def test_matrix_derivative_xy_weight():
a = np.array(wm.W(point_test, point_test[1], 80, {
'order': 2,
'var': 'xy'
}))
b = np.array([[0.000114519242018, 0, 0, 0], [0, 0, 0, 0],
[0, 0, 0.0000983135044506, 0], [0, 0, 0, 0.000150574165798]])
assert np.allclose(a, b) is True
def test_matrix_derivative_x_weight():
a = np.array(wm.W(point_test, point_test[1], 80, {'order': 1, 'var': 'x'}))
b = np.array([[0.0057259621009, 0, 0, 0], [0, 0, 0, 0],
[0, 0, -0.0122891880563, 0], [0, 0, 0, -0.00941088536234]])
assert np.allclose(a, b) is True
def test_matrix_weight():
a = np.array(wm.W(point_test, point_test[1], 80))
b = np.array([[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0.420675747852, 0],
[0, 0, 0, 0]])
assert np.allclose(a, b) is True
def test_matrix_derivative_xx_weight():
a = np.array(wm.W(point_test, point_test[1], 80, {'order': 2, 'var': 'x'}))
b = np.array([[0.000057259621009, 0, 0, 0], [0, -0.000423094551838, 0, 0],
[0, 0, -0.000208916196958, 0], [0, 0, 0,
0.0000329380987683]])
assert np.allclose(a, b) is True
from numpy import linalg as la
import basismatrix as bm
import basis as b
import coefficients as c
import minimumradius as mr
r_data = [[0, 1], [0.5, 1.5], [1, 2], [1.5, 2.5], [2, 3], [2.5, 3.5], [3, 4], [3.5, 4.5], [4, 5]]
contour_point = [[0, 0], [4, 4]]
radius_approximation = mr.get_radius(r_data, r_data[4], 3, contour_point)
print(radius_approximation)
base = b.pde_basis(1)[0]
P = bm.create_basis(base, r_data, r_data[4], radius_approximation)
Pt = np.transpose(P)
Peso = wm.W(r_data, r_data[4], radius_approximation)
print('P = ', P)
print('Pt = ', Pt)
print('W = ', Peso)
A = Pt @ Peso @ P
print('A = ', A)
B_matrix = Pt @ Peso
pt = bm.create_basis(base, [r_data[4]])
print('pt = ', pt)
phi = pt @ la.inv(A) @ B_matrix
def coefficients(data, point, basis_order, derivative=None):
basis = b.pde_basis(basis_order)[0]
m = len(basis)
r = mr.get_radius(data, point, m)
while True:
P = bm.create_basis(basis, data, point, r) # Basis matrix
Pt = np.transpose(P)
weight_ = wm.W(data, point, r)
pt = bm.create_basis(basis, [point])
B = Pt @ weight_
A = B @ P
_, det = la.slogdet(A)
determinante = det
if det < np.log(1e-6) and m < len(data) - 1:
r *= 1.05
continue
else:
pass
if not derivative:
return pt @ la.inv(A) @ B
else:
# For dx or dy
dptd_ = bm.create_basis(derivative['base1'], [point])
dWd_ = wm.W(data, point, r, {'order': 1, 'var': derivative['var']})
dAd_ = Pt @ dWd_ @ P
dBd_ = Pt @ dWd_
invA = la.inv(A) # A inverse
# For dx² or dy²
dptd_2 = bm.create_basis(derivative['base2'], [point])
d2Wd_ = wm.W(data, point, r, {
'order': 2,
'var': derivative['var']
})
d2Bd_2 = Pt @ d2Wd_
d2Ad_2 = d2Bd_2 @ P
# For dxy and dyx:
dptd_x = bm.create_basis(b.pde_basis(basis_order)[1], [point])
dptd_y = bm.create_basis(b.pde_basis(basis_order)[2], [point])
dxyWd_ = wm.W(data, point, r, {
'order': 2,
'var': derivative['var']
})
dxWd_ = wm.W(data, point, r, {'order': 1, 'var': 'x'})
dyWd_ = wm.W(data, point, r, {'order': 1, 'var': 'y'})
dxyBd = Pt @ dxyWd_
dxBd = Pt @ dxWd_
dyBd = Pt @ dyWd_
dxyAd = dxyBd @ P
dxAd = dxBd @ P
dyAd = dyBd @ P
# First derivative:
d1 = dptd_ @ invA @ B - pt @ invA @ dAd_ @ invA @ B + pt @ invA @ dBd_
# Second derivative:
d2 = dptd_2 @ invA @ B + np.array(
[[2]]
) @ pt @ invA @ dAd_ @ invA @ dAd_ @ invA @ B - pt @ invA @ d2Ad_2 @ invA @ B + pt @ invA @ d2Bd_2 - np.array(
[[2]]) @ dptd_ @ invA @ dAd_ @ invA @ B + np.array(
[[2]]) @ dptd_ @ invA @ dBd_ - np.array(
[[2]]) @ pt @ invA @ dAd_ @ invA @ dBd_
# Derivative for xy:
dxy = dptd_2 @ invA @ B - dptd_y @ invA @ dxAd @ invA @ B + dptd_y @ invA @ dxBd - dptd_x @ invA @ dyAd @ invA @ B + pt @ invA @ dxAd @ invA @ dyAd @ invA @ B - pt @ invA @ dxyAd @ invA @ B + pt @ invA @ dyAd @ invA @ dxAd @ invA @ B - pt @ invA @ dyAd @ invA @ dxBd + dptd_x @ invA @ dyBd - pt @ invA @ dxAd @ invA @ dyBd + pt @ invA @ dxyBd
if derivative['order'] == 1:
return d1
elif derivative['order'] == 2 and derivative['var'] != 'xy':
return d2
elif derivative['order'] == 2 and derivative['var'] == 'xy':
return dxy
break