如何将标量函数重塑为网格上的标量函数 [英] How to reshape a scalar funcction to a scalar function on a grid

问题描述

我的问题更多是关于如何组织np.meshgrid以便更好地理解它的一般问题.因此，我有一组3d点，对于每个点，我都有一个与之关联的标量值.因此，对于此函数，其形状为n x 1，但是现在我想使用相同的值将其重塑为np.meshgrid，这意味着使其成为3D numpy数组.但是，我不知道如何开始执行此操作，因为我不知道它的外观.您知道我该怎么做以及其背后的原因吗?

My question is more of a general question about how np.meshgrid is organized to understand it better. So I have a set of 3d points and for each point I have a scalar value associated with it. So for this function is shaped as n x 1, however now I want to reshape this function with the same values, to a np.meshgrid this means to make it to a 3D numpy array. However I don't understand how can I begin to do that this, since I don't know how it supposed to look like. Do you know how I can do this and the reasoning behind it?

谢谢，我真的是np.meshgrids的新手，我仍然无法完全理解它.

Thank you I'm really new to np.meshgrids and I still can't comprehend it fully.

推荐答案

我将以2D方式对其进行解释(如果您很容易理解，则可以使用3D).

I will explain it in 2D (going to 3D if you understand it is quite easy).

假设您有一个二维平面的截面.可以说它是一个长度和宽度为5的正方形.但是x的坐标在[10,15]中 和[15,20]中的y.

Just imagine you have a section from the two dimensional plane. Lets say its a square with 5 in length and width. But the coordinates for x are in [10,15] and for y in [15,20], respectively.

现在，您要在此部分评估函数(假设分辨率为0.5). Numpys meshgrid 现在为您提供了两个矩阵，其中保存了每个像素"(0.5 x 0.5区域)的x和y坐标.

Now you want to evaluate a function on this section (lets say with a resolution of 0.5). Numpys meshgrid now gives you two matrices in which the x and y coordinates for each "pixel" (0.5 x 0.5 area) are saved.

在某些代码中，它看起来像:

In some code this looks like:

import numpy as np

x = np.arange(10,15,.5)
y = np.arange(15,20,.5)

xx, yy = np.meshgrid(x,y, indexing = 'ij')

我们的区域被分成10x10像素，因此我们希望形状为:

our area is dived into 10x10 pixels and therefore we expect the shapes to be:

xx.shape
>>> (10, 10)

yy.shape
>>> (10, 10)

看着xx:

array([[10. , 10. , 10. , 10. , 10. , 10. , 10. , 10. , 10. , 10. ],
       [10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5],
       [11. , 11. , 11. , 11. , 11. , 11. , 11. , 11. , 11. , 11. ],
       [11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5, 11.5],
       [12. , 12. , 12. , 12. , 12. , 12. , 12. , 12. , 12. , 12. ],
       [12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5],
       [13. , 13. , 13. , 13. , 13. , 13. , 13. , 13. , 13. , 13. ],
       [13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5, 13.5],
       [14. , 14. , 14. , 14. , 14. , 14. , 14. , 14. , 14. , 14. ],
       [14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5, 14.5]])

和yy:

array([[15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5],
       [15. , 15.5, 16. , 16.5, 17. , 17.5, 18. , 18.5, 19. , 19.5]])

所以对于x方向为4像素，y方向为5像素的坐​​标，您可以得到:

so to the the coordinates for the 4 pixel into x and 5 pixel into y direction you can just get:

x_coord = xx[4,5]
y_coord = yy[4,5]

x_coord
>>> 12.0

y_coord
>>> 17.5

如果要在3D模式下使用，则只有三个立方体，而不是两个矩阵.

If you want in 3D you have three cubes instead of two matrices that's basically it.

现在，如果您要对此求值，请说:

Now if you want to evaluate a function on this lets say:

def fun(x,y):
    return np.sin(x)*np.cos(y)

您可以像这样使用xx和yy:

zz = fun(xx,yy)
zz.shape

>>> (10, 10)

它看起来像:

import matplotlib.pyplot as plt
plt.contourf(xx,yy,zz)

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