如何将某些函数应用于 python 网格网格? [英] How do I apply some function to a python meshgrid?

问题描述

假设我想为网格上的每个点计算一个值.我会定义一些函数 func，它接受两个值 x 和 y 作为参数并返回第三个值.在下面的示例中，计算此值需要在外部字典中查找.然后我会生成一个点网格并在每个点上评估 func 以获得我想要的结果.

下面的代码正是这样做的，但有点迂回.首先，我将 X 和 Y 坐标矩阵都重新整形为一维数组，计算所有值，然后将结果重新整形为矩阵.我的问题是，这可以以更优雅的方式完成吗?

将集合导入为 c# 一些任意的查找表a = c.defaultdict(int)[1] = 2[2] = 3[3] = 2[4] = 3定义函数(x，y):# 一些任意函数返回 a[x] + a[y]X,Y = np.mgrid[1:3, 1:4]X = X.TY = Y.TZ = np.array([func(x,y) for (x,y) in zip(X.ravel(), Y.ravel())]).reshape(X.shape)打印 Z

此代码的目的是生成一组值，我可以将这些值与 matplotlib 中的 pcolor 一起使用以创建热图类型的图.

解决方案

我会使用 numpy.vectorize 来矢量化"你的函数.请注意，尽管名称如此，vectorize 并不是为了让您的代码运行得更快——只是稍微简化一下.

以下是一些示例:

<预><代码>>>>将 numpy 导入为 np>>>@np.vectorize... def foo(a, b):...返回 a + b...>>>foo([1,3,5], [2,4,6])数组([ 3, 7, 11])>>>foo(np.arange(9).reshape(3,3), np.arange(9).reshape(3,3))数组([[ 0, 2, 4],[ 6, 8, 10],[12, 14, 16]])

使用您的代码，用 np.vectorize 装饰 func 应该就足够了，然后您可以将其称为 func(X, Y) -- 不需要 raveling 或 reshapeing :

将 numpy 导入为 np将集合导入为 c# 一些任意的查找表a = c.defaultdict(int)[1] = 2[2] = 3[3] = 2[4] = [e-mail]定义函数(x，y):# 一些任意函数返回 a[x] + a[y]X,Y = np.mgrid[1:3, 1:4]X = X.TY = Y.TZ = func(X, Y)

Say I want to calculate a value for every point on a grid. I would define some function func that takes two values x and y as parameters and returns a third value. In the example below, calculating this value requires a look-up in an external dictionary. I would then generate a grid of points and evaluate func on each of them to get my desired result.

The code below does precisely this, but in a somewhat roundabout way. First I reshape both the X and Y coordinate matrices into one-dimensional arrays, calculate all the values, and then reshape the result back into a matrix. My questions is, can this be done in a more elegant manner?

import collections as c

# some arbitrary lookup table
a = c.defaultdict(int)
a[1] = 2
a[2] = 3
a[3] = 2
a[4] = 3

def func(x,y):
    # some arbitrary function
    return a[x] + a[y]

X,Y = np.mgrid[1:3, 1:4]
X = X.T
Y = Y.T

Z = np.array([func(x,y) for (x,y) in zip(X.ravel(), Y.ravel())]).reshape(X.shape)
print Z

The purpose of this code is to generate a set of values that I can use with pcolor in matplotlib to create a heatmap-type plot.

解决方案

I'd use numpy.vectorize to "vectorize" your function. Note that despite the name, vectorize is not intended to make your code run faster -- Just simplify it a bit.

Here's some examples:

>>> import numpy as np
>>> @np.vectorize
... def foo(a, b):
...    return a + b
... 
>>> foo([1,3,5], [2,4,6])
array([ 3,  7, 11])
>>> foo(np.arange(9).reshape(3,3), np.arange(9).reshape(3,3))
array([[ 0,  2,  4],
       [ 6,  8, 10],
       [12, 14, 16]])

With your code, it should be enough to decorate func with np.vectorize and then you can probably just call it as func(X, Y) -- No raveling or reshapeing necessary:

import numpy as np
import collections as c

# some arbitrary lookup table
a = c.defaultdict(int)
a[1] = 2
a[2] = 3
a[3] = 2
a[4] = 3

@np.vectorize
def func(x,y):
    # some arbitrary function
    return a[x] + a[y]

X,Y = np.mgrid[1:3, 1:4]
X = X.T
Y = Y.T

Z = func(X, Y)

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