Scipy学习

Exercise 10.1: Least squares

代码：

import scipy.linalg as lina
import numpy as np

m = 10
n = 6
A = np.random.random_sample((m, n))
x = np.random.random_sample((n,))
b = A.dot(x) + np.random.normal(0, 1, (m,))
x_ = lina.inv(A.T.dot(A)).dot(A.T).dot(b)
print(lina.norm(A.dot(x_) - b))

结果：

2.7711555872938862
[Finished in 3.8s]

Exercise 10.2: Optimization

代码：

import scipy.optimize as so
from math import sin, exp

def f(x):
    return -(sin(x - 2) ** 2) * exp(-(x ** 2))

a = so.fminbound(f, 0, 1)

print("the max of f(x) = ", -f(a),"when x = ", a)

结果：

the max of f(x) =  0.9116854118471066 when x =  0.216241170568
[Finished in 1.8s]

Exercise 10.3: Pairwise distances

Let X be a matrix with n rows and m columns. How can you compute the pairwise distances between every two rows?

As an example application, consider nn cities, and we are given their coordinates in two columns. Now we want a nice table that tells us for each two cities, how far they are apart.

Again, make sure you make use of Scipy’s functionality instead of writing your own routine.

代码：

import numpy as np
import scipy.spatial.distance as dis

m = 10
n = 6
X = np.random.rand(m, n)
Y = dis.pdist(X)
z = dis.squareform(Y)
print(z)

结果：

[[ 0.          1.06563785  0.8991295   1.11523718  0.68486272  0.84821488
   0.69147257  0.76578426  0.84108407  0.97179401]
 [ 1.06563785  0.          1.05035582  1.25618603  1.13114483  0.95785648
   0.84361886  1.15080478  0.79948917  0.67902661]
 [ 0.8991295   1.05035582  0.          0.85992237  1.3830768   1.26597884
   1.23922916  1.26570587  1.10687948  1.257172  ]
 [ 1.11523718  1.25618603  0.85992237  0.          1.37042936  1.62495922
   1.20311556  1.2376298   1.17202273  1.45872162]
 [ 0.68486272  1.13114483  1.3830768   1.37042936  0.          0.79638965
   0.80060998  0.90885248  0.75235086  1.00716696]
 [ 0.84821488  0.95785648  1.26597884  1.62495922  0.79638965  0.
   0.95381021  1.0311819   0.63747946  0.86866474]
 [ 0.69147257  0.84361886  1.23922916  1.20311556  0.80060998  0.95381021
   0.          0.67373532  0.76295439  0.78899356]
 [ 0.76578426  1.15080478  1.26570587  1.2376298   0.90885248  1.0311819
   0.67373532  0.          0.97081342  0.74455982]
 [ 0.84108407  0.79948917  1.10687948  1.17202273  0.75235086  0.63747946
   0.76295439  0.97081342  0.          0.97669933]
 [ 0.97179401  0.67902661  1.257172    1.45872162  1.00716696  0.86866474
   0.78899356  0.74455982  0.97669933  0.        ]]
[Finished in 1.6s]