Python/NumPy中meshgrid的目的是什么? [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 函数的用途是什么吗?我知道它为绘图创建了某种坐标网格，但我看不出它的直接好处.

我正在学习 Sebastian Raschka 的Python 机器学习"，他用它来绘制决策边界.请参阅输入 11

显然，这会变得非常乏味，尤其是对于大范围的 x 和 y.相反，meshgrid 实际上可以为我们生成:我们需要指定的只是唯一的 x 和 y 值.

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，我们会自动获得之前的输出.

xx, yy = np.meshgrid(xvalues, yvalues)plt.plot(xx, yy, 标记='.', color='k', linestyle='none')

创建这些矩形网格对许多任务很有用.在您在帖子中提供的示例中，它只是一种对函数进行采样的方法 (sin(x**2 + y**2)/(x**2 + y**2)) 在 x 和 y 的值范围内.

由于此函数已在矩形网格上采样，因此现在可以将该函数可视化为图像".

此外，现在可以将结果传递给需要矩形网格数据的函数(即contourf)

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.

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

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)

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

解决方案

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

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.

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

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

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

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

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]);

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')

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.

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

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

这篇关于Python/NumPy中meshgrid的目的是什么?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！