SciPy 是一个很强大的Python科学算法库，里面提供了很多科学计算方法和可视化的命令。这篇文章我不打算详细介绍SciPy，我只介绍几个我常用的结合NumPy可以发挥很大作用的功能，等年底有时间了我在好好研究一下完善教程。
import numpy as np
A = np.array([[1,2,3],[4,5,6],[7,8,8]])
线性代数（Linear Algebra）
linalg
from scipy import linalg
计算矩阵的行列式： 计算方法如图： https://wikimedia.org/api/rest_v1/media/math/render/svg/caae8224e861040e4075b43438a5beee31b9f700
# Compute the determinant of a matrix
linalg.det(A)
2.999999999999997
LU分解：
可以将矩阵分为一个上三角和一个下三角的乘积
A = P L U
P:置换矩阵 L：下单位三角矩阵 U：上单位三角矩阵
P, L, U = linalg.lu(A)
P
array([[ 0., 1., 0.],
[ 0., 0., 1.],
[ 1., 0., 0.]])
L
array([[ 1. , 0. , 0. ],
[ 0.14285714, 1. , 0. ],
[ 0.57142857, 0.5 , 1. ]])
U
array([[ 7. , 8. , 8. ],
[ 0. , 0.85714286, 1.85714286],
[ 0. , 0. , 0.5 ]])
np.dot(L,U)
array([[ 7., 8., 8.],
[ 1., 2., 3.],
[ 4., 5., 6.]])
还可以获得矩阵的特征值和特征量
EW, EV = linalg.eig(A)
EW
array([ 15.55528261+0.j, -1.41940876+0.j, -0.13587385+0.j])
EV
array([[-0.24043423, -0.67468642, 0.51853459],
[-0.54694322, -0.23391616, -0.78895962],
[-0.80190056, 0.70005819, 0.32964312]])
线性方程的求解：
v = np.array([[2],[3],[5]])
v
array([[2],
[3],
[5]])
s = linalg.solve(A,v)
s
array([[-2.33333333],
[ 3.66666667],
[-1. ]])
稀疏线性代数（Sparse Linear Algebra）
from scipy import sparse
# Row-based linked list sparse matrix
A = sparse.lil_matrix((1000, 1000))
A
<1000x1000 sparse matrix of type '<class 'numpy.float64'>'
with 0 stored elements in LInked List format>
A[0,:100] = np.random.rand(100)
A[1,100:200] = A[0,:100]
A.setdiag(np.random.rand(1000))
A
<1000x1000 sparse matrix of type '<class 'numpy.float64'>'
with 1199 stored elements in LInked List format>
线性代数稀疏矩阵（Linear Algebra for Sparse Matrices）
python
from scipy.sparse import linalg
# Convert this matrix to Compressed Sparse Row format.
A.tocsr()
<1000x1000 sparse matrix of type '<class 'numpy.float64'>'
with 1199 stored elements in Compressed Sparse Row format>
A = A.tocsr()
b = np.random.rand(1000)
linalg.spsolve(A, b)
array([ -5.95139017e+01, -2.11676791e+02, 8.71500295e-01,
8.80692794e+00, 3.92509926e-01, 4.07735642e+00,
1.03953304e+00, 8.67487093e-01, 1.04239180e+00,
5.64067865e-01, 5.66852537e-01, 1.44603822e+01,
3.08908787e-01, 3.84755428e+00, 2.59572317e-01,
2.01455584e+00, 7.22529398e-01, 3.10774145e-01,
5.99430111e-01, 9.94908214e-01, 8.16556218e-01,
6.13388488e-01, 5.14511939e-01, 5.93379845e-01,
7.16747945e+00, 1.12059905e+00, 2.57598133e+00,
7.23065380e-01, 1.11316273e+00, 5.71046430e-01,
6.07181161e-01, 1.88477643e+00, 2.30443811e+00,
2.57915718e-01, 6.98913445e+00, 1.64715697e+00,
4.05564022e-04, 4.70426767e+00, 1.72471960e+00,
2.96000041e+00, 6.40251397e-01, 1.48918343e+00,
8.51904053e-01, 1.02156309e-01, 1.46841021e+00,
8.74947320e-01, 7.52231106e-01, 1.51041285e-01,
7.01065652e-01, 6.27547877e-02, 1.70077118e+00,
9.52613806e-01, 1.42793388e-01, 1.96810160e+00,
6.17217022e-01, 7.49727082e-01, 5.33575097e-01,
1.03863941e+00, 7.95971011e-01, 4.07624501e-01,
9.92555378e-01, 2.56062399e+00, 8.64957711e-02,
3.78215912e-01, 2.93218489e+00, 1.35306106e+01,
3.60303628e-01, 1.85928272e+00, 5.91817421e-01,
6.39544270e-01, 3.47595949e+00, 3.22209117e-01,
1.04924603e+00, 1.12719687e+00, 1.55112764e-01,
1.16219431e+00, 3.65473227e+00, 4.04119747e+01,
4.85477473e-01, 1.03664719e+00, 2.00128063e+00,
1.11899447e+00, 1.09863788e+00, 6.99312178e-02,
1.27631136e-01, 7.01354698e-01, 1.28109561e+00,
3.17288887e+01, 1.94713261e+00, 6.06807841e-01,
2.16209114e+00, 3.16510515e-01, 3.46509075e-01,
3.87765636e-02, 7.49454229e-01, 1.89014767e+00,
9.56446406e-01, 1.39753660e+00, 1.64642641e-01,
1.11291261e+01, 2.59032211e-01, 4.09694844e+00,
3.50564965e-01, 1.46250570e+00, 9.09778475e-01,
1.00302659e+00, 1.05869890e+00, 1.37089837e+00,
1.46232392e+00, 2.26817086e+01, 2.54763517e+00,
1.72015651e-02, 3.93255428e-01, 9.05958975e-01,
6.44712395e-01, 3.32435819e-01, 6.50999863e-01,
6.53226070e+00, 4.11673234e-01, 1.08365682e+00,
7.05694616e+00, 7.80275599e-01, 8.77392585e+00,
1.05755003e+00, 4.67625818e-01, 6.68668107e-01,
3.40272305e+00, 1.50823944e+00, 5.82878212e-01,
3.05452189e+00, 6.32187436e-01, 3.42986659e+00,
5.57600878e-01, 3.25931305e-01, 7.97981917e+00,
6.44587244e+00, 1.42597878e+00, 3.70319360e-01,
3.71126567e-01, 1.70236004e+00, 1.03518121e-01,
8.82578313e-01, 6.23178047e+00, 2.16298869e+00,
3.75789585e-01, 5.75937620e-01, 5.72292769e+00,
4.28934757e-01, 1.55494164e+01, 2.15574198e+00,
1.27592849e+01, 2.49707772e+00, 3.12333905e+00,
9.29220586e-01, 1.16302042e+01, 5.39818008e-01,
8.34891177e-02, 3.59769306e-01, 2.65254890e+00,
6.87899732e-01, 4.16599825e-01, 2.99188085e-01,
7.21288043e-01, 1.21894551e+00, 1.25676521e-01,
2.44136202e+00, 2.62319992e-01, 3.63697530e-01,
1.52798424e+01, 6.23493693e-01, 9.69426593e-01,
8.86230339e-01, 9.87246007e+00, 1.18514195e+00,
3.00611256e+00, 3.98091656e+00, 1.57167221e+00,
1.58944113e-01, 1.77849706e-01, 8.97924127e-01,
5.17795100e-01, 8.20969996e+00, 6.63180609e-01,
7.10304409e-01, 1.68782434e+00, 3.96113024e-01,
1.19060186e+00, 8.50783915e-02, 6.13803494e-01,
1.73269913e+00, 8.55969584e-01, 1.64131594e+00,
8.58613893e-02, 9.81661750e-02, 2.78759789e+00,
9.59956310e-01, 2.29773958e-01, 1.61492699e+00,
1.01034599e+00, 7.18872588e-01, 1.62706127e+00,
5.32838042e-01, 1.30215206e+01, 1.94416009e+00,
1.41992387e+00, 8.87928409e-01, 1.11943087e+00,
1.31482739e+00, 8.77962887e+00, 2.42889940e+00,
4.75109403e-01, 7.85464398e-01, 1.40331539e+01,
7.98775271e-01, 9.71203096e-01, 2.10326002e-01,
7.51093550e-01, 7.55866212e-01, 5.08198076e+00,
8.73035578e-01, 8.18731976e-01, 7.57240126e-01,
9.17577513e-01, 2.58378134e+00, 9.68288124e-01,
2.58742199e-01, 8.87906654e-01, 8.73528970e-01,
4.12566626e+00, 6.16232432e-01, 1.18261196e+00,
5.78051511e-02, 4.06421396e-01, 5.28898986e-01,
4.34687315e-01, 1.17460558e+00, 1.86055543e+00,
2.28451450e+00, 1.17556012e+00, 1.16568311e+00,
5.76192882e-01, 2.64970486e+00, 3.64037778e-02,
3.36642247e+00, 2.79562791e-01, 4.77165389e-01,
2.02370419e+00, 5.61602158e-01, 6.80329496e-01,
4.44305421e-01, 2.39866548e-01, 2.39478161e-01,
5.85566976e+00, 9.70503483e-01, 2.92538702e-02,
4.08999104e-01, 1.04275923e+00, 9.11360662e-01,
1.63302059e+01, 6.13895392e-01, 6.41138518e-01,
4.38856073e-01, 7.55595165e-01, 4.52787289e-01,
9.17066028e-01, 9.98960005e-01, 9.05609764e-01,
1.17912414e+01, 4.76532638e+00, 3.83256190e-01,
7.45918534e-01, 2.63845808e-01, 4.92929460e-01,
4.41060765e+00, 1.18395740e+00, 6.44723212e-01,
9.50190133e-01, 5.26943393e+00, 3.41989856e-01,
1.46151390e-01, 9.91187341e-01, 3.74914605e-01,
3.50475564e-01, 3.99430120e-01, 4.57232247e+00,
8.87295603e-01, 4.56169268e+01, 6.09452849e-01,
1.25562620e+00, 2.04728410e-01, 1.85450443e-01,
3.03317551e-01, 8.13703930e-01, 8.21422397e-01,
1.00470432e+00, 1.39683388e+00, 2.75117273e+00,
8.97235732e-01, 4.80145610e-01, 2.80744313e-01,
2.25000729e+00, 1.04329198e+00, 7.37398006e-01,
4.57503851e-02, 6.21536872e-01, 3.50722773e+00,
1.07869960e+00, 1.24943756e+01, 4.24462972e-01,
7.56106525e-01, 2.06938220e+01, 7.79192078e-01,
3.87813245e+00, 3.91382246e-01, 3.91356634e+00,
1.55792478e+00, 8.12813562e-01, 1.80971685e+00,
3.04944417e-01, 1.62720395e+00, 1.15431632e+00,
6.07205565e+02, 1.25670235e+00, 5.47683106e-01,
1.32949275e+00, 3.73279210e-01, 3.17136980e+00,
7.14185444e-01, 3.81929796e-01, 5.59392996e-01,
1.05444945e+00, 1.31831189e+00, 4.40927090e-01,
5.85441303e-01, 2.23901127e+00, 1.33555183e+00,
2.16869335e-01, 1.55244225e+00, 1.45194147e+00,
4.22463028e-01, 1.37626564e-02, 8.15412765e-02,
2.58923475e-01, 1.30671965e+00, 3.06151599e+00,
4.69780031e+00, 1.17041119e+00, 1.24183673e+00,
1.16139820e+00, 3.54258641e-01, 1.06363253e-01,
9.50671285e-01, 1.49640632e-02, 2.74874442e+01,
2.32426650e-01, 1.45632953e+00, 8.32217316e-01,
1.74344901e+00, 3.51001660e-02, 7.65829653e-01,
6.79054740e-01, 4.03101698e-01, 2.27105338e+00,
3.05077796e-01, 2.70275626e+00, 2.44444801e+01,
1.27223220e+00, 1.15518156e+00, 9.88358832e-01,
2.40284960e+01, 2.19696964e+00, 7.19168306e-01,
5.88514603e-01, 5.36372643e-02, 1.02985215e+00,
1.39317432e+00, 1.20417993e+00, 3.92851264e+00,
2.55098064e-01, 2.97730572e+00, 1.47670272e+00,
1.75931540e+01, 1.50416383e+00, 9.98194194e-01,
1.05608100e+00, 1.19696332e+00, 8.04538184e-01,
2.49083176e+00, 4.94317238e+00, 5.99041563e-01,
1.29165325e+00, 9.11602128e-01, 1.18541479e+00,
2.75998541e+00, 3.36211447e-01, 5.52752812e+00,
5.36822909e-01, 1.44384595e+00, 8.51859461e-01,
1.84727089e-01, 1.78105607e+00, 9.45413833e-01,
3.91464470e-01, 1.45226927e+00, 4.56882417e+00,
3.23279597e-01, 5.02394650e-01, 2.79720834e-01,
5.47264809e-03, 6.95355196e-01, 1.73857472e-01,
1.11905975e-01, 1.61306002e-01, 4.10279860e-01,
1.43009922e+00, 9.52697148e-01, 9.43767688e-01,
4.28221334e-01, 4.82637180e-01, 8.62936895e-01,
3.86295549e-01, 2.30748171e+00, 3.63177336e+00,
6.35588687e+00, 2.92472429e-01, 2.94631479e+00,
2.64917015e+00, 1.12598059e+00, 3.84818978e-01,
1.49288106e+00, 1.24625027e+00, 2.34147082e+01,
3.89642879e-01, 2.08088477e+00, 1.25491453e+00,
2.31193434e+00, 6.31704680e-01, 3.77210234e+01,
5.96381662e-01, 4.17912618e-01, 1.28741137e+00,
1.85405769e+00, 1.58868381e+00, 4.77873333e-02,
7.69661151e-01, 3.82832446e-01, 2.98955927e-01,
3.59762258e-01, 4.21588739e-01, 1.09121551e+02,
8.18140677e-01, 2.24792875e+00, 5.76122690e-01,
6.14704460e-01, 2.74946311e+00, 1.73384942e+00,
2.72619296e-01, 1.15108058e+00, 1.46532017e+00,
4.17238825e-01, 1.63569547e-01, 2.26101389e-01,
1.96898497e-01, 8.55290767e-01, 1.48079444e-01,
6.15021566e-02, 3.47629488e+00, 1.02068555e+00,
1.58379582e-01, 1.07779376e+00, 1.27776343e+00,
5.65660969e-01, 3.06580278e+00, 8.54103197e-01,
9.33322363e-01, 1.32288837e+00, 2.89292170e+00,
2.68079471e+00, 6.27513798e+00, 2.68216517e+00,
1.38120367e+00, 2.24789440e+00, 1.12590323e+01,
1.23183287e+01, 3.66972973e-01, 7.19549163e-01,
6.60821304e-01, 8.49577332e-01, 1.28567018e+00,
7.14888833e-01, 5.30359306e+00, 8.98886709e-02,
8.06354980e-01, 6.59172910e-01, 1.23160059e+00,
2.67672781e-01, 1.50102275e+01, 8.45912032e-01,
6.46388460e-01, 3.64657520e-01, 2.26484271e-01,
2.78816249e-01, 6.40678324e-01, 1.82318162e+00,
1.78446252e+00, 2.06668518e+00, 8.30151119e-01,
1.99972811e+00, 1.46512107e+01, 2.23154714e-01,
4.71803572e-01, 7.56309045e-01, 1.60380769e+00,
1.84611117e+00, 6.73622304e-01, 4.30974937e+00,
1.21070892e+00, 4.99101724e+00, 3.62506823e-01,
3.94076851e-01, 1.23144585e+00, 3.59183830e-01,
1.49975229e+00, 7.30241214e-01, 1.68231874e+00,
1.13429555e+00, 2.49510181e-02, 3.52321515e-01,
1.15308477e+00, 4.08429269e-02, 2.98791751e+00,
8.58213860e-01, 1.94847847e+00, 2.19283657e+00,
6.23860542e+00, 3.62673574e-01, 2.41864620e-01,
5.58436437e-01, 1.39445544e+00, 1.07374472e+00,
6.23670544e-01, 7.55377374e-01, 5.58119238e+00,
4.82231548e-01, 7.35472783e-01, 2.42858054e-01,
4.54670098e-01, 3.04494738e+00, 1.09559174e+00,
2.21414319e+00, 4.37506420e-01, 3.04225393e+00,
4.69762750e-01, 3.53285106e-02, 1.61053319e+00,
9.46049993e-01, 2.13176623e+00, 6.56490324e+00,
4.54721600e-01, 8.66697614e-01, 1.49813900e-01,
9.99016325e-01, 3.49589382e-02, 1.72876257e+00,
6.75318339e+00, 1.25179457e+00, 2.87434908e+00,
1.65881458e-01, 3.44844290e-01, 3.22442461e-01,
7.13531793e-01, 2.56645729e+01, 3.49984781e-02,
6.53521779e-01, 1.92608042e+00, 4.69987292e+00,
3.04844477e-01, 7.63258624e-01, 6.32631492e+00,
5.16499746e-01, 1.68561775e-01, 1.21631737e+01,
1.30254464e-01, 3.73551128e-01, 9.01656335e-01,
3.47538474e+00, 5.54407958e-01, 6.06577068e-01,
5.25718123e-02, 1.99584536e+00, 2.62262341e+00,
5.73845021e+00, 7.67138350e-01, 1.62829046e+00,
8.89296667e-01, 1.76769651e+00, 3.01282820e-01,
2.09902968e+00, 2.32301545e+00, 1.29588604e+00,
4.42909374e+00, 1.56959146e+00, 1.43703626e-01,
7.74386019e-01, 5.03951021e+00, 3.86259107e-01,
1.44829349e+00, 2.37116079e+00, 4.11286746e+02,
4.94131442e+00, 6.66596198e+00, 1.58143271e+00,
3.12085788e-01, 2.20713118e-01, 2.09247355e-01,
3.46340670e+00, 7.04042560e-01, 6.92874418e-01,
1.56423634e+00, 9.28070670e-01, 1.31806533e-01,
7.15207750e+00, 8.51460646e+00, 3.45632181e-01,
1.13211459e-01, 1.75798662e+00, 3.14147324e+01,
4.26560842e-02, 6.34004827e-01, 9.63519070e-01,
4.60200962e-01, 3.68819611e-01, 8.11043445e-01,
7.37632165e+00, 3.44169194e+00, 6.65366189e-01,
6.43898766e-02, 4.06345350e-02, 6.16398986e-01,
1.36997303e+00, 6.59559293e+00, 6.44207470e-01,
2.79782796e-01, 1.87760230e+00, 2.54048927e-01,
3.93564453e-01, 1.97701197e+00, 5.41135616e-01,
1.59509689e+00, 1.65483552e-01, 9.51726557e-01,
8.82626231e-01, 2.50313359e+00, 8.19505104e-02,
9.77979207e-01, 1.02052071e+00, 1.04343251e-02,
1.04393983e+00, 1.35985716e+00, 2.41348282e+01,
2.62046847e-01, 1.20275124e-01, 1.08012358e+00,
2.59032843e+00, 8.51322683e-01, 1.89421261e+00,
1.16194584e+00, 1.33509032e+00, 1.48539229e+00,
3.32759007e+00, 1.37455503e+00, 2.59205548e+00,
4.36490393e+00, 9.48565955e-01, 2.89089235e-01,
3.20038387e-01, 5.82801362e-01, 2.64818460e+00,
4.73021948e+00, 1.12491733e+00, 3.35185527e-01,
6.50282688e-02, 1.95711561e+00, 9.69271689e+00,
9.65951614e-01, 3.44899023e+01, 1.43652827e+00,
1.84985657e+00, 5.91662966e-01, 6.16489728e-01,
6.80730097e-02, 2.27350122e+00, 1.45862062e-01,
7.22501658e-01, 1.17074912e+00, 6.59522079e-01,
7.09843470e-01, 2.66670390e-01, 1.14142051e+00,
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