FooBar
Reputation: 16528
Iterated 2d grid interpolation with holes (missing values)
I have the following problem:
I have two grids, s0B and s1B, both 20x20, and a function s_0(s0, s1) evaluated at these grid points.
However, for some corners, s_0(s0, s1) cannot be evaluated, and returns np.nan.
I would like to have an interpolated function of my evaluated grid points that I can then use in a root solving problem (Fixed point in s_0 and the analogue s_1). Here is a rough sketch of the code right now:
# mesh 1d grids:
ss0 = np.array([ 0.38445455, 0.40388198, 0.42110923, 0.43626859, 0.44949237,
0.46091287, 0.47066239, 0.47887323, 0.48567771, 0.49120811,
0.49559675, 0.49897593, 0.50147794, 0.50323509, 0.50437969,
0.50504404, 0.50536044, 0.50546118, 0.50547859, 0.50554495])
ss1 = np.array([ 0.43490909, 0.50764658, 0.5719651 , 0.62838234, 0.67741596,
0.71958365, 0.75540309, 0.78539195, 0.81006791, 0.82994865,
0.84555185, 0.85739519, 0.86599635, 0.87187299, 0.87554281,
0.87752348, 0.87833267, 0.87848808, 0.87850736, 0.87890821])
s0B, s1B = np.meshgrid(ss0, ss1, indexing='ij')
# generate interpolated functions
idx = ~np.isnan(s0Max)
if idx.sum() == 0:
# check if there are any points at all
raise notImplementedError
s0MaxInterp = interpolate.interp2d(
s0B[idx], s1B[idx], s0Max[idx],
fill_value=np.nan, kind='linear')
idx = ~np.isnan(s1Max)
s1MaxInterp = interpolate.interp2d(
s0B[idx], s1B[idx], s1Max[idx],
fill_value=np.nan, kind='linear')
def errorFixedPoint(x, s0MaxInterp, s1MaxInterp, grids):
s0, s1 = x
# I skip some checks whether s0, s1 are inside the interpolation range
return np.array([s0 - s0MaxInterp(s0, s1)[0], s1 - s1MaxInterp(s0, s1)[0]])
result = optimize.root(errorFixedPoint, np.array([0.5, 0.9]),
args=(s0MaxInterp, s1MaxInterp, (ss0, ss1)), method='lm')
However, when trying this, I'm getting a RunTimeWarning:
RuntimeWarning: No more knots can be added because the number of B-spline
coefficients already exceeds the number of data points m.
Probable causes: either s or m too small. (fp>s)
kx,ky=1,1 nx,ny=20,20 m=314 fp=0.000001 s=0.000000
warnings.warn(RuntimeWarning(_iermess2[ierm][0] + _mess))
The interpolation appears sometimes quite off the mark:
However, this can be because the function is quite nonlinear over both dimensions:
I read on other places that scipy.interpolate.griddata is recommended as opposed to interpolate2d. However, I have to iteratively interpolate (for the root finding process), and grid data does not support that.
How can I attack this problem?
For reproducibility, I paste the values of s0Max and s1Max here:
nan = np.nan
s0Max = np.array([[ nan, nan, nan, nan, nan,
nan, nan, nan, nan, nan,
0.51494141, 0.51347656, 0.51210937, 0.51210937, 0.51210937,
0.51210937, 0.51210937, 0.51210937, 0.51210937, 0.51210937],
[ nan, nan, nan, nan, nan,
0.51337891, 0.5109375 , 0.51083984, 0.50253906, 0.50175781,
0.50429687, 0.50957031, 0.50859375, 0.50849609, 0.50839844,
0.50839844, 0.50839844, 0.50839844, 0.50839844, 0.50839844],
[ nan, nan, nan, 0.51347656, 0.50527344,
0.50009766, 0.49824219, 0.49746094, 0.49746094, 0.496875 ,
0.49746094, 0.49941406, 0.50742187, 0.50732422, 0.50732422,
0.50732422, 0.50732422, 0.50732422, 0.50732422, 0.50732422],
[ nan, nan, 0.51347656, 0.5015625 , 0.49863281,
0.49746094, 0.49628906, 0.49619141, 0.49570313, 0.49570313,
0.49619141, 0.49746094, 0.50722656, 0.50634766, 0.50625 ,
0.50625 , 0.50625 , 0.50625 , 0.50625 , 0.50625 ],
[ nan, nan, 0.50253906, 0.49824219, 0.496875 ,
0.49619141, 0.49560547, 0.49511719, 0.49511719, 0.49511719,
0.49550781, 0.49677734, 0.50625 , 0.50625 , 0.50625 ,
0.50625 , 0.50625 , 0.50625 , 0.50625 , 0.50625 ],
[ nan, 0.51210937, 0.49941406, 0.49746094, 0.49619141,
0.49560547, 0.49511719, 0.49453125, 0.49453125, 0.49453125,
0.49511719, 0.49628906, 0.50625 , 0.50527344, 0.50527344,
0.50527344, 0.50527344, 0.50527344, 0.50527344, 0.50527344],
[ nan, 0.50341797, 0.49804688, 0.49628906, 0.49570313,
0.49511719, 0.49453125, 0.49414062, 0.49404297, 0.49404297,
0.49453125, 0.49570313, 0.50527344, 0.50527344, 0.50527344,
0.50527344, 0.50527344, 0.50527344, 0.50527344, 0.50527344],
[ nan, 0.50078125, 0.49746094, 0.49619141, 0.49511719,
0.49453125, 0.49414062, 0.49404297, 0.49394531, 0.49394531,
0.49453125, 0.49570313, 0.50527344, 0.50527344, 0.50527344,
0.50527344, 0.50527344, 0.50527344, 0.50527344, 0.50527344],
[ nan, 0.49941406, 0.496875 , 0.49570313, 0.49511719,
0.49453125, 0.49404297, 0.49394531, 0.49355469, 0.49394531,
0.49414062, 0.49570313, 0.50527344, 0.50527344, 0.50517578,
0.50517578, 0.50507812, 0.50507812, 0.50507812, 0.50449219],
[ nan, 0.49873047, 0.49667969, 0.49560547, 0.49462891,
0.49414062, 0.49394531, 0.49355469, 0.49345703, 0.49355469,
0.49453125, 0.49628906, 0.50527344, 0.50517578, 0.50429687,
0.50429687, 0.50429687, 0.50429687, 0.50429687, 0.50429687],
[ 0.51347656, 0.49863281, 0.49628906, 0.49511719, 0.49453125,
0.49404297, 0.49394531, 0.49355469, 0.49355469, 0.49404297,
0.49570313, 0.50527344, 0.50429687, 0.50429687, 0.50429687,
0.50429687, 0.50429687, 0.50429687, 0.50429687, 0.50429687],
[ 0.51347656, 0.49814453, 0.49628906, 0.49511719, 0.49453125,
0.49404297, 0.49394531, 0.49355469, 0.49404297, 0.49570313,
0.50527344, 0.50429687, 0.50429687, 0.50429687, 0.50351563,
0.50351563, 0.50341797, 0.50341797, 0.50341797, 0.50341797],
[ 0.51347656, 0.49814453, 0.49619141, 0.49511719, 0.49453125,
0.49404297, 0.49394531, 0.49404297, 0.49511719, 0.50527344,
0.50429687, 0.50429687, 0.50351563, 0.50341797, 0.50341797,
0.50332031, nan, nan, nan, nan],
[ 0.51347656, 0.49814453, 0.49619141, 0.49511719, 0.49453125,
0.49404297, 0.49404297, 0.49453125, 0.49873047, 0.50507812,
0.50429687, 0.50351563, 0.50341797, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49814453, 0.49619141, 0.49511719, 0.49453125,
0.49404297, 0.49404297, 0.49511719, 0.50527344, 0.50429687,
0.50429687, 0.50341797, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49804688, 0.49619141, 0.49511719, 0.49453125,
0.49404297, 0.49453125, 0.49570313, 0.50527344, 0.50429687,
0.50429687, 0.50341797, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49804688, 0.49619141, 0.49511719, 0.49453125,
0.49414062, 0.49453125, 0.49619141, 0.50527344, 0.50429687,
0.50429687, 0.50341797, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49804688, 0.49619141, 0.49511719, 0.49453125,
0.49414062, 0.49453125, 0.49628906, 0.50527344, 0.50429687,
0.50351563, 0.50341797, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49804688, 0.49619141, 0.49511719, 0.49453125,
0.49414062, 0.49453125, 0.49628906, 0.50527344, 0.50429687,
0.50351563, 0.50341797, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.51347656, 0.49804688, 0.49619141, 0.49511719, 0.49453125,
0.49414062, 0.49453125, 0.49628906, 0.50527344, 0.50429687,
0.50351563, 0.50332031, nan, nan, nan,
nan, nan, nan, nan, nan]])
and
s1Max = np.array([[ nan, nan, nan, nan, nan,
nan, nan, nan, nan, nan,
0.99894531, 0.99895996, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, nan, nan, nan, nan,
0.99895996, 0.99895996, 0.99895996, 0.98726563, 0.98429688,
0.99896118, 0.99895996, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, nan, nan, 0.99895996, 0.99896118,
0.97 , 0.95265625, 0.93984375, 0.93195313, 0.930625 ,
0.93929688, 0.96421875, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, nan, 0.99895996, 0.98117188, 0.95429688,
0.93351563, 0.91695313, 0.90453125, 0.89703125, 0.896875 ,
0.908125 , 0.93789063, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, nan, 0.98648438, 0.95296875, 0.9278125 ,
0.9075 , 0.89101563, 0.87859375, 0.8715625 , 0.8725 ,
0.88617188, 0.92085938, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, 0.99895996, 0.9640625 , 0.93265625, 0.90789063,
0.88757813, 0.87109375, 0.85875 , 0.85210938, 0.8540625 ,
0.86992188, 0.90914063, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, 0.99023438, 0.94773438, 0.91703125, 0.89234375,
0.87203125, 0.85546875, 0.84320313, 0.83695313, 0.83976563,
0.85757813, 0.9009375 , 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, 0.97570313, 0.93515625, 0.90476563, 0.88015625,
0.8596875 , 0.843125 , 0.8309375 , 0.825 , 0.82867188,
0.84820313, 0.8953125 , 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, 0.96515625, 0.92546875, 0.89515625, 0.87046875,
0.85 , 0.83335938, 0.82140625, 0.81585938, 0.82046875,
0.84203125, 0.89390625, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ nan, 0.95757813, 0.918125 , 0.88773438, 0.86296875,
0.8425 , 0.82609375, 0.8146875 , 0.81054688, 0.81820313,
0.84664063, 0.91648438, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ 0.99896484, 0.953125 , 0.913125 , 0.88242188, 0.8575 ,
0.83726563, 0.821875 , 0.81289062, 0.81414063, 0.83429688,
0.89601563, 0.99895996, 0.99895996, 0.99895996, 0.99895996,
0.99895996, 0.99895996, 0.99895996, 0.99895996, 0.99895996],
[ 0.99896484, 0.95078125, 0.90992188, 0.87867188, 0.85390625,
0.83453125, 0.82164063, 0.81859375, 0.83421875, 0.89546875,
0.99895996, 0.99895996, 0.99895996, 0.99896484, 0.99125 ,
0.9909375 , 0.99078125, 0.99078125, 0.99078125, 0.99070313],
[ 0.99896484, 0.94945313, 0.9078125 , 0.87632813, 0.85195313,
0.83429688, 0.82554688, 0.83273438, 0.87804688, 0.99895996,
0.99895996, 0.99895996, 0.99117188, 0.99023438, 0.98945313,
0.98890625, nan, nan, nan, nan],
[ 0.99896484, 0.94859375, 0.90640625, 0.875 , 0.85125 ,
0.835625 , 0.83203125, 0.8534375 , 0.9571875 , 0.99895996,
0.99895996, 0.99125 , 0.98992188, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.948125 , 0.905625 , 0.87429688, 0.85125 ,
0.83757813, 0.83914063, 0.87632813, 0.99895996, 0.99895996,
0.99896484, 0.99046875, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.94789063, 0.90523438, 0.87398438, 0.85148438,
0.83929688, 0.8446875 , 0.89546875, 0.99895996, 0.99895996,
0.99896484, 0.98992188, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.94773438, 0.905 , 0.87382813, 0.85164063,
0.84023438, 0.84789063, 0.906875 , 0.99895996, 0.99895996,
0.99140625, 0.98960938, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.94773438, 0.90492188, 0.87382813, 0.85171875,
0.84054688, 0.84890625, 0.9109375 , 0.99895996, 0.99895996,
0.99132813, 0.98953125, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.94773438, 0.90492188, 0.87375 , 0.85171875,
0.840625 , 0.84914063, 0.91164063, 0.99895996, 0.99895996,
0.99132813, 0.98945313, nan, nan, nan,
nan, nan, nan, nan, nan],
[ 0.99896484, 0.94765625, 0.90492188, 0.87375 , 0.85179688,
0.84085938, 0.84984375, 0.91445313, 0.99895996, 0.99895996,
0.99132813, 0.989375 , nan, nan, nan,
nan, nan, nan, nan, nan]])
Upvotes: 0
Views: 1543
Answers (1)
Niklas
Reputation: 1380
According to this excellent answer here, using interp2d will not work for more complex data. It is suggested to use radial basis function interpolation.
This seemed to work and to give better interpolation results,
import scipy.optimize as optimize
from scipy.interpolate import Rbf
s0MaxInterp = Rbf(s0B[idx], s1B[idx], s0Max[idx], function='cubic')
s1MaxInterp = Rbf(s0B[idx], s1B[idx], s1Max[idx], function='cubic')
def errorFixedPoint(x, s0MaxInterp, s1MaxInterp, grids):
s0, s1 = x
# I skip some checks whether s0, s1 are inside the interpolation range
return np.array([s0 - s0MaxInterp(s0, s1), s1 - s1MaxInterp(s0, s1)])
result = optimize.root(errorFixedPoint, np.array([0.5, 0.9]),
args=(s0MaxInterp, s1MaxInterp, (ss0, ss1)), method='lm')
Note that I removed the [0] in the errorFixedPoint function.
Upvotes: 0
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