Added linear algebra section #36
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| ">>> np.dot(a, b)\n", | ||
| "32\n", | ||
| "```\n", | ||
| "With an N-D vector `a` and a 1-D vector `b`, the product is computed over the last axis of a.\n", |
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last axis of a <- code mode
| "```\n", | ||
| "\n", | ||
| "### Matrix multiplication\n", | ||
| "The numpy matrix multiplication operator `np.matmul` is unique because it does not operate on arrays of arbitrary dimension. Instead, it prefers to operate on 2-D arrays. Accordingly\n", |
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For consistency, NumPy should be stylized
| "```\n", | ||
| "\n", | ||
| "### Matrix multiplication\n", | ||
| "The numpy matrix multiplication operator `np.matmul` is unique because it does not operate on arrays of arbitrary dimension. Instead, it prefers to operate on 2-D arrays. Accordingly\n", |
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It might be good to provide examples illustrating each of these cases for clarity
| "### Matrix multiplication\n", | ||
| "The numpy matrix multiplication operator `np.matmul` is unique because it does not operate on arrays of arbitrary dimension. Instead, it prefers to operate on 2-D arrays. Accordingly\n", | ||
| "\n", | ||
| "* Arguments to np.matmul cannot be scalars\n", |
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code style for np.matmul
| " [ 8, 10, 12],\n", | ||
| " [12, 15, 18]])\n", | ||
| "```\n", | ||
| "The @-operator is equivalent to np.matmul and is defined if either argument is a numpy array\n", |
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code for np.matmul and stylize NumPy
| "```\n", | ||
| "\n", | ||
| "### np.einsum\n", | ||
| "`np.einsum` is a very powerful tool available in Numpy that uses [**Ein**stein **sum**mation notation](https://en.wikipedia.org/wiki/Einstein_notation), where repeated indices are summed over to compute the final product. For example, you can use Einstein notation to compute a matrix outer product like so\n", |
| " [ 8, 10, 12],\n", | ||
| " [12, 15, 18]])\n", | ||
| "```\n", | ||
| "It's flexible notation means you can basically perform any arbitrary operation on a pair of numpy arrays. As an example, consider the folling arrays\n", |
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It's -> Its
Stylize NumPy
| ">>> b = np.arange(12).reshape(3, 4)\n", | ||
| "```\n", | ||
| "\n", | ||
| "These arrays cannot be broadcast together, so if I want to multiply them together, I need to add a new axis to array `a`.\n", |
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'I' should be 'we' for consistency (I think?)
| " [24, 27, 30, 33]])\n", | ||
| "```\n", | ||
| "\n", | ||
| "This example can be extended further with operations that take place on the resulting array (e.g. summing over rows and columns in the result).\n", |
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Changing the wording here is up to you, but it sounds weird to me to say "operations that take place on the resulting array." I guess operations would operate on the resulting array but there's got to be better wording than that.
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@davidmascharka addressed comments! The only one I didn't fix was adding explicit examples for each matrix multiply case. It's just a lot of examples that are kind of tedious so I think they're better left out. Will defer to you and ryan for that judgement call though! |
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I need to revisit this after refactoring other numpy material |
Added a linear algebra section hitting all the points talked about in issue #33 .
I found that there were a ton of edge cases for almost all of these methods and I mentioned almost none of them. I touched on the very basics with np.einsum and directed peopel to this blog which is probably the best description I've found of einsum so far!