如何最小化 Python 上的多变量函数？

问题描述

我是 stackoverflow（和 Python）的新手，如果这个问题很乱，我很抱歉！尝试使用最小二乘法最小化函数 myfit(M,P)。这是我的代码：

import matplotlib.pylab as plt
import matplotlib.pyplot as plt
import numpy as np 
import math 
from fractions import Fraction
import cmath
from matplotlib import colors as c
from scipy.optimize import curve_fit,minimize
from mpl_toolkits.mplot3d import Axes3D
import csv
from matplotlib.colors import ListedColormap,LinearSegmentedColormap


theta = ((np.pi)/4)*0
eta = (3*(np.pi)/2)*0

# Quarter-wave plate and Half-wave plate
QWP = np.matrix([[complex(1 +0j),complex(0 +0j)],[complex(0 +0j),complex(0+1j)]])
HWP = np.matrix([[1,0],[0,-1]])

ydata= np.linspace(0,np.pi,50)
xdata= np.linspace(0,np.pi/2,25)
X,Y = np.meshgrid(xdata,ydata)

z=[]
zdata = []

with open('.//Caoilainn//Data//CoPt//18112020//TR-MOKE_CoPt_Delay@Max_QWP_0to180deg_HWP_0to90deg.tsv','r') as csvfile:
    plots = csv.reader(csvfile,delimiter='\t')
    next(plots,None)
    for row in plots:
        z.append(float(row[2]))
  
Z = np.zeros((50,25))
for i in range(0,50):
    for j in range(0,25):
        Z[i,j] = z[i*25+j]

def d(theta):
    return theta + 0.01*np.pi/180
    
# Rotation Matrix,R(theta)
def R(theta):
    return np.matrix([[np.cos(theta),np.sin(theta)],[-np.sin(theta),np.cos(theta)]])
# R(theta+d)
def D(theta):
    return np.matrix([[np.cos(d(theta)),np.sin(d(theta))],[-np.sin(d(theta)),np.cos(d(theta))]])

def signal(x,y):
    E = np.matrix([[np.sin(eta)*1j],[np.cos(eta)]]) 
    J = R(theta)*E
    V= R(y)*QWP*R(-y)*R(x)*HWP*R(-x)*J
    return float(abs(V[0])*abs(V[0]) - abs(V[1])*abs(V[1]))

def moke(x,[np.cos(eta)]]) 
    J = D(theta)*E
    V= R(y)*QWP*R(-y)*R(x)*HWP*R(-x)*J
    return (float(abs(V[0])*abs(V[0]) - abs(V[1])*abs(V[1])) - signal(x,y))/d(theta)

def mcd(x,[np.cos(eta)]]) 
    J = R(theta)*np.matrix([[np.sin(eta + (0.01*np.pi)/180)*1j],[np.cos(eta+ (0.01*np.pi)/180)]])
    V= R(y)*QWP*R(-y)*R(x)*HWP*R(-x)*J
    return (float(abs(V[0])*abs(V[0]) - abs(V[1])*abs(V[1])) - signal(x,y))/ (0.01*np.pi/180)

# Plot the 3D figure of the fitted function
fig = plt.figure(1)
ax = fig.gca(projection='3d')
ax.plot_surface(X,Y,Z,cmap="viridis")
plt.show()

# Our function to fit 
def myfit(M,P):
    x,y = M
    return P[0]*signal(x-P[3],y-P[4]) + P[1]*moke(x-P[3],y-P[4]) + P[2]*mcd(x-P[3],y-P[4])



def khi(P,xdata,ydata,zdata):
    out = 0.0
    for itemp,i in enumerate(xdata):
        for jtemp,j in enumerate(ydata):
           out = out + float((zdata[jtemp,itemp] - myfit(i,j,P))**2)
    return out            

def myfit2(x,y,P):
    out = np.empty([y.size,x.size ])
    for itemp,i in enumerate(x):
        for jtemp,j in enumerate(y):
           out[jtemp,itemp] = P[0]*signal(i-P[3],j-P[4]) + P[1]*moke(i-P[3],j-P[4]) + P[2]*mcd(i-P[3],j-P[4])
    return out  
 
P0 = np.array([0.3,1.0,0.1,7*np.pi/180,-70*np.pi/180]) 
xdata = np.vstack((X.ravel(),Y.ravel()))
popt,pcov = curve_fit(myfit,Z.ravel(),P0)
res = minimize(khi,P0,(xdata,zdata))
vtemp = myfit(xdata,popt)   

出现的错误是

" File "//anaconda3/lib/python3.7/site-packages/scipy/optimize/minpack.py",line 458,in func_wrapped 返回 func(xdata,*params) - ydata

TypeError: myfit() 需要 2 个位置参数，但给出了 6 个"

非常感谢任何帮助

解决方法

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