numpy 簡介
numpy的存在使得python擁有強大的矩陣計算能力，不亞於matlab。
官方文檔(https://docs.scipy.org/doc/numpy-dev/user/quickstart.html)
各種用法介紹
首先是numpy中的數據類型，ndarray類型，和標准庫中的array.array並不一樣。
ndarray的一些屬性
ndarray.ndim
the number of axes (dimensions) of the array. In the Python world, the number of dimensions is referred to as rank.
ndarray.shape
the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the rank, or number of dimensions, ndim.
ndarray.size
the total number of elements of the array. This is equal to the product of the elements of shape.
ndarray.dtype
an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples.
ndarray.itemsize
the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize.
ndarray.data
the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we will access the elements in an array using indexing facilities.
ndarray的創建
>>> import numpy as np
>>> a = np.array([2,3,4])
>>> a
array([2, 3, 4])
>>> a.dtype
dtype('int64')
>>> b = np.array([1.2, 3.5, 5.1])
>>> b.dtype
dtype('float64')
二維的數組
>>> b = np.array([(1.5,2,3), (4,5,6)])
>>> b
array([[ 1.5, 2. , 3. ],
[ 4. , 5. , 6. ]])
創建時指定類型
>>> c = np.array( [ [1,2], [3,4] ], dtype=complex )
>>> c
array([[ 1.+0.j, 2.+0.j],
[ 3.+0.j, 4.+0.j]])
創建一些特殊的矩陣
>>> np.zeros( (3,4) )
array([[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.],
[ 0., 0., 0., 0.]])
>>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified
array([[[ 1, 1, 1, 1],
[ 1, 1, 1, 1],
[ 1, 1, 1, 1]],
[[ 1, 1, 1, 1],
[ 1, 1, 1, 1],
[ 1, 1, 1, 1]]], dtype=int16)
>>> np.empty( (2,3) ) # uninitialized, output may vary
array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260],
[ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]])
創建一些有特定規律的矩陣
>>> np.arange( 10, 30, 5 )
array([10, 15, 20, 25])
>>> np.arange( 0, 2, 0.3 ) # it accepts float arguments
array([ 0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8])
>>> from numpy import pi
>>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2
array([ 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ])
>>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points
>>> f = np.sin(x)
一些基本的運算
加減乘除三角函數邏輯運算
>>> a = np.array( [20,30,40,50] )
>>> b = np.arange( 4 )
>>> b
array([0, 1, 2, 3])
>>> c = a-b
>>> c
array([20, 29, 38, 47])
>>> b**2
array([0, 1, 4, 9])
>>> 10*np.sin(a)
array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854])
>>> a<35
array([ True, True, False, False], dtype=bool)
矩陣運算
matlab中有.* ,./等等
但是在numpy中，如果使用+，-，×，/優先執行的是各個點之間的加減乘除法
如果兩個矩陣（方陣）可既以元素之間對於運算，又能執行矩陣運算會優先執行元素之間的運算
>>> import numpy as np
>>> A = np.arange(10,20)
>>> B = np.arange(20,30)
>>> A + B
array([30, 32, 34, 36, 38, 40, 42, 44, 46, 48])
>>> A * B
array([200, 231, 264, 299, 336, 375, 416, 459, 504, 551])
>>> A / B
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
>>> B / A
array([2, 1, 1, 1, 1, 1, 1, 1, 1, 1])
如果需要執行矩陣運算，一般就是矩陣的乘法運算
>>> A = np.array([1,1,1,1])
>>> B = np.array([2,2,2,2])
>>> A.reshape(2,2)
array([[1, 1],
[1, 1]])
>>> B.reshape(2,2)
array([[2, 2],
[2, 2]])
>>> A * B
array([2, 2, 2, 2])
>>> np.dot(A,B)
8
>>> A.dot(B)
8
一些常用的全局函數
>>> B = np.arange(3)
>>> B
array([0, 1, 2])
>>> np.exp(B)
array([ 1. , 2.71828183, 7.3890561 ])
>>> np.sqrt(B)
array([ 0. , 1. , 1.41421356])
>>> C = np.array([2., -1., 4.])
>>> np.add(B, C)
array([ 2., 0., 6.])
矩陣的索引分片遍歷
>>> a = np.arange(10)**3
>>> a
array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729])
>>> a[2]
8
>>> a[2:5]
array([ 8, 27, 64])
>>> a[:6:2] = -1000 # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000
>>> a
array([-1000, 1, -1000, 27, -1000, 125, 216, 343, 512, 729])
>>> a[ : :-1] # reversed a
array([ 729, 512, 343, 216, 125, -1000, 27, -1000, 1, -1000])
>>> for i in a:
... print(i**(1/3.))
...
nan
1.0
nan
3.0
nan
5.0
6.0
7.0
8.0
9.0
矩陣的遍歷
>>> import numpy as np
>>> b = np.arange(16).reshape(4, 4)
>>> for row in b:
... print(row)
...
[0 1 2 3]
[4 5 6 7]
[ 8 9 10 11]
[12 13 14 15]
>>> for node in b.flat:
... print(node)
...
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
矩陣的特殊運算
改變矩陣形狀--reshape
>>> a = np.floor(10 * np.random.random((3,4)))
>>> a
array([[ 6., 5., 1., 5.],
[ 5., 5., 8., 9.],
[ 5., 5., 9., 7.]])
>>> a.ravel()
array([ 6., 5., 1., 5., 5., 5., 8., 9., 5., 5., 9., 7.])
>>> a
array([[ 6., 5., 1., 5.],
[ 5., 5., 8., 9.],
[ 5., 5., 9., 7.]])
resize和reshape的區別
resize會改變原來的矩陣，reshape並不會
>>> a
array([[ 6., 5., 1., 5.],
[ 5., 5., 8., 9.],
[ 5., 5., 9., 7.]])
>>> a.reshape(2,-1)
array([[ 6., 5., 1., 5., 5., 5.],
[ 8., 9., 5., 5., 9., 7.]])
>>> a
array([[ 6., 5., 1., 5.],
[ 5., 5., 8., 9.],
[ 5., 5., 9., 7.]])
>>> a.resize(2,6)
>>> a
array([[ 6., 5., 1., 5., 5., 5.],
[ 8., 9., 5., 5., 9., 7.]])
矩陣的合並
>>> a = np.floor(10*np.random.random((2,2)))
>>> a
array([[ 8., 8.],
[ 0., 0.]])
>>> b = np.floor(10*np.random.random((2,2)))
>>> b
array([[ 1., 8.],
[ 0., 4.]])
>>> np.vstack((a,b))
array([[ 8., 8.],
[ 0., 0.],
[ 1., 8.],
[ 0., 4.]])
>>> np.hstack((a,b))
array([[ 8., 8., 1., 8.],
[ 0., 0., 0., 4.]])