python/scipy中的多元样条插值? [英] Multivariate spline interpolation in python/scipy?
问题描述
是否有库模块或其他简单的方法可以在python中实现多元样条插值?
Is there a library module or other straightforward way to implement multivariate spline interpolation in python?
具体来说，我在规则排列的三维网格上有一组标量数据，需要在散布在整个域中的少量点处进行插值.对于两个维度，我一直在使用 scipy.interpolate.RectBivariateSpline ，而我本质上是在寻找将其扩展到三维数据的方法.
Specifically, I have a set of scalar data on a regularly-spaced three-dimensional grid which I need to interpolate at a small number of points scattered throughout the domain. For two dimensions, I have been using scipy.interpolate.RectBivariateSpline, and I'm essentially looking for an extension of that to three-dimensional data.
The N-dimensional interpolation routines I have found are not quite good enough: I would prefer splines over LinearNDInterpolator for smoothness, and I have far too many data points (often over one million) for, e.g., a radial basis function to work.
如果有人知道可以执行此操作的python库，或者可能会调用或移植另一种语言的python库，我将不胜感激.
If anyone knows of a python library that can do this, or perhaps one in another language that I could call or port, I'd really appreciate it.
推荐答案
如果我正确地理解了您的问题，那么您输入的观测"数据会定期网格化吗?
If I'm understanding your question correctly, your input "observation" data is regularly gridded?
如果是这样， scipy.ndimage.map_coordinates 完全满足您的要求.
If so, scipy.ndimage.map_coordinates does exactly what you want.
乍一看有点难理解，但是从本质上讲，您只是向它提供了一系列要在像素/体素/n维指数坐标中插值网格值的坐标.
It's a bit hard to understand at first pass, but essentially, you just feed it a sequence of coordinates that you want to interpolate the values of the grid at in pixel/voxel/n-dimensional-index coordinates.
作为2D示例:
import numpy as np
from scipy import ndimage
import matplotlib.pyplot as plt
# Note that the output interpolated coords will be the same dtype as your input
# data. If we have an array of ints, and we want floating point precision in
# the output interpolated points, we need to cast the array as floats
data = np.arange(40).reshape((8,5)).astype(np.float)
# I'm writing these as row, column pairs for clarity...
coords = np.array([[1.2, 3.5], [6.7, 2.5], [7.9, 3.5], [3.5, 3.5]])
# However, map_coordinates expects the transpose of this
coords = coords.T
# The "mode" kwarg here just controls how the boundaries are treated
# mode='nearest' is _not_ nearest neighbor interpolation, it just uses the
# value of the nearest cell if the point lies outside the grid. The default is
# to treat the values outside the grid as zero, which can cause some edge
# effects if you're interpolating points near the edge
# The "order" kwarg controls the order of the splines used. The default is
# cubic splines, order=3
zi = ndimage.map_coordinates(data, coords, order=3, mode='nearest')
row, column = coords
nrows, ncols = data.shape
im = plt.imshow(data, interpolation='nearest', extent=[0, ncols, nrows, 0])
plt.colorbar(im)
plt.scatter(column, row, c=zi, vmin=data.min(), vmax=data.max())
for r, c, z in zip(row, column, zi):
plt.annotate('%0.3f' % z, (c,r), xytext=(-10,10), textcoords='offset points',
arrowprops=dict(arrowstyle='->'), ha='right')
plt.show()
要在n维中执行此操作，我们只需要传递适当大小的数组即可:
To do this in n-dimensions, we just need to pass in the appropriate sized arrays:
import numpy as np
from scipy import ndimage
data = np.arange(3*5*9).reshape((3,5,9)).astype(np.float)
coords = np.array([[1.2, 3.5, 7.8], [0.5, 0.5, 6.8]])
zi = ndimage.map_coordinates(data, coords.T)
就扩展和内存使用而言，如果您使用的顺序> 1(即非线性插值)，则map_coordinates将创建数组的过滤副本.如果只想在极少的点进行插值，则这是相当大的开销.但是，它不会随着要插入的点数而增加.只要有足够的RAM用于输入数据数组的单个临时副本，就可以了.
As far as scaling and memory usage goes, map_coordinates will create a filtered copy of the array if you're using an order > 1 (i.e. not linear interpolation). If you just want to interpolate at a very small number of points, this is a rather large overhead. It doesn't increase with the number points you want to interpolate at, however. As long as have enough RAM for a single temporary copy of your input data array, you'll be fine.
如果无法将数据副本存储在内存中，则可以a)指定prefilter=False和order=1并使用线性插值，或者b)使用ndimage.spline_filter用过滤后的版本替换原始数据，然后使用prefilter=False调用map_coordinates.
If you can't store a copy of your data in memory, you can either a) specify prefilter=False and order=1 and use linear interpolation, or b) replace your original data with a filtered version using ndimage.spline_filter, and then call map_coordinates with prefilter=False.
即使您有足够的内存，如果需要多次调用map_coordinates(例如，交互式使用等)，则保持过滤后的数据集也可以大大提高速度.
Even if you have enough ram, keeping the filtered dataset around can be a big speedup if you need to call map_coordinates multiple times (e.g. interactive use, etc).
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