In [156]: np.ones(3)
Out[156]: array([1., 1., 1.])
In [157]: np.ones((3,5))
Out[157]:
array([[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1.]])
In [158]:
In [158]: np.zeros(4)
Out[158]: array([0., 0., 0., 0.])
In [159]: np.zeros((2,5))
Out[159]:
array([[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.]])
In [160]:
In [146]: a = np.array([[1,3,5,2],[4,2,6,1]])
In [147]: print(a)
[[1 3 5 2]
[4 2 6 1]]
In [148]:
In [161]: np.arange(10)
Out[161]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
In [162]: np.arange(3,13)
Out[162]: array([ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])
In [163]: np.arange(3,13).reshape((2,5))
Out[163]:
array([[ 3, 4, 5, 6, 7],
[ 8, 9, 10, 11, 12]])
In [164]:
In [169]: np.arange(2,25,2)
Out[169]: array([ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24])
In [170]: np.arange(2,25,2).reshape(3,4)
Out[170]:
array([[ 2, 4, 6, 8],
[10, 12, 14, 16],
[18, 20, 22, 24]])
In [171]:
In [176]: np.linspace(1,10,4)
Out[176]: array([ 1., 4., 7., 10.])
In [177]:
In [7]: a = np.array([[1,2],[3,4]])
In [8]: b = np.arange(5,9).reshape((2,3))
In [10]: print(a)
[[1 2]
[3 4]]
In [11]: print(b)
[[5 6]
[7 8]]
In [12]:
In [12]: a+b
Out[12]:
array([[ 6, 8],
[10, 12]])
In [13]: a-b
Out[13]:
array([[-4, -4],
[-4, -4]])
In [14]: a*b # 对应元素相乘
Out[14]:
array([[ 5, 12],
[21, 32]])
In [17]: a/b
Out[17]:
array([[0, 0],
[0, 0]])
In [18]:
In [18]: a**2
Out[18]:
array([[ 1, 4],
[ 9, 16]])
In [19]:
In [15]: np.dot(a,b) # 矩阵乘法
Out[15]:
array([[19, 22],
[43, 50]])
In [16]: a.dot(b)
Out[16]:
array([[19, 22],
[43, 50]])
In [17]:
In [54]: print(a)
[[ 2 3 4 5]
[ 6 7 8 9]
[10 11 12 13]]
In [55]: np.sum(a)
Out[55]: 90
In [56]: np.min(a)
Out[56]: 2
In [57]: np.max(a)
Out[57]: 13
In [58]:
In [58]: np.sum(a,axis=1)
Out[58]: array([14, 30, 46])
In [59]: np.sum(a,axis=0)
Out[59]: array([18, 21, 24, 27])
In [60]:
# 三角函数结合random生成一组随机数据
In [74]: N = 10
In [75]: t = np.linspace(0, 2*np.pi, N)
In [76]: print(t)
[0. 0.6981317 1.3962634 2.0943951 2.7925268 3.4906585
4.1887902 4.88692191 5.58505361 6.28318531]
In [77]: y = np.sin(t) + 0.02*np.random.randn(N)
In [78]: print(y)
[-0.00947902 0.64196198 0.96567468 0.89394571 0.33830193 -0.3015316
-0.86943758 -0.95954123 -0.62526393 0.02872202]
In [79]: M = 3
In [80]: for ii, vv in zip(np.random.rand(M)*N, np.random.randn(M)):
...: y[int(ii):] += vv
...:
In [81]: print(y)
[-0.00947902 0.64196198 1.47685437 1.55309848 0.99745469 0.35762117
-0.21028481 -0.30038846 -0.29746375 0.35652221]
In [82]:
In [101]: a = np.arange(2,14).reshape((3,4))
In [102]: print(a)
[[ 2 3 4 5]
[ 6 7 8 9]
[10 11 12 13]]
In [103]: print(np.argmin(a)) # 最小值的索引
0
In [104]: print(np.argmax(a)) # 最大值的索引
11
In [105]: np.cumsum(a) # 从0元素开始的累计和
Out[105]: array([ 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90])
In [106]: np.cumprod(a) # 从1元素开始的累计乘
Out[106]:
array([ 2, 6, 24, 120, 720,
5040, 40320, 362880, 3628800, 39916800,
479001600, 6227020800])
In [107]:
In [129]: a
Out[129]:
array([[ 2, 3, 4, 5],
[ 6, 7, 8, 9],
[10, 11, 12, 13]])
In [130]: np.cumsum(a,axis=1)
Out[130]:
array([[ 2, 5, 9, 14],
[ 6, 13, 21, 30],
[10, 21, 33, 46]])
In [131]: np.cumsum(a,axis=0)
Out[131]:
array([[ 2, 3, 4, 5],
[ 8, 10, 12, 14],
[18, 21, 24, 27]])
In [132]:
In [133]: np.cumprod(a,axis=1)
Out[133]:
array([[ 2, 6, 24, 120],
[ 6, 42, 336, 3024],
[ 10, 110, 1320, 17160]])
In [134]: np.cumprod(a,axis=0)
Out[134]:
array([[ 2, 3, 4, 5],
[ 12, 21, 32, 45],
[120, 231, 384, 585]])
In [135]:
In [146]: a = np.array([[1,3,5,2],[4,2,6,1]])
In [147]: print(a)
[[1 3 5 2]
[4 2 6 1]]
In [148]: a.shape
Out[148]: (2, 4)
In [149]: a.ndim
Out[149]: 2
In [150]: a.size
Out[150]: 8
In [151]: np.diff(a) # 累差运算
Out[151]:
array([[ 2, 2, -3],
[-2, 4, -5]])
In [152]: np.diff(a,axis=1)
Out[152]:
array([[ 2, 2, -3],
[-2, 4, -5]])
In [153]: np.diff(a,axis=0)
Out[153]: array([[ 3, -1, 1, -1]])
In [154]:
In [108]: a = np.array([10,7,11,9,8,13,12,9])
In [109]: a.ndim
Out[109]: 1
In [110]: a.shape
Out[110]: (8,)
In [111]: a.size
Out[111]: 8
In [112]: a.mean() # 均值
Out[112]: 9.875
In [113]: a.var() # 方差
Out[113]: 3.609375
In [114]: a.std() # 标准差
Out[114]: 1.899835519196333
In [115]:
In [117]: np.median(a) # 中位数
Out[117]: 9.5
In [118]:
In [138]: z = (a-a.mean())/a.std() # z-score
In [139]: print(z)
[ 0.06579517 -1.5132889 0.59215653 -0.46056619 -0.98692754 1.64487924
1.11851788 -0.46056619]
In [140]:
In [198]: a = np.arange(-3,3).reshape((2,3))
In [199]: a
Out[199]:
array([[-3, -2, -1],
[ 0, 1, 2]])
In [200]: np.nonzero(a) # 查找非0元素
Out[200]: (array([0, 0, 0, 1, 1]), array([0, 1, 2, 1, 2]))
In [201]: print(np.nonzero(a))
(array([0, 0, 0, 1, 1]), array([0, 1, 2, 1, 2]))
In [202]:
In [207]: a = np.arange(14,2,-1).reshape((3,4))
In [208]: print(a)
[[14 13 12 11]
[10 9 8 7]
[ 6 5 4 3]]
In [209]: np.sort(a) # 排序
Out[209]:
array([[11, 12, 13, 14],
[ 7, 8, 9, 10],
[ 3, 4, 5, 6]])
In [210]:
In [210]: np.sort(a,axis=1)
Out[210]:
array([[11, 12, 13, 14],
[ 7, 8, 9, 10],
[ 3, 4, 5, 6]])
In [211]: np.sort(a,axis=0)
Out[211]:
array([[ 6, 5, 4, 3],
[10, 9, 8, 7],
[14, 13, 12, 11]])
In [212]:
# 矩阵的转置
In [212]: a = np.arange(14,2,-1).reshape((3,4))
In [213]: print(a)
[[14 13 12 11]
[10 9 8 7]
[ 6 5 4 3]]
In [214]:
In [215]: print(np.transpose(a))
[[14 10 6]
[13 9 5]
[12 8 4]
[11 7 3]]
In [216]: a.T
Out[216]:
array([[14, 10, 6],
[13, 9, 5],
[12, 8, 4],
[11, 7, 3]])
In [217]:
In [220]: a.T.dot(a) # 先转置，再进行矩阵乘法
Out[220]:
array([[332, 302, 272, 242],
[302, 275, 248, 221],
[272, 248, 224, 200],
[242, 221, 200, 179]])
In [221]:
# 矩阵的clip，处理最大值和最小值
In [221]: print(a)
[[14 13 12 11]
[10 9 8 7]
[ 6 5 4 3]]
In [222]: np.clip(a,5,11)
Out[222]:
array([[11, 11, 11, 11],
[10, 9, 8, 7],
[ 6, 5, 5, 5]])
In [223]:
numpy.convolve(weights,array)
weight = [a,b,c]
array = [i,j,k,m,n]
Result：[ai, bi+aj, ci+bj+ak, cj+bk+am, ck+bm+an, cm+bn, cn][N-1:-N+1]
针对移动平均算法来预测下一个数据，越接近待预测点的数据权重越大，
那么就需要让 i, j, k, m, n 的系数逐渐增大即可；即让 a > b > c ，并且 a+b+c=1 。
示例：
In [223]: weight = np.ones(3)/3
In [224]: print(weight)
[0.33333333 0.33333333 0.33333333]
In [225]: arr = np.array([8,11,9,7,10])
In [226]: np.convolve(weight,arr)
Out[226]:
array([2.66666667, 6.33333333, 9.33333333, 9. , 8.66666667,
5.66666667, 3.33333333])
In [227]:
In [227]: weight = np.array([0.8,0.1,0.1])
In [228]: np.convolve(weight,arr)
Out[228]: array([6.4, 9.6, 9.1, 7.6, 9.6, 1.7, 1. ])
In [229]:
# 生成随机浮点数，范围是在0.0~1.0之间
In [19]: a = np.random.random((2,3))
In [20]: print(a)
[[0.02185901 0.69585563 0.04555439]
[0.37331857 0.32903986 0.62448246]]
In [21]:
# 生成随机整数，可指定起止范围
In [48]: np.random.randint(3)
Out[48]: 2
In [49]: np.random.randint(low=3,high=9)
Out[49]: 6
In [50]: np.random.randint(low=3,high=9,size=(3,4))
Out[50]:
array([[5, 6, 7, 8],
[8, 7, 3, 8],
[5, 4, 5, 5]])
In [51]:
In [68]: np.random.randint(low=-5,high=2,size=(3,4))
Out[68]:
array([[-4, -4, -2, 1],
[ 1, 0, 0, 1],
[-4, -3, 1, -5]])
In [69]:
# 生成正态分布，又名高斯分布（Gaussian distribution）随机数
In [64]: np.random.normal()
Out[64]: -0.5399414561419419
In [65]: np.random.normal(loc=0,scale=1,size=(2,3))
Out[65]:
array([[-0.50318082, -0.38614219, 0.30450427],
[ 0.41711087, 0.29990928, -0.7843322 ]])
In [66]:
In [66]: np.random.normal(loc=2,scale=3,size=(2,3))
Out[66]:
array([[ 3.37067379, 6.23517315, 2.3267659 ],
[ 6.46832646, -2.76363304, 5.77883853]])
In [67]:
# 生成标准正态分布（"standard normal" distribution）随机数，标准正态分布的平均值为0，方差为1，服从u（0，1）分布。
In [83]: np.random.randn()
Out[83]: 0.502482341264108
In [84]: np.random.randn(3,4)
Out[84]:
array([[ 0.34507555, -0.26868132, -0.56103417, 0.86176617],
[-0.16535555, -0.38045904, 0.48176385, -1.09005206],
[-0.60780266, 1.74113117, -0.72427329, -0.51232408]])
In [85]:
# 生成[0, 1)间随机数
In [99]: np.random.rand()
Out[99]: 0.607701127768974
In [100]: np.random.rand(3,4)
Out[100]:
array([[0.73020695, 0.53993878, 0.46693879, 0.82611629],
[0.76117076, 0.16522599, 0.85129611, 0.74448772],
[0.6450236 , 0.49994053, 0.04115063, 0.30081311]])
In [101]: