def test_wrong_derivative(tol=1e-9):
field = np.random.random([nx, ny])
interp = Bicubic(field)
with pytest.raises(ValueError):
interp(1, 1, derivative=3)
with pytest.raises(ValueError):
interp(1, 1, derivative=-1)
def test_grid_derivatives(tol=1e-9):
field = np.random.random([nx, ny])
derx = np.random.random([nx, ny])
dery = np.random.random([nx, ny])
interp = Bicubic(field, derx, dery)
for i in range(nx):
for j in range(ny):
assert abs(interp(i, j) - field[i, j]) < tol
x, y = np.mgrid[:nx, :ny]
interp_field, interp_derx, interp_dery = interp(x, y, derivative=1)
assert np.allclose(interp_field, field)
assert np.allclose(interp_derx, derx)
assert np.allclose(interp_dery, dery)
def test_grid_values(tol=1e-9):
field = np.random.random([nx, ny])
interp = Bicubic(field)
for i in range(nx):
for j in range(ny):
assert abs(interp(i, j) - field[i, j]) < tol
x, y = np.mgrid[:nx, :ny]
for der in [0, 1, 2]:
if der == 0:
interp_field = interp(x, y, derivative=der)
elif der == 1:
interp_field, _, _ = interp(x, y, derivative=der)
else:
interp_field, _, _, _, _, _ = interp(x, y, derivative=der)
assert np.allclose(interp_field, field)
# %% check bicubic interpolation against fourier interpolation
# %%
fig, ax = plt.subplots()
x, y = topography.positions()
ax.plot(x[:, 0], topography.heights()[:, 0], ".k", label="original")
skips = [4, 8, 16, 32, 64]
rms_err = []
max_err = []
for skip in skips:
grid_slice = (slice(None, None, skip), slice(None, None, skip))
interp = Bicubic(topography.heights()[grid_slice],
dx[grid_slice] * topography.pixel_size[0] * skip,
dy[grid_slice] * topography.pixel_size[1] * skip
)
interp_field, interp_derx, interp_dery = interp(
x / (topography.pixel_size[0] * skip),
y / (topography.pixel_size[1] * skip), derivative=1)
l, = ax.plot(x[grid_slice][:, 0], topography.heights()[grid_slice][:, 0],
"+")
ax.plot(x[:, 0], interp_field[:, 0], color=l.get_color(),
label=r"bicubic, $l_{{cor}} / \Delta_x={}$"
.format(hc / (skip * topography.pixel_size[0])))
rms_err.append(
np.sqrt(np.mean((interp_field - topography.heights()) ** 2)))
max_err.append(np.max(abs(interp_field - topography.heights())))
ax.legend()
def test_bicubic_between(plot=False):
# grid points based on which the interpolation is made
nx = 32
ny = 17
sx = nx
sy = ny
x = np.arange(nx).reshape(-1, 1)
y = np.arange(ny).reshape(1, -1)
def fun(x, y):
return np.sin(2 * np.pi * x / sx) * np.cos(2 * np.pi * y / sy)
def dfun_dx(x, y):
return 2 * np.pi / sx * np.cos(2 * np.pi * x / sx) * np.cos(
2 * np.pi * y / sy)
def dfun_dy(x, y):
return -2 * np.pi / sy * np.sin(2 * np.pi * x / sx) * np.sin(
2 * np.pi * y / sy)
interp = Bicubic(fun(x, y), dfun_dx(x, y), dfun_dy(x, y))
interp_field, interp_derx, interp_dery = interp(x * np.ones_like(y),
y * np.ones_like(x),
derivative=1)
if plot:
import matplotlib.pyplot as plt
fig, (ax, axdx, axdy) = plt.subplots(3, 1)
ax.plot(x, fun(x, y)[:, 0], "k+")
ax.plot(x, interp_field[:, 0], "ko", mfc="none")
axdx.plot(x, dfun_dx(x, y)[:, 0], "r+")
axdx.plot(x, interp_derx[:, 0], "ro", mfc="none")
axdy.plot(y.flat, dfun_dy(x, y)[0, :], "g+")
axdy.plot(y.flat, interp_dery[0, :], "go", mfc="none")
# interpolate between the points used for definition
fac = 8
x_fine = np.arange(fac * nx).reshape(-1, 1) / fac
y_fine = np.arange(fac * ny).reshape(1, -1) / fac
interp_field0 = interp(x_fine * np.ones_like(y_fine),
y_fine * np.ones_like(x_fine),
derivative=0)
interp_field1, interp_derx1, interp_dery1 = interp(
x_fine * np.ones_like(y_fine),
y_fine * np.ones_like(x_fine),
derivative=1)
interp_field2, interp_derx2, interp_dery2, interp_derxx2, interp_deryy2, \
interp_derxy2 = interp(
x_fine * np.ones_like(y_fine), y_fine * np.ones_like(x_fine),
derivative=2)
if plot:
ax.plot(x_fine, interp_field1[:, 0], 'k-')
axdx.plot(x_fine.flat, interp_derx1[:, 0], 'r-')
axdy.plot(y_fine.flat, interp_dery1[0, :], 'g-')
fig.show()
np.testing.assert_allclose(interp_field0, fun(x_fine, y_fine), atol=1e-2)
np.testing.assert_allclose(interp_field1, fun(x_fine, y_fine), atol=1e-2)
np.testing.assert_allclose(interp_derx1,
dfun_dx(x_fine, y_fine),
atol=1e-2)
np.testing.assert_allclose(interp_dery1,
dfun_dy(x_fine, y_fine),
atol=1e-2)
np.testing.assert_allclose(interp_field2, fun(x_fine, y_fine), atol=1e-2)
def test_wrong_grid(tol=1e-9):
field = np.random.random([nx, ny])
derx = np.random.random([nx, ny - 1])
dery = np.random.random([nx, ny])
with pytest.raises(ValueError):
Bicubic(field, derx, dery)