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33 lines
973 B
33 lines
973 B
# Impl routines common for all backends
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from itertools import combinations_with_replacement
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from math import comb
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def _monomial_powers_impl(ndim, degree):
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"""Return the powers for each monomial in a polynomial.
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Parameters
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----------
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ndim : int
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Number of variables in the polynomial.
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degree : int
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Degree of the polynomial.
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Returns
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-------
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(nmonos, ndim) int ndarray
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Array where each row contains the powers for each variable in a
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monomial.
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"""
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nmonos = comb(degree + ndim, ndim)
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out = [[0]*ndim for _ in range(nmonos)]
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count = 0
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for deg in range(degree + 1):
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for mono in combinations_with_replacement(range(ndim), deg):
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# `mono` is a tuple of variables in the current monomial with
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# multiplicity indicating power (e.g., (0, 1, 1) represents x*y**2)
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for var in mono:
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out[count][var] += 1
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count += 1
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return out
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