下面是一个示例曲面拟合，它可以生成三维散射图、三维曲面图和等高线图。在import numpy, scipy,
import matplotlib
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
f = (figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
xModel = (min(x_data), max(x_data), 20)
yModel = (min(y_data), max(y_data), 20)
X, Y = (xModel, yModel)
Z = func(numpy.array([X, Y]), *fittedParameters)
axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=, linewidth=1, antialiased=True)
(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
()
('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
f = (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 = (min(x_data), max(x_data), 20)
yModel = (min(y_data), max(y_data), 20)
X, Y = (xModel, yModel)
Z = func(([X, Y]), *fittedParameters)
(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 = (X, Y, Z, numberOfContourLines, colors='k')
(CS, inline=1, fontsize=10) # labels for contours
()
('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
f = (figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
(True)
axes = Axes3D(f)
x_data = data[0]
y_data = data[1]
z_data = data[2]
(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')
()
('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 = ([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
yData = ([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
zData = ([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
data = [xData, yData, zData]
initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example
# here a non-linear surface fit is made with scipy's curve_fit()
fittedParameters, pcov = .curve_fit(func, [xData, yData], zData, p0 = initialParameters)
ScatterPlot(data)
SurfacePlot(func, data, fittedParameters)
ContourPlot(func, data, fittedParameters)
print('fitted prameters', fittedParameters)
modelPredictions = func(data, *fittedParameters)
absError = modelPredictions - zData
SE = (absError) # squared errors
MSE = (SE) # mean squared errors
RMSE = (MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - ((absError) / (zData))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)