Note that, if you just picked a kernel with a 1 in the middle and 0s elsewhere, you would just get the same grid of numbers (which can represent an image) back. The convolution is also central to a method of machine learning in structures called convolutional neural networks, which can be made to do pretty amazing things. The convolution also often appears as a one-dimensional operation as well as a continuous operation between two functions, as well as through a very similar but slightly different operation called the cross-correlation, which has uses in astronomy and other fields. Then, line up the kernel on the second pixel: We then assign that number to the top-left pixel: We then multiply the overlapping numbers together, and then add the results all together. We first line up the kernel with the top left pixel: For example, if we start with the following arrayĪnd convolve it with the following set of weights (also called a “kernel”)
Another way of thinking about this is that a convolution takes an array and adds to each point the value of its neighbors, modulated by (possibly negative) weights. In this context, convolutions are operations that take two arrays of numbers and return another array of numbers that quantifies, in some way, how much the arrays overlap.
However, in this case, NumPy didn’t provide all the tools necessary to execute this speed-processing vision sufficiently. After having waited for my computer for twenty or thirty minutes to do many simple operations to large numbers of numbers, I have gained a newfound appreciation of efficient data manipulation. As a test case, it demonstrates how fast the speedup is. Now, 293 ms is still not bad, but we have to keep it within the context that usually, in data analysis, there isn’t utility in adding 1 to a million random numbers. Doing the same exact operation to the same exact numbers with NumPy arrays only took 2 ms. I wasn’t able to notice a difference between these last two examples, but suppose, instead of working with twenty elements, we were working with one million? There is a massive speedup! Using for-loops, adding 1 to each element in a list of one million numbers took me 293 ms. However, while aesthetics and intuition definitely matter, what really gives NumPy its power is the efficiency at which it can process operations like this. Whereas the NumPy array route is more direct: Suppose I wanted to add 1 to every number in a list. The first advantage is that NumPy is more succinct than for-loops, although this is, of course, just aesthetic.
While adding lists simply appends the second list to the end of the first, adding arrays is element-wise, adding each element together one-by-one, but all at once. You can see this immediately when you try and add two lists together, and when you add two arrays together: While, at first, arrays appear to serve a very similar function as lists, they are actually quite different. NumPy handles data in a way that stock Python cannot by utilizing objects called arrays. Luckily, there are some very common modules in Python which provide alternatives to for-loops in many cases, one of which is NumPy (I recognize that it’s probably intended to be pronounced “Num-Pai,” but I find the pronunciation “Num-Pee” more affectionate).
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Luckily for my friend, the code ran quite quickly, but I thought about whether there was a faster way. While they often seem like a natural course of action, in many settings they are often unwieldy and slower than desirable.
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Interested, I asked to look into the code.Īs I expected, the lines that checked whether a player had achieved a five-in-a-row was a verbose series of nested for-loops checking a plethora of cases. She and her partner created a game in the style of tic-tac-toe, with opposing sides, black and white, placing markers on a grid until one side creates a line of five pieces in a row: Recently, one of my good friends was telling me about her final project in an introductory programming class for physics.
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