Jupter Notebook高级 - 魔法命令
%timeit
696 µs ± 104 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
1.08 µs ± 105 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)
46.7 ms ± 3.45 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
%%timeit
L = []
for n in range(1000):
L.append(n**2)
506 µs ± 47.7 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
%time
Wall time: 997 µs
%%time
L = []
for n in range(1000):
L.append(n**2)
Wall time: 996 µs
03 Numpy.array基础
import numpy
numpy.__version__
'1.16.2'
import numpy as np
Python List的特点
L = [i for i in range(10)]
L
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
5
L
[0, 1, 2, 3, 4, 'Machine Learing', 6, 7, 8, 9]
import array
arr = array.array('i', [i for i in range(10)])
arr
array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
5
numpy.array
nparr = np.array([i for i in range(10)])
nparr
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
5
nparr[5] = 100
nparr
array([ 0, 1, 2, 3, 4, 100, 6, 7, 8, 9])
nparr.dtype
dtype('int32')
nparr
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
nparr.dtype
dtype('int32')
nparr2.dtype
dtype('float64')
其他创建 numpy.array的方法
array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
np.zeros(10).dtype
dtype('float64')
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
array([[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.]])
array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])
array([[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.]])
array([[666.6, 666.6, 666.6, 666.6, 666.6],
[666.6, 666.6, 666.6, 666.6, 666.6],
[666.6, 666.6, 666.6, 666.6, 666.6]])
arange
[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])
array([ 0. , 0.2, 0.4, 0.6, 0.8, 1. , 1.2, 1.4, 1.6, 1.8, 2. ,
2.2, 2.4, 2.6, 2.8, 3. , 3.2, 3.4, 3.6, 3.8, 4. , 4.2,
4.4, 4.6, 4.8, 5. , 5.2, 5.4, 5.6, 5.8, 6. , 6.2, 6.4,
6.6, 6.8, 7. , 7.2, 7.4, 7.6, 7.8, 8. , 8.2, 8.4, 8.6,
8.8, 9. , 9.2, 9.4, 9.6, 9.8, 10. , 10.2, 10.4, 10.6, 10.8,
11. , 11.2, 11.4, 11.6, 11.8, 12. , 12.2, 12.4, 12.6, 12.8, 13. ,
13.2, 13.4, 13.6, 13.8, 14. , 14.2, 14.4, 14.6, 14.8, 15. , 15.2,
15.4, 15.6, 15.8, 16. , 16.2, 16.4, 16.6, 16.8, 17. , 17.2, 17.4,
17.6, 17.8, 18. , 18.2, 18.4, 18.6, 18.8, 19. , 19.2, 19.4, 19.6,
19.8])
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
linspace
array([ 0. , 2.22222222, 4.44444444, 6.66666667, 8.88888889,
11.11111111, 13.33333333, 15.55555556, 17.77777778, 20. ])
array([ 0., 2., 4., 6., 8., 10., 12., 14., 16., 18., 20.])
random
array([9, 5, 9, 5, 1, 8, 4, 1, 2, 1])
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
array([3, 4, 0, 9, 4, 3, 6, 4, 6, 0])
array([[2, 5, 0, 8, 9],
[8, 7, 8, 8, 6],
[6, 6, 2, 8, 0]])
# 指定种子，每次产生的数都一样
np.random.seed(666)
np.random.randint(0, 10, size=(3, 5))
array([[2, 6, 9, 4, 3],
[1, 0, 8, 7, 5],
[2, 5, 5, 4, 8]])
0.7315955468480113
array([[0.8578588 , 0.76741234, 0.95323137, 0.29097383, 0.84778197],
[0.3497619 , 0.92389692, 0.29489453, 0.52438061, 0.94253896],
[0.07473949, 0.27646251, 0.4675855 , 0.31581532, 0.39016259]])
0.9047266176428719
# 均值为10，方差为100的正态分布
np.random.normal(10, 100)
-72.62832650185376
array([[ 92.1013692 , 46.7125916 , 175.39958581, 23.94647258],
[-111.71535503, -89.49473667, -146.44858645, -152.87900441],
[ 133.17486561, -81.36003361, -17.08440668, 152.02491357]])
np.random.normal?
np.random?
Help on built-in function normal:
normal(...) method of mtrand.RandomState instance
normal(loc=0.0, scale=1.0, size=None)
Draw random samples from a normal (Gaussian) distribution.
The probability density function of the normal distribution, first
derived by De Moivre and 200 years later by both Gauss and Laplace
independently [2]_, is often called the bell curve because of
its characteristic shape (see the example below).
The normal distributions occurs often in nature. For example, it
describes the commonly occurring distribution of samples influenced
by a large number of tiny, random disturbances, each with its own
unique distribution [2]_.
Parameters
----------
loc : float or array_like of floats
Mean ("centre") of the distribution.
scale : float or array_like of floats
Standard deviation (spread or "width") of the distribution.
size : int or tuple of ints, optional
Output shape. If the given shape is, e.g., ``(m, n, k)``, then
``m * n * k`` samples are drawn. If size is ``None`` (default),
a single value is returned if ``loc`` and ``scale`` are both scalars.
Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn.
Returns
-------
out : ndarray or scalar
Drawn samples from the parameterized normal distribution.
See Also
--------
scipy.stats.norm : probability density function, distribution or
cumulative density function, etc.
Notes
-----
The probability density for the Gaussian distribution is
.. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }}
e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },
where :math:`\mu` is the mean and :math:`\sigma` the standard
deviation. The square of the standard deviation, :math:`\sigma^2`,
is called the variance.
The function has its peak at the mean, and its "spread" increases with
the standard deviation (the function reaches 0.607 times its maximum at
:math:`x + \sigma` and :math:`x - \sigma` [2]_). This implies that
`numpy.random.normal` is more likely to return samples lying close to
the mean, rather than those far away.
References
----------
.. [1] Wikipedia, "Normal distribution",
https://en.wikipedia.org/wiki/Normal_distribution
.. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability,
Random Variables and Random Signal Principles", 4th ed., 2001,
pp. 51, 51, 125.
Examples
--------
Draw samples from the distribution:
>>> mu, sigma = 0, 0.1 # mean and standard deviation
>>> s = np.random.normal(mu, sigma, 1000)
Verify the mean and the variance:
>>> abs(mu - np.mean(s)) < 0.01
True
>>> abs(sigma - np.std(s, ddof=1)) < 0.01
True
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 30, density=True)
>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *
... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
... linewidth=2, color='r')
>>> plt.show()
05 Numpy.array的基本操作
import numpy as np
x = np.arange(10)
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
X = np.arange(15).reshape(3, 5)
X
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
x.ndim
1
X.ndim
2
x.shape
(10,)
X.shape
(3, 5)
x.size
10
X.size
15
numpy.array的数据访问
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
9
X
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
10
array([0, 1, 2, 3, 4])
array([0, 1, 2, 3, 4])
array([5, 6, 7, 8, 9])
array([0, 2, 4, 6, 8])
array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])
X
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
array([[0, 1, 2],
[5, 6, 7]])
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
array([[0, 2, 4],
[5, 7, 9]])
array([[14, 13, 12, 11, 10],
[ 9, 8, 7, 6, 5],
[ 4, 3, 2, 1, 0]])
array([0, 1, 2, 3, 4])
array([0, 1, 2, 3, 4])
X[0, :].ndim
1
array([ 0, 5, 10])
X[:, 0].ndim
1
subX = X[:2, :3]
subX
array([[0, 1, 2],
[5, 6, 7]])
subX[0, 0] = 100
subX
array([[100, 1, 2],
[ 5, 6, 7]])
X
array([[100, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[ 10, 11, 12, 13, 14]])
subX = X[:2, :3].copy()
subX[0, 0] = 0
X
array([[100, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[ 10, 11, 12, 13, 14]])
Reshape
x.shape
(10,)
x.ndim
1
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
A = x.reshape(2, 5)
A
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
B
array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
B.ndim
2
B.shape
(1, 10)
x.shape
(10,)
array([[0],
[1],
[2],
[3],
[4],
[5],
[6],
[7],
[8],
[9]])
array([[0, 1, 2, 3, 4],
[5, 6, 7, 8, 9]])
array([[0, 1],
[2, 3],
[4, 5],
[6, 7],
[8, 9]])
x = np.array([1,2,3])
y = np.array([3,2,1])
x
array([1, 2, 3])
y
array([3, 2, 1])
array([1, 2, 3, 3, 2, 1])
z = np.array([666, 666, 666])
np.concatenate([x,y,z])
array([ 1, 2, 3, 3, 2, 1, 666, 666, 666])
A = np.array([[1,2,3],
[4,5,6]])
array([[1, 2, 3],
[4, 5, 6],
[1, 2, 3],
[4, 5, 6]])
# 沿着x轴拼接
np.concatenate([A,A], axis=1)
array([[1, 2, 3, 1, 2, 3],
[4, 5, 6, 4, 5, 6]])
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-348-abdc54b54f98> in <module>
----> 1 np.concatenate([A,z])
ValueError: all the input arrays must have same number of dimensions
array([[ 1, 2, 3],
[ 4, 5, 6],
[666, 666, 666]])
A
array([[1, 2, 3],
[4, 5, 6]])
A2 = np.concatenate([A,z.reshape(1, -1)])
A2
array([[ 1, 2, 3],
[ 4, 5, 6],
[666, 666, 666]])
array([[ 1, 2, 3],
[ 4, 5, 6],
[666, 666, 666]])
B = np.full((2,2) ,100)
B
array([[100, 100],
[100, 100]])
array([[ 1, 2, 3, 100, 100],
[ 4, 5, 6, 100, 100]])
分割操作
x = np.arange(10)
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
x1, x2, x3 = np.split(x, [3,7])
x1, x2, x3
(array([0, 1, 2]), array([3, 4, 5, 6]), array([7, 8, 9]))
A = np.arange(16).reshape((4, 4))
A
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
A1, A2 = np.split(A, [2])
A1
array([[0, 1, 2, 3],
[4, 5, 6, 7]])
A2
array([[ 8, 9, 10, 11],
[12, 13, 14, 15]])
A1, A2 = np.split(A, [2], axis=1)
A1
array([[ 0, 1],
[ 4, 5],
[ 8, 9],
[12, 13]])
A2
array([[ 2, 3],
[ 6, 7],
[10, 11],
[14, 15]])
upper
array([[0, 1, 2, 3],
[4, 5, 6, 7]])
lower
array([[ 8, 9, 10, 11],
[12, 13, 14, 15]])
data = np.arange(16).reshape((4, 4))
data
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
X, y = np.hsplit(data, [-1])
X
array([[ 0, 1, 2],
[ 4, 5, 6],
[ 8, 9, 10],
[12, 13, 14]])
y
array([[ 3],
[ 7],
[11],
[15]])
numpy.array中的运算
给定一个向量，让向量中每一个数乘以2
a=(0,1,2)
a*2=(0,2,4)
n = 10
L = [i for i in range(n)]
2*L
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
A=[]
for e in L:
A.append(2*e)
A
[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]
L = np.arange(n)
A = 2*L
A
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])
Universal Functions
X = np.arange(1, 16).reshape((3,5))
X
array([[ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15]])
array([[ 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16]])
array([[ 2, 4, 6, 8, 10],
[12, 14, 16, 18, 20],
[22, 24, 26, 28, 30]])
1/X
array([[1. , 0.5 , 0.33333333, 0.25 , 0.2 ],
[0.16666667, 0.14285714, 0.125 , 0.11111111, 0.1 ],
[0.09090909, 0.08333333, 0.07692308, 0.07142857, 0.06666667]])
array([[ 0.84147098, 0.90929743, 0.14112001, -0.7568025 , -0.95892427],
[-0.2794155 , 0.6569866 , 0.98935825, 0.41211849, -0.54402111],
[-0.99999021, -0.53657292, 0.42016704, 0.99060736, 0.65028784]])
array([[ 3, 9, 27, 81, 243],
[ 729, 2187, 6561, 19683, 59049],
[ 177147, 531441, 1594323, 4782969, 14348907]], dtype=int32)
矩阵运算
X+Y
array([[ 2, 3, 4, 5, 6],
[ 7, 8, 9, 10, 11],
[12, 13, 14, 15, 16]])
X*Y
array([[ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15]])
X.T
array([[ 1, 6, 11],
[ 2, 7, 12],
[ 3, 8, 13],
[ 4, 9, 14],
[ 5, 10, 15]])
X.T.shape
(5, 3)
向量和矩阵的运算
聚合操作
import numpy as np
L = np.random.random(100)
L
array([0.95619151, 0.73353358, 0.71210247, 0.2427146 , 0.57043673,
0.57773404, 0.89274848, 0.12138544, 0.66083873, 0.16459271,
0.09435837, 0.5876144 , 0.86014445, 0.82936987, 0.65091808,
0.51832728, 0.00355049, 0.80309176, 0.35932938, 0.42014544,
0.2026436 , 0.63279787, 0.18935861, 0.1308497 , 0.75765845,
0.34158167, 0.52138487, 0.88302327, 0.44914216, 0.23902229,
0.33014086, 0.26650938, 0.79768204, 0.05551712, 0.12980746,
0.82262638, 0.36076783, 0.56970121, 0.83023273, 0.44767601,
0.2132831 , 0.56115445, 0.71657783, 0.7493205 , 0.58624783,
0.54759891, 0.0817732 , 0.40852941, 0.63205157, 0.12168885,
0.27480879, 0.07770505, 0.15726591, 0.14978044, 0.38535367,
0.70941476, 0.44518764, 0.01584702, 0.99491381, 0.90632665,
0.05199571, 0.86100897, 0.51224649, 0.0111548 , 0.49310591,
0.55102356, 0.27260476, 0.2311436 , 0.95858105, 0.66579831,
0.84015904, 0.14691185, 0.14394403, 0.30843116, 0.37016398,
0.31852964, 0.56240025, 0.4640979 , 0.80066784, 0.78735522,
0.84323067, 0.68824287, 0.31854825, 0.93794112, 0.40711455,
0.75336448, 0.5065076 , 0.8242313 , 0.48603164, 0.17872445,
0.79322194, 0.13924006, 0.71347858, 0.38300909, 0.70410853,
0.82867258, 0.58154578, 0.38693726, 0.39648041, 0.15039198])
48.824427939282955
48.82442793928298
0.0035504869521352234
0.9949138071844505
![TestLink导出用例转换工具(XML2Excel)[图]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACwAAAAAAQABAAACAkQBADs=)