插复数整个阵列 [英] Interpolate whole arrays of complex numbers

问题描述

我公司拥有一批2维np.arrays（所有大小相同的）含有复数。他们每个人都属于一个位置在4维空间。这些职位是稀疏和不规则分布（拉丁超立方体被precise）。
我想在同样的4维空间插值这个数据到其他点。

I have a number of 2-dimensional np.arrays (all of equal size) containing complex numbers. Each of them belongs to one position in a 4-dimensional space. Those positions are sparse and distributed irregularly (a latin hypercube to be precise). I would like to interpolate this data to other points in the same 4-dimensional space.

我能成功地做到了简单的数字，即使用 sklearn.kriging（）， scipy.interpolate.Rbf（）（或其它）：

I can successfully do this for simple numbers, using either sklearn.kriging(), scipy.interpolate.Rbf() (or others):

# arrayof co-ordinates: 2 4D sets
X = np.array([[1.0, 0.0, 0.0, 0.0],\
              [0.0, 1.0, 0.0, 0.0]])

# two numbers, one for each of the points above 
Y = np.array([1,\
              0])

# define the type of gaussian process I want
kriging = gp.GaussianProcess(theta0=1e-2, thetaL=1e-4, thetaU=4.0,\
            corr='linear', normalize=True, nugget=0.00001, optimizer='fmin_cobyla')

# train the model on the data
kmodel = kriging.fit(X,Y)

# interpolate
kmodel.predict(np.array([0.5, 0.5, 0.0, 0.0]))
# returns: array([ 0.5])

如果我尝试使用阵列（或只是复数）数据，这不起作用：

If I try to use arrays (or just complex numbers) as data, this doesn't work:

# two arrays of complex numbers, instead of the numbers 
Y = np.array([[1+1j, -1-1j],\
              [0+0j,  0+0j]])

kmodel = kriging.fit(X,Y)
# returns: ValueError: The number of features in X (X.shape[1] = 1) should match the sample size used for fit() which is 4.

这是显而易见的，因为文档字符串为 kriging.fit（）明确指出，它需要ñ标量的数组，每个每个元素之一，X的第一维

This is obvious since the docstring for kriging.fit() clearly states that it needs an array of n scalars, one per each element in the first dimension of X.

一种解决方案是分解阵列Y中成单个数字，这些成实部和虚部，使各那些的一个单独的内插，然后再次把它们放在一起。我可以循环的正确组合和一些艺术性做到这一点，但如果有一个方法，这将是很好（如 scipy.interpolate ），可以处理整个NP。数组，而不是标量值。

One solution is to decompose the arrays in Y into individual numbers, those into real and imaginary parts, make a separate interpolation of each of those and then put them together again. I can do this with the right combination of loops and some artistry but it would be nice if there was a method (e.g. in scipy.interpolate) that could handle an entire np.array instead of scalar values.

我不是固定在一个特定的算法（还），所以我很乐意知道任何能够使用复数阵列的变量来进行插值。因为 - 正如我所说的 - 有空间很少，不规则的点（和无网格内插的），简单的线性插值不会做，当然，

I'm not fixed on a specific algorithm (yet), so I'd be happy to know about any that can use arrays of complex numbers as the "variable" to be interpolated. Since -- as I said -- there are few and irregular points in space (and no grid to interpolate on), simple linear interpolation won't do, of course.

推荐答案

有看着复数两种方式：

1. 直角坐标形式（A + BI）和


2. 极地/ Euler格式（A * EXP（我* PHI））

当你说你想要两个极坐标之间进行插值，你想相对于实/虚部（1）进行插值，或相对于数字的幅度和相位（2）？

When you say you want to interpolate between two polar coordinates, do you want to interpolate with respect to the real/imaginary components (1), or with respect to the number's magnitude and phase (2)?

您可以打破的东西分解成实部和虚部，

You CAN break things down into real and imaginary components,

X = 2 * 5j
X_real = np.real(X)
X_imag = np.imag(X)

# Interpolate the X_real and X_imag

# Reconstruct X
X2 = X_real + 1j * X_imag

然而，使用涉及到复杂的数字，如数字滤波器设计真实生活中的应用，则经常要在极性/指数形式编号，以正常工作。

However, With real-life applications that involve complex numbers, such as digital filter design, you quite often want to work with numbers in Polar/exponential form.

。因此，而不是插值np.real（）和np.imag（）组件，您可能需要把它分解成幅度和放大器;使用np.abs（）阶段和角度或< A HREF =htt​​p://docs.scipy.org/doc/numpy/reference/generated/numpy.arctan2.html#numpy.arctan2相对=nofollow> Arctan2 ，并分别插值。你可以这样做，例如，试图插值傅立叶变换的数字滤波器的时候。

Therefore instead of interpolating the np.real() and np.imag() components, you may want to break it down into magnitude & phase using np.abs() and Angle or Arctan2, and interpolate separately. You might do this, for example, when trying to interpolate the Fourier Transform of a digital filter.

Y = 1+2j
mag = np.abs(Y)
phase = np.angle(Y)

该插补值可以被转换回使用欧拉公式络合物（笛卡尔）编号

The interpolated values can be converted back into complex (Cartesian) numbers using the Eulers formula

# Complex number
y = mag * np.exp( 1j * phase)

# Or if you want the real and imaginary complex components separately,
realPart, imagPart = mag * np.cos(phase) , mag * np.sin(phase)

根据你在做什么，这让你与你使用插值方法一些真正的灵活性。

Depending on what you're doing, this gives you some real flexibility with the interpolation methods you use.

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