1 import numpy as np 2 x = np.array([2,0,1,4]) 3 print(x) 4 print(len(x)) 5 print(x[1]) : 1 [ ] / 57
17 array : 1 import numpy as np 2 A = np.array([[1,2,3],[4,5,6]]) 3 print(a) 4 print(len(a)) 5 print(a[1][1]) : 1 [[1 2 3] 2 [4 5 6]] , 3, 4,... array 17 / 57
18 array 1 import numpy as np 2 x = np.array([2,0,1,4]) 3 y = np.array([5,6,7,8]) 4 print(x + y) 5 print(x * y) # 6 print(x.dot(y)) 1 [ ] 2 [ ] # * 3 49 # 18 / 57
19 array ( ) : 1 import numpy 2 A = numpy.array([[1,2,3],[4,5,6]]) 3 x = numpy.array([2,4,6]) 4 print(a.dot(x)) 1 [28 64] 1 import numpy 2 A = numpy.array([[1,2,3],[4,5,6]]) 3 B = numpy.array([[2,3],[4,5],[6,7]]) 4 print(a.dot(b)) 1 [[28 34] 2 [64 79]] 19 / 57
20 matrix : * array,, (, * ) matrix 1 import numpy as np 2 A = np.matrix([[1,2,3],[4,5,6]]) 3 B = np.matrix([[2,3],[4,5],[6,7]]) 4 print(a * B) 1 [[28 34] 2 [64 79]], array, matrix 20 / 57
21 array (1) ( ) 1 >>> np.arange(2,3,0.2) 2 array([ 2., 2.2, 2.4, 2.6, 2.8]) ( ) 1 >>> np.linspace(2,3,6) 2 array([ 2., 2.2, 2.4, 2.6, 2.8, 3. ]) >>> np.zeros((3,2)) 2 array([[ 0., 0.], 3 [ 0., 0.], 4 [ 0., 0.]]) 1 np.ones((2,3)) 2 array([[ 1., 1., 1.], 3 [ 1., 1., 1.]]) 21 / 57
22 array (2), zeros, 1 import numpy as np 2 3 def make_diag(n): 4 A = np.zeros((n,n)) 5 for i in range(n): 6 A[i,i] = i return A 8 9 print(make_diag(4)) 1 [[ ] 2 [ ] 3 [ ] 4 [ ]] 22 / 57
23 array (3) reshape, ( ) (1 ) (2 ) A = np.arange(0, 15, 1).reshape(3, 5) 2 print(a) 3 B = A.reshape(5, 3) 4 print(b) 1 [[ ] 2 [ ] 3 [ ]] 4 [[ 0 1 2] 5 [ 3 4 5] 6 [ 6 7 8] 7 [ ] 8 [ ]] 23 / 57
24 array (4) 1 >>> np.random.random((3,3)) 2 array([[ , , ], 3 [ , , ], 4 [ , , ]]) 1 >>> def f(i,j): 2... return I + J >>> np.fromfunction(f, (3,3)) 5 array([[ 0., 1., 2.], 6 [ 1., 2., 3.], 7 [ 2., 3., 4.]]) 24 / 57
25 ,,,, 1 import numpy 2 A = np.arange(0, 15, 1).reshape(3, 5) 3 >>> A 4 array([[ 0, 1, 2, 3, 4], 5 [ 5, 6, 7, 8, 9], 6 [10, 11, 12, 13, 14]]) 7 >>> A[1,2] >>> A[1:3,2:4] 10 array([[ 7, 8], 11 [12, 13]]) 25 / 57
26 ,, 1 >>> A[1:3,:] # = A[1:3,0:5] 2 array([[ 5, 6, 7, 8, 9], 3 [10, 11, 12, 13, 14]]) 4 >>> A[:,2:4] # = A[0:3,2:4] 5 array([[ 2, 3], 6 [ 7, 8], 7 [12, 13]]) 8 >>> A[:,2] 9 array([ 2, 7, 12]) 10 >>> A[:,:] 11 array([[ 0, 1, 2, 3, 4], 12 [ 5, 6, 7, 8, 9], 13 [10, 11, 12, 13, 14]]) 26 / 57
27 Universal (1) array 1 >>> import numpy as np 2 >>> r = np.linspace(0, 0.5 * math.pi, 6) 3 >>> r 4 array([ 0., , , , , ]) 5 >>> r array([ 2., , , , , ]) 7 >>> r ** 2 8 array([ 0., , , , , ]) 27 / 57
28 Universal (2) sin, cos math array array numpy 1 >>> import numpy as np 2 >>> import math 3 >>> r = np.linspace(0, 0.5 * math.pi, 6) 4 >>> math.sin(r) 5 Traceback (most recent call last): 6 File "<stdin>", line 1, in <module> 7 TypeError: only length-1 arrays can be converted to Python scalars 8 >>> np.sin(0.5 * math.pi) >>> np.sin(r) 11 array([ 0., , , , , 1. ]) 28 / 57
29 Numpy (Ax = b) 1 x = np.linalg.solve(a, b) 1 d,p = np.linalg.eig(a) 1 rank = np.linalg.det(a) 1 rank = np.linalg.matrix_rank(a) / 57
30 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 30 / 57
31 Scipy (scipy.integrate) (scipy.odeint) (scipy.optimize)... scipy 31 / 57
32 Contents 1 2 Visual Python 3 Numpy Scipy 4 Scipy 5 Matplotlib 32 / 57
33 Matplotlib Visual,, ( ) Matplotlib, numpy array, + 33 / 57
34 Matplotlib,.. document : user s guide: Pyplot tutorial ( y = f(x) ) mplot3d (3D ) Gallery ( ) Plotting Command Summary ( ) 34 / 57
35 1 (y = f(x)) : matplotlib.pyplot, plot show, 1 import matplotlib.pyplot as plt 2 plt.plot(...) 3 plt.show(...) : x, y array, plot, show 1 import matplotlib.pyplot as plt 2 import numpy as np 3 x = np.arange(0, 10, 0.1) # [ ] 4 y = np.sin(x) # universal 5 # y = [sin(0) sin(0.1) sin(0.2)... ] 6 plt.plot(x, y) 7 plt.show() 35 / 57
36 1 (y = f(x)) 1 import matplotlib.pyplot as plt 2 import numpy as np 3 x = np.arange(0, 10, 0.1) # [ ] 4 y = np.sin(x) # universal 5 # y = [sin(0) sin(0.1) sin(0.2)... ] 6 plt.plot(x, y) 7 plt.show() 36 / 57
37 (,,... etc.) plot bar, scatter pyplot tutorial, gallery? help 1 >>> import matplotlib.pyplot as plt 2 >>> help(plt.plot) 37 / 57
38 2 (z = f(x, y)) : 1 plot 2 1 pcolor ( ) 2 contour ( ) 3 etc. (gallery plotting command summary ) 2 (x i, y i, z i), x i, y i, z i 2 (x, y) [0, 2] [0, 3] x 2 y 2 1 import matplotlib.pyplot as plt 2 import numpy as np 3 X = np.array([[0,0,0,0],[1,1,1,1],[2,2,2,2]]) 4 Y = np.array([[0,1,2,3],[0,1,2,3],[0,1,2,3]]) 5 Z = X ** 2 - Y ** 2 # universal 6 # Z = array([[0,-1,-4,-9],[1,0,-3,-8],[4,3,0,-5]]) 7 plt.pcolor(x, Y, Z) 8 plt.show() X, Y ( ) 38 / 57
39 2 (z = f(x, y)) np.meshgrid 1 import matplotlib.pyplot as plt 2 import numpy as np 3 X = np.array([0,1,2]) 4 Y = np.array([0,1,2,3]) 5 X,Y = np.meshgrid(x, Y) 6 Z = X ** 2 - Y ** 2 7 plt.pcolor(x, Y, Z) 8 plt.show() 39 / 57
40 2 (y = f(x, y)) 1 import matplotlib.pyplot as plt 2 import numpy as np 3 X = np.arange(0, 10, 0.1) 4 Y = np.arange(0, 10, 0.1) 5 X,Y = np.meshgrid(x, Y) 6 Z = X ** 2 - Y ** 2 7 plt.pcolor(x, Y, Z) 8 plt.show() 40 / 57
41 3D 1 import matplotlib.pyplot as plt 2 fig = plt.figure() # windows 3 ax = fig.add_subplot(,, ) # 4 ax.plot(...) 5 fig.show(...) (3x2 ) 1 import matplotlib.pyplot as plt 2 fig = plt.figure() 3 ax0 = fig.add_subplot(3,2,1) # fig.add_subplot(321) 4 ax1 = fig.add_subplot(3,2,2) # fig.add_subplot(322) ax0.plot(...) 7 ax1.plot(...) fig.show(...) 41 / 57
42 2 (z = f(x, y)) 3D : plot plot surface plot wireframe etc. 1 import matplotlib.pyplot as plt 2 import numpy as np 3 import mpl toolkits.mplot3d.axes3d 4 fig = plt.figure() 5 ax = fig.add_subplot(1,1,1, projection= 3d ) 6 X = np.arange(0, 10, 0.1) 7 Y = np.arange(0, 10, 0.1) 8 X,Y = np.meshgrid(x, Y) 9 Z = X ** 2 - Y ** 2 10 ax.plot_surface(x, Y, Z) 11 plt.show() 42 / 57
43 3D 1 import matplotlib.pyplot as plt 2 import numpy as np 3 import mpl_toolkits.mplot3d.axes3d 4 fig = plt.figure() 5 ax = fig.add_subplot(1,1,1, projection= 3d ) 6 X = np.arange(0, 10, 0.1) 7 Y = np.arange(0, 10, 0.1) 8 X,Y = np.meshgrid(x, Y) 9 Z = X ** 2 - Y ** 2 10 ax.plot_surface(x, Y, Z) 11 plt.show() 43 / 57
44 Matplotlib,,,, Jupyter, 44 / 57
45 : y = sin kx (0 x 2π), k = 1, 2, 3, 5 : k (= 3) 1 import matplotlib.pyplot as plt 2 import numpy as np 3 4 x = np.linspace(0.0, 2.0 * np.pi, 100) 5 plt.plot(x, np.sin(3 * x)) 6 plt.show() 45 / 57
46 1 import matplotlib.pyplot as plt 2 import numpy as np 3 4 x = np.linspace(0.0, 2.0 * np.pi, 100) 5 for k in range(1, 6): 6 plt.plot(x, np.sin(k * x)) 7 plt.show() : 5 ( ) 46 / 57
47 3, ( ), Jupyter, 1 Jupyter ( ) python 47 / 57
48 1 plt.plot(...), ( ) ( ), animation.artistsanimation, %matplotlib notebook 1 %matplotlib notebook 2 import matplotlib.pyplot as plt 3 import matplotlib.animation as animation 4 import numpy as np 5 6 x = np.linspace(0.0, 2.0 * np.pi, 100) 7 plots = [] 8 for k in range(1, 6): 9 plots.append(plt.plot(x, np.sin(k * x))) 10 a = animation.artistanimation(plt.gcf(), plots, repeat=0) 11 plt.show() 48 / 57
49 1. max frames 1 n_steps = max_frames = 50 3 interval = math.ceil(n_steps / max_frames) 4 plots = [] 5 for t in range(n_steps): 6 if t % interval == 0: 7 plots.append(...), : 2, 3, Jupyter 49 / 57
50 ( ) 2 plt.plot(...) ( ) ( ) set data ( ) pause ( ) ( ) Jupyter (python. ) 1 x = np.linspace(0.0, 2.0 * np.pi, 100) 2 for k in range(1, 6): 3 if k == 1: 4 [ line ] = plt.plot(x, np.sin(k * x)) # ( ) 5 else: 6 line.set data(x, np.sin(k * x)) # ( ) 7 plt.pause(0.1) # ( ) : plt.plot(...), ( 1 ) ; 50 / 57
51 ( ) 3 (Jupyter, ) 2., yield ( ) 1 def generate_plots(): 2 x = np.linspace(0.0, 2.0 * np.pi, 100) 3 for k in range(1, 6): 4 if k == 1: 5 [line] = plt.plot(x, np.sin(k * x)) 6 else: 7 line.set_data(x, np.sin(k * x)) 8 yield [line] # ( ), 1 animate iterator(generate plots(), interval=100) animate iterator 51 / 57
52 animate iterator ( ) 1 import matplotlib.pyplot as plt 2 import matplotlib.animation as animation 3 4 def animate_iterator(iterator, **kwargs): 5 def fun(*args): 6 try: 7 return next(iterator) 8 except StopIteration: 9 return [] 10 ani = animation.funcanimation(plt.gcf(), fun, 11 **kwargs) 12 plt.show() 52 / 57
53 2 次元 (pcolor) の場合 復習: アニメーションなしで静止画 (z = y sin 3x) を書くだけの例 %matplotlib notebook import matplotlib.pyplot as plt import numpy as np x = np.linspace(0.0, 1.0, 100) y = np.linspace(0.0, 1.0, 100) x,y = np.meshgrid(x, y) plt.pcolor(x, y, np.sin(y - np.sin(3 * x))) plt.show() 53 / 57
54 2 (pcolor) 1 1 (pcolor, animation.artistanimation ) 1 %matplotlib notebook 2 import matplotlib.pyplot as plt 3 import matplotlib.animation as animation 4 import numpy as np 5 x = np.linspace(0.0, 1.0, 100) 6 y = np.linspace(0.0, 1.0, 100) 7 x,y = np.meshgrid(x, y) 8 pcolors = [] 9 for k in range(1, 20): 10 pcolors.append([ plt.pcolor(x,y,y-np.sin(k*x)) ]) 11 a = animation.artistanimation(plt.gcf(), pcolors, 12 repeat=0) 13 plt.show() plt.plot, ( )plt.pcolor, 1 ( ) 54 / 57
55 ( ) 2 (pcolor) 2 : Jupyter 1 (plot) set data, 2 (pcolor) set array, z 1, 1 ( ) 1 import matplotlib.pyplot as plt 2 import numpy as np 3 x = np.linspace(0.0, 1.0, 100) 4 y = np.linspace(0.0, 1.0, 100) 5 x,y = np.meshgrid(x, y) 6 for k in range(1, 20): 7 if k == 1: 8 f = plt.pcolor(x, y, y - np.sin(k * x)) 9 else: 10 f.set array(shrink1(y - np.sin(k * x))) 11 plt.pause(0.1) shrink1 55 / 57
56 shrink1 1 def shrink1(z): 2 m,n = z.shape 3 return z[:m-1,:n-1].flatten() 56 / 57
57 ( ) 2 (pcolor) 3 (Jupyter, ) 1 def generate_pcolors(): 2 x = np.linspace(0.0, 1.0, 100) 3 y = np.linspace(0.0, 1.0, 100) 4 x,y = np.meshgrid(x, y) 5 for k in range(1, 20): 6 if k == 1: 7 f = plt.pcolor(x, y, y - np.sin(k * x)) 8 else: 9 f.set_array(shrink1(y - np.sin(k * x))) 10 yield [ f ], 1 animate_iterator(generate_pcolors(), interval=100) animate iterator 1 57 / 57
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2018/03/15 第 版 本書は全球降 観測衛星 (GPM) のデータを読み込むプログラム (Python) の作成 法についてまとめたものです 本書で解説するサンプルプログラムは GPM はプロダクトバージョン 5 GSMaP はプロダクトバージョン 4 で動作を確認しています 目次 1. はじめに... 3 2.GPM データの 法... 4 3. 関連 書 サンプルプログラムの 法...
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