如何用matplotlib绘制4d图

3条回答

网友

1楼 · 编辑于 2024-04-27 02:35:35

我知道这个问题已经很老了，但是我想提出一个替代方案，在这个方案中，我们没有使用“散点图”，而是有一个基于第4维的颜色的三维曲面图。就我个人而言，我并没有真正看到“散点图”中的空间关系，因此使用三维曲面帮助我更容易理解图形。

主要的想法和公认的答案是一样的，但我们有一个三维图形的表面，让视觉上更好地看到点之间的距离。下面的代码主要基于this question给出的答案。

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

# The values related to each point. This can be a "Dataframe pandas" 
# for example where each column is linked to a variable <-> 1 dimension. 
# The idea is that each line = 1 pt in 4D.
do_random_pt_example = True;

index_x = 0; index_y = 1; index_z = 2; index_c = 3;
list_name_variables = ['x', 'y', 'z', 'c'];
name_color_map = 'seismic';

if do_random_pt_example:
    number_of_points = 200;
    x = np.random.rand(number_of_points);
    y = np.random.rand(number_of_points);
    z = np.random.rand(number_of_points);
    c = np.random.rand(number_of_points);
else:
    # Example where we have a "Pandas Dataframe" where each line = 1 pt in 4D.
    # We assume here that the "data frame" "df" has already been loaded before.
    x = df[list_name_variables[index_x]]; 
    y = df[list_name_variables[index_y]]; 
    z = df[list_name_variables[index_z]]; 
    c = df[list_name_variables[index_c]];
#end
#-----

# We create triangles that join 3 pt at a time and where their colors will be
# determined by the values of their 4th dimension. Each triangle contains 3
# indexes corresponding to the line number of the points to be grouped. 
# Therefore, different methods can be used to define the value that 
# will represent the 3 grouped points and I put some examples.
triangles = mtri.Triangulation(x, y).triangles;

choice_calcuation_colors = 1;
if choice_calcuation_colors == 1: # Mean of the "c" values of the 3 pt of the triangle
    colors = np.mean( [c[triangles[:,0]], c[triangles[:,1]], c[triangles[:,2]]], axis = 0);
elif choice_calcuation_colors == 2: # Mediane of the "c" values of the 3 pt of the triangle
    colors = np.median( [c[triangles[:,0]], c[triangles[:,1]], c[triangles[:,2]]], axis = 0);
elif choice_calcuation_colors == 3: # Max of the "c" values of the 3 pt of the triangle
    colors = np.max( [c[triangles[:,0]], c[triangles[:,1]], c[triangles[:,2]]], axis = 0);
#end
#----------
# Displays the 4D graphic.
fig = plt.figure();
ax = fig.gca(projection='3d');
triang = mtri.Triangulation(x, y, triangles);
surf = ax.plot_trisurf(triang, z, cmap = name_color_map, shade=False, linewidth=0.2);
surf.set_array(colors); surf.autoscale();

#Add a color bar with a title to explain which variable is represented by the color.
cbar = fig.colorbar(surf, shrink=0.5, aspect=5);
cbar.ax.get_yaxis().labelpad = 15; cbar.ax.set_ylabel(list_name_variables[index_c], rotation = 270);

# Add titles to the axes and a title in the figure.
ax.set_xlabel(list_name_variables[index_x]); ax.set_ylabel(list_name_variables[index_y]);
ax.set_zlabel(list_name_variables[index_z]);
plt.title('%s in function of %s, %s and %s' % (list_name_variables[index_c], list_name_variables[index_x], list_name_variables[index_y], list_name_variables[index_z]) );

plt.show();

对于我们绝对希望每个点都具有第4维原始值的情况，另一个解决方案是简单地使用“散点图”与三维曲面图相结合，该图将简单地链接它们，以帮助您查看它们之间的距离。

name_color_map_surface = 'Greens';  # Colormap for the 3D surface only.

fig = plt.figure(); 
ax = fig.add_subplot(111, projection='3d');
ax.set_xlabel(list_name_variables[index_x]); ax.set_ylabel(list_name_variables[index_y]);
ax.set_zlabel(list_name_variables[index_z]);
plt.title('%s in fcn of %s, %s and %s' % (list_name_variables[index_c], list_name_variables[index_x], list_name_variables[index_y], list_name_variables[index_z]) );

# In this case, we will have 2 color bars: one for the surface and another for 
# the "scatter plot".
# For example, we can place the second color bar under or to the left of the figure.
choice_pos_colorbar = 2;

#The scatter plot.
img = ax.scatter(x, y, z, c = c, cmap = name_color_map);
cbar = fig.colorbar(img, shrink=0.5, aspect=5); # Default location is at the 'right' of the figure.
cbar.ax.get_yaxis().labelpad = 15; cbar.ax.set_ylabel(list_name_variables[index_c], rotation = 270);

# The 3D surface that serves only to connect the points to help visualize 
# the distances that separates them.
# The "alpha" is used to have some transparency in the surface.
surf = ax.plot_trisurf(x, y, z, cmap = name_color_map_surface, linewidth = 0.2, alpha = 0.25);

# The second color bar will be placed at the left of the figure.
if choice_pos_colorbar == 1: 
    #I am trying here to have the two color bars with the same size even if it 
    #is currently set manually.
    cbaxes = fig.add_axes([1-0.78375-0.1, 0.3025, 0.0393823, 0.385]);  # Case without tigh layout.
    #cbaxes = fig.add_axes([1-0.844805-0.1, 0.25942, 0.0492187, 0.481161]); # Case with tigh layout.

    cbar = plt.colorbar(surf, cax = cbaxes, shrink=0.5, aspect=5);
    cbar.ax.get_yaxis().labelpad = 15; cbar.ax.set_ylabel(list_name_variables[index_z], rotation = 90);

# The second color bar will be placed under the figure.
elif choice_pos_colorbar == 2: 
    cbar = fig.colorbar(surf, shrink=0.75, aspect=20,pad = 0.05, orientation = 'horizontal');
    cbar.ax.get_yaxis().labelpad = 15; cbar.ax.set_xlabel(list_name_variables[index_z], rotation = 0);
#end
plt.show();

最后，也可以使用“plot_surface”，在这里我们定义将用于每个面的颜色。在这样的情况下，我们每个维度有一个值向量，问题是我们必须插值得到二维网格。在第4维插值的情况下，仅根据X-Y定义，不考虑Z。因此，颜色表示C（x，y），而不是C（x，y，z）。以下代码主要基于以下响应：plot_surface with a 1D vector for each dimension；plot_surface with a selected color for each surface。请注意，与以前的解决方案相比，计算量相当大，显示可能需要一些时间。

import matplotlib
from scipy.interpolate import griddata

# X-Y are transformed into 2D grids. It's like a form of interpolation
x1 = np.linspace(x.min(), x.max(), len(np.unique(x))); 
y1 = np.linspace(y.min(), y.max(), len(np.unique(y)));
x2, y2 = np.meshgrid(x1, y1);

# Interpolation of Z: old X-Y to the new X-Y grid.
# Note: Sometimes values can be < z.min and so it may be better to set 
# the values too low to the true minimum value.
z2 = griddata( (x, y), z, (x2, y2), method='cubic', fill_value = 0);
z2[z2 < z.min()] = z.min();

# Interpolation of C: old X-Y on the new X-Y grid (as we did for Z)
# The only problem is the fact that the interpolation of C does not take
# into account Z and that, consequently, the representation is less 
# valid compared to the previous solutions.
c2 = griddata( (x, y), c, (x2, y2), method='cubic', fill_value = 0);
c2[c2 < c.min()] = c.min(); 

#--------
color_dimension = c2; # It must be in 2D - as for "X, Y, Z".
minn, maxx = color_dimension.min(), color_dimension.max();
norm = matplotlib.colors.Normalize(minn, maxx);
m = plt.cm.ScalarMappable(norm=norm, cmap = name_color_map);
m.set_array([]);
fcolors = m.to_rgba(color_dimension);

# At this time, X-Y-Z-C are all 2D and we can use "plot_surface".
fig = plt.figure(); ax = fig.gca(projection='3d');
surf = ax.plot_surface(x2, y2, z2, facecolors = fcolors, linewidth=0, rstride=1, cstride=1,
                       antialiased=False);
cbar = fig.colorbar(m, shrink=0.5, aspect=5);
cbar.ax.get_yaxis().labelpad = 15; cbar.ax.set_ylabel(list_name_variables[index_c], rotation = 270);
ax.set_xlabel(list_name_variables[index_x]); ax.set_ylabel(list_name_variables[index_y]);
ax.set_zlabel(list_name_variables[index_z]);
plt.title('%s in fcn of %s, %s and %s' % (list_name_variables[index_c], list_name_variables[index_x], list_name_variables[index_y], list_name_variables[index_z]) );
plt.show();

网友

2楼 · 编辑于 2024-04-27 02:35:35

一种可能是使用颜色空间，例如RGBA或HSVA，它们是四维的，但是很好地显示alpha（透明度）可能是一个问题。

另一种可能是带有滑块的动态绘图。其中一个维度将由滑块表示。

不过，我不确定你是不是在问这个问题。

网友

3楼 · 编辑于 2024-04-27 02:35:35

很好的问题腾吉斯，所有的数学人都喜欢用给定的函数来展示浮华的曲面图，而忽略了处理真实世界的数据。您提供的示例代码使用渐变，因为变量的关系是使用函数建模的。对于这个例子，我将使用标准正态分布生成随机数据。

无论如何，这里是如何快速绘制4D随机（任意）数据的方法，前三个变量在轴上，第四个是颜色：

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

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x = np.random.standard_normal(100)
y = np.random.standard_normal(100)
z = np.random.standard_normal(100)
c = np.random.standard_normal(100)

img = ax.scatter(x, y, z, c=c, cmap=plt.hot())
fig.colorbar(img)
plt.show()

注：第4维度使用了热色调方案（黄色到红色）的热图

结果：

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