如何用兩組自變量擬合數據

Question

我有一個方程a *（t ^ alpha）*（p_p ^ beta），我想擬合它以獲得alpha和beta值，其中t和p_p是自變量。 我的問題是如何編寫最終擬合模型（結果）表達式。

result = model.fit(S_L1, params, t=t, p_p=p_p)

我嘗試了類似上述表達式的操作，但出現此錯誤：

ValueError: The input contains nan values


# Calculating unburned mass temperature
T_u = T_i*(p_filter/p_i)**((k_u-1)/k_u)                     # Linear unburned temperature
t = T_u/T_i
p_p = p_filter/p_i


# Model function.
def mod_m(t, p_p, a=1, alpha=1,beta=1):                             # Define function with initial guesses
    return a*(t**alpha)*(p_p**beta)                                 # Function for fitting


# Fitting model.
model = Model(mod_m, independent_vars=['t','p_p'] )

# Making a set of parameters:
params = model.make_params(a=10)

# Setting  min/max bounds on parameters:
params['alpha'].min = 0.0
params['beta'].min = 0.0
params['a'].min = 0.0
params['a'].max = 1e6


# Run the fit with Model.fit(Data_Array, Parameters, independent vars).
result = model.fit(S_L1, params, t=t, p_p=p_p)

Answer 1

這是將您的函數與測試數據結合使用的Python 3示例。 這將scipy.optimize.curve_fit（）用於多元回歸，並創建3D數據散點圖，擬合函數的3D表面圖和擬合函數的輪廓圖。 請注意，我為Curve_fit使用了默認的scipy初始參數。

import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import  Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt

graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels

# 3D contour plot lines
numberOfContourLines = 16


def SurfacePlot(func, data, fittedParameters):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = func(numpy.array([X, Y]), *fittedParameters)

    axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)

    axes.scatter(x_data, y_data, z_data) # show data along with plotted surface

    axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label
    axes.set_zlabel('Z Data') # Z axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ContourPlot(func, data, fittedParameters):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = func(numpy.array([X, Y]), *fittedParameters)

    axes.plot(x_data, y_data, 'o')

    axes.set_title('Contour Plot') # add a title for contour plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
    matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ScatterPlot(data):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    axes.scatter(x_data, y_data, z_data)

    axes.set_title('Scatter Plot (click-drag with mouse)')
    axes.set_xlabel('X Data')
    axes.set_ylabel('Y Data')
    axes.set_zlabel('Z Data')

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def func(data, a, alpha, beta):
    t = data[0]
    p_p = data[1]
    return a * (t**alpha) * (p_p**beta)


if __name__ == "__main__":
    xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
    yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
    zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])

    data = [xData, yData, zData]

    # this example uses curve_fit()'s default initial paramter values
    fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData)

    ScatterPlot(data)
    SurfacePlot(func, data, fittedParameters)
    ContourPlot(func, data, fittedParameters)

    print('fitted prameters', fittedParameters)

Answer 2

您的問題是“如何編寫最終擬合模型（結果）表達式？”。 您已經自己回答了這個問題

def mod_m(t, p_p, a=1, alpha=1,beta=1): 
    return a*(t**alpha)*(p_p**beta)

model = Model(mod_m, independent_vars=['t','p_p'] )

是的，這正是編寫擬合模型的方法。

本身不會導致異常

ValueError: The input contains nan values

導致ValueError原因在於，您的fit函數會使用您提供的參數值和自變量來生成nan值。 那么...您為這些傳遞的價值是什么？

我建議打印出模型函數中參數的值以及自變量的值。 需要明確的是，求冪很容易產生大於1e308的值，這將產生inf並引起您看到的異常。 因此，您可能必須更加小心允許使用哪些參數值，這可能對自變量的值很敏感。