Python-Scipy(第十四周作业)

Exercise 10.1: Least squares

题目要求

给出矩阵A,向量b,用最小二乘法求x,并求出残差的模
代码:

import scipy
import scipy.spatial

m = 8
n = 7
A = scipy.random.rand(m, n) * scipy.random.randint(1, 10)
b = scipy.random.rand(m) * scipy.random.randint(1, 10)
x, resid, rnk, s = scipy.linalg.lstsq(A, b)
print('A :\n', A)
print('b :\n', b)
print('x :\n', x)
print('Norm of residual : ', resid / n)

结果:

Exercise 10.2: Optimization

题目要求

求给出函数f(x)=(sin(x−2))2∗e−x2$f(x)=(sin(x-2){)}^2\ast e^{-x^2}$的最大值
代码:

import scipy
import math
import scipy.optimize as opt

func = lambda x: (math.sin(x - 2) ** 2) * math.exp(-x * x)
maximum = opt.fmin(lambda x: -func(x), 1, full_output=True, disp=False)
print('max point is', maximum[0], ',value is', -maximum[1])
print('iterations is', maximum[2], ',function evaluations is', maximum[3])

结果:

Exercise 10.3: Pairwise distances

题目要求

计算N个点中每两个点间的距离,这里取4个点
代码:

import scipy
import math
import scipy.spatial
import scipy.optimize as opt

m, n = 2, 4
X = scipy.random.rand(n, m) * scipy.random.randint(1, 10)
Y = scipy.spatial.distance.pdist(X)
print('points:\n', X)
print('distance:', Y)

结果: