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Numpy快速上手指南 —- 进阶篇

python

1 2	import numpy as np import math

高级索引技巧

一维数组索引

python

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a = np.arange(12)**2
i = np.array([1,1,3,8,5])
a[i]

array([ 1,  1,  9, 64, 25], dtype=int32)

python

1 2	j = np.array( [ [ 3, 4], [ 9, 7 ] ] ) # a bidimensional array of indices a[j]

array([[ 9, 16],
       [81, 49]], dtype=int32)

python

palette = np.array( [ [0,0,0],                # 黑色
                   [255,0,0],              # 红色
                   [0,255,0],              # 绿色
                   [0,0,255],              # 蓝色
                   [255,255,255] ] )       # 白色
image = np.array( [ [ 0, 1, 2, 0 ],           # each value corresponds to a color in the palette
                 [ 0, 3, 4, 0 ]  ] )
palette[image]

array([[[  0,   0,   0],
        [255,   0,   0],
        [  0, 255,   0],
        [  0,   0,   0]],

       [[  0,   0,   0],
        [  0,   0, 255],
        [255, 255, 255],
        [  0,   0,   0]]])

python

1 2	a = np.arange(12).reshape(3,4) a

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

多维数组索引

多维的索引数组也是可以的.每一维的数组必须有相同的形状.

python

1 2	i = np.array( [ [0,1], # indices for the first dim of a [1,2] ] )

python

1 2	j = np.array( [ [2,1], # indices for the second dim [3,3] ] )

python

a[i,j]

array([[ 2,  5],
       [ 7, 11]])

python

1	a[i,j] #broadcast

array([[ 2,  5],
       [ 7, 11]])

python

a[:,j]

array([[[ 2,  1],
        [ 3,  3]],

       [[ 6,  5],
        [ 7,  7]],

       [[10,  9],
        [11, 11]]])

把i,j放在一个tuple里当成索引也可以

python

1 2	l = (i,j) a[l]

array([[ 2,  5],
       [ 7, 11]])

例子: 寻找多个数列的最大值

python

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time = np.linspace(20, 145, 5)                 # time scale
data = np.sin(np.arange(20)).reshape(5,4)         # 4 time-dependent series
time

array([ 20.  ,  51.25,  82.5 , 113.75, 145.  ])

python

data

array([[ 0.        ,  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],
       [-0.28790332, -0.96139749, -0.75098725,  0.14987721]])

python

1 2	ind = data.argmax(axis=0) # index of the maxima for each series ind

array([2, 0, 3, 1], dtype=int64)

python

1 2	data_max = data[ind, range(data.shape[1])] # => data[ind[0],0], data[ind[1],1]... data_max

array([0.98935825, 0.84147098, 0.99060736, 0.6569866 ])

python

1	np.all(data_max == data.max(axis=0))

True

例子: 数组索引作为目标赋值

python

1	a = np.arange(5)

python

array([0, 1, 2, 3, 4])

python

1 2	a[[1,2,3]] = 0 a

array([0, 0, 0, 0, 4])

例子:当一个索引列表包含重复时，赋值被多次完成，保留最后的值

python

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a = np.arange(5)
a[[0,0,2]]=[1,2,3]
a

array([2, 1, 3, 3, 4])

通过布尔数组索引

索引

python

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a = np.arange(12).reshape(3,4)
b = a > 4
b       # b is a boolean with a's shape

array([[False, False, False, False],
       [False,  True,  True,  True],
       [ True,  True,  True,  True]])

赋值

python

1 2	a[b] = 0 # All elements of 'a' higher than 4 become 0 a

array([[0, 1, 2, 3],
       [4, 0, 0, 0],
       [0, 0, 0, 0]])

多维布尔数组索引

python

1 2	a = np.arange(12).reshape(3,4) a

array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

python

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b1 = np.array([False,True,True])
b2 = np.array([True,False,True,False])
a[b1,:]

array([[ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

python

a[b1]

array([[ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

python

a[:,b2]

array([[ 0,  2],
       [ 4,  6],
       [ 8, 10]])

python

a[b1,b2]

array([ 4, 10])

np.ix_索引

np.ix_返回每一维相互组合的索引

python

1	a = ap.arange(10).reshape(2, 5)

python

1	ixgrid = np.ix_([0, 1], [2, 4])

python

a[ixgrid]

array([[2, 4],
       [7, 9]])

高级例子, 用np.ix_来计算所有元素组合的结果

python

a = np.array([2,3,4,5])
b = np.array([8,5,4])
c = np.array([5,4,6,8,3])
ax,bx,cx = np.ix_(a,b,c)

python

ax

array([[[2]],

       [[3]],

       [[4]],

       [[5]]])

python

bx

array([[[8],
        [5],
        [4]]])

python

cx

array([[[5, 4, 6, 8, 3]]])

python

1	ax.shape, bx.shape, cx.shape

((4, 1, 1), (1, 3, 1), (1, 1, 5))

python

1	result = ax + bx * cx

python

result

array([[[42, 34, 50, 66, 26],
        [27, 22, 32, 42, 17],
        [22, 18, 26, 34, 14]],

       [[43, 35, 51, 67, 27],
        [28, 23, 33, 43, 18],
        [23, 19, 27, 35, 15]],

       [[44, 36, 52, 68, 28],
        [29, 24, 34, 44, 19],
        [24, 20, 28, 36, 16]],

       [[45, 37, 53, 69, 29],
        [30, 25, 35, 45, 20],
        [25, 21, 29, 37, 17]]])

python

1	result[3, 2, 4]

python

1	a[3] + b[2] * c[4]

线性代数

运算

python

1 2	a = np.array([[1.0, 2.0], [3.0, 4.0]]) print (a)

[[1. 2.]
 [3. 4.]]

转置

python

1	a.transpose()

Object `solve` not found.

逆矩阵

python

1	np.linalg.inv(a)

array([[-2. ,  1. ],
       [ 1.5, -0.5]])

单位对角矩阵

python

np.eye(2)

array([[1., 0.],
       [0., 1.]])

点积

python

1 2	j = np.array([[0.0, -1.0], [1.0, 0.0]]) np.dot(j, j) # matrix product

array([[-1.,  0.],
       [ 0., -1.]])

对角数据和

python

1	a = np.array([[1.0, 2.0], [3.0, 4.0]])

python

1	np.trace(a)

5.0

矩阵点乘方程求解

python

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a = np.array([[1.0, 2.0], [3.0, 4.0]])
y = np.array([[5.], [7.]])
np.linalg.solve(a, y)

array([[-3.],
       [ 4.]])

1(-3) + 24 = 3(-3) + 44 = 7

python

1	np.dot(np.array([[1.0, 2.0], [3.0, 4.0]]), np.array([[-3.], [ 4.]]))

array([[5.],
       [7.]])

特征值和特征向量

python

1 2	j = np.array([[0.0, -1.0], [1.0, 0.0]]) np.linalg.eig(j)

(array([0.+1.j, 0.-1.j]),
 array([[0.70710678+0.j        , 0.70710678-0.j        ],
        [0.        -0.70710678j, 0.        +0.70710678j]]))

矩阵

略. 参考 Numpy快速上手指南 —- 进阶篇