def test_linear_interpolation_outside_domain(self):
"""Interpolation library sensibly handles values outside the domain
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Simple example first for debugging
xis = numpy.linspace(0.9, 4.0, 4)
etas = numpy.linspace(5, 9.1, 3)
points = combine_coordinates(xis, etas)
refs = linear_function(points[:, 0], points[:, 1])
vals = interpolate2d(x, y, A, points, mode='linear',
bounds_error=False)
msg = ('Length of interpolation points %i differs from length '
'of interpolated values %i' % (len(points), len(vals)))
assert len(points) == len(vals), msg
for i, (xi, eta) in enumerate(points):
if xi < x[0] or xi > x[-1] or eta < y[0] or eta > y[-1]:
assert numpy.isnan(vals[i])
else:
msg = ('Got %.15f for (%f, %f), expected %.15f'
% (vals[i], xi, eta, refs[i]))
assert numpy.allclose(vals[i], refs[i],
rtol=1.0e-12, atol=1.0e-12), msg
# Try a range of combinations of points outside domain
# with error_bounds True
print
for lox in [x[0], x[0] - 1]:
for hix in [x[-1], x[-1] + 1]:
for loy in [y[0], y[0] - 1]:
for hiy in [y[-1], y[-1] + 1]:
# Then test that points outside domain can be handled
xis = numpy.linspace(lox, hix, 4)
etas = numpy.linspace(loy, hiy, 4)
points = combine_coordinates(xis, etas)
if lox < x[0] or hix > x[-1] or \
loy < y[0] or hiy > y[-1]:
try:
vals = interpolate2d(x, y, A, points,
mode='linear',
bounds_error=True)
except BoundsError, e:
assert 'bounds_error was requested' in str(e)
else:
msg = 'Should have raised bounds error'
raise Exception(msg)
def test_interpolation_corner_cases(self):
"""Interpolation library returns NaN for incomplete grid points
"""
# Define four pixel centers
x = [2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test that interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 3)
etas = numpy.linspace(y[0], y[-1], 3)
points = combine_coordinates(xis, etas)
# Interpolate to cropped grids
for xc, yc, Ac in [
([x[0]], [y[0]], numpy.array([[A[0, 0]]])), # 1 x 1
([x[0]], y, numpy.array([A[0, :]])), # 1 x 2
]:
vals = interpolate2d(xc, yc, Ac, points, mode='linear')
msg = 'Expected NaN when grid %s is incomplete' % str(Ac.shape)
assert numpy.all(numpy.isnan(vals)), msg
def test_linear_interpolation_nan_array(self):
"""Interpolation library works (linear mode) with grid points being NaN
"""
# Define pixel centers along each direction
x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
y = [4.0, 5.0, 7.0, 9.0, 11.0, 13.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
A[2, 3] = numpy.nan # (x=2.0, y=9.0): NaN
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 12)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
# Set reference result with expected NaNs and compare
for i, (xi, eta) in enumerate(points):
if (1.0 < xi <= 3.0) and (7.0 < eta <= 11.0):
refs[i] = numpy.nan
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_nan_points(self):
"""Interpolation library works with interpolation points being NaN
This is was the reason for bug reported in:
https://github.com/AIFDR/riab/issues/155
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
xis[6:7] = numpy.nan
etas[3] = numpy.nan
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_nan_points(self):
"""Interpolation library works with interpolation points being NaN
This is was the reason for bug reported in:
https://github.com/AIFDR/riab/issues/155
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
xis[6:7] = numpy.nan
etas[3] = numpy.nan
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_constant_interpolation_basic(self):
"""Interpolation library works for piecewise constant function
"""
# Define pixel centers along each direction
x = numpy.array([1.0, 2.0, 4.0])
y = numpy.array([5.0, 9.0])
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points are always assigned value of
# closest neighbour
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='constant')
# Find upper neighbours for each interpolation point
xi = points[:, 0]
eta = points[:, 1]
idx = numpy.searchsorted(x, xi, side='left')
idy = numpy.searchsorted(y, eta, side='left')
# Get the four neighbours for each interpolation point
x0 = x[idx - 1]
x1 = x[idx]
y0 = y[idy - 1]
y1 = y[idy]
z00 = A[idx - 1, idy - 1]
z01 = A[idx - 1, idy]
z10 = A[idx, idy - 1]
z11 = A[idx, idy]
# Location coefficients
alpha = (xi - x0) / (x1 - x0)
beta = (eta - y0) / (y1 - y0)
refs = numpy.zeros(len(vals))
for i in range(len(refs)):
if alpha[i] < 0.5 and beta[i] < 0.5:
refs[i] = z00[i]
if alpha[i] >= 0.5 and beta[i] < 0.5:
refs[i] = z10[i]
if alpha[i] < 0.5 and beta[i] >= 0.5:
refs[i] = z01[i]
if alpha[i] >= 0.5 and beta[i] >= 0.5:
refs[i] = z11[i]
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_interpolation_corner_cases(self):
"""Interpolation library returns NaN for incomplete grid points
"""
# Define four pixel centers
x = [2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test that interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 3)
etas = numpy.linspace(y[0], y[-1], 3)
points = combine_coordinates(xis, etas)
# Interpolate to cropped grids
for xc, yc, Ac in [([x[0]], [y[0]], numpy.array([[A[0, 0]]])), # 1 x 1
([x[0]], y, numpy.array([A[0, :]])), # 1 x 2
]:
vals = interpolate2d(xc, yc, Ac, points, mode='linear')
msg = 'Expected NaN when grid %s is incomplete' % str(Ac.shape)
assert numpy.all(numpy.isnan(vals)), msg
def test_linear_interpolation_basic(self):
"""Interpolation library works for linear function - basic test
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test first that original points are reproduced correctly
for i, xi in enumerate(x):
for j, eta in enumerate(y):
val = interpolate2d(x, y, A, [(xi, eta)], mode='linear')[0]
ref = linear_function(xi, eta)
assert numpy.allclose(val, ref, rtol=1e-12, atol=1e-12)
# Then test that genuinly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_nan_array(self):
"""Interpolation library works (linear mode) with grid points being NaN
"""
# Define pixel centers along each direction
x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
y = [4.0, 5.0, 7.0, 9.0, 11.0, 13.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
A[2, 3] = numpy.nan # (x=2.0, y=9.0): NaN
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 12)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
# Set reference result with expected NaNs and compare
for i, (xi, eta) in enumerate(points):
if (1.0 < xi <= 3.0) and (7.0 < eta <= 11.0):
refs[i] = numpy.nan
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_basic(self):
"""Interpolation library works for linear function - basic test
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test first that original points are reproduced correctly
for i, xi in enumerate(x):
for j, eta in enumerate(y):
val = interpolate2d(x, y, A, [(xi, eta)], mode='linear')[0]
ref = linear_function(xi, eta)
assert numpy.allclose(val, ref, rtol=1e-12, atol=1e-12)
# Then test that genuinly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_constant_interpolation_basic(self):
"""Interpolation library works for piecewise constant function
"""
# Define pixel centers along each direction
x = numpy.array([1.0, 2.0, 4.0])
y = numpy.array([5.0, 9.0])
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points are always assigned value of
# closest neighbour
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='constant')
# Find upper neighbours for each interpolation point
xi = points[:, 0]
eta = points[:, 1]
idx = numpy.searchsorted(x, xi, side='left')
idy = numpy.searchsorted(y, eta, side='left')
# Get the four neighbours for each interpolation point
x0 = x[idx - 1]
x1 = x[idx]
y0 = y[idy - 1]
y1 = y[idy]
z00 = A[idx - 1, idy - 1]
z01 = A[idx - 1, idy]
z10 = A[idx, idy - 1]
z11 = A[idx, idy]
# Location coefficients
alpha = (xi - x0) / (x1 - x0)
beta = (eta - y0) / (y1 - y0)
refs = numpy.zeros(len(vals))
for i in range(len(refs)):
if alpha[i] < 0.5 and beta[i] < 0.5:
refs[i] = z00[i]
if alpha[i] >= 0.5 and beta[i] < 0.5:
refs[i] = z10[i]
if alpha[i] < 0.5 and beta[i] >= 0.5:
refs[i] = z01[i]
if alpha[i] >= 0.5 and beta[i] >= 0.5:
refs[i] = z11[i]
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_interpolation_raster_data(self):
"""Interpolation library works for raster data
This shows interpolation of data arranged with
latitudes bottom - up and
longitudes left - right
"""
# Create test data
lon_ul = 100 # Longitude of upper left corner
lat_ul = 10 # Latitude of upper left corner
numlon = 8 # Number of longitudes
numlat = 5 # Number of latitudes
# Define array where latitudes are rows and longitude columns
A = numpy.zeros((numlat, numlon))
# Establish coordinates for lower left corner
lat_ll = lat_ul - numlat
lon_ll = lon_ul
# Define pixel centers along each direction
longitudes = numpy.linspace(lon_ll + 0.5, lon_ll + numlon - 0.5,
numlon)
latitudes = numpy.linspace(lat_ll + 0.5, lat_ll + numlat - 0.5, numlat)
# Define raster with latitudes going bottom-up (south to north).
# Longitudes go left-right (west to east)
for i in range(numlat):
for j in range(numlon):
A[numlat - 1 - i, j] = linear_function(longitudes[j],
latitudes[i])
# Then test that interpolated points are correct
xis = numpy.linspace(lon_ll + 1, lon_ll + numlon - 1, 100)
etas = numpy.linspace(lat_ll + 1, lat_ll + numlat - 1, 100)
points = combine_coordinates(xis, etas)
vals = interpolate_raster(longitudes,
latitudes,
A,
points,
mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_interpolation_raster_data(self):
"""Interpolation library works for raster data
This shows interpolation of data arranged with
latitudes bottom - up and
longitudes left - right
"""
# Create test data
lon_ul = 100 # Longitude of upper left corner
lat_ul = 10 # Latitude of upper left corner
numlon = 8 # Number of longitudes
numlat = 5 # Number of latitudes
# Define array where latitudes are rows and longitude columns
A = numpy.zeros((numlat, numlon))
# Establish coordinates for lower left corner
lat_ll = lat_ul - numlat
lon_ll = lon_ul
# Define pixel centers along each direction
longitudes = numpy.linspace(lon_ll + 0.5,
lon_ll + numlon - 0.5, numlon)
latitudes = numpy.linspace(lat_ll + 0.5,
lat_ll + numlat - 0.5, numlat)
# Define raster with latitudes going bottom-up (south to north).
# Longitudes go left-right (west to east)
for i in range(numlat):
for j in range(numlon):
A[numlat - 1 - i, j] = linear_function(longitudes[j],
latitudes[i])
# Then test that interpolated points are correct
xis = numpy.linspace(lon_ll + 1, lon_ll + numlon - 1, 100)
etas = numpy.linspace(lat_ll + 1, lat_ll + numlat - 1, 100)
points = combine_coordinates(xis, etas)
vals = interpolate_raster(longitudes, latitudes, A, points,
mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_range(self):
"""Interpolation library works for linear function - a range of cases
"""
for x in [[1.0, 2.0, 4.0], [-20, -19, 0], numpy.arange(200) + 1000]:
for y in [[5.0, 9.0], [100, 200, 10000]]:
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test that linearly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 100)
etas = numpy.linspace(y[0], y[-1], 100)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_range(self):
"""Interpolation library works for linear function - a range of cases
"""
for x in [[1.0, 2.0, 4.0], [-20, -19, 0], numpy.arange(200) + 1000]:
for y in [[5.0, 9.0], [100, 200, 10000]]:
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test that linearly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 100)
etas = numpy.linspace(y[0], y[-1], 100)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_interpolation_random_array_and_nan(self):
"""Interpolation library (constant and linear) works with NaN
"""
# Define pixel centers along each direction
x = numpy.arange(20) * 1.0
y = numpy.arange(25) * 1.0
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define arbitrary values for each x, y pair
numpy.random.seed(17)
A = numpy.random.random((len(x), len(y))) * 10
# Create islands of NaN
A[5, 13] = numpy.nan
A[6, 14] = A[6, 18] = numpy.nan
A[7, 14:18] = numpy.nan
A[8, 13:18] = numpy.nan
A[9, 12:19] = numpy.nan
A[10, 14:17] = numpy.nan
A[11, 15] = numpy.nan
A[15, 5:6] = numpy.nan
# Creat interpolation points
xis = numpy.linspace(x[0], x[-1], 39) # Hit all mid points
etas = numpy.linspace(y[0], y[-1], 73) # Hit thirds
points = combine_coordinates(xis, etas)
for mode in ['linear', 'constant']:
vals = interpolate2d(x, y, A, points, mode=mode)
# Calculate reference result with expected NaNs and compare
i = j = 0
for k, (xi, eta) in enumerate(points):
# Find indices of nearest higher value in x and y
i = numpy.searchsorted(x, xi)
j = numpy.searchsorted(y, eta)
if i > 0 and j > 0:
# Get four neigbours
A00 = A[i - 1, j - 1]
A01 = A[i - 1, j]
A10 = A[i, j - 1]
A11 = A[i, j]
if numpy.allclose(xi, x[i]):
alpha = 1.0
else:
alpha = 0.5
if numpy.allclose(eta, y[j]):
beta = 1.0
else:
beta = eta - y[j - 1]
if mode == 'linear':
if numpy.any(numpy.isnan([A00, A01, A10, A11])):
ref = numpy.nan
else:
ref = (A00 * (1 - alpha) * (1 - beta) +
A01 * (1 - alpha) * beta +
A10 * alpha * (1 - beta) +
A11 * alpha * beta)
elif mode == 'constant':
assert alpha >= 0.5 # Only case in this test
if beta < 0.5:
ref = A10
else:
ref = A11
else:
msg = 'Unknown mode: %s' % mode
raise Exception(msg)
#print i, j, xi, eta, alpha, beta, vals[k], ref
assert nan_allclose(vals[k], ref, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_outside_domain(self):
"""Interpolation library sensibly handles values outside the domain
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Simple example first for debugging
xis = numpy.linspace(0.9, 4.0, 4)
etas = numpy.linspace(5, 9.1, 3)
points = combine_coordinates(xis, etas)
refs = linear_function(points[:, 0], points[:, 1])
vals = interpolate2d(x,
y,
A,
points,
mode='linear',
bounds_error=False)
msg = ('Length of interpolation points %i differs from length '
'of interpolated values %i' % (len(points), len(vals)))
assert len(points) == len(vals), msg
for i, (xi, eta) in enumerate(points):
if xi < x[0] or xi > x[-1] or eta < y[0] or eta > y[-1]:
assert numpy.isnan(vals[i])
else:
msg = ('Got %.15f for (%f, %f), expected %.15f' %
(vals[i], xi, eta, refs[i]))
assert numpy.allclose(vals[i],
refs[i],
rtol=1.0e-12,
atol=1.0e-12), msg
# Try a range of combinations of points outside domain
# with error_bounds True
print
for lox in [x[0], x[0] - 1]:
for hix in [x[-1], x[-1] + 1]:
for loy in [y[0], y[0] - 1]:
for hiy in [y[-1], y[-1] + 1]:
# Then test that points outside domain can be handled
xis = numpy.linspace(lox, hix, 4)
etas = numpy.linspace(loy, hiy, 4)
points = combine_coordinates(xis, etas)
if lox < x[0] or hix > x[-1] or \
loy < y[0] or hiy > y[-1]:
try:
vals = interpolate2d(x,
y,
A,
points,
mode='linear',
bounds_error=True)
except BoundsError, e:
assert 'bounds_error was requested' in str(e)
else:
msg = 'Should have raised bounds error'
raise Exception(msg)
class Test_interpolate(unittest.TestCase):
def test_linear_interpolation_basic(self):
"""Interpolation library works for linear function - basic test
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test first that original points are reproduced correctly
for i, xi in enumerate(x):
for j, eta in enumerate(y):
val = interpolate2d(x, y, A, [(xi, eta)], mode='linear')[0]
ref = linear_function(xi, eta)
assert numpy.allclose(val, ref, rtol=1e-12, atol=1e-12)
# Then test that genuinly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_constant_interpolation_basic(self):
"""Interpolation library works for piecewise constant function
"""
# Define pixel centers along each direction
x = numpy.array([1.0, 2.0, 4.0])
y = numpy.array([5.0, 9.0])
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points are always assigned value of
# closest neighbour
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='constant')
# Find upper neighbours for each interpolation point
xi = points[:, 0]
eta = points[:, 1]
idx = numpy.searchsorted(x, xi, side='left')
idy = numpy.searchsorted(y, eta, side='left')
# Get the four neighbours for each interpolation point
x0 = x[idx - 1]
x1 = x[idx]
y0 = y[idy - 1]
y1 = y[idy]
z00 = A[idx - 1, idy - 1]
z01 = A[idx - 1, idy]
z10 = A[idx, idy - 1]
z11 = A[idx, idy]
# Location coefficients
alpha = (xi - x0) / (x1 - x0)
beta = (eta - y0) / (y1 - y0)
refs = numpy.zeros(len(vals))
for i in range(len(refs)):
if alpha[i] < 0.5 and beta[i] < 0.5:
refs[i] = z00[i]
if alpha[i] >= 0.5 and beta[i] < 0.5:
refs[i] = z10[i]
if alpha[i] < 0.5 and beta[i] >= 0.5:
refs[i] = z01[i]
if alpha[i] >= 0.5 and beta[i] >= 0.5:
refs[i] = z11[i]
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_range(self):
"""Interpolation library works for linear function - a range of cases
"""
for x in [[1.0, 2.0, 4.0], [-20, -19, 0], numpy.arange(200) + 1000]:
for y in [[5.0, 9.0], [100, 200, 10000]]:
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Test that linearly interpolated points are correct
xis = numpy.linspace(x[0], x[-1], 100)
etas = numpy.linspace(y[0], y[-1], 100)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert numpy.allclose(vals, refs, rtol=1e-12, atol=1e-12)
test_linear_interpolation_range.slow = True
def test_linear_interpolation_nan_points(self):
"""Interpolation library works with interpolation points being NaN
This is was the reason for bug reported in:
https://github.com/AIFDR/riab/issues/155
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 10)
etas = numpy.linspace(y[0], y[-1], 10)
xis[6:7] = numpy.nan
etas[3] = numpy.nan
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_linear_interpolation_nan_array(self):
"""Interpolation library works (linear mode) with grid points being NaN
"""
# Define pixel centers along each direction
x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
y = [4.0, 5.0, 7.0, 9.0, 11.0, 13.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
A[2, 3] = numpy.nan # (x=2.0, y=9.0): NaN
# Then test that interpolated points can contain NaN
xis = numpy.linspace(x[0], x[-1], 12)
etas = numpy.linspace(y[0], y[-1], 10)
points = combine_coordinates(xis, etas)
vals = interpolate2d(x, y, A, points, mode='linear')
refs = linear_function(points[:, 0], points[:, 1])
# Set reference result with expected NaNs and compare
for i, (xi, eta) in enumerate(points):
if (1.0 < xi <= 3.0) and (7.0 < eta <= 11.0):
refs[i] = numpy.nan
assert nan_allclose(vals, refs, rtol=1e-12, atol=1e-12)
def test_interpolation_random_array_and_nan(self):
"""Interpolation library (constant and linear) works with NaN
"""
# Define pixel centers along each direction
x = numpy.arange(20) * 1.0
y = numpy.arange(25) * 1.0
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define arbitrary values for each x, y pair
numpy.random.seed(17)
A = numpy.random.random((len(x), len(y))) * 10
# Create islands of NaN
A[5, 13] = numpy.nan
A[6, 14] = A[6, 18] = numpy.nan
A[7, 14:18] = numpy.nan
A[8, 13:18] = numpy.nan
A[9, 12:19] = numpy.nan
A[10, 14:17] = numpy.nan
A[11, 15] = numpy.nan
A[15, 5:6] = numpy.nan
# Creat interpolation points
xis = numpy.linspace(x[0], x[-1], 39) # Hit all mid points
etas = numpy.linspace(y[0], y[-1], 73) # Hit thirds
points = combine_coordinates(xis, etas)
for mode in ['linear', 'constant']:
vals = interpolate2d(x, y, A, points, mode=mode)
# Calculate reference result with expected NaNs and compare
i = j = 0
for k, (xi, eta) in enumerate(points):
# Find indices of nearest higher value in x and y
i = numpy.searchsorted(x, xi)
j = numpy.searchsorted(y, eta)
if i > 0 and j > 0:
# Get four neigbours
A00 = A[i - 1, j - 1]
A01 = A[i - 1, j]
A10 = A[i, j - 1]
A11 = A[i, j]
if numpy.allclose(xi, x[i]):
alpha = 1.0
else:
alpha = 0.5
if numpy.allclose(eta, y[j]):
beta = 1.0
else:
beta = eta - y[j - 1]
if mode == 'linear':
if numpy.any(numpy.isnan([A00, A01, A10, A11])):
ref = numpy.nan
else:
ref = (A00 * (1 - alpha) * (1 - beta) + A01 *
(1 - alpha) * beta + A10 * alpha *
(1 - beta) + A11 * alpha * beta)
elif mode == 'constant':
assert alpha >= 0.5 # Only case in this test
if beta < 0.5:
ref = A10
else:
ref = A11
else:
msg = 'Unknown mode: %s' % mode
raise Exception(msg)
#print i, j, xi, eta, alpha, beta, vals[k], ref
assert nan_allclose(vals[k], ref, rtol=1e-12, atol=1e-12)
test_interpolation_random_array_and_nan.slow = True
def test_linear_interpolation_outside_domain(self):
"""Interpolation library sensibly handles values outside the domain
"""
# Define pixel centers along each direction
x = [1.0, 2.0, 4.0]
y = [5.0, 9.0]
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define values for each x, y pair as a linear function
for i in range(len(x)):
for j in range(len(y)):
A[i, j] = linear_function(x[i], y[j])
# Simple example first for debugging
xis = numpy.linspace(0.9, 4.0, 4)
etas = numpy.linspace(5, 9.1, 3)
points = combine_coordinates(xis, etas)
refs = linear_function(points[:, 0], points[:, 1])
vals = interpolate2d(x,
y,
A,
points,
mode='linear',
bounds_error=False)
msg = ('Length of interpolation points %i differs from length '
'of interpolated values %i' % (len(points), len(vals)))
assert len(points) == len(vals), msg
for i, (xi, eta) in enumerate(points):
if xi < x[0] or xi > x[-1] or eta < y[0] or eta > y[-1]:
assert numpy.isnan(vals[i])
else:
msg = ('Got %.15f for (%f, %f), expected %.15f' %
(vals[i], xi, eta, refs[i]))
assert numpy.allclose(vals[i],
refs[i],
rtol=1.0e-12,
atol=1.0e-12), msg
# Try a range of combinations of points outside domain
# with error_bounds True
print
for lox in [x[0], x[0] - 1]:
for hix in [x[-1], x[-1] + 1]:
for loy in [y[0], y[0] - 1]:
for hiy in [y[-1], y[-1] + 1]:
# Then test that points outside domain can be handled
xis = numpy.linspace(lox, hix, 4)
etas = numpy.linspace(loy, hiy, 4)
points = combine_coordinates(xis, etas)
if lox < x[0] or hix > x[-1] or \
loy < y[0] or hiy > y[-1]:
try:
vals = interpolate2d(x,
y,
A,
points,
mode='linear',
bounds_error=True)
except BoundsError, e:
assert 'bounds_error was requested' in str(e)
else:
msg = 'Should have raised bounds error'
raise Exception(msg)
# Try a range of combinations of points outside domain with
# error_bounds False
for lox in [x[0], x[0] - 1, x[0] - 10]:
for hix in [x[-1], x[-1] + 1, x[-1] + 5]:
for loy in [y[0], y[0] - 1, y[0] - 10]:
for hiy in [y[-1], y[-1] + 1, y[-1] + 10]:
# Then test that points outside domain can be handled
xis = numpy.linspace(lox, hix, 10)
etas = numpy.linspace(loy, hiy, 10)
points = combine_coordinates(xis, etas)
refs = linear_function(points[:, 0], points[:, 1])
vals = interpolate2d(x,
y,
A,
points,
mode='linear',
bounds_error=False)
assert len(points) == len(vals), msg
for i, (xi, eta) in enumerate(points):
if xi < x[0] or xi > x[-1] or\
eta < y[0] or eta > y[-1]:
msg = 'Expected NaN for %f, %f' % (xi, eta)
assert numpy.isnan(vals[i]), msg
else:
msg = ('Got %.15f for (%f, %f), expected '
'%.15f' % (vals[i], xi, eta, refs[i]))
assert numpy.allclose(vals[i],
refs[i],
rtol=1.0e-12,
atol=1.0e-12), msg
def test_interpolation_random_array_and_nan(self):
"""Interpolation library (constant and linear) works with NaN
"""
# Define pixel centers along each direction
x = numpy.arange(20) * 1.0
y = numpy.arange(25) * 1.0
# Define ny by nx array with corresponding values
A = numpy.zeros((len(x), len(y)))
# Define arbitrary values for each x, y pair
numpy.random.seed(17)
A = numpy.random.random((len(x), len(y))) * 10
# Create islands of NaN
A[5, 13] = numpy.nan
A[6, 14] = A[6, 18] = numpy.nan
A[7, 14:18] = numpy.nan
A[8, 13:18] = numpy.nan
A[9, 12:19] = numpy.nan
A[10, 14:17] = numpy.nan
A[11, 15] = numpy.nan
A[15, 5:6] = numpy.nan
# Creat interpolation points
xis = numpy.linspace(x[0], x[-1], 39) # Hit all mid points
etas = numpy.linspace(y[0], y[-1], 73) # Hit thirds
points = combine_coordinates(xis, etas)
for mode in ['linear', 'constant']:
vals = interpolate2d(x, y, A, points, mode=mode)
# Calculate reference result with expected NaNs and compare
i = j = 0
for k, (xi, eta) in enumerate(points):
# Find indices of nearest higher value in x and y
i = numpy.searchsorted(x, xi)
j = numpy.searchsorted(y, eta)
if i > 0 and j > 0:
# Get four neigbours
A00 = A[i - 1, j - 1]
A01 = A[i - 1, j]
A10 = A[i, j - 1]
A11 = A[i, j]
if numpy.allclose(xi, x[i]):
alpha = 1.0
else:
alpha = 0.5
if numpy.allclose(eta, y[j]):
beta = 1.0
else:
beta = eta - y[j - 1]
if mode == 'linear':
if numpy.any(numpy.isnan([A00, A01, A10, A11])):
ref = numpy.nan
else:
ref = (A00 * (1 - alpha) * (1 - beta) + A01 *
(1 - alpha) * beta + A10 * alpha *
(1 - beta) + A11 * alpha * beta)
elif mode == 'constant':
assert alpha >= 0.5 # Only case in this test
if beta < 0.5:
ref = A10
else:
ref = A11
else:
msg = 'Unknown mode: %s' % mode
raise Exception(msg)
#print i, j, xi, eta, alpha, beta, vals[k], ref
assert nan_allclose(vals[k], ref, rtol=1e-12, atol=1e-12)