37 lines
893 B
Python
37 lines
893 B
Python
"""
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Here we perform some symbolic computations required for the N-D
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interpolation routines in `interpnd.pyx`.
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"""
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from sympy import symbols, binomial, Matrix # type: ignore[import]
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def _estimate_gradients_2d_global():
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#
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# Compute
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#
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#
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f1, f2, df1, df2, x = symbols(['f1', 'f2', 'df1', 'df2', 'x'])
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c = [f1, (df1 + 3*f1)/3, (df2 + 3*f2)/3, f2]
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w = 0
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for k in range(4):
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w += binomial(3, k) * c[k] * x**k*(1-x)**(3-k)
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wpp = w.diff(x, 2).expand()
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intwpp2 = (wpp**2).integrate((x, 0, 1)).expand()
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A = Matrix([[intwpp2.coeff(df1**2), intwpp2.coeff(df1*df2)/2],
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[intwpp2.coeff(df1*df2)/2, intwpp2.coeff(df2**2)]])
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B = Matrix([[intwpp2.coeff(df1).subs(df2, 0)],
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[intwpp2.coeff(df2).subs(df1, 0)]]) / 2
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print("A")
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print(A)
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print("B")
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print(B)
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print("solution")
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print(A.inv() * B)
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