blocks|key|4428003|text|假设你有一个函数：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|4428004|def+sinus2d(x,+y):
++++return+np.sin(x)+%2B+np.sin(y)|code-block|syntax|javascript|4428005|例如，你想看看它在0到2*pi的范围内是什么样子的。你会怎么做？下面是np.meshgrid的用法：|offset|length|style|CODE|4428006|xx,+yy+=+np.meshgrid(np.linspace(0,2*np.pi,100),+np.linspace(0,2*np.pi,100))
z+=+sinus2d(xx,+yy)+#+Create+the+image+on+this+grid|4428007|这样的图应该是这样的：|4428008|import+matplotlib.pyplot+as+plt
plt.imshow(z,+origin='lower',+interpolation='none')
plt.show()|4428009|​|4428010|📷|atomic|4428011|4428012|所以np.meshgrid只是一种便利。原则上，同样的工作可以通过以下方式完成：|4428013|z2+=+sinus2d(np.linspace(0,2*np.pi,100)[:,None],+np.linspace(0,2*np.pi,100)[None,:])|4428014|但是你需要注意你的维度(假设你有两个以上的维度...)以及正确的广播。np.meshgrid为您完成了所有这些工作。|4428015|例如，如果您想要进行插值，但排除某些值，则meshgrid还允许您删除坐标和数据：|4428016|condition+=+z>0.6
z_new+=+z[condition]+#+This+will+make+your+array+1D|4428017|那么现在如何进行插值呢？您可以将x和y赋给像scipy.interpolate.interp2d这样的插值函数，因此您需要一种方法来知道删除了哪些坐标：|4428018|x_new+=+xx[condition]
y_new+=+yy[condition]|4428019|然后你仍然可以使用“正确的”坐标进行插值(试着不使用网格，你会有很多额外的代码)：|4428020|from+scipy.interpolate+import+interp2d
interpolated+=+interp2d(x_new,+y_new,+z_new)|4428021|原始网格允许您再次在原始网格上进行插值：|4428022|interpolated_grid+=+interpolated(xx[0],+yy[:,+0]).reshape(xx.shape)|4428023|这些只是我使用meshgrid的一些例子，可能还有更多的例子。|4428024|entityMap|0|IMAGE|mutability|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/a97ef97520976f833b9a0926e2a669d4.png|imageAlt^0|0|0|Z|B|0|0|0|0|0|0|1|0|0|0|2|B|0|0|Z|B|0|0|0|G|1|I|1|M|Q|0|0|0|0|0|0|7|8|0^^$0|@$1|2|3|4|5|6|7|1V|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|1W|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|1X|8|@$I|1Y|J|1Z|K|L]]|9|@]|A|$]]|$1|M|3|N|5|D|7|20|8|@]|9|@]|A|$E|F]]|$1|O|3|P|5|6|7|21|8|@]|9|@]|A|$]]|$1|Q|3|R|5|D|7|22|8|@]|9|@]|A|$E|F]]|$1|S|3|T|5|6|7|23|8|@]|9|@]|A|$]]|$1|U|3|V|5|W|7|24|8|@]|9|@$I|25|J|26|1|27]]|A|$]]|$1|X|3|T|5|6|7|28|8|@]|9|@]|A|$]]|$1|Y|3|Z|5|6|7|29|8|@$I|2A|J|2B|K|L]]|9|@]|A|$]]|$1|10|3|11|5|D|7|2C|8|@]|9|@]|A|$E|F]]|$1|12|3|13|5|6|7|2D|8|@$I|2E|J|2F|K|L]]|9|@]|A|$]]|$1|14|3|15|5|6|7|2G|8|@]|9|@]|A|$]]|$1|16|3|17|5|D|7|2H|8|@]|9|@]|A|$E|F]]|$1|18|3|19|5|6|7|2I|8|@$I|2J|J|2K|K|L]|$I|2L|J|2M|K|L]|$I|2N|J|2O|K|L]]|9|@]|A|$]]|$1|1A|3|1B|5|D|7|2P|8|@]|9|@]|A|$E|F]]|$1|1C|3|1D|5|6|7|2Q|8|@]|9|@]|A|$]]|$1|1E|3|1F|5|D|7|2R|8|@]|9|@]|A|$E|F]]|$1|1G|3|1H|5|6|7|2S|8|@]|9|@]|A|$]]|$1|1I|3|1J|5|D|7|2T|8|@]|9|@]|A|$E|F]]|$1|1K|3|1L|5|6|7|2U|8|@$I|2V|J|2W|K|L]]|9|@]|A|$]]|$1|1M|3|-4|5|6|7|2X|8|@]|9|@]|A|$]]]|1N|$1O|$5|1P|1Q|1R|A|$1S|1T|1U|-4]]]]

Suppose you have a function:

<pre><code>def sinus2d(x, y):
 return np.sin(x) + np.sin(y)
</code></pre>

and you want, for example, to see what it looks like in the range 0 to 2*pi. How would you do it? There <code>np.meshgrid</code> comes in:

<pre><code>xx, yy = np.meshgrid(np.linspace(0,2*np.pi,100), np.linspace(0,2*np.pi,100))
z = sinus2d(xx, yy) # Create the image on this grid
</code></pre>

and such a plot would look like:

<pre><code>import matplotlib.pyplot as plt
plt.imshow(z, origin='lower', interpolation='none')
plt.show()
</code></pre>

<a href="https://i.stack.imgur.com/vceRQ.png" rel="noreferrer"><img src="https://i.stack.imgur.com/vceRQ.png" alt="enter image description here"></a>

So <code>np.meshgrid</code> is just a convenience. In principle the same could be done by:

<pre><code>z2 = sinus2d(np.linspace(0,2*np.pi,100)[:,None], np.linspace(0,2*np.pi,100)[None,:])
</code></pre>

but there you need to be aware of your dimensions (suppose you have more than two ...) and the right broadcasting. <code>np.meshgrid</code> does all of this for you.

Also meshgrid allows you to delete coordinates together with the data if you, for example, want to do an interpolation but exclude certain values:

<pre><code>condition = z&gt;0.6
z_new = z[condition] # This will make your array 1D
</code></pre>

so how would you do the interpolation now? You can give <code>x</code> and <code>y</code> to an interpolation function like <code>scipy.interpolate.interp2d</code> so you need a way to know which coordinates were deleted:

<pre><code>x_new = xx[condition]
y_new = yy[condition]
</code></pre>

and then you can still interpolate with the "right" coordinates (try it without the meshgrid and you will have a lot of extra code):

<pre><code>from scipy.interpolate import interp2d
interpolated = interp2d(x_new, y_new, z_new)
</code></pre>

and the original meshgrid allows you to get the interpolation on the original grid again:

<pre><code>interpolated_grid = interpolated(xx[0], yy[:, 0]).reshape(xx.shape)
</code></pre>

These are just some examples where I used the <code>meshgrid</code> there might be a lot more.

blocks|key|4427981|text|由Microsoft+Excel提供：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|4427982|​|4427983|📷|atomic|offset|length|4427984|4427985|entityMap|0|IMAGE|mutability|IMMUTABLE|imageUrl|https://ask.qcloudimg.com/http-save/yehe-900000/88b4897b9b92cbd2d801fb026c1eb550.png|imageAlt^0|0|0|0|1|0|0|0^^$0|@$1|2|3|4|5|6|7|S|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|T|8|@]|9|@]|A|$]]|$1|D|3|E|5|F|7|U|8|@]|9|@$G|V|H|W|1|X]]|A|$]]|$1|I|3|C|5|6|7|Y|8|@]|9|@]|A|$]]|$1|J|3|-4|5|6|7|Z|8|@]|9|@]|A|$]]]|K|$L|$5|M|N|O|A|$P|Q|R|-4]]]]

Courtesy of Microsoft Excel:&nbsp;

<a href="https://i.stack.imgur.com/8Mbig.png" rel="noreferrer"><img src="https://i.stack.imgur.com/8Mbig.png" alt="enter image description here"></a>

blocks|key|4428028|text|网格有助于从两个一维阵列创建矩形网格，该阵列由两个阵列中的所有点对组成。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|4428029|x+=+np.array([0,+1,+2,+3,+4])
y+=+np.array([0,+1,+2,+3,+4])|code-block|syntax|javascript|4428030|现在，如果你已经定义了一个函数f(x，y)，并且你想将这个函数应用于数组'x‘和'y’中所有可能的点组合，那么你可以这样做：|4428031|f(*np.meshgrid(x,+y))|4428032|比方说，如果你的函数只产生两个元素的乘积，那么这就是笛卡尔乘积如何实现的，对于大型数组来说是有效的。|4428033|引用自here|offset|length|4428034|entityMap|0|LINK|mutability|MUTABLE|url|https://codereview.stackexchange.com/questions/90005/efficient-element-wise-function-computation-in-python^0|0|0|0|0|0|3|4|0|0^^$0|@$1|2|3|4|5|6|7|Y|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|Z|8|@]|9|@]|A|$E|F]]|$1|G|3|H|5|6|7|10|8|@]|9|@]|A|$]]|$1|I|3|J|5|D|7|11|8|@]|9|@]|A|$E|F]]|$1|K|3|L|5|6|7|12|8|@]|9|@]|A|$]]|$1|M|3|N|5|6|7|13|8|@]|9|@$O|14|P|15|1|16]]|A|$]]|$1|Q|3|-4|5|6|7|17|8|@]|9|@]|A|$]]]|R|$S|$5|T|U|V|A|$W|X]]]]

meshgrid helps in creating a rectangular grid from two 1-D arrays of all pairs of points from the two arrays.

<pre><code>x = np.array([0, 1, 2, 3, 4])
y = np.array([0, 1, 2, 3, 4])
</code></pre>

Now, if you have defined a function f(x,y) and you wanna apply this function to all the possible combination of points from the arrays 'x' and 'y', then you can do this:

<pre><code>f(*np.meshgrid(x, y))
</code></pre>

Say, if your function just produces the product of two elements, then this is how a cartesian product can be achieved, efficiently for large arrays.

Referred from <a href="https://codereview.stackexchange.com/questions/90005/efficient-element-wise-function-computation-in-python">here</a>

blocks|key|4428057|text|大多数情况下，您只需要在list(zip(X,Y))中使用X+=+np.linspace(x)和Y+=+np.linspace(y)|type|unstyled|depth|inlineStyleRanges|offset|length|style|CODE|entityRanges|data|4428058|entityMap^0|C|E|T|I|1C|I|0^^$0|@$1|2|3|4|5|6|7|H|8|@$9|I|A|J|B|C]|$9|K|A|L|B|C]|$9|M|A|N|B|C]]|D|@]|E|$]]|$1|F|3|-4|5|6|7|O|8|@]|D|@]|E|$]]]|G|$]]

Most of the times you just need <code>list(zip(X,Y))</code>
where <code>X = np.linspace(x)</code> and <code>Y = np.linspace(y)</code>

Can someone explain to me what is the purpose of <code>meshgrid</code> 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 <a href="https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch03/ch03.ipynb" rel="noreferrer">here</a>.

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

<pre><code>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)
</code></pre>

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

What is the purpose of meshgrid in Python / NumPy?

Python

谁能给我解释一下meshgrid函数在Numpy中的作用？我知道它为绘图创建了某种坐标网格，但我真的看不到它的直接好处。我正在学习Sebastian Raschka的"Python Machine Learning“，他正在用它来绘制决策边界。请参见输入11 。我也尝试过官方文档中的这段代码，但同样，输出对我来说没有什...

问在Python / NumPy中，网格的作用是什么？
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