3&4.numpy.array基础,创建numpy数组和矩阵

3.numpy.array基础

导入numpy

import numpy

numpy.__version__

'1.16.5'

也可以将numpy这个包命名

import numpy as np

np.__version__

'1.16.5'

python 中 list 的的特点

格式自由 list中的元素类型可以不统一

但效率低

L = [i for i in range(10)]
L

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

L[5] = 88
L

[0, 1, 2, 3, 4, 88, 6, 7, 8, 9]

L[3] = 'Machine'
L

[0, 1, 2, 'Machine', 4, 88, 6, 7, 8, 9]

限定元素类型的数组

import array

arr = array.array('i', [n for n in range(10)])
#括号中的 'i' 表示整型变量
arr

array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

arr[4]

4

arr[4] = 888
arr

array('i', [0, 1, 2, 3, 888, 5, 6, 7, 8, 9])

但不能使用 arr[4] = 'Machine' 修改元素的值，因为arr是整型数组

array的缺点是，没有将数组作为向量来看，因此没有向量或矩阵相关的运算

因此用到numpy

nparr = np.array([i for i in range(10)])
#已经将numpy命名为np
nparr

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

nparr[4] = 888
nparr

array([  0,   1,   2,   3, 888,   5,   6,   7,   8,   9])

nparr.dtype
#查看存储的哪种类型的数据

dtype('int32')

#如果传给nparr一个浮点数，会自动取整
nparr[3] = 9.99
nparr

array([ 0, 1, 2, 9, 888, 5, 6, 7, 8, 9])

#如果传给numpy.array的元素中包含浮点数，则数组类型会变为浮点型
nparr1 = np.array([0, 1, 2.2])
nparr1.dtype

dtype('float64')

其他创建numpy.array的方法

np.zeros(10)

array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])

np.zeros(10).dtype
# 默认类型为浮点型

dtype('float64')

#创建整型零数组
np.zeros(10, dtype = int)

array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])

#创建二维数组
np.zeros((3, 5))

array([[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.]])

np.zeros(shape = (3, 5), dtype = int)

array([[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])

#全为1的数组
np.ones(10)

array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

np.ones((3, 5))

array([[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.]])

#创建一个全为指定数据的二维数组
np.full((3, 5), 233)
#注：默认数据类型为整型

array([[233, 233, 233, 233, 233],
[233, 233, 233, 233, 233],
[233, 233, 233, 233, 233]])

#也可以用如下格式
np.full(shape = (3, 5), fill_value = 233.6)

array([[233.6, 233.6, 233.6, 233.6, 233.6],
[233.6, 233.6, 233.6, 233.6, 233.6],
[233.6, 233.6, 233.6, 233.6, 233.6]])

#如果写出了参数名字，则可以调换顺序
np.full(fill_value = 233, shape = (3, 5))

array([[233, 233, 233, 233, 233],
[233, 233, 233, 233, 233],
[233, 233, 233, 233, 233]])

numpy.arange

L = [i for i in range(0, 20, 2)]
#(起始，终止，步长)，不包含终止数,步长不可以是浮点数
L

[0, 2, 4, 6, 8, 10, 12, 14, 16, 18]

np.arange(0, 20, 2)

array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18])

np.arange(0, 10)

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

np.arange(10)

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

np.arange(0, 1, 0.1)
#步长可以是浮点数

array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])

linspace

np.linspace(0, 20, 10)
#起始点0，终止点20，共截取10个点，包含0和20

array([ 0. , 2.22222222, 4.44444444, 6.66666667, 8.88888889,
11.11111111, 13.33333333, 15.55555556, 17.77777778, 20. ])

#如果要以步长为2进行截取
np.linspace(0, 20, 11)

array([ 0., 2., 4., 6., 8., 10., 12., 14., 16., 18., 20.])

random

np.random.randint(0, 10)
#生成0到9之间的随机数，不包含10

8

np.random.randint(0, 10, 5)
#生成5个随机数组成的数组

array([5, 8, 2, 9, 2])

np.random.randint(3, 12, size = 10)

array([ 7, 6, 4, 6, 11, 4, 11, 5, 5, 6])

#也可生成二维数组
np.random.randint(1, 20, size = (4, 4))

array([[ 1, 14, 12, 5],
[ 7, 14, 4, 3],
[14, 17, 14, 7],
[19, 12, 8, 10]])

在python中，上述随机数通过随机种子产生，如果在以后的实验中想使用同一组随机数，则要指定种子，如下

np.random.seed(89)

np.random.randint(1, 20, size = (4, 4))

array([[ 5, 14, 12, 6],
[ 9, 19, 2, 8],
[ 1, 18, 7, 2],
[ 7, 8, 14, 18]])

np.random.seed(89)
np.random.randint(1, 20, size = (4, 4))

array([[ 5, 14, 12, 6],
[ 9, 19, 2, 8],
[ 1, 18, 7, 2],
[ 7, 8, 14, 18]])

#生成0到1之间的随机浮点数
np.random.random()

0.49308492335080867

np.random.random(10)

array([0.37258734, 0.9756292 , 0.40189585, 0.89878196, 0.71335081,
0.20629155, 0.23740199, 0.09838872, 0.38509579, 0.83206468])

np.random.random(size = 10)

array([0.53031515, 0.61196362, 0.24538715, 0.04081728, 0.86292302,
0.09864514, 0.75721596, 0.84735109, 0.59883511, 0.72059833])

np.random.random((3, 4))

array([[0.64352003, 0.94103595, 0.5552627 , 0.04702374],
[0.56098571, 0.31018331, 0.33095341, 0.95772773],
[0.81792851, 0.01927153, 0.75940938, 0.40838984]])

以上的随机数是在0到1之间均匀分布，而我们有时想得到正态分布的随机数

np.random.normal()
#均值为0，方差为1的随机浮点数

1.289513432712115

np.random.normal(10,100)
#均值为10，方差为100的随机数

21.288798339880664

np.random.normal(0, 1, size = (3, 4))
#均值为0，方差为1 ，三行四列随机数组

array([[-0.84328947, -0.16348222, -1.26849029, -2.3224809 ],
[ 0.28296887, -0.4126417 , -0.34244338, -0.48110948],
[-0.13713219, 1.20263041, 0.43110683, -1.71883176]])

help(np.random.normal)
#查看函数或模块文档，也可以用如下格式
# 函数名? 模块名?

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()

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