机器学习测试笔记（4）——scipy

# coding:utf-8
import numpy asnp
from scipyimport constants as C
from scipyimport linalg
from scipyimport integrate
fromscipy.interpolate import interp1d
importmatplotlib.pyplot as plt

def get_const():
    print("圆周率：\n",C.pi)
    print("黄金分割率：\n",C.golden)
    print("真空中的光束：\n",C.c)
    print("普朗克常数：\n",C.h)
    print("一英里等于多少米：\n",C.mile)
    print("一英寸等于多少米：\n",C.inch)
    print("一度等于多少弧度：\n",C.degree)
    print("一分钟等于多少秒：\n",C.minute)
    print("标准重力加速度：\n",C.g)

defsystem_of_linear_equations():
#2x + y = 5
#3x -4y = -9
    a = np.array([[2,1],[3,-4]])
    b = np.array([5,-9])
    x,y = np.round(linalg.solve(a,b))
print("x=",x,"y=",y)
#x= 1.0 y= 3.0
#2x + y +z = 8
#3x -4y +2z= -3
#x + y + z = 7
    a = np.array([[2,1,1],[3,-4,2],[1,1,1]])
    b = np.array([8,-3,7])
    x,y,z = np.round(linalg.solve(a,b))
print("x=",x,"y=",y,"z=",z)
#x= 1.0 y= 3.0 z= 3.0

defmatrix_operation():
    A = np.array([[2,3],[4,5]])
#3.1 矩阵绝对值
#|A| = det(A) = 2*5-3*4 = 10-12=-2
    x = linalg.det(A)
print("A的矩阵行列式",x)
#A的矩阵行列式 -2.000000000000001
#3.2矩阵的逆矩阵
    iA = linalg.inv(A)
print("A的矩阵的逆矩阵",iA)
#A的矩阵的逆矩阵 [[-2.5  1.5]
#                 [ 2.  -1. ]]
#设A是一个n阶矩阵，若存在另一个n阶矩阵B，使得：AB=BA=E ，则称方阵A可逆，并称方阵B是A的逆矩阵
#3.3矩阵的特征值和特征向量
    λ, v = linalg.eig(A)
print("A的矩阵的特征值",λ)
#设 A 是n阶方阵，如果存在数m和非零n维列向量 x，使得 Ax=mx 成立，则称 m 是矩阵A的一个特征值（characteristic value)或本征值（eigenvalue)。
#A的矩阵的特征值 [-0.27491722+0.j 7.27491722+0.j]
print("A的矩阵的特征向量",v)
#A的矩阵的特征向量 [[-0.79681209 -0.49436913]
#                   [ 0.60422718 -0.86925207]]

#半圆看做对y的积分，y=(1-x^2)^0.5
defhalf_circle(x):
return (1-x**2)**0.5
#z=(1-x^2-y^2)^0.5
defhalf_sphere(x,y):
return (1-x**2-y**2)**0.5
defnumerical_integration():
#单位圆的面积：x^2+y^2 = 1
    pi_half, err = integrate.quad(half_circle,-1,1)#err为误差
#integrate.quad(f,from,end)f:求积分的函数名,[from,end]: 积分区间
    print("半圆面积:",pi_half,"误差:",err)
    print("2*pi_half:",2*pi_half)
#半圆面积: 1.5707963267948983 误差: 1.0002354500215915e-09
#2*pi_half: 3.1415926535897967
#单位球的体积
    pi_sphere, err = integrate.dblquad(half_sphere,-1,1,
lambda x:-half_circle(x),
lambda x:half_circle(x))
    print("2*pi_sphere",2*pi_sphere)
#2*pi_sphere 4.188790204786397

definterpolation():
    x = np.linspace(0,10,num=11,endpoint=True)
    y = np.cos(x)
    f1 = interp1d(x,y,kind='linear')
    f2 = interp1d(x,y,kind='cubic')
    xnew = np.linspace(0,10,num=41,endpoint=True)
    plt.plot(x,y,'o',xnew,f1(xnew),'-',xnew,f2(xnew),'--')
    plt.legend(['data','linear','cubic'],loc='best')
    plt.show()

if__name__=="__main__":
    get_const()
    system_of_linear_equations()
    matrix_operation()
    numerical_integration()
    interpolation()