我正在尝试使用scipy.interpolate.LinearNDInterpolator()来对8维空间中的数据点进行插值，并且遇到一个我不理解的错误：
scipy.spatial.qhull.QhullError: QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point)
之后是更多文本，我将在下面发布。使用我可以在网上找到的内容，我无法对代码中的错误进行优化。在我看来一切正常（我只复制了相关部分）：
from scipy import interpolate as inter
from numpy import array
npPoints = array(points)
npS = array(s)
inter.LinearNDInterpolator(npPoints, npS)
其中points是Nx8的嵌套浮点列表，s是Nx1的浮点列表，两者均已预先定义。
从我在documentation中看到的情况看，我似乎做得对。我的错误在哪里？我应该使用其他方法吗？
这是完整的Qhull错误：
Traceback (most recent call last):
File "BellDataFit", line 83, in <module>
inter.LinearNDInterpolator(npPoints, npS)
File "interpnd.pyx", line 248, in scipy.interpolate.interpnd.LinearNDInterpolator.__init__
File "qhull.pyx", line 1826, in scipy.spatial.qhull.Delaunay.__init__
File "qhull.pyx", line 354, in scipy.spatial.qhull._Qhull.__init__
scipy.spatial.qhull.QhullError: QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point)
While executing: | qhull d Qbb Qx Qz Q12 Qt Qc
Options selected for Qhull 2015.2.r 2016/01/18:
run-id 704299719 delaunay Qbbound-last Qxact-merge Qz-infinity-point
Q12-no-wide-dup Qtriangulate Qcoplanar-keep _zero-centrum Qinterior-keep
Q3-no-merge-vertices-dim-high Pgood _max-width 5.6 Error-roundoff 3.5e-14
_one-merge 6.7e-13 Visible-distance 2.1e-13 U-coplanar-distance 2.1e-13
Width-outside 4.2e-13 _wide-facet 1.3e-12
precision problems (corrected unless 'Q0' or an error)
2 flipped facets
11 nearly singular or axis-parallel hyperplanes
11 zero divisors during back substitute
119436 zero divisors during gaussian elimination
The input to qhull appears to be less than 9 dimensional, or a
computation has overflowed.
Qhull could not construct a clearly convex simplex from points:
- p3(v9): -0.89 -0.89 0 0 0 -1.7 -3.1 -3.1 2.1
- p2(v8): -0.89 -0.89 0 0 0 -2.1 -3.1 -3.1 2.7
- p1(v7): -0.89 -0.89 0 0 0 -2.4 -3.1 -3.1 3.4
- p16(v6): -0.89 -0.89 0 0 0 2.8 -3.1 -3.1 4.3
- p2720(v5): 0 0 -0.89 0.89 0 -2.8 -3.1 -3.1 4.3
- p2448(v4): 0 0 -0.89 -0.89 0 -2.8 -3.1 -3.1 4.3
- p7055(v3): 0 0 0.89 -0.89 0 -2.8 -3.1 -3.1 4.3
- p272(v2): -0.89 0.89 0 0 0 -2.8 -3.1 -3.1 4.3
- p0(v1): -0.89 -0.89 0 0 0 -2.8 -3.1 -3.1 4.3
- p9503(v0): 0.89 -0.89 0 0 0 -2.8 -3.1 -3.1 4.3
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 3.5e-14. The center point, facets and distances
to the center point are as follows:
center point -0.4444 -0.4444 -0.08889 -0.08889 0 -2.025 -3.142 -3.142 3.806
facet p2 p1 p16 p2720 p2448 p7055 p272 p0 p9503 distance= 0
facet p3 p1 p16 p2720 p2448 p7055 p272 p0 p9503 distance= 0
facet p3 p2 p16 p2720 p2448 p7055 p272 p0 p9503 distance= 0
facet p3 p2 p1 p2720 p2448 p7055 p272 p0 p9503 distance= 0
facet p3 p2 p1 p16 p2448 p7055 p272 p0 p9503 distance= 0
facet p3 p2 p1 p16 p2720 p7055 p272 p0 p9503 distance= -0.13
facet p3 p2 p1 p16 p2720 p2448 p272 p0 p9503 distance= 0
facet p3 p2 p1 p16 p2720 p2448 p7055 p0 p9503 distance= 0
facet p3 p2 p1 p16 p2720 p2448 p7055 p272 p9503 distance= 0
facet p3 p2 p1 p16 p2720 p2448 p7055 p272 p0 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.
Because of the high dimension, the min x-coordinate and max-coordinate
points are used if the determinant is non-zero. Option 'Qs' will
do a better, though much slower, job. Instead of 'Qs', you can change
the points by randomly rotating the input with 'QR0'.
The min and max coordinates for each dimension are:
0: -0.8889 0.8889 difference= 1.778
1: -0.8889 0.8889 difference= 1.778
2: -0.8889 0.8889 difference= 1.778
3: -0.8889 0.8889 difference= 1.778
4: 0 0 difference= 0
5: -2.793 2.793 difference= 5.585
6: -3.142 -2.225e-308 difference= 3.142
7: -3.142 -2.225e-308 difference= 3.142
8: 1.776e-15 5.585 difference= 5.585
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 3.5e-14.
- 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.
答案 0 :(得分：1)
在我看来，出现此问题的原因是，正如错误所指出的，即使您要传递的是9列数组，您的数据（或给定的一组数据）实际上都小于9维。您可以在错误消息中打印出的数据中看到，第5、7和8列是恒定的。这意味着这些列是线性相关的，并且该数据集只有7个维度。在进行过程中，它试图形成一个9维的simplex，但不能形成一个convex的物体。
当我编写一个运行Xfoil的airfoil database时，这个问题对我出现了，它获得了不同的迎角，雷诺数，襟翼偏斜等情况下的机翼系数。该空间中很多点的任何结果。那意味着我最终得到了一个数据库，其中所有点都在相同的雷诺数下。即使我说过，这也使数据库不依赖于雷诺数。我的数据比我的数据要少。
我将通过确保数据中的所有点都是唯一的并且每列实际上为集合添加维度来解决此问题。