You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
40 lines
935 B
Python
40 lines
935 B
Python
6 years ago
|
"""
|
||
|
|
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 symbols, binomial, Matrix
|
||
|
|
|
||
|
|
|
||
|
|
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)
|