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