Question

我发布了an earlier version of this yesterday，但我似乎无法将此版本添加到该帖子中，因为有人似乎关闭了该帖子进行编辑，所以这是新版本中的新版本。

我在下面的脚本中执行以下操作：
1.）在S形数据上绘制最佳拟合曲线 2.）根据x和y的新的最大和最小坐标重新调整数据大小 3.）为调整大小的数据计算并绘制新的最佳拟合曲线。

步骤1和2似乎工作正常，但步骤3没有。如果您运行该脚本，您将看到它为重新调整大小的数据绘制了完全无效的曲线。

任何人都可以告诉我如何修改下面的代码，以便为重新调整大小的数据创建和绘制真正最合适的S形曲线吗？ 这需要是在可能的最大值和最小值的范围内重新调整大小时可重现。

我似乎能够将问题跟踪到New_p，后者在以下代码行中定义：

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)

但我无法弄清楚如何更深入地解决这个问题。我认为这个问题可能与全局变量和局部变量之间的差异有关，但也许是其他变量。

以下是我的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()

Answer 1

试试这个：

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(arr,lower=0.0,upper=1.0):
    # Create local copy
    result=arr.copy()
    # If the mins are greater than the maxs, then flip them.
    if lower>upper: lower,upper=upper,lower
    #----------------------------------------------------------------------------------------------    
    # 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
    #----------------------------------------------------------------------------------------------    
    # Subtracts right operand from the left operand and assigns the result to the left operand.
    # Note: c -= a is equivalent to c = c - a
    result -= result.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
    result *= (upper-lower)/result.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
    result += lower
    return result


# 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
# x[-1] returns the last value in x
minLVET=(y[-1]/x[-1])*MinRR
maxLVET=(y[0]/x[0])*MaxRR

print(MinRR, MaxRR)
#x,y=resize(x,y,xmin=0.3, ymin=0.3) 
NewX=resize(x,lower=MinRR,upper=MaxRR)
NewY=resize(y,lower=minLVET,upper=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.min(y),np.max(y),0.01) 
New_p_guess=(np.median(NewX),np.min(NewY),np.max(NewY),0.01) 

# 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()

alt text

您的其他相关问题尚未结束，您似乎已注册了两次，并且stackoverflow不允许您编辑其他问题，因为它无法识别this user与this user相同

我在上面的代码中所做的主要是改变New_p_guess。为初始猜测找到正确的值是一种艺术。如果它可以通过算法完成，scipy不会要求你这样做。一点分析可以帮助您，也可以为您的数据提供“感觉”。事先知道解决方案应该大致是什么样的，因此在问题的背景下哪些值是合理的也有帮助。（这只是一个很长的路要说我猜我选择k = 0.01的方式。）

另一个S形回归方程问题

1 个答案: