Numpy 使用Scipy进行线性回归曲线拟合-不确定有什么问题

我一直在尝试学习如何使用线性回归和scipy拟合曲线

下面是我从另一个帮助别人的用户那里得到的一些代码

我的问题在于：我为

xData

和

yData

拟合了一些自己的数据。 但是如果我翻转

xData

和

yData

，那么

如何修复它，使曲线适合原始

xData

和

yData

位置

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
import math
# det value in dbm
ytoBeConverted = numpy.array([7.76,5.00,1.70,-1.33,-4.77,-7.75,-10.78,-13.76,-16.70,-19.97,-23.04,-25.88,-28.92,-32.05,-34.67,-37.08,-39.33])
#power meter value
lst = []
for y in ytoBeConverted:
    lst.append(math.pow(10, (y/10)))

############ These X and Y data points don't work, but if I flip them as X and Y, it works##########
yData = numpy.asarray(lst)
xData = numpy.array([0.8475,0.7108,0.3853,0.2108,0.1026,0.0537,0.0277,0.0147,0.0079,0.0043,0.0027,0.0019,0.0015,0.0013,0.0012,0.0011,0.0011])


def func(x, a, b, Offset): # Sigmoid A With Offset from zunzun.com
    return  1.0 / (1.0 + numpy.exp(-a * (x-b))) + Offset


# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
    warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
    val = func(xData, *parameterTuple)
    return numpy.sum((yData - val) ** 2.0)


def generate_Initial_Parameters():
    # min and max used for bounds
    maxX = max(xData)
    minX = min(xData)
    maxY = max(yData)
    minY = min(yData)

    parameterBounds = []
    parameterBounds.append([minX, maxX]) # seach bounds for a
    parameterBounds.append([minX, maxX]) # seach bounds for b
    parameterBounds.append([0.0, maxY]) # seach bounds for Offset

    # "seed" the numpy random number generator for repeatable results
    result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
    return result.x

# generate initial parameter values
geneticParameters = generate_Initial_Parameters()

# curve fit the test data
fittedParameters, pcov = curve_fit(func, xData, yData, geneticParameters)

print('Parameters', fittedParameters)

modelPredictions = func(xData, *fittedParameters) 
absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('Power Meter Value (mW)') # X axis data label
    axes.set_ylabel('Detector Value') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight) 

---

数据似乎没有S形，因此代码中的等式与数据拟合得不好。我对你的数据进行了方程搜索，一个三参数双曲型方程得到了一个OK拟合。这是你的代码，使用这个方程和更新的遗传算法搜索新方程的范围

---

什么是因变量，什么是自变量？你想预测什么？我不确定这是否回答了你的问题，但我想根据我提供的x值预测y值。更具体地说，我试图找到望远镜数据、探测器值（X）和功率计值（Y）之间的关系。探测器值随着功率计值的减小而减小，我希望能够在样本数据点之间插值和预测值。更具体地说，我可以在我的示例中使用正确拟合的曲线从Y预测X吗？混淆之处在于首先将值

[7.76，5.00…]

命名为X，然后对它们执行一些操作并将其称为Y。然后再次提供

[0.845071…]

作为x。其次，在第二幅图像中，通过反转x和y轴，y轴标签是

[0.845071…]的“检测器值”

。因此，

[0.845071…]

值是x还是y？

[0.845071…]

是x值。我图片中的“错误拟合”曲线就是我想要修正的曲线。@VivekKumar请看我对这个问题的回答。

import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
import math
# det value in dbm
xtoBeConverted = numpy.array([7.76,5.00,1.70,-1.33,-4.77,-7.75,-10.78,-13.76,-16.70,-19.97,-23.04,-25.88,-28.92,-32.05,-34.67,-37.08,-39.33])
#power meter value
lst = []
for x in xtoBeConverted:
    lst.append(math.pow(10, (x/10)))

############ These X and Y data points don't work, but if I flip them as X and Y, it works##########
yData = numpy.asarray(lst)
xData = numpy.array([0.8475,0.7108,0.3853,0.2108,0.1026,0.0537,0.0277,0.0147,0.0079,0.0043,0.0027,0.0019,0.0015,0.0013,0.0012,0.0011,0.0011])


def func(x, a, b, c): # Hyperbolic F from zunzun.com
    return  a * x / (b + x) + c * x


# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
    warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
    val = func(xData, *parameterTuple)
    return numpy.sum((yData - val) ** 2.0)


def generate_Initial_Parameters():
    # min and max used for bounds
    maxX = max(xData)
    minX = min(xData)
    maxY = max(yData)
    minY = min(yData)

    parameterBounds = []
    parameterBounds.append([-1.0, 0.0]) # seach bounds for a
    parameterBounds.append([-1.0, 0.0]) # seach bounds for b
    parameterBounds.append([minY, maxY]) # seach bounds for c

    # "seed" the numpy random number generator for repeatable results
    result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
    return result.x


# generate initial parameter values
geneticParameters = generate_Initial_Parameters()

# curve fit the data
fittedParameters, pcov = curve_fit(func, xData, yData, geneticParameters)

print('Parameters', fittedParameters)

modelPredictions = func(xData, *fittedParameters) 
absError = modelPredictions - yData

SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)

print()


##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(xData, yData,  'D')

    # create data for the fitted equation plot
    xModel = numpy.linspace(min(xData), max(xData))
    yModel = func(xModel, *fittedParameters)

    # now the model as a line plot
    axes.plot(xModel, yModel)

    axes.set_xlabel('Power Meter Value (mW)') # X axis data label
    axes.set_ylabel('Detector Value') # Y axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot

graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)