def test_quadratic_basis_xy():
assert bm.create_basis(pde2_xy, data_test) == [[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1],
[0, 0, 0, 0, 0, 1]]
def test_quadratic_basis_y():
assert bm.create_basis(pde2_y, data_test) == [[0, 0, 0, 1, 0, 0],
[0, 0, 0, 1, 4, 4],
[0, 0, 0, 1, 8, 4]]
def test_quadratic_basis_yy():
assert bm.create_basis(pde2_yy, data_test) == [[0, 0, 0, 0, 2, 0],
[0, 0, 0, 0, 2, 0],
[0, 0, 0, 0, 2, 0]]
def test_quadratic_basis():
assert bm.create_basis(pde2, data_test) == [[1, 0, 0, 0, 0, 0],
[1, 4, 16, 2.0, 4.0, 8.0],
[1, 4, 16, 4, 16, 16]]
def test_quadratic_basis_x():
assert bm.create_basis(pde2_x, data_test) == [[0, 1, 0, 0, 0, 0],
[0, 1, 8, 0, 0, 2],
[0, 1, 8, 0, 0, 4]]
def test_linear_basis_y():
assert bm.create_basis(pde1_y, data_test) == [[0, 0, 1], [0, 0, 1],
[0, 0, 1]]
def test_linear_basis_xy():
assert bm.create_basis(pde1_xy, data_test) == [[0, 0, 0], [0, 0, 0],
[0, 0, 0]]
def test_cubic_basis_xy():
assert bm.create_basis(pde3_xy,
data_test) == [[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 8, 4, 0],
[0, 0, 0, 0, 1, 0, 0, 8, 8, 0]]
def test_linear_basis():
assert bm.create_basis(pde1, data_test) == [[1, 0, 0], [1, 4, 2],
[1, 4, 4]]
def test_cubic_basis_xx():
assert bm.create_basis(pde3_xx,
data_test) == [[0, 0, 0, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 2, 0, 0, 24, 4, 0, 0],
[0, 0, 0, 2, 0, 0, 24, 8, 0, 0]]
def test_cubic_basis_yy():
assert bm.create_basis(pde3_yy,
data_test) == [[0, 0, 0, 0, 0, 2, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 2, 0, 0, 8, 12],
[0, 0, 0, 0, 0, 2, 0, 0, 8, 24]]
def test_cubic_basis_y():
assert bm.create_basis(pde3_y,
data_test) == [[0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 4, 4, 0, 16, 16, 12],
[0, 0, 1, 0, 4, 8, 0, 16, 32, 48]]
def test_cubic_basis_x():
assert bm.create_basis(pde3_x,
data_test) == [[0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 8, 2, 0, 48, 16, 4, 0],
[0, 1, 0, 8, 4, 0, 48, 32, 16, 0]]
def test_cubic_basis():
assert bm.create_basis(
pde3, data_test) == [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 4, 2, 16, 8, 4, 64, 32, 16, 8],
[1, 4, 4, 16, 16, 16, 64, 64, 64, 64]]
import numpy as np
import weightmatrix as wm
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)
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
