69 lines
1.6 KiB
Python
69 lines
1.6 KiB
Python
#!/usr/bin/env python3
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# implementing: https://web.media.mit.edu/~crtaylor/calculator.html
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import numpy as np
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# from math import factorial
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_factorials = ( # all the factorials that fit into 53 bits
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1,
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1,
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2,
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6,
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24,
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120,
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720,
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5040,
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40320,
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362880,
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3628800,
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39916800,
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479001600,
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6227020800,
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87178291200,
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1307674368000,
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20922789888000,
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355687428096000,
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6402373705728000,
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)
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__noisy = False
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def fd(offsets, degree):
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if degree < 0:
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raise RuntimeError("the degree must be greater than or equal to zero")
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elif degree > 18:
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raise RuntimeError("degrees greater than 18 are unsupported")
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if len(offsets) <= degree:
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raise RuntimeError("the number of offsets must be greater than the degree")
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mat = np.array([[o**n for o in offsets] for n in range(len(offsets))])
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vec = np.array([_factorials[i] if i == degree else 0 for i in range(len(offsets))])
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if __noisy:
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print("mat:", mat, "vec:", vec, sep="\n")
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res = np.linalg.lstsq(mat, vec, rcond=None)[0]
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return res
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if __name__ == "__main__":
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__noisy = True
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assert np.allclose(fd([-2, 0, 2], 1), [-1 / 4, 0, 1 / 4])
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# + A * f(x - 2 * h)
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# + B * f(x - 1 * h)
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# + C * f(x)
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# + D * f(x + 1 * h)
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# + E * f(x + 2 * h)
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assert np.allclose(fd([-2, -1, 0, 1, 2], 4), [1, -4, 6, -4, 1])
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print("", "#" * 40, "", sep="\n")
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ans = fd([-2, 7], 1)
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print("ans:", ans)
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ans = fd([-2, 0, 7], 1)
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print("ans:", ans)
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ans = fd([-0.2, 0.0, 0.7], 1)
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print("ans:", ans)
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__all__ = ("fd",)
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