3D 数组上的快速插值 [英] Fast interpolation over 3D array

问题描述

我有一个 3D 数组，需要在一个轴(最后一个维度)上进行插值.假设 y.shape = (nx, ny, nz)，我想在 nz 中为每个 (nx, ny) 进行插值.但是，我想在每个 [i, j] 中插入不同的值.

I have a 3D array that I need to interpolate over one axis (the last dimension). Let's say y.shape = (nx, ny, nz), I want to interpolate in nz for every (nx, ny). However, I want to interpolate for a different value in each [i, j].

这是一些示例代码.如果我想插入单个值，比如 new_z，我会像这样使用 scipy.interpolate.interp1d

Here's some code to exemplify. If I wanted to interpolate to a single value, say new_z, I'd use scipy.interpolate.interp1d like this

# y is a 3D ndarray
# x is a 1D ndarray with the abcissa values
# new_z is a number
f = scipy.interpolate.interp1d(x, y, axis=-1, kind='linear')
result = f(new_z)

然而，对于这个问题，我真正想要的是为每个 y[i, j] 插入一个不同的 new_z.所以我这样做:

However, for this problem what I actually want is to interpolate to a different new_z for each y[i, j]. So I do this:

# y is a 3D ndarray
# x is a 1D ndarray with the abcissa values
# new_z is a 2D array
result = numpy.empty(y.shape[:-1])
for i in range(nx):
    for j in range(ny):
        f = scipy.interpolate.interp1d(x, y[i, j], axis=-1, kind='linear')
        result[i, j] = f(new_z[i, j])

不幸的是，如果有多个循环，这会变得低效且缓慢.有没有更好的方法来做这种插值?线性插值就足够了.一种可能性是在 Cython 中实现这一点，但我试图避免这种情况，因为我希望能够灵活地更改为三次插值，并且不想在 Cython 中手动完成.

Unfortunately, with multiple loops this becomes inefficient and slow. Is there a better way to do this kind of interpolation? Linear interpolation is sufficient. A possibility is to implement this in Cython, but I was trying to avoid that because I want to have the flexibility of changing to cubic interpolation and don't want to do it by hand in Cython.

推荐答案

为了加速高阶插值，你可以只调用一次 interp1d()，然后使用 _spline> 属性和 _fitpack 模块中的低级函数 _bspleval().代码如下:

To speedup high order interpolate, you can call interp1d() only once, and then use the _spline attribute and the low level function _bspleval() in the _fitpack module. Here is the code:

from scipy.interpolate import interp1d
import numpy as np

nx, ny, nz = 30, 40, 50
x = np.arange(0, nz, 1.0)
y = np.random.randn(nx, ny, nz)
new_x = np.random.random_integers(1, (nz-1)*10, size=(nx, ny))/10.0

def original_interpolation(x, y, new_x):
    result = np.empty(y.shape[:-1])
    for i in xrange(nx):
        for j in xrange(ny):
            f = interp1d(x, y[i, j], axis=-1, kind=3)
            result[i, j] = f(new_x[i, j])
    return result

def fast_interpolation(x, y, new_x):
    from scipy.interpolate._fitpack import _bspleval
    f = interp1d(x, y, axis=-1, kind=3)
    xj,cvals,k = f._spline
    result = np.empty_like(new_x)
    for (i, j), value in np.ndenumerate(new_x):
        result[i, j] = _bspleval(value, x, cvals[:, i, j], k, 0)
    return result

r1 = original_interpolation(x, y, new_x)
r2 = fast_interpolation(x, y, new_x)

>>> np.allclose(r1, r2)
True

%timeit original_interpolation(x, y, new_x)
%timeit fast_interpolation(x, y, new_x)
1 loops, best of 3: 3.78 s per loop
100 loops, best of 3: 15.4 ms per loop

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