scipyTest.py

# -*- coding: UTF-8 -*-

import numpy as np
from pylab import *

def main():
    #1--Integral
    from scipy.integrate import quad,dblquad,nquad #积分和二元积分
    print(quad(lambda x:np.exp(-x),0,np.inf))
    print(dblquad(lambda t,x:np.exp(-x*t)/t**3,0,np.inf,lambda X:1,lambda x:np.inf))
    def f(x,y):
        return x*y
    def bound_y():
        return [0,0.5]
    def bound_x(y):
        return [0,1-2*y]
    print(nquad(f,[bound_x,bound_y]))

    #2--Optimizer
    from scipy.optimize import minimize
    def rosen(x):
        return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0+(1-x[:-1])**2.0)
    x0=np.array([1.3,0.7,0.8,1.9,1.2])
    res=minimize(rosen,x0,method="nelder-mead",options={"xtol":1e-8,"disp":True})
    #求函数的全局最小值
    print("ROSE MINI:",res) #res可以改成res.x,打印res的一个属性
    #求函数在某个约束下的最小值
    def func(x):
        return (2*x[0]*x[1]+2*x[0]-x[0]**2-2*x[1]**2)
    def func_deriv(x):
        dfdx0=(-2*x[0]+2*x[1]+2)
        dfdx1=(2*x[0]-4*x[1])
        return np.array([dfdx0,dfdx1])
    #cons是约束条件,jac 雅可比行列式，求偏导
    cons=({"type":"eq","fun":lambda x:np.array([x[0]**3-x[1]]),"jac":lambda x:np.array([3.0*(x[0]**2.0),-1.0])},
          {"type":"ineq","fun":lambda x:np.array([x[1]-1]),'jac':lambda x:np.array([0.0,1.0])})
    res=minimize(func,[-1.0,1.0],jac=func_deriv,constraints=cons,method='SLSQP',options={'disp':True})
    print("RESTRICT:",res)
    from scipy.optimize import root
    def fun(x):
        return x+2*np.cos(x)
    sol=root(fun,0.1)
    print("ROOT:",sol.x,sol.fun)

    #3--Interpolation
    x=np.linspace(0,1,10)
    y=np.sin(2*np.pi*x)
    from scipy.interpolate import interp1d
    li=interp1d(x,y,kind="cubic")
    x_new=np.linspace(0,1,50)
    y_new=li(x_new)
    figure()
    plot(x,y,"r")
    plot(x_new,y_new,"k")
    show()
    print(y_new)
    #新的数据线比原来的数据线平滑

    #4————Linear
    from scipy import linalg as lg
    arr=np.array([[1,2],[3,4]])
    print("Dev:",lg.det(arr))
    print("Inv:",lg.inv(arr))
    b=np.array([6,14])
    print("Sol:",lg.solve(arr,b))
    #以上是解线性方程组x+2y=6，3x+4y=14
    print("Eig:",lg.eig(arr)) #特征值和特征向量
    #以下几个是矩阵分解
    print("LU:",lg.lu(arr))
    print("QR:",lg.qr(arr))
    print("SVD:",lg.svd(arr))
    print("Schur:",lg.schur(arr))








if __name__ == "__main__":
    main()