I am trying to create an above-head view heat map of relatively sparse EEG data (27 electrodes). I convert x,y cartesian coordinates of the EEG electrodes to polar, and attempt to map them as such. Each x,y coordinate corresponds to a given value (if you want to know: Hurst exponent) to which I would like the color around that location to correspond.
I started with working code from this page and tried to adapt it to my problem. Unfortunately, my adaptation is not working.
Here is my code:
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()
I get an error:
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
The bolded portion is what I am trying to understand. When I add more points (that is, when I add more points to the lists X and Y that become polar coordinates), the number of points the error claims to need keeps increasing, always two steps ahead of how many points I have input.
Does anyone have any idea how to deal with this?
The first argument to griddata must have shape (n, D), where n is the number of points, and D is the dimension of those points. You passed in points = [Thetas,Rs], where Thetas and Rs are lists with length 31. When that input is converted to a two-dimensional array, it will have shape (2, 31). So griddata thinks you have passed in just two 31-dimensional points.
To fix this, you can create points using numpy.column_stack so that it is an array with shape (31, 2), e.g.:
points = np.column_stack((Thetas, Rs))