python学习—scipy知识点
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2022-07-12 22:32:40
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1.1 integral积分运算
import numpy as np
from scipy.integrate import quad,dblquad,nquad #quad是一元积分，dblquad是二元积分,nquad表示n维的积分
print(quad(lambda x:np.exp(-x),0,np.inf))#在进行一元积分时此处0是x的下界，np.inf是x的上界
print(dblquad(lambda t,x:np.exp(-x*t)/t**3,0,np.inf,lambda x:1,lambda x:np.inf))#在进行二元积分时需要定义两个变量，x的取值范围可以和t有关
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]))#可将自定义的函数代入nquad中进行积分运算(1.0000000000000002, 5.842607038578007e-11) (0.3333333333366853, 1.3888461883425516e-08) (0.010416666666666668, 4.101620128472366e-16)
1.2 优化器 Optimizer
可以自定义拉格朗日乘子法的运算过程，也可以实现凸优化的相关计算
from scipy.optimize import minimize
def rosen(x):
return np.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})
print(res)Optimization terminated successfully.
Current function value: 0.000000
Iterations: 339
Function evaluations: 571
final_simplex: (array([[ 1. , 1. , 1. , 1. , 1. ],
[ 1. , 1. , 1. , 1. , 1. ],
[ 1. , 1. , 1. , 1.00000001, 1.00000001],
[ 1. , 1. , 1. , 1. , 1. ],
[ 1. , 1. , 1. , 1. , 1. ],
[ 1. , 1. , 1. , 1. , 0.99999999]]), array([ 4.86115343e-17, 7.65182843e-17, 8.11395684e-17,
8.63263255e-17, 8.64080682e-17, 2.17927418e-16]))
fun: 4.8611534334221152e-17
message: 'Optimization terminated successfully.'
nfev: 571
nit: 339
status: 0
success: True
x: array([ 1., 1., 1., 1., 1.])
1.3 插值 interpolation
from pylab import * #绘图模块
#from scipy import interpolate
from scipy.interpolate import interp1d
x = np.linspace(0,1,10)
y = np.sin(2*np.pi*x)
li = interpolate.interp1d(x,y,kind = 'cubic')
x_new = np.linspace(0,1,50)
y_new = li(x_new)
plot(x,y,'r')
plot(x_new,y_new,'k')
print(y_new)
show()[ 0.00000000e+00 1.31268478e-01 2.58058896e-01 3.79095818e-01 4.93103803e-01 5.98807414e-01 6.94931212e-01 7.80199759e-01 8.53337617e-01 9.13069347e-01 9.58119510e-01 9.87213058e-01 9.99462682e-01 9.95096409e-01 9.74541587e-01 9.38225564e-01 8.86575689e-01 8.20078818e-01 7.39913600e-01 6.47705004e-01 5.45085433e-01 4.33687295e-01 3.15143957e-01 1.91245093e-01 6.41081509e-02 -6.41081509e-02 -1.91245093e-01 -3.15143957e-01 -4.33687295e-01 -5.45085433e-01 -6.47705004e-01 -7.39913600e-01 -8.20078818e-01 -8.86575689e-01 -9.38225564e-01 -9.74541587e-01 -9.95096409e-01 -9.99462682e-01 -9.87213058e-01 -9.58119510e-01 -9.13069347e-01 -8.53337617e-01 -7.80199759e-01 -6.94931212e-01 -5.98807414e-01 -4.93103803e-01 -3.79095818e-01 -2.58058896e-01 -1.31268478e-01 -2.44929360e-16]
1.4 线性计算和矩阵分解
from scipy import linalg as lg
arr = np.array([[1,2],[3,4]])
print(lg.det(arr)) #计算矩阵的行列式
print(lg.inv(arr)) #计算矩阵的逆矩阵
b = np.array([6,14])
print(lg.solve(arr,b))#解线性方程组，此时arr是系数矩阵，b是目标值，可直接代入lg.solve()进行线性方程组的求解
print(lg.eig(arr)) #计算矩阵的特征值和特征向量
print('LU:\n',lg.lu(arr))#进行矩阵分解中的LU分解
print('QR:\n',lg.qr(arr))#进行矩阵分解中的QR分解
print('SVD:\n',lg.svd(arr))#进行矩阵分解中的SVD分解（奇异值分解）-2.0
[[-2. 1. ]
[ 1.5 -0.5]]
[ 2. 2.]
(array([-0.37228132+0.j, 5.37228132+0.j]), array([[-0.82456484, -0.41597356],
[ 0.56576746, -0.90937671]]))
LU:
(array([[ 0., 1.],
[ 1., 0.]]), array([[ 1. , 0. ],
[ 0.33333333, 1. ]]), array([[ 3. , 4. ],
[ 0. , 0.66666667]]))
QR:
(array([[-0.31622777, -0.9486833 ],
[-0.9486833 , 0.31622777]]), array([[-3.16227766, -4.42718872],
[ 0. , -0.63245553]]))
SVD:
(array([[-0.40455358, -0.9145143 ],
[-0.9145143 , 0.40455358]]), array([ 5.4649857 , 0.36596619]), array([[-0.57604844, -0.81741556],
[ 0.81741556, -0.57604844]]))