问题
I'm having a strange issue using scipy.interpolate.griddata. It's a QhullError. It says center point is coplanar with a facet, or a vertex is coplanar with a neighboring facet.. What does this error mean? How can it be overcome?
from scipy.interpolate import griddata
import numpy as np
def f(x, y): return (1 - x) ** 2 * 10 * (y - x**2) ** 2
X = np.linspace(-3, 3)
Y = np.linspace(-3, 3)
Z = f(X, Y)
xi = np.linspace(X.min(), X.max(), 1000)
yi = np.linspace(Y.min(), Y.max(), 1000)
zi = griddata((X, Y), Z, (xi[None,:], yi[:,None]), method='cubic')
QhullError Traceback (most recent call last)
~/Documents/SAStatement/sss.py in <module>
7 xi = np.linspace(X.min(), X.max(), 1000)
8 yi = np.linspace(Y.min(), Y.max(), 1000)
----> 9 zi = griddata((X, Y), Z, (xi[None,:], yi[:,None]), method='cubic')
/anaconda3/lib/python3.7/site-packages/scipy/interpolate/ndgriddata.py in griddata(points, values, xi, method, fill_value, rescale)
224 elif method == 'cubic' and ndim == 2:
225 ip = CloughTocher2DInterpolator(points, values, fill_value=fill_value,
--> 226 rescale=rescale)
227 return ip(xi)
228 else:
interpnd.pyx in scipy.interpolate.interpnd.CloughTocher2DInterpolator.__init__()
qhull.pyx in scipy.spatial.qhull.Delaunay.__init__()
qhull.pyx in scipy.spatial.qhull._Qhull.__init__()
QhullError: QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point)
While executing: | qhull d Qz Qt Qc Q12 Qbb
Options selected for Qhull 2015.2.r 2016/01/18:
run-id 62852831 delaunay Qz-infinity-point Qtriangulate Qcoplanar-keep
Q12-no-wide-dup Qbbound-last _pre-merge _zero-centrum Qinterior-keep
Pgood _max-width 6 Error-roundoff 8.3e-15 _one-merge 5.8e-14
Visible-distance 1.7e-14 U-coplanar-distance 1.7e-14 Width-outside 3.3e-14
_wide-facet 1e-13
precision problems (corrected unless 'Q0' or an error)
2 flipped facets
The input to qhull appears to be less than 3 dimensional, or a
computation has overflowed.
Qhull could not construct a clearly convex simplex from points:
- p38(v3): 1.7 1.7 1.7
- p50(v2): 8.9e-17 8.9e-17 6
- p49(v1): 3 3 5.5
- p0(v0): -3 -3 5.5
The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet. The maximum round off error for
computing distances is 8.3e-15. The center point, facets and distances
to the center point are as follows:
center point 0.4133 0.4133 4.641
facet p50 p49 p0 distance= 0
facet p38 p49 p0 distance= 0
facet p38 p50 p0 distance= 0
facet p38 p50 p49 distance= 0
These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates. Trial points
are first selected from points that maximize a coordinate.
The min and max coordinates for each dimension are:
0: -3 3 difference= 6
1: -3 3 difference= 6
2: -4.337e-19 6 difference= 6
If the input should be full dimensional, you have several options that
may determine an initial simplex:
- use 'QJ' to joggle the input and make it full dimensional
- use 'QbB' to scale the points to the unit cube
- use 'QR0' to randomly rotate the input for different maximum points
- use 'Qs' to search all points for the initial simplex
- use 'En' to specify a maximum roundoff error less than 8.3e-15.
- trace execution with 'T3' to see the determinant for each point.
If the input is lower dimensional:
- use 'QJ' to joggle the input and make it full dimensional
- use 'Qbk:0Bk:0' to delete coordinate k from the input. You should
pick the coordinate with the least range. The hull will have the
correct topology.
- determine the flat containing the points, rotate the points
into a coordinate plane, and delete the other coordinates.
- add one or more points to make the input full dimensional.
回答1:
Because your X and Y are identical, wich means all the points you provided to interpolate are the on the plane x=y.
X = np.linspace(-3, 3)
Y = (np.random.random(50)-0.5)*6 # Just make sure X and Y are non-linear.
Z = f(X, Y)
xi = np.linspace(X.min(), X.max(), 1000)
yi = np.linspace(Y.min(), Y.max(), 1000)
zi = griddata((X, Y), Z, (xi[None,:], yi[:,None]), method='cubic')
来源：https://stackoverflow.com/questions/56654686/scipy-griddata-qhullerror-center-point-is-coplanar-with-a-facet-or-a-vertex-is