scipy

10.1 Least squares

使用lstsq进行线性回归

import numpy as np

from scipy.linalg import *

m = 20

n = 15

A = np.random.random((m, n))

b = np.random.random((m,))

cc, re, rank, sigma = lstsq(A, b)

b1 = A.dot(cc)

delta = b - b1

print(norm(delta))

10.2 optimization

使用fmin即可

import numpy as np

from scipy.linalg import *

from scipy.optimize import fmin

def f( x):

return -( 1 * np.sin(x- 2)** 2 * np.e**(- 1*x** 2))

opt = fmin(f, 0)

print(-f(opt)[ 0])

10.3 pairwise distances

可以直接使用scipy的距离计算函数 pdist求出

import numpy as np

import scipy.spatial.distance

n = 20

m = 15

A = np.random.rand(n,m)

X = scipy.spatial.distance.pdist(A)

Y = scipy.spatial.distance.squareform(X)

print(Y)

[[0.         1.70723364 1.67232394 2.14848234 1.81661124 1.52028073
  1.72870584 1.44979784 1.91241827 1.6690722  1.57910147 1.81669617
  2.14387069 1.70279202 1.70946341 1.47205802 1.91203106 1.88894804
  1.72074019 1.33649791]
 [1.70723364 0.         1.66529196 1.56321923 1.31698055 1.44271224
  1.5209942  1.39646947 1.29319299 1.4415709  1.34903143 1.70376255
  1.71089653 1.70809496 1.85715285 1.53346995 1.90699968 1.53557633
  1.69210972 1.4356786 ]
 [1.67232394 1.66529196 0.         2.16537299 1.61166394 1.62408598
  1.99695736 1.39343426 1.95026217 1.37335845 1.82294837 2.07437076
  2.06216394 2.17549423 1.74777236 1.46421705 1.68179628 1.85163016
  2.15962043 1.57020591]
 [2.14848234 1.56321923 2.16537299 0.         1.61744096 1.88851528
  1.34413788 1.89398291 1.46709356 1.51890132 1.54229883 1.65237536
  1.02859956 1.68758486 1.42972634 2.11055697 1.61379488 1.55930157
  1.69316533 1.61673748]
 [1.81661124 1.31698055 1.61166394 1.61744096 0.         1.57506447
  1.64856206 1.54462691 1.26073619 1.67646547 1.67084812 1.81246537
  1.58863275 1.56247758 1.86333648 1.42115663 1.56454956 1.36803946
  1.61047539 1.34794565]
 [1.52028073 1.44271224 1.62408598 1.88851528 1.57506447 0.
  1.93076771 1.80667192 1.62390781 1.62131565 1.22412401 1.89877188
  2.2287198  1.8424469  1.97116297 1.50919167 1.8116297  1.81767725
  1.93822376 1.49301997]
 [1.72870584 1.5209942  1.99695736 1.34413788 1.64856206 1.93076771
  0.         1.5984583  1.3739134  1.73435405 1.32009888 1.46882034
  1.29935889 1.17612914 1.35878312 2.07095613 1.67426578 1.64686582
  1.42055562 1.35513523]
 [1.44979784 1.39646947 1.39343426 1.89398291 1.54462691 1.80667192
  1.5984583  0.         1.8219781  1.21034371 1.96697615 1.9136222
  1.7131313  1.85591055 1.8493316  1.52669117 1.88982055 1.83252903
  1.7503535  1.56149337]
 [1.91241827 1.29319299 1.95026217 1.46709356 1.26073619 1.62390781
  1.3739134  1.8219781  0.         1.63035212 1.34622488 1.36837991
  1.515803   0.87209497 1.78371141 1.76672116 1.58975982 0.97117112
  1.40584691 1.46286706]
 [1.6690722  1.4415709  1.37335845 1.51890132 1.67646547 1.62131565
  1.73435405 1.21034371 1.63035212 0.         1.65543959 1.83492604
  1.55897106 1.8694899  1.83625683 1.38260266 1.81402838 1.52835775
  2.00287105 1.53885769]
 [1.57910147 1.34903143 1.82294837 1.54229883 1.67084812 1.22412401
  1.32009888 1.96697615 1.34622488 1.65543959 0.         1.55108518
  1.82778351 1.5795985  1.52008291 1.91682534 1.72790657 1.63059121
  1.83492781 1.31934342]
 [1.81669617 1.70376255 2.07437076 1.65237536 1.81246537 1.89877188
  1.46882034 1.9136222  1.36837991 1.83492604 1.55108518 0.
  1.52766165 1.50209549 1.65426736 2.1394657  2.11508613 1.98777079
  1.35365351 1.6889287 ]
 [2.14387069 1.71089653 2.06216394 1.02859956 1.58863275 2.2287198
  1.29935889 1.7131313  1.515803   1.55897106 1.82778351 1.52766165
  0.         1.61023629 1.56312161 2.14209356 1.51085459 1.53239633
  1.69013196 1.69610014]
 [1.70279202 1.70809496 2.17549423 1.68758486 1.56247758 1.8424469
  1.17612914 1.85591055 0.87209497 1.8694899  1.5795985  1.50209549
  1.61023629 0.         1.84857612 1.89971775 1.65491187 1.21571993
  1.37919973 1.56664618]
 [1.70946341 1.85715285 1.74777236 1.42972634 1.86333648 1.97116297
  1.35878312 1.8493316  1.78371141 1.83625683 1.52008291 1.65426736
  1.56312161 1.84857612 0.         2.19546315 1.28728038 1.81340596
  1.4690638  1.17895255]
 [1.47205802 1.53346995 1.46421705 2.11055697 1.42115663 1.50919167
  2.07095613 1.52669117 1.76672116 1.38260266 1.91682534 2.1394657
  2.14209356 1.89971775 2.19546315 0.         1.99391454 1.57438674
  2.17212559 1.65971252]
 [1.91203106 1.90699968 1.68179628 1.61379488 1.56454956 1.8116297
  1.67426578 1.88982055 1.58975982 1.81402838 1.72790657 2.11508613
  1.51085459 1.65491187 1.28728038 1.99391454 0.         1.20761278
  1.7316566  1.35060886]
 [1.88894804 1.53557633 1.85163016 1.55930157 1.36803946 1.81767725
  1.64686582 1.83252903 0.97117112 1.52835775 1.63059121 1.98777079
  1.53239633 1.21571993 1.81340596 1.57438674 1.20761278 0.
  1.81923254 1.58007452]
 [1.72074019 1.69210972 2.15962043 1.69316533 1.61047539 1.93822376
  1.42055562 1.7503535  1.40584691 2.00287105 1.83492781 1.35365351
  1.69013196 1.37919973 1.4690638  2.17212559 1.7316566  1.81923254
  0.         1.15343142]
 [1.33649791 1.4356786  1.57020591 1.61673748 1.34794565 1.49301997
  1.35513523 1.56149337 1.46286706 1.53885769 1.31934342 1.6889287
  1.69610014 1.56664618 1.17895255 1.65971252 1.35060886 1.58007452
  1.15343142 0.        ]]