這是使用scipy.optimize.curve_fit擬合表面的示例Python代碼,它使原始數據生成3D散點圖,對錯誤進行3D散點圖繪制,繪制表面圖和輪廓圖.更改它以使用您自己的數據和功能,您應該已完成.

import numpy, scipy

import 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(equationFunc, data, params):

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 = equationFunc(numpy.array([X, Y]), *params)

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(equationFunc, data, params):

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 = equationFunc(numpy.array([X, Y]), *params)

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, title):

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, depthshade=False, color='k')

axes.set_title(title)

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 EquationFunc(data, *params):

p0 = params[0]

p1 = params[1]

return p0 + numpy.sqrt(data[0]) + numpy.cos(data[1] / p1)

if __name__ == "__main__":

# raw data

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])

pInitial = (1.0, 1.0)

popt, pcov = scipy.optimize.curve_fit(EquationFunc,(xData,yData),zData, p0=pInitial)

dataForPlotting = [xData, yData, zData]

ScatterPlot([xData, yData, zData], 'Data Scatter Plot (click-drag with mouse)')

SurfacePlot(EquationFunc, [xData, yData, zData], popt)

ContourPlot(EquationFunc, [xData, yData, zData], popt)

absError = zData - EquationFunc((xData,yData), *popt)

ScatterPlot([xData, yData, absError], 'Error Scatter Plot (click-drag with mouse)')

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