另一个S型回归方程问题

Question

我昨天发过一个早期版本的帖子，但是我发现无法在那个帖子里添加这个新版本，因为好像有人把那个帖子关闭了，不能编辑了，所以我在这里发一个新的帖子。

我有下面这个脚本，它做了以下几件事：
1.) 为S型数据绘制最佳拟合曲线。
2.) 根据新的最大和最小坐标调整数据的大小。
3.) 计算并绘制调整大小后数据的新的最佳拟合曲线。

步骤1和步骤2似乎都没问题，但步骤3却不行。如果你运行这个脚本，你会发现它为调整大小后的数据绘制了一条完全不正确的曲线。

有没有人能告诉我如何修改下面的代码，让它为调整大小后的数据创建并绘制一条真正的最佳拟合S型曲线？ 这个过程需要在不同的最大和最小值范围内都能重复进行。

我发现问题可能出在New_p这个变量上，它在下面这行代码中定义：

New_p, New_cov, New_infodict, New_mesg, New_ier = scipy.optimize.leastsq( 
    residuals,New_p_guess,args=(NewX,NewY),full_output=1,warning=True)

但我不知道如何更深入地解决这个问题。我觉得问题可能和全局变量和局部变量的区别有关，但也可能是其他原因。

这是我完整代码的当前草稿：

import numpy as np 
import matplotlib.pyplot as plt 
import scipy.optimize 

def GetMinRR(age):
    MaxHR = 208-(0.7*age)
    MinRR = (60/MaxHR)*1000
    return MinRR

def sigmoid(p,x):
    x0,y0,c,k=p 
    y = c / (1 + np.exp(-k*(x-x0))) + y0 
    return y 

def residuals(p,x,y): 
    return y - sigmoid(p,x) 

def resize(x,y,xmin=0.0,xmax=1.0,ymin=0.0,ymax=1.0):
    # Create local variables
    NewX = [t for t in x]
    NewY = [t for t in y]
    # If the mins are greater than the maxs, then flip them.
    if xmin>xmax: xmin,xmax=xmax,xmin 
    if ymin>ymax: ymin,ymax=ymax,ymin
    #----------------------------------------------------------------------------------------------    
    # The rest of the code below re-calculates all the values in x and then in y with these steps:
    #       1.) Subtract the actual minimum of the input x-vector from each value of x
    #       2.) Multiply each resulting value of x by the result of dividing the difference
    #           between the new xmin and xmax by the actual maximum of the input x-vector
    #       3.) Add the new minimum to each value of x
    # Note: I wrote in x-notation, but the identical process is also repeated for y
    #----------------------------------------------------------------------------------------------    
    # Subtracts right operand from the left operand and assigns the result to the left operand.
    # Note: c -= a is equivalent to c = c - a
    NewX -= x.min()

    # Multiplies right operand with the left operand and assigns the result to the left operand.
    # Note: c *= a is equivalent to c = c * a
    NewX *= (xmax-xmin)/NewX.max()

    # Adds right operand to the left operand and assigns the result to the left operand.
    # Note: c += a is equivalent to c = c + a
    NewX += xmin

    # Subtracts right operand from the left operand and assigns the result to the left operand.
    # Note: c -= a is equivalent to c = c - a
    NewY -= y.min()

    # Multiplies right operand with the left operand and assigns the result to the left operand.
    # Note: c *= a is equivalent to c = c * a
    NewY *= (ymax-ymin)/NewY.max()

    # Adds right operand to the left operand and assigns the result to the left operand.
    # Note: c += a is equivalent to c = c + a
    NewY += ymin

    return (NewX,NewY)

# Declare raw data for use in creating logistic regression equation
x = np.array([821,576,473,377,326],dtype='float') 
y = np.array([255,235,208,166,157],dtype='float') 

# Call resize() function to re-calculate coordinates that will be used for equation
MinRR=GetMinRR(50)
MaxRR=1200
minLVET=(y[4]/x[4])*MinRR
maxLVET=(y[0]/x[0])*MaxRR

#x,y=resize(x,y,xmin=0.3, ymin=0.3) 
NewX,NewY=resize(x,y,xmin=MinRR,xmax=MaxRR,ymin=minLVET,ymax=maxLVET) 
print 'x is:  ',x 
print 'y is:  ',y
print 'NewX is:  ',NewX
print 'NewY is:  ',NewY

# p_guess is the starting estimate for the minimization
p_guess=(np.median(x),np.median(y),1.0,1.0) 
New_p_guess=(np.median(NewX),np.median(NewY),1.0,1.0) 

# Calls the leastsq() function, which calls the residuals function with an initial
# guess for the parameters and with the x and y vectors.  The full_output means that
# the function returns all optional outputs.  Note that the residuals function also
# calls the sigmoid function.  This will return the parameters p that minimize the
# least squares error of the sigmoid function with respect to the original x and y
# coordinate vectors that are sent to it.
p, cov, infodict, mesg, ier = scipy.optimize.leastsq( 
    residuals,p_guess,args=(x,y),full_output=1,warning=True)   

New_p, New_cov, New_infodict, New_mesg, New_ier = scipy.optimize.leastsq( 
    residuals,New_p_guess,args=(NewX,NewY),full_output=1,warning=True)   

# Define the optimal values for each element of p that were returned by the leastsq() function.
x0,y0,c,k=p 
print('''Reference data:\ 
x0 = {x0} 
y0 = {y0} 
c = {c} 
k = {k} 
'''.format(x0=x0,y0=y0,c=c,k=k)) 

New_x0,New_y0,New_c,New_k=New_p 
print('''New data:\ 
New_x0 = {New_x0} 
New_y0 = {New_y0} 
New_c = {New_c} 
New_k = {New_k} 
'''.format(New_x0=New_x0,New_y0=New_y0,New_c=New_c,New_k=New_k))

# Create a numpy array of x-values
xp = np.linspace(x.min(), x.max(), x.max()-x.min())
New_xp = np.linspace(NewX.min(), NewX.max(), NewX.max()-NewX.min())
# Return a vector pxp containing all the y values corresponding with the x-values in xp
pxp=sigmoid(p,xp)
New_pxp=sigmoid(New_p,New_xp)

# Plot the results 
plt.plot(x, y, '>', xp, pxp, 'g-')
plt.plot(NewX, NewY, '^',New_xp, New_pxp, 'r-')
plt.xlabel('x')
plt.ylabel('y',rotation='horizontal')
plt.grid(True)
plt.show()

全局变量代码调试局部变量数学建模最大最小值 s型回归拟合曲线数据调整

另一个S型回归方程问题

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