def test_non_array_input():
ramp = np.linspace(-100, 100, 500).tolist()
reflected = reflect(ramp, 30, 40)
# Check boundaries
assert not np.any(reflected < 30)
assert not np.any(reflected > 40)
def test_non_array_input():
ramp = np.linspace(-100, 100, 500).tolist()
reflected = reflect(ramp, 30, 40)
# Check boundaries
assert not np.any(reflected < 30)
assert not np.any(reflected > 40)
def _upsample_columns(X, method=None):
"""
The centre of columns of X, an M-columned matrix, are assumed to have co-ordinates
{ 0, 1, 2, ... , M-1 } which means that the up-sampled matrix's columns should sample
from { -0.25, 0.25, 0.75, ... , M-1.25 }. We can view that as an interleaved set of teo
*convolutions* of X. The first, A, using a kernel equivalent to sampling the { -0.25, 0.75,
1.75, 2.75, ... M-1.25 } columns and the second, B, sampling the { 0.25, 1.25, ... , M-0.75 }
columns.
"""
if method is None:
method = 'lanczos'
X = np.atleast_2d(asfarray(X))
out_shape = list(X.shape)
out_shape[1] *= 2
output = np.zeros(out_shape, dtype=X.dtype)
# Centres of sampling for A and B convolutions
M = X.shape[1]
A_columns = np.linspace(-0.25, M-1.25, M)
B_columns = A_columns + 0.5
# For A columns sample at x = ceil(x) - 0.25 with ceil(x) = { 0, 1, 2, ..., M-1 }
# For B columns sample at x = floor(x) + 0.25 with floor(x) = { 0, 1, 2, ..., M-1 }
int_columns = np.linspace(0, M-1, M)
if method == 'lanczos':
# Lanczos kernel width
a = 3.0
sample_offsets = np.arange(-a, a+1)
# For A: if i = ceil(x) + di, => ceil(x) - i = -0.25 - di
# For B: if i = floor(x) + di, => floor(x) - i = 0.25 - di
l_as = np.sinc(-0.25-sample_offsets)*np.sinc((-0.25-sample_offsets)/a)
l_bs = np.sinc(0.25-sample_offsets)*np.sinc((0.25-sample_offsets)/a)
elif method == 'nearest':
# Nearest neighbour kernel width is 1
sample_offsets = [0,]
l_as = l_bs = [1,]
elif method == 'bilinear':
# Bilinear kernel width is technically 2 but we need to offset the kernels differently
# for A and B columns:
sample_offsets = [-1,0,1]
l_as = [0.25, 0.75, 0]
l_bs = [0, 0.75, 0.25]
else:
raise ValueError('Unknown interpolation mode: {0}'.format(mode))
# Convolve
for di, l_a, l_b in zip(sample_offsets, l_as, l_bs):
columns = reflect(int_columns + di, -0.5, M-0.5).astype(np.int)
output[:,0::2,...] += l_a * X[:,columns,...]
output[:,1::2,...] += l_b * X[:,columns,...]
return output
def _sample_clipped(im, xs, ys):
"""Truncated and symmatric sampling."""
sym_xs = reflect(xs, -0.5, im.shape[1]-0.5).astype(np.int)
sym_ys = reflect(ys, -0.5, im.shape[0]-0.5).astype(np.int)
return im[sym_ys, sym_xs, ...]
def setup():
global ramp, reflected
# Create a simple linear ramp and reflect it
ramp = np.linspace(-100, 100, 500)
reflected = reflect(ramp, 30, 40)
def _sample_clipped(im, xs, ys):
"""Truncated and symmatric sampling."""
sym_xs = reflect(xs, -0.5, im.shape[1] - 0.5).astype(np.int)
sym_ys = reflect(ys, -0.5, im.shape[0] - 0.5).astype(np.int)
return im[sym_ys, sym_xs, ...]
def _upsample_columns(X, method=None):
"""
The centre of columns of X, an M-columned matrix, are assumed to have co-ordinates
{ 0, 1, 2, ... , M-1 } which means that the up-sampled matrix's columns should sample
from { -0.25, 0.25, 0.75, ... , M-1.25 }. We can view that as an interleaved set of teo
*convolutions* of X. The first, A, using a kernel equivalent to sampling the { -0.25, 0.75,
1.75, 2.75, ... M-1.25 } columns and the second, B, sampling the { 0.25, 1.25, ... , M-0.75 }
columns.
"""
if method is None:
method = 'lanczos'
X = np.atleast_2d(asfarray(X))
out_shape = list(X.shape)
out_shape[1] *= 2
output = np.zeros(out_shape, dtype=X.dtype)
# Centres of sampling for A and B convolutions
M = X.shape[1]
A_columns = np.linspace(-0.25, M - 1.25, M)
B_columns = A_columns + 0.5
# For A columns sample at x = ceil(x) - 0.25 with ceil(x) = { 0, 1, 2, ..., M-1 }
# For B columns sample at x = floor(x) + 0.25 with floor(x) = { 0, 1, 2, ..., M-1 }
int_columns = np.linspace(0, M - 1, M)
if method == 'lanczos':
# Lanczos kernel width
a = 3.0
sample_offsets = np.arange(-a, a + 1)
# For A: if i = ceil(x) + di, => ceil(x) - i = -0.25 - di
# For B: if i = floor(x) + di, => floor(x) - i = 0.25 - di
l_as = np.sinc(-0.25 - sample_offsets) * np.sinc(
(-0.25 - sample_offsets) / a)
l_bs = np.sinc(0.25 - sample_offsets) * np.sinc(
(0.25 - sample_offsets) / a)
elif method == 'nearest':
# Nearest neighbour kernel width is 1
sample_offsets = [
0,
]
l_as = l_bs = [
1,
]
elif method == 'bilinear':
# Bilinear kernel width is technically 2 but we need to offset the kernels differently
# for A and B columns:
sample_offsets = [-1, 0, 1]
l_as = [0.25, 0.75, 0]
l_bs = [0, 0.75, 0.25]
else:
raise ValueError('Unknown interpolation mode: {0}'.format(mode))
# Convolve
for di, l_a, l_b in zip(sample_offsets, l_as, l_bs):
columns = reflect(int_columns + di, -0.5, M - 0.5).astype(np.int)
output[:, 0::2, ...] += l_a * X[:, columns, ...]
output[:, 1::2, ...] += l_b * X[:, columns, ...]
return output
def setup():
global ramp, reflected
# Create a simple linear ramp and reflect it
ramp = np.linspace(-100, 100, 500)
reflected = reflect(ramp, 30, 40)
