2次元多重線形回帰のmatplotlib plot_surface

Question

x1、x2、yの3つの次元を持つ多くのデータ点があります。私はこれらの点の複数の線形回帰を計算することができ、私は3次元散布図上にその点を表示することができますが、私はそれらの点について計算した複数の線形回帰をプロットする方法を知らない： 1次元線形回帰で最良の線を描く方法で、私は2D線形回帰の「最良適合平面」をプロットすることに興味があります。

私のコードは次のとおりです。

import numpy as np 
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 

# collect data into numpy arrays 
X = [] 
Y = [] 
for line in open('data_2d.csv'): 
    x1, x2, y = line.split(',') 
    X.append([1, float(x1), float(x2)]) # here X[i][0] represents x0 = 1 
    Y.append(float(y)) 
X = np.array(X) 
Y = np.array(Y) 

# calculate weights 
w = np.linalg.solve(np.dot(X.T,X), np.dot(X.T, Y)) 
Yhat = np.dot(X, w) # results of linear regression for data points 

# plot results 
fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 
ax.scatter(X[:,1], X[:,2], Y) 
ax.plot_surface(X[:,1], X[:,2], Yhat) # doesn't seem to work 
plt.show() 

Answer 1

はplot_surfaceは、その入力の各々は、私が以前使用していたように、行列ではなく値のリストを調整する必要が判明しました。

import numpy as np 
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 

# collect data into numpy arrays 
X = [] 
Y = [] 
for line in open('data_2d.csv'): # contains 3 columns: x1, x2, and y 
    x1, x2, y = line.split(',') 
    X.append([1, float(x1), float(x2)]) # here X[i][0] represents x0 = 1 
    Y.append(float(y)) 
X = np.array(X) 
Y = np.array(Y) 

# calculate weights for computing solutions 
w = np.linalg.solve(X.T.dot(X), X.T.dot(Y)) 

# calculate r-squared error given weights 
Yhat = X.dot(w) 
d1 = Y - Yhat 
d2 = Y - Y.mean() 
r2 = 1 - d1.dot(d1)/d2.dot(d2) 
print("r-squared value of", r2) 

# calculate plane of best fit 
divs = 2 # number of divisions in surface: generates divs^2 points. 
     # The surface is a plane, so just 2^2 = 4 points can define it. 
# plane spans all values of x1 and x2 from data 
x1_range = np.linspace(min(X[:,1]),max(X[:,1]),divs) 
x2_range = np.linspace(min(X[:,2]),max(X[:,2]),divs) 
X_plane = [] 
for i in range(divs): 
    for j in range(divs): 
     X_plane.append([1, x1_range[i], x2_range[j]]) 
X_plane = np.array(X_plane) 
# values of y are equal to the linear regression of points on the plane 
Yhat2 = X_plane.dot(w) 

# rearrange Yhat2 into a coordinate matrix for display as a surface 
Yhat2_surface = [] 
for i in range(divs): 
    Yhat2_surface.append(Yhat2[ divs*i : divs*i+divs ]) 
Yhat2_surface = np.array(Yhat2_surface) 
Yhat2 = Yhat2_surface 

# generate coordinate matrices for x1 and x2 values 
X2, X1 = np.meshgrid(x1_range, x2_range) # intentional ordering: X2, *then* X1 

# plot results 
fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 
ax.scatter(X[:,1], X[:,2], Y) # supplied data 
ax.plot_surface(X1, X2, Yhat2, color='y', alpha=0.1) # plane of best fit 
plt.show() 

The output is shown here.ドットが入力されたデータを表し、黄色の矩形がplot_surfaceで描かれたベストフィットのその平面を表し、次のように私のソリューションです。

Answer 2

をここで私は一緒に3D散布図、3D表面プロットと等高線プロットを実証投げた簡単な例です。

import numpy, scipy 
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): 
    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])) 

    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): 
    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])) 

    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 EquationFunc(data): 
    return 5.0 + numpy.sqrt(data[0]) + numpy.cos(data[1]/5.0) 


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] 

    ScatterPlot(data) 
    SurfacePlot(EquationFunc, data) 
    ContourPlot(EquationFunc, data)