griddata：QH6214 qhull输入错误：没有足够的points（2）来构造初始单纯形

Question

我正在尝试创建一个相对稀疏的EEG数据（27个电极）的俯视图热图。 我将EEG电极的x，y直角坐标转换为极性，并尝试将它们映射为极性。 每个x，y坐标都对应一个给定的值（如果您想知道：赫斯特指数），我希望该位置周围的颜色与之对应。

我从此页面上的工作代码开始，并尝试使其适应我的问题。 不幸的是，我的修改无法正常工作。

这是我的代码：

from __future__ import division, print_function, absolute_import
from pylab import *
import numpy as np
from scipy.interpolate import griddata


# Setting the paremeters that define the circle
max_r = 1
max_theta = 2.0 * np.pi

###Cartesian coordinates of the 27 electrodes
###x axis goes from back of head to nose, with nose being the positive direction
###y axis goes from ear to ear, with toward right ear (from perspective of self) being the negative direction
# X coordinates
X = [0.95, 0.95, 0.673, 0.673, 0.000000000000000044, 0.000000000000000044,
     -0.673, -0.673, -0.95, -0.95, 0.587, 0.587, 0.0000000000000000612, 0.0000000000000000612,
     -0.587, -0.587, 0.719, 0.00000000000000000000000000000000375, -0.719,
     0.375, 0.375, 0.999, -0.999, -0.375, -0.375, -0.9139, -0.9139,.5,.6,.7,.8]
# Y coordinates
Y = [0.309, -0.309, 0.545, -0.545, 0.719, -0.719, 0.545, -0.545,
     0.309, -0.309, 0.809, -0.809, 0.999, -0.999, 0.809, -0.809, 0, -0.0000000000000000612,
     -0.0000000000000000881, 0.375, -0.375, 0, -0.000000000000000122, 0.375, -0.375, 0.2063, -0.2063,.5,.6,.7,.8]


# Convert cartesian coordinates to polar
def convert_to_polar(x, y):
    theta = np.arctan2(y, x)
    r = np.sqrt(x ** 2 + y ** 2)
    return theta, r

# Arrays that house the theta and radii from converted cartesian coordinates.
Thetas = []
Rs = []

# Converting cartesian coordinates to polar, for each electrode
for i in range(0, 31):
    theta, r = convert_to_polar(X[i], Y[i])
    Thetas.append(theta)
    Rs.append(r)

# Making a two column list that contains the converted thetas and radii, so the appropriate shape is attained.
points = [Thetas,Rs]
values = [[.51,.71,.81,.91,.72,.87,.90,.67,.78,.89,.56,.45,.68,.96,.69,.63,.37,.85,.92,.70,.74,.97,.35,.76,.68,.46,.68,90,91,92,93],
    [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,30,78,56,90]]

# now we create a grid of values, interpolated from our random sample above
theta = np.linspace(0.0, max_theta, 100)
r = np.linspace(0, max_r, 200)
grid_r, grid_theta = np.meshgrid(r, theta)
data = griddata(points, values, (grid_r, grid_theta),fill_value=0)

# Create a polar projection
ax1 = plt.subplot(projection="polar")
ax1.pcolormesh(theta, r, data.T)
plt.show()

我收到一个错误：

Traceback (most recent call last):
File "/Users/mac/NIH/EEG/Python/Testing heat map", line 50, in <module>
    data = griddata(points, values, (grid_r, grid_theta),fill_value=0)
File "/Users/mac/anaconda/lib/python2.7/site-packages/scipy/interpolate/ndgriddata.py", line 217, in griddata rescale=rescale)
File "scipy/interpolate/interpnd.pyx", line 246, in scipy.interpolate.interpnd.LinearNDInterpolator.__init__
    (scipy/interpolate/interpnd.c:4980)
File "scipy/spatial/qhull.pyx", line 1747, in scipy.spatial.qhull.Delaunay.__init__
    (scipy/spatial/qhull.c:15918)
File "scipy/spatial/qhull.pyx", line 415, in scipy.spatial.qhull._Qhull.__init__
    (scipy/spatial/qhull.c:5108) scipy.spatial.qhull.**QhullError: QH6214 qhull input error: not enough points(2) to construct initial simplex (need 33)**

While executing:  | qhull d Qbb Qt Q12 Qx Qz Qc Options selected for
Qhull 2015.2.r 2016/01/18:   run-id 1980533833  delaunay  Qbbound-last
Qtriangulate  Q12-no-wide-dup   Qxact-merge  Qz-infinity-point 
Qcoplanar-keep  _zero-centrum  Qinterior-keep  
Q3-no-merge-vertices-dim-high

粗体部分是我想了解的内容。 当我添加更多点时（也就是说，当我在列表X和Y中添加更多点成为极坐标时），错误声称需要的点数一直在增加，始终比输入的点数多两步。

有谁知道如何处理吗？

Answer 1

griddata的第一个参数必须具有形状(n, D) ，其中n是点的数量， D是这些点的尺寸。 您传入了points = [Thetas,Rs] ，其中Thetas和Rs是长度为31的列表。当该输入转换为二维数组时，它将具有形状(2, 31) Thetas (2, 31) 。 因此， griddata认为您仅传递了两个31维点。

要解决此问题，您可以使用numpy.column_stack创建points ，使其成为形状为(31, 2) numpy.column_stack ）的数组，例如：

points = np.column_stack((Thetas, Rs))