Python/NumPy中的meshgrid的用途是什么? [英] What is the purpose of meshgrid in Python / NumPy?

问题描述

有人可以向我解释Numpy中meshgrid函数的目的是什么?我知道它会创建某种用于绘制的坐标网格，但我真的看不到它的直接好处.

Can someone explain to me what is the purpose of meshgrid function in Numpy? I know it creates some kind of grid of coordinates for plotting, but I can't really see the direct benefit of it.

我正在研究Sebastian Raschka的"Python机器学习"，他正在使用它来绘制决策边界.请参见输入11 此处.

I am studying "Python Machine Learning" from Sebastian Raschka, and he is using it for plotting the decision borders. See input 11 here.

我也在官方文档中尝试过此代码，但是，再次，输出对我来说真的没有意义.

I have also tried this code from official documentation, but, again, the output doesn't really make sense to me.

x = np.arange(-5, 5, 1)
y = np.arange(-5, 5, 1)
xx, yy = np.meshgrid(x, y, sparse=True)
z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2)
h = plt.contourf(x,y,z)

如果可能的话，还请给我展示很多真实的例子.

Please, if possible, also show me a lot of real-world examples.

推荐答案

meshgrid的目的是根据x值数组和y值数组创建矩形网格.

The purpose of meshgrid is to create a rectangular grid out of an array of x values and an array of y values.

因此，例如，如果要创建一个网格，则在x和y方向上每个介于0和4之间的整数值处都有一个点.要创建矩形网格，我们需要x和y点的每种组合.

So, for example, if we want to create a grid where we have a point at each integer value between 0 and 4 in both the x and y directions. To create a rectangular grid, we need every combination of the x and y points.

这将是25分，对吧?因此，如果我们想为所有这些点创建一个x和y数组，我们可以执行以下操作.

This is going to be 25 points, right? So if we wanted to create an x and y array for all of these points, we could do the following.

x[0,0] = 0    y[0,0] = 0
x[0,1] = 1    y[0,1] = 0
x[0,2] = 2    y[0,2] = 0
x[0,3] = 3    y[0,3] = 0
x[0,4] = 4    y[0,4] = 0
x[1,0] = 0    y[1,0] = 1
x[1,1] = 1    y[1,1] = 1
...
x[4,3] = 3    y[4,3] = 4
x[4,4] = 4    y[4,4] = 4

这将导致以下x和y矩阵，这样，每个矩阵中对应元素的配对将给出网格中某个点的x和y坐标.

This would result in the following x and y matrices, such that the pairing of the corresponding element in each matrix gives the x and y coordinates of a point in the grid.

x =   0 1 2 3 4        y =   0 0 0 0 0
      0 1 2 3 4              1 1 1 1 1
      0 1 2 3 4              2 2 2 2 2
      0 1 2 3 4              3 3 3 3 3
      0 1 2 3 4              4 4 4 4 4

然后我们可以绘制这些图形以确认它们是网格:

We can then plot these to verify that they are a grid:

plt.plot(x,y, marker='.', color='k', linestyle='none')

显然，这变得非常乏味，尤其是对于大范围的x和y.实际上，meshgrid可以为我们生成此代码:我们只需指定唯一的x和y值即可.

Obviously, this gets very tedious especially for large ranges of x and y. Instead, meshgrid can actually generate this for us: all we have to specify are the unique x and y values.

xvalues = np.array([0, 1, 2, 3, 4]);
yvalues = np.array([0, 1, 2, 3, 4]);

现在，当我们调用meshgrid时，我们将自动获得先前的输出.

Now, when we call meshgrid, we get the previous output automatically.

xx, yy = np.meshgrid(xvalues, yvalues)

plt.plot(xx, yy, marker='.', color='k', linestyle='none')

创建这些矩形网格对于许多任务很有用.在您的帖子中提供的示例中，这只是在x和y的值范围内对函数(sin(x**2 + y**2) / (x**2 + y**2))进行采样的一种简单方法.

Creation of these rectangular grids is useful for a number of tasks. In the example that you have provided in your post, it is simply a way to sample a function (sin(x**2 + y**2) / (x**2 + y**2)) over a range of values for x and y.

由于此功能已在矩形网格上采样，因此现在可以将其可视化为图像".

Because this function has been sampled on a rectangular grid, the function can now be visualized as an "image".

另外，现在可以将结果传递给期望在矩形网格上显示数据的函数(即contourf)

Additionally, the result can now be passed to functions which expect data on rectangular grid (i.e. contourf)

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