“视之不见名曰夷，听之不闻名曰希，搏之不得名曰微。
此三者不可致诘，故混而为一。
一者，其上不皦，其下不昧。
绳绳不可名，复归于无物，是谓无状之状、无物之象，是谓惚恍。
迎之不见其首，随之不见其后。
执古之道，以御今之有，能知古始，是谓道纪。”[1]
SciPy
世界上著名的Python开源科学计算库。
官网（scipy.org）：能啃英文的还是经常去这里看看。
SciPy函数库在NumPy库的基础上增加了众多的数学、科学以及工程计算中常用的库函数。它的不同子模块相应于不同的应用，像插值、积分、优化、图像处理、统计、特殊函数等等。
常用子模块
| 子模块 | 描述 |
|---|---|
| scipy.cluster | 聚类工具：矢量量化 / K-均值 |
| scipy.constants | 物理和数学常数 |
| scipy.fftpack | 快速傅里叶变换 |
| scipy.integrate | 数值积分 |
| scipy.interpolate | 插值：进行数据处理和可视化分析的常见操作，基于Python的SciPy支持一维和二维的插值运算。 |
| scipy.io | 数据输入输出 |
| scipy.linalg | 线性代数函数库，如：解线性方程组、最小二乘解、特征值和特征向量、奇异值分解等 |
| scipy.ndimage | n维图像包，提供了有关数学形态学的方法 |
| scipy.odr | 正交距离回归 |
| scipy.optimize | 优化和拟合库 |
| scipy.signal | 信号处理 |
| scipy.sparse | 稀疏矩阵 |
| scipy.spatial | 空间数据结构和算法 |
| scipy.special | 特殊数学函数 |
| scipy.stats | 统计 |
使用scipy之前要先导入包，建议不能像numpy那样全部导入，使用哪个子模块导入哪个子模块，如下：
import numpy as np
import pandas as pd
from scipy import io as spio
scipy.io文件的输入和输出
numpy、pandas、scipy.io均可以对文件进行操作。
- numpy
np.load()
np.loadtxt()
np.genfromtxt()
np.recfromcsv()
np.recfromtxt()
……
- pandas
pd.read_csv()
pd.read_excel()
pd.read_html()
……
- scipy.io
spio.loadmat()
spio.savemat()
对上述方法的使用，在之后的分解文章中在介绍，现在先以spio举个例子，创建一个3行4列的矩阵，保存然后读取：
a = np.arange(12).reshape(3,4)
spio.savemat('file.mat',{'a':a})
datas = spio.loadmat('file.mat',struct_as_record=True)
datas
输出：
{'__globals__': [],
'__header__': b'MATLAB 5.0 MAT-file Platform: posix, Created on: Sun Mar 18 10:41:36 2018',
'__version__': '1.0',
'a': array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])}
统计：分析随机数
scipy.stats包括统计工具和随机过程的概率过程。各个随机过程的随机数生成器可以从numpy.random中找到。
生成20个正态分布的随机数：
from scipy import stats
generates = stats.norm.rvs(size=20)
generates
输出：
array([ 0.09644491, -0.07552055, 2.4406988 , 0.22137236, -0.2266991 ,
1.93962117, 0.57879661, -0.03147269, -0.19289511, 0.40454166,
0.668479 , -1.27321257, -1.55462663, -0.73369392, 0.55564607,
0.85396381, -2.17697731, -1.02549411, 0.19205101, 2.7793757 ])
还记得reshape()方法吗，现在强化记忆一下，将generates改变为一个4行5列的矩阵：
generates.reshape(4,5)
输出：
array([[ 0.09644491, -0.07552055, 2.4406988 , 0.22137236, -0.2266991 ],
[ 1.93962117, 0.57879661, -0.03147269, -0.19289511, 0.40454166],
[ 0.668479 , -1.27321257, -1.55462663, -0.73369392, 0.55564607],
[ 0.85396381, -2.17697731, -1.02549411, 0.19205101, 2.7793757 ]])
接下来，我们拟合生成的一维数据，来生成均值和标准差：
mean,std = stats.norm.fit(generates)
mean,std
输出：
(0.17201995571492329, 1.2122988177111329)
stats.norm.rvs(size=xxx,loc=xxx,scale=xxx)有三个参数，其中loc为均值，scale为标准差
上述生成的正态分布的数据数量太小，我们增加到size=1000，来看几个校验方法：
array([ 5.17903592e-01, -4.84819825e-01, -2.17331819e+00,
-2.71978120e-03, 3.43398473e-01, -1.53672137e+00,
-7.80230954e-01, -1.38493510e-01, 8.64678941e-01,
-5.23193564e-01, 1.00355735e+00, 9.93139686e-02,
4.46330129e-01, -1.95042024e-01, -7.78248002e-01,
4.94678411e-01, 9.24668576e-01, 9.91269886e-01,
-3.34111264e-01, 5.35049208e-01, 4.66624215e-01,
8.74805164e-01, 1.21823570e-01, 5.81397820e-01,
-4.45018479e-01, 1.04672648e-01, 7.56344139e-01,
1.60198846e-01, -1.46477267e-01, -5.80502049e-01,
3.99681665e-02, 2.67920793e+00, -1.49332545e+00,
-1.39485255e+00, -1.62184979e-01, -3.05899731e-02,
4.97657829e-02, -2.30222899e-01, -9.49411984e-01,
-1.31184285e+00, -1.41967163e-01, -4.34813954e-01,
7.38725143e-01, 4.00598883e-01, 4.36436960e-01,
-4.09986450e-01, -2.07197222e-01, -3.25044931e-01,
-7.43910151e-01, -6.13570624e-01, -1.26727223e+00,
-3.73803851e-01, -8.48694345e-01, -2.75244179e+00,
-9.64321271e-01, 7.00534558e-01, 1.86793945e-01,
7.46039130e-01, -8.10518097e-01, 1.67235474e+00,
-1.50856260e+00, 5.20941828e-01, -7.67878811e-02,
2.32584136e+00, 1.49835809e+00, -9.05440571e-01,
-1.24178395e+00, 2.43911036e-01, -1.20667049e+00,
-9.16536280e-01, -4.49705301e-02, 2.30834507e-01,
-6.92527685e-02, -5.85348401e-02, 4.23071961e-01,
-1.07815974e-01, 5.28821852e-01, -3.22449511e-01,
-7.12439336e-01, -1.11656371e+00, 1.20476418e+00,
2.19543599e+00, -2.04023860e+00, 1.83482542e+00,
-1.49249174e+00, -2.68834446e-01, 1.95818755e-01,
-3.16677583e-01, -3.52805238e-01, 7.55090436e-01,
2.11162353e+00, -1.53078202e+00, 8.45645296e-01,
-5.20684353e-01, 8.41674068e-01, 1.27422749e+00,
-7.00928060e-01, -5.80290714e-01, 1.00358607e+00,
3.58235810e-01, -8.06690609e-01, -1.97432494e-01,
-1.85253776e+00, 1.21471527e+00, -1.32575833e+00,
2.20498984e-01, -7.59459595e-01, 6.54102341e-01,
-1.91811635e-01, -2.17006655e+00, 1.22757153e+00,
-1.46243654e-01, -6.36676291e-01, 3.02682605e-01,
1.36671612e+00, 1.57930512e+00, 4.04263941e-01,
1.28662572e+00, 2.49968315e-01, 4.06608797e-01,
-8.93212197e-01, 1.63066508e+00, 1.23779907e+00,
-7.84025604e-01, 3.12265366e-02, 6.51420464e-01,
1.78509544e-01, -2.68839046e-01, 1.15181648e-01,
-7.85364176e-01, 1.25247067e+00, 7.72137479e-01,
-1.18110763e+00, -1.78637662e-01, -1.13501810e+00,
-2.69113774e+00, 2.43586397e-01, 1.07776230e+00,
-1.33571329e+00, 1.56412663e+00, 7.68541531e-01,
-3.88497111e-01, -4.13440012e-01, 1.48619082e+00,
-2.81005932e+00, 4.76974689e-01, -4.83140098e-02,
-2.09960292e+00, -1.21598418e+00, 5.96742283e-01,
9.15847172e-01, 2.25765097e-03, 1.54535341e+00,
-1.47931509e+00, -2.10377317e+00, -1.45037025e+00,
4.57123894e-01, -1.94574739e+00, -6.80606280e-01,
4.76905629e-01, -1.23517489e+00, -6.88355573e-01,
9.43119808e-01, 1.67302968e+00, 7.11875143e-01,
1.64127917e+00, -2.94041677e-01, 1.54103126e-01,
-5.85416826e-01, 2.05999042e+00, 1.18738940e+00,
1.99531518e-01, -2.11101357e+00, -1.09363755e+00,
1.67983335e+00, 2.99285489e-01, 1.27744550e+00,
7.36959152e-01, 1.39125694e+00, -7.56751182e-01,
-5.90793756e-01, -3.86542077e-02, 1.81986351e+00,
-1.06014546e+00, -1.32346285e+00, -7.39927880e-01,
1.38212086e+00, -5.88060104e-01, -2.88610199e+00,
6.45039997e-01, 8.05223241e-01, 1.50847871e+00,
5.66306325e-01, -2.22879103e-02, -5.32065838e-01,
9.29596147e-01, -1.00062920e+00, -7.22940989e-01,
-6.88290586e-01, 1.49974723e-01, -3.69190936e-01,
6.43570526e-01, 1.40973583e+00, -1.09694233e+00,
-1.04788396e+00, 1.19138652e+00, -2.64696938e-01,
5.66860287e-01, 1.94722056e+00, 7.82355235e-01,
-9.22911261e-01, -7.43748090e-01, -7.18312223e-01,
3.61035218e-01, -8.02051485e-01, -1.25629229e+00,
-1.11254930e+00, -2.17500089e+00, -5.61117834e-01,
7.75492006e-01, 2.35203990e-01, 4.92911832e-01,
-4.41602973e-01, -1.43134294e+00, 1.24202334e+00,
-1.27805897e+00, -9.99866924e-01, -1.71438632e+00,
-1.79810070e+00, -1.03384505e+00, -7.38840610e-01,
2.59881883e+00, 7.58599225e-01, -2.91227055e-03,
-1.08525899e+00, -5.77098348e-01, 6.44084281e-02,
1.75831702e+00, -5.28591510e-01, 7.91843955e-01,
-1.61140464e-01, 5.41977031e-01, -2.29088856e-01,
-1.94228622e-01, 7.53444460e-01, -1.88985082e-01,
1.58162684e+00, -3.77083620e-01, 2.17144773e-01,
1.02065186e+00, 4.34620425e-01, -1.39747820e+00,
-1.61820516e+00, 1.56519909e+00, 1.17291478e+00,
9.61580854e-01, -1.12329763e+00, -7.24531012e-01,
-8.60033707e-01, -4.65461266e-01, 2.43657234e-01,
1.74302788e+00, 1.45065256e-01, 5.57160946e-01,
-3.26106670e-01, 2.32550557e-01, 1.06177286e+00,
-6.52730310e-01, 5.12634301e-02, 7.23664099e-03,
-5.97796521e-01, 2.94120803e-01, -2.00167304e+00,
-1.67558293e+00, -6.90594381e-01, 8.05322517e-01,
5.99708010e-01, 1.39946854e+00, -9.12745996e-01,
1.75628885e-01, -9.52621164e-01, -1.63553595e+00,
-5.73909001e-02, -2.13752327e-01, 9.08843189e-01,
7.54338387e-01, 6.86448693e-01, 6.37414903e-01,
-1.31553804e-01, -6.14035005e-02, 3.17722855e-01,
1.00010564e+00, 5.66189109e-01, -3.31229887e-01,
-1.26784197e+00, 5.65865115e-01, -1.34827415e+00,
-2.51836250e-02, 2.35383999e+00, -1.25618785e+00,
-8.50225265e-01, 1.85219586e-02, -1.19282292e+00,
1.79456724e-01, -7.46712449e-01, 2.14327724e+00,
-1.88544573e+00, -9.50946030e-01, 1.29378603e-01,
-2.16246079e+00, 1.50783186e+00, 2.31836239e-01,
3.67135954e-01, 9.25395949e-01, -7.43659199e-01,
-4.63261176e-01, 9.17578865e-01, 6.31962811e-01,
9.28821246e-01, 2.66833595e-01, 8.04378911e-01,
3.66038122e-01, 6.52047153e-01, 1.56307516e+00,
-8.89518014e-01, 3.75768229e-01, -1.09131872e+00,
4.55578487e-01, -7.76866845e-01, 1.80204670e-02,
-2.21759004e+00, 8.42415305e-01, 3.01510583e-02,
-7.76409734e-02, -4.11547372e-01, -7.55102539e-01,
2.10526334e-01, -1.58522602e+00, -1.35755283e+00,
-8.58103811e-01, -6.07561434e-01, 4.98475784e-01,
-4.65715879e-01, 6.33148206e-01, 2.60342758e-01,
5.99091782e-01, -2.26842082e+00, 1.40177396e+00,
-1.10198446e+00, 1.97454968e+00, 1.08095331e+00,
1.02132766e+00, 1.17832728e+00, 9.30481505e-01,
-1.38002873e+00, -6.23477342e-01, 7.77572604e-01,
-4.16849947e-02, 5.85935975e-02, -3.43723693e-01,
-1.29803389e+00, -7.85437549e-01, 2.09918513e+00,
-8.32242053e-02, 1.34756860e+00, 4.20666337e-01,
-6.23077815e-01, 3.83333826e-01, 1.07637533e+00,
-5.36798669e-01, 2.26184723e-01, -1.71843124e+00,
2.88628271e+00, -1.66953870e+00, -1.04128898e+00,
7.29756517e-02, 9.16548743e-01, 1.00785434e+00,
8.87834244e-01, 8.51919889e-01, -3.92304884e-01,
-2.90512265e-01, 5.32853057e-01, -7.79351441e-01,
-3.38995321e-01, -1.78560587e-01, -1.47718052e-01,
-1.22337547e+00, -4.14363367e-01, 1.78478385e+00,
8.81224994e-01, -2.86509296e-01, -1.47140331e+00,
2.00232111e-01, -1.08666985e+00, 8.80514936e-01,
8.45693941e-01, -1.26209911e+00, -1.43224161e+00,
1.29518395e+00, 7.95465444e-01, 5.34646568e-01,
-1.54851329e-01, -1.34519089e-01, 8.43642647e-01,
-7.02888200e-01, 1.10989002e+00, 7.10434593e-01,
1.27288284e+00, -7.02412620e-01, -2.47260071e-02,
1.86315225e+00, 3.18732128e-01, 2.85852319e-01,
-2.89281323e-02, 1.64308914e+00, 6.78905592e-01,
-2.23898207e+00, 6.45227361e-01, -2.10722006e-01,
-5.15334081e-02, 5.21718062e-01, -4.28589133e-01,
-3.32994850e-01, -9.96564936e-01, 4.43139233e-02,
8.34243415e-01, 2.17024275e-01, 6.48832946e-01,
1.39552210e+00, 5.45378253e-01, 1.23680500e+00,
1.36330855e+00, -6.91938875e-01, -1.32466443e+00,
1.40977288e-01, 1.87758626e+00, 3.10942400e-01,
-5.41959267e-01, 1.65385704e+00, 9.33377795e-01,
8.91428028e-02, -8.52805953e-01, 1.58607271e-01,
-5.52939995e-01, 3.30720367e-01, -9.75222073e-02,
9.08906746e-01, -4.77320009e-01, -6.70020450e-01,
-1.72473895e+00, 1.25450455e-02, 1.54247857e-02,
4.77084668e-01, 9.74026348e-01, 4.66092420e-01,
-1.86742467e-01, 5.19324577e-02, -1.79982729e+00,
-3.79270866e-01, 1.94272791e-02, -2.28700755e-02,
-1.44835613e+00, -6.77897503e-01, -3.76212765e-01,
8.90054522e-01, 1.25702761e+00, -1.17640677e-01,
1.73785564e+00, 3.47620655e-01, -9.67679848e-01,
9.38381020e-01, -2.02956574e+00, 1.03903973e-01,
6.89777724e-01, 1.15719338e+00, 5.02387689e-01,
1.65414778e+00, -4.79422190e-02, 4.71465797e-01,
4.71210862e-01, -2.95445178e-01, -9.27952481e-01,
-2.84518822e-01, 4.50762651e-01, 3.57838417e-01,
1.05556381e+00, -1.25461973e+00, 5.25710748e-01,
1.18346547e+00, -6.36131832e-02, 1.99996624e+00,
-4.05626343e-01, 5.02440229e-01, 3.06722159e-01,
1.12961182e+00, 2.71252139e-01, 1.02751704e+00,
6.58981355e-01, -1.33754483e+00, -1.88208047e+00,
9.65909726e-02, 2.17877879e+00, 1.25656355e-01,
1.97683689e+00, 1.88306505e+00, 3.93711759e-01,
1.11480906e+00, 5.43163950e-02, -9.70974509e-01,
5.91343120e-01, 6.03472480e-01, -1.41207708e-01,
-3.57354046e-01, 8.83769732e-01, -7.98277396e-01,
5.34234315e-01, -1.76017958e-01, -6.70988950e-01,
-9.92681894e-01, 1.02535613e+00, 7.86056043e-01,
1.08465761e+00, 9.28624272e-01, -1.29234470e-01,
-8.71688683e-01, -1.43193619e+00, -9.92240568e-01,
4.50317041e-01, -7.83975597e-01, 3.25406806e-01,
2.16974723e+00, -8.98345345e-01, -1.21821660e+00,
-2.05393549e-01, -6.97514681e-01, -9.84930653e-01,
2.92589293e-01, 1.75465316e+00, 2.89391096e-02,
-5.70833465e-01, -8.26878492e-01, 9.38516497e-02,
-1.10404029e+00, 4.79417673e-01, 9.06859139e-01,
2.84728627e-01, 7.81807537e-01, 5.94857977e-01,
-2.39704052e+00, -3.95317906e-01, 6.00154490e-01,
-2.21365308e+00, 9.59143039e-01, 6.61087230e-01,
-2.11076654e-01, -6.53571930e-01, 2.17956383e+00,
1.16704615e-01, 9.98712389e-01, -1.62361914e+00,
-2.50632371e-02, -4.45459791e-01, -2.28138155e-02,
-3.59760026e-01, -1.25357919e+00, 4.71340851e-02,
1.40328071e+00, -4.12591851e-01, 7.85809019e-01,
-1.70616337e+00, 1.88482833e+00, 1.96424743e+00,
-1.76543942e-01, -3.80571853e-01, 6.87730233e-01,
-1.71387963e-01, -2.61269664e-01, 1.94983128e+00,
7.46702909e-01, -1.55802291e-01, 1.54348840e-01,
4.84993880e-01, -6.36064763e-01, -7.77626949e-01,
6.92906103e-01, 5.86780454e-01, -1.71396865e+00,
1.12970593e+00, -7.31194601e-01, 1.44478155e+00,
6.40973401e-01, -3.27758206e-01, -4.14741504e-01,
-5.04916600e-01, -9.43490941e-01, 1.74154128e+00,
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-1.13579394e+00, 1.45329400e-01, -5.20324531e-01,
1.00047710e+00])
- 偏度 skewnes
概率分布的偏斜程度，我们需要做一个偏度检验。该检验有两个返回值，其中第二个返回值是p-value，即观察到的数据服从正态分布的概率，取值为0-1
stats.skewtest(generates)
输出：
SkewtestResult(statistic=0.73500197175279103, pvalue=0.4623382932849327)
- 峰度 kurtosis
概率分布的陡峭程度。该检验和偏度检验类似。
stats.skewtest(generates)
输出：
KurtosistestResult(statistic=0.45424860606802309, pvalue=0.64964990231896591)
- 正态性检验 normality test
检验数据服从正太分布的程度。
stats.normaltest(generates)
输出：
NormaltestResult(statistic=5.2884112715980525, pvalue=0.07106178025936169)
使用Scipy我们很方便的得到数据所在区域中某一百分比处的数值:
例如：得到75%处的值：
stats.scoreatpercentile(generates,75)
输出：
0.66404134087859246
或者反过来，给定一个值，获取处在的百分位：
stats.percentileofscore(generates,0.66)
输出：
74.8888888888889
文到此处，可以用matplotlib库画个图看看了，关于matlotlib我单独出一篇笔记来记录。
import matplotlib.pyplot as plt
plt.hist(generates)
plt.show()
输出图形：
normaltest.png
先写到这儿，scipy分多篇来记录吧。
-
老子《道德经》第十四章，老子故里，中国鹿邑。 ↩
