def test_dist_2():
r"""Test squared distance function."""
x0 = 0
y0 = 0
x1 = 10
y1 = 10
truth = 200
dist2 = dist_2(x0, y0, x1, y1)
assert_almost_equal(truth, dist2)
def test_dist_2():
r"""Test squared distance function."""
x0 = 0
y0 = 0
x1 = 10
y1 = 10
truth = 200
dist2 = dist_2(x0, y0, x1, y1)
assert_almost_equal(truth, dist2)
def test_cressman_point(test_data):
r"""Test Cressman interpolation for a point function."""
xp, yp, z = test_data
r = 40
obs_tree = cKDTree(list(zip(xp, yp)))
indices = obs_tree.query_ball_point([30, 30], r=r)
dists = dist_2(30, 30, xp[indices], yp[indices])
values = z[indices]
truth = 1.05499444404
value = cressman_point(dists, values, r)
assert_almost_equal(truth, value)
def test_cressman_point(test_data):
r"""Test Cressman interpolation for a point function."""
xp, yp, z = test_data
r = 40
obs_tree = cKDTree(list(zip(xp, yp)))
indices = obs_tree.query_ball_point([30, 30], r=r)
dists = dist_2(30, 30, xp[indices], yp[indices])
values = z[indices]
truth = 1.05499444404
value = cressman_point(dists, values, r)
assert_almost_equal(truth, value)
def test_barnes_point(test_data):
r"""Test Barnes interpolation for a point function."""
xp, yp, z = test_data
r = 40
obs_tree = cKDTree(list(zip(xp, yp)))
indices = obs_tree.query_ball_point([60, 60], r=r)
dists = dist_2(60, 60, xp[indices], yp[indices])
values = z[indices]
truth = 4.08718241061
ave_spacing = np.mean((cdist(list(zip(xp, yp)), list(zip(xp, yp)))))
kappa = calc_kappa(ave_spacing)
value = barnes_point(dists, values, kappa)
assert_almost_equal(truth, value)
def test_barnes_point(test_data):
r"""Test Barnes interpolation for a point function."""
xp, yp, z = test_data
r = 40
obs_tree = cKDTree(list(zip(xp, yp)))
indices = obs_tree.query_ball_point([60, 60], r=r)
dists = dist_2(60, 60, xp[indices], yp[indices])
values = z[indices]
truth = 4.08718241061
ave_spacing = np.mean((cdist(list(zip(xp, yp)), list(zip(xp, yp)))))
kappa = calc_kappa(ave_spacing)
value = barnes_point(dists, values, kappa)
assert_almost_equal(truth, value)
def inverse_distance(xp,
yp,
variable,
grid_x,
grid_y,
r,
gamma=None,
kappa=None,
min_neighbors=3,
kind='cressman'):
r"""Generate an inverse distance weighting interpolation of the given
points to the given grid based on either Cressman (1959) or Barnes (1964).
The Barnes implementation used here based on Koch et al. (1983).
Parameters
----------
xp: (N, ) ndarray
x-coordinates of observations.
yp: (N, ) ndarray
y-coordinates of observations.
variable: (N, ) ndarray
observation values associated with (xp, yp) pairs.
IE, variable[i] is a unique observation at (xp[i], yp[i]).
grid_x: (M, 2) ndarray
Meshgrid associated with x dimension.
grid_y: (M, 2) ndarray
Meshgrid associated with y dimension.
r: float
Radius from grid center, within which observations
are considered and weighted.
gamma: float
Adjustable smoothing parameter for the barnes interpolation. Default None.
kappa: float
Response parameter for barnes interpolation. Default None.
min_neighbors: int
Minimum number of neighbors needed to perform barnes or cressman interpolation
for a point. Default is 3.
kind: str
Specify what inverse distance weighting interpolation to use.
Options: 'cressman' or 'barnes'. Default 'cressman'
Returns
-------
img: (M, N) ndarray
Interpolated values on a 2-dimensional grid
"""
obs_tree = cKDTree(list(zip(xp, yp)))
grid_points = points.generate_grid_coords(grid_x, grid_y)
indices = obs_tree.query_ball_point(grid_points, r=r)
img = np.empty(shape=(grid_points.shape[0]), dtype=variable.dtype)
img.fill(np.nan)
for idx, (matches, grid) in enumerate(zip(indices, grid_points)):
if len(matches) >= min_neighbors:
x1, y1 = obs_tree.data[matches].T
values = variable[matches]
dists = triangles.dist_2(grid[0], grid[1], x1, y1)
if kind == 'cressman':
img[idx] = cressman_point(dists, values, r)
elif kind == 'barnes':
img[idx] = barnes_point(dists, values, kappa)
else:
raise ValueError(str(kind) + ' interpolation not supported.')
img = img.reshape(grid_x.shape)
return img
########################################### # Set up a cKDTree object and query all of the observations within "radius" of each grid point. # # The variable ``indices`` represents the index of each matched coordinate within the # cKDTree's ``data`` list. grid_points = np.array(list(zip(sim_gridx, sim_gridy))) radius = 40 obs_tree = cKDTree(list(zip(xp, yp))) indices = obs_tree.query_ball_point(grid_points, r=radius) ########################################### # For grid 0, we will use Cressman to interpolate its value. x1, y1 = obs_tree.data[indices[0]].T cress_dist = dist_2(sim_gridx[0], sim_gridy[0], x1, y1) cress_obs = zp[indices[0]] cress_val = cressman_point(cress_dist, cress_obs, radius) ########################################### # For grid 1, we will use barnes to interpolate its value. # # We need to calculate kappa--the average distance between observations over the domain. x2, y2 = obs_tree.data[indices[1]].T barnes_dist = dist_2(sim_gridx[1], sim_gridy[1], x2, y2) barnes_obs = zp[indices[1]] ave_spacing = np.mean((cdist(list(zip(xp, yp)), list(zip(xp, yp))))) kappa = calc_kappa(ave_spacing)
