NumPy + Matplotlib
December 3, 2019
1 NumPy
• de facto standard pro numerické výpočty v Pythonu
• velké množství dalších modulů postavených nad NumPy (SciPy, scikit-learn, pandas, …)
[142]: import numpy as np
1.1 NumPy pole
• základní objekt, se kterým NumPy pracuje
• pouze prvky stejného typu
• fixní velikost
[143]: np.array([1, 3, 4])
[143]: array([1, 3, 4])
[144]: np.arange(10)
[144]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
[145]: np.linspace(0, 1, 11)
[145]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])
[146]: np.random.sample(10)
[146]: array([0.62666803, 0.07045182, 0.20550107, 0.36733577, 0.38851806,
0.03756064, 0.90113418, 0.6652082 , 0.43018563, 0.6772363 ])
1.2 Základní operace
[147]: a = np.arange(10)
a
[147]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
[148]: len(a)
1
[148]: 10
Operace se provádějí nad celým polem, není nutné používat for cyklus.
[149]: a + 1
[149]: array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
[150]: a ** 2
[150]: array([ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81])
1.3 Vícerozměrná pole
[151]: a = np.arange(25)
a
[151]: array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24])
[152]: a.shape
[152]: (25,)
[153]: b = a.reshape(5, 5)
b
[153]: array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24]])
[154]: b.shape
[154]: (5, 5)
[155]: b[2, :]
[155]: array([10, 11, 12, 13, 14])
[156]: b[:, 4]
[156]: array([ 4, 9, 14, 19, 24])
[157]: b[3:6, 2]
2
[157]: array([17, 22])
[158]: np.zeros((3, 3))
[158]: array([[0., 0., 0.],
[0., 0., 0.],
[0., 0., 0.]])
[159]: x = np.ones((3, 3))
x
[159]: array([[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.]])
[160]: x[:, 1] = 4
x
[160]: array([[1., 4., 1.],
[1., 4., 1.],
[1., 4., 1.]])
[161]: x.T
[161]: array([[1., 1., 1.],
[4., 4., 4.],
[1., 1., 1.]])
[162]: np.eye(3)
[162]: array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
[163]: 3 * np.eye(3) + np.arange(9).reshape(3, 3)
[163]: array([[ 3., 1., 2.],
[ 3., 7., 5.],
[ 6., 7., 11.]])
1.4 Užitečné funkce
[164]: a = np.arange(30).reshape(5, 6)
a
[164]: array([[ 0, 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10, 11],
3
[12, 13, 14, 15, 16, 17],
[18, 19, 20, 21, 22, 23],
[24, 25, 26, 27, 28, 29]])
[165]: np.min(a), np.max(a), np.sum(a), np.mean(a)
[165]: (0, 29, 435, 14.5)
Všechny zmíněné funkce mají parametr axis, který určuje, zda provést funkci přes řádky nebo
sloupce.
[166]: np.sum(a, axis=0)
[166]: array([60, 65, 70, 75, 80, 85])
[167]: np.sum(a, axis=1)
[167]: array([ 15, 51, 87, 123, 159])
1.5 NumPy a lineární algebra
• np.linalg
• velké množství funkcí (determinanty, inverzní matice, vlastní hodnoty, …)
1.5.1 Příklad - soustava lineárních rovnic
x + y = 1
2x − y = 2
je ekvivalentní: [
1 1
2 −1
]
·
[
x
y
]
=
[
1
2
]
[168]: A = np.array([[1, 1], [2, -1]])
A
[168]: array([[ 1, 1],
[ 2, -1]])
[169]: b = np.array([1, 2])
b
[169]: array([1, 2])
[170]: np.linalg.solve(A, b)
[170]: array([1., 0.])
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1.6 Vizualizace dat - matplotlib
• asi nejrozšířenější modul
• podobná syntaxe jako v Matlabu
• velké možnosti nastavení, typu grafů
• pracuje nad NumPy poli
[171]: import matplotlib.pyplot as plt
[172]: xs = np.linspace(0, 10, 50)
[173]: plt.plot(xs, np.sin(xs))
[173]: [<matplotlib.lines.Line2D at 0x7fef25f51250>]
[174]: plt.grid()
plt.plot(xs, np.sin(xs), '-o', color='red')
[174]: [<matplotlib.lines.Line2D at 0x7fef25eb2950>]
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[175]: plt.grid()
plt.xlim(-1, 11)
plt.ylim(-2, 2)
plt.title('Goniometrické funkce')
plt.plot(xs, np.sin(xs), label='$y = \sin{x}$')
plt.plot(xs, np.cos(xs), label='$y = \cos{x}$')
plt.legend()
[175]: <matplotlib.legend.Legend at 0x7fef25e975d0>
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1.6.1 Bar plot
[176]: x = np.random.randint(10, size=10)
x
[176]: array([1, 4, 4, 8, 6, 3, 4, 7, 1, 3])
[177]: plt.bar(np.arange(10), x)
[177]: <BarContainer object of 10 artists>
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1.6.2 Histogram
[178]: plt.hist(np.random.sample(100), bins=15)
[178]: (array([ 4., 9., 5., 4., 5., 5., 10., 5., 5., 7., 8., 12., 5.,
11., 5.]),
array([0.02412496, 0.08896623, 0.1538075 , 0.21864877, 0.28349004,
0.34833131, 0.41317258, 0.47801385, 0.54285512, 0.60769639,
0.67253765, 0.73737892, 0.80222019, 0.86706146, 0.93190273,
0.996744 ]),
<a list of 15 Patch objects>)
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1.6.3 Scatter plot
[179]: xs = np.random.sample(50)
ys = np.random.sample(50)
sizes = np.random.randint(100, size=50)
colors = np.random.randint(3, size=50)
[180]: plt.scatter(xs, ys, c=colors, s=sizes)
[180]: <matplotlib.collections.PathCollection at 0x7fef25eba6d0>
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1.7 NumPy - masky
[181]: a = np.random.randint(100, size=16).reshape(4, 4)
a
[181]: array([[54, 23, 7, 62],
[28, 53, 69, 81],
[72, 76, 11, 63],
[67, 40, 41, 61]])
[182]: mask = a > 20
mask
[182]: array([[ True, True, False, True],
[ True, True, True, True],
[ True, True, False, True],
[ True, True, True, True]])
[183]: a[mask]
[183]: array([54, 23, 62, 28, 53, 69, 81, 72, 76, 63, 67, 40, 41, 61])
[184]: a[~mask]
[184]: array([ 7, 11])
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[185]: xs = np.arange(100)
ys = np.random.sample(100)
plt.scatter(xs, ys)
[185]: <matplotlib.collections.PathCollection at 0x7fef25c884d0>
[186]: for threshold in np.linspace(0, 1, 6):
mask = (ys > threshold) & (ys < threshold + 0.2)
plt.scatter(xs[mask], ys[mask])
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1.7.1 Příklad - náhodnostní výpočet π
[187]: xs = np.random.sample(10000) * 2 - 1
ys = np.random.sample(10000) * 2 - 1
[188]: plt.figure(figsize=(5, 5))
plt.scatter(xs, ys, s=1)
[188]: <matplotlib.collections.PathCollection at 0x7fef25b6c810>
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Jednotkový kruh je množina bodů, pro které platí x2 + y2 ≤ 1.
[189]: mask = xs ** 2 + ys ** 2 <= 1
[190]: plt.figure(figsize=(5, 5))
plt.scatter(xs[mask], ys[mask], s=1)
plt.scatter(xs[~mask], ys[~mask], s=1)
[190]: <matplotlib.collections.PathCollection at 0x7fef25b02dd0>
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počet bodů
počet bodů v kruhu
˜=
(2r)2
πr2
=
4r2
πr2
=
4
π
π ˜=
4 · počet bodů v kruhu
počet bodů
[191]: 4 * np.sum(mask) / len(mask)
[191]: 3.138
1.8 NumPy vstup a výstup
• textový
– np.savetxt a np.loadtxt
– pracuje se standardním CSV
– potřeba nastavit způsob uložení a načtení
• binární
– np.save a np.load
– rychlejší, menší velikost
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[192]: a = np.random.randint(100, size=50).reshape(5, 10)
a
[192]: array([[31, 30, 49, 83, 7, 14, 30, 30, 53, 92],
[77, 50, 38, 98, 48, 81, 58, 93, 60, 19],
[29, 51, 41, 55, 84, 61, 96, 22, 72, 95],
[30, 47, 13, 74, 98, 58, 67, 48, 61, 69],
[17, 99, 27, 25, 91, 64, 93, 56, 33, 18]])
[193]: np.savetxt('data.csv', a, fmt='%d')
[194]: np.loadtxt('data.csv', dtype=np.int)
[194]: array([[31, 30, 49, 83, 7, 14, 30, 30, 53, 92],
[77, 50, 38, 98, 48, 81, 58, 93, 60, 19],
[29, 51, 41, 55, 84, 61, 96, 22, 72, 95],
[30, 47, 13, 74, 98, 58, 67, 48, 61, 69],
[17, 99, 27, 25, 91, 64, 93, 56, 33, 18]])
[195]: np.save('data.npy', a)
[196]: np.load('data.npy')
[196]: array([[31, 30, 49, 83, 7, 14, 30, 30, 53, 92],
[77, 50, 38, 98, 48, 81, 58, 93, 60, 19],
[29, 51, 41, 55, 84, 61, 96, 22, 72, 95],
[30, 47, 13, 74, 98, 58, 67, 48, 61, 69],
[17, 99, 27, 25, 91, 64, 93, 56, 33, 18]])
1.9 NumPy - rychlost
[197]: %%timeit
[x ** 2 for x in range(1000)]
185 µs ± 967 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
[198]: %%timeit
np.arange(1000) ** 2
2.46 µs ± 23.4 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
1.9.1 Součet dvou seznamů/polí
[199]: a_np = np.random.randint(100, size=10 ** 6)
b_np = np.random.randint(100, size=10 ** 6)
a_py = list(a_np)
15
b_py = list(b_np)
Python - tři způsoby:
[204]: %%timeit
c_py = []
for i in range(len(a_py)):
c_py.append(a_py[i] + b_py[i])
167 ms ± 1.53 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
[201]: %%timeit
c_py = []
for x, y in zip(a_py, b_py):
c_py.append(x + y)
124 ms ± 636 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
[202]: %%timeit
c_py = [x + y for x, y in zip(a_py, b_py)]
99.7 ms ± 223 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
NumPy
[203]: %%timeit
c_np = a_np + b_np
913 µs ± 6.16 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
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