pyhton第13周作业

Exercise 10.1: Least squares
Generate matrix A ∈ Rm×n with m > n. Also generate some vector b ∈ Rm.
Now find x = arg minx kAx − bk2.

Print the norm of the residual.

import numpy as np 

A = np.random.randint(0, 10, (10, 5))
B = np.random.randint(0, 10, (10, 1))

l = np.linalg.lstsq(A, B, rcond=0)
print(l[0])
print(l[1])

Exercise 10.2: Optimization
Find the maximum of the function
f(x) = sin2(x − 2)e−x2

import numpy as np 
from scipy import optimize 

fun = lambda x : (-1)*(np.sin(x-2))**2*np.exp((-1)*(x**2))
m = optimize.fmin(fun, 0)
print((-1)*m[0])

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 n 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.

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

d = np.random.randint(0, 10, (10, 10))
dd = dis.pdist(d, 'euclidean')
print(dd)