Implement gaussian elimination in python #370
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june128
added
the
Implementation
berquist
requested changes
Sep 14, 2018
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Hi!
- I didn't mark them, but there are quite a few PEP 8 violations. The most important here are missing spaces after commas and missing spaces between binary operators. This line
A[r,:] = A[r,:] + frac*A[pivot_row,:]should change to
A[r, :] = A[r, :] + frac * A[pivot_row, :]A tool like pylint will help you catch a lot of these.
- This is not a requirement, but if you have
A[r, :]with NumPy, the colon is redundant. In fact, if you have a quantity liketensor[a, b, c, d, e], and want to take all of the last four dimension but have a specific index into the first dimension,tensor[r]does the same thing astensor[r, :, :, :, :]. Choose what you think is clearer.
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| print("Back subsitution") | ||
| print(back_substitution(A)) | ||
| print() |
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Can you make this more consistent with the other printing sections?
print("Back substitution")
print(back_substitution(A), "\n")|
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| def main(): | ||
| A = np.matrix('2. 3 4 6; 1 2 3 4; 3 -4 0 10') |
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- Generally, you want
arrayand notmatrix. - The explicit form of initialization, rather than a string, is clearer.
- The single float to force the type is too easy to overlook. Either do
A = np.array([[2, 3, 4, 6],
[1, 2, 3, 4],
[3, -4, 0, 10]], dtype=float)or
A = np.array([[2.0, 3.0, 4.0, 6.0],
[1.0, 2.0, 3.0, 4.0],
[3.0, -4.0, 0.0, 10.0]])|
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| """ | ||
| Assumes A is already ref | ||
| """ |
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If you want a code comment and not an actual function docstring (which would go under the def), use the usual # syntax. Better to say "row echelon form" than "ref".
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| """ | ||
| Assumes A has a unique solution and A in ref | ||
| """ |
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Same docstring and ref comment.
| print(A, "\n") | ||
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| gaussian_elimination(A) | ||
| print("Gaussian elimination, REF") |
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I would not abbreviate REF in print output.
| """ | ||
| Assumes A is already ref | ||
| """ | ||
| def gauss_jordon_elimination(A): |
| print(back_substitution(A)) | ||
| print() | ||
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| gauss_jordon_elimination(A) |
| # Step 3: Get fraction | ||
| frac = -A[r,pivot_col] / A[pivot_row,pivot_col] | ||
| # Step 4: Add rows | ||
| A[r,:] = A[r,:] + frac*A[pivot_row,:] |
| continue | ||
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| # Set each pivot to one via row scaling | ||
| A[row,:] = A[row,:] / A[row,col] |
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| # Zero out elements above pivot | ||
| for r in range(row): | ||
| A[r,:] = A[r,:] - A[r,col] * A[row,:] |
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Hey guys, checking up on this PR. Are you happy with the current code @berquist ? If so, I'll approve. Otherwise, I'll also do my own review. |
berquist
requested changes
Sep 22, 2018
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The windows for viewing code in the book are ok too. |
berquist
approved these changes
Sep 23, 2018
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Python implementation using numpy