Scipy Curve_fit For Two Dimensions Not Working - Object Too Deep?

I have a 2400 by 2400 array of data which looks something like this: data = [[-2.302670298082603040e-01 -2.304885241061924717e-01 -2.305029774024092148e-01 -2.304807100897505734e-0

Solution 1:

OK guys, I've fixed the problem myself. As I suspected, it's a dimensionality issue.

The appropriate dimensions for curve_fit applied to a 2D array are as follows:

• Function - One Dimension, which in this case carries the same dimensions as the data set unless enforced
• x data - (2, n*m), where n and m are the dimensions of the data array
• y data - (n*m)
• List of Initial Parameters - A 1D array simply containing all the parameters in the same order as stated in the function

I therefore left my parameter array unchanged, but made the following change to the function:

def Gauss2D(x, mux, muy, sigmax, sigmay, amplitude, offset, rotation):
    assert len(x) == 2
    X = x[0]
    Y = x[1]
    A = (np.cos(rotation)**2)/(2*sigmax**2) + (np.sin(rotation)**2)/(2*sigmay**2)
    B = (np.sin(rotation*2))/(4*sigmay**2) - (np.sin(2*rotation))/(4*sigmax**2)
    C = (np.sin(rotation)**2)/(2*sigmax**2) + (np.cos(rotation)**2)/(2*sigmay**2)
    G = amplitude*np.exp(-((A * (X - mux) ** 2) + (2 * B * (X - mux) * (Y - muy)) + (C * (Y - muy) ** 2))) + offset
    return G.ravel()

and I passed the following to the x data argument:

x = np.vstack((HORIZ.ravel(), VERT.ravel()))

and this to the y data argument:

y = data.ravel()

Thus, I optimised it using:

curve_fit(Gauss2D, x, y, po)

which works just fine.

Solution 2:

Per the comments, here is a 3D surface fitter using curve_fit() that has 3D scatterplot, 3D surface plot, and contour plot.

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

graphWidth = 800# units are pixels
graphHeight = 600# units are pixels# 3D contour plot lines
numberOfContourLines = 16defSurfacePlot(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 problemsdefContourPlot(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 problemsdefScatterPlot(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 problemsdeffunc(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]

    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 = scipy.optimize.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 = 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(zData))
    print('RMSE:', RMSE)
    print('R-squared:', Rsquared)