def test_2d(self):
a = array([
[1.0, 2],
[3, 8]
])
za = array([
[1, 1, 0, 1],
[1.5, 2, 0, 2],
[0, 0, 0, 0],
[1.5, 2, 0, 2]
])
self.assertArraysClose(za, mm.zpadf(a, 2))
self.assertArraysClose(za, mm.zpadf(a, (2, 2)))
za = array([
[1, 2],
[1.5, 4],
[0, 0],
[1.5, 4]
])
self.assertArraysClose(za, mm.zpadf(a, (2, 0)))
za = array([
[1, 1, 0, 1],
[3, 4, 0, 4],
])
self.assertArraysClose(za, mm.zpadf(a, (0, 2)))
def test_2d(self):
a = array([[1.0, 2], [3, 8]])
za = array([[1, 1, 0, 1], [1.5, 2, 0, 2], [0, 0, 0, 0], [1.5, 2, 0,
2]])
self.assertArraysClose(za, mm.zpadf(a, 2))
self.assertArraysClose(za, mm.zpadf(a, (2, 2)))
za = array([[1, 2], [1.5, 4], [0, 0], [1.5, 4]])
self.assertArraysClose(za, mm.zpadf(a, (2, 0)))
za = array([
[1, 1, 0, 1],
[3, 4, 0, 4],
])
self.assertArraysClose(za, mm.zpadf(a, (0, 2)))
def test_full_array(self):
nx = self.nx
ny = self.ny
upsample = self.upsample
aa = rand(ny, nx)
aa[:-5, :-5] += 1
aa[:-2, :] += 2
a = fft2(aa)
aa, a = self.remove_nyquist(aa, a)
## calculate the slow way
extra_zeros = ((upsample - 1)*ny, (upsample - 1)*nx)
padded = mm.zpadf(a, extra_zeros)
b_slow_big = ifft2(padded)
# calculate the fast way
b_fast_big = mm.upsampled_idft2(a, upsample, upsample*ny, upsample*nx, 0, 0)
b_slow_big = b_slow_big/mean(abs(b_slow_big))
b_fast_big = b_fast_big/mean(abs(b_fast_big))
if PLOTTING:
subplot(131)
imshow(abs(b_fast_big - b_slow_big))
colorbar()
subplot(132)
imshow(angle(b_fast_big))
colorbar()
subplot(133)
imshow(angle(b_slow_big))
colorbar()
show()
self.assertArraysClose(abs(b_fast_big), abs(b_slow_big), rtol=1e-2)
def test_1d(self):
a = array([1.0, 1.0])
za = array([1.0, 0.5, 0, 0.5])
self.assertArraysClose(za, mm.zpadf(a, 2))
self.assertArraysClose(za, mm.zpadf(a, (2, )))
a = array([1.0, 2, 3])
za = array([1, 2, 0, 0, 3])
self.assertArraysClose(za, mm.zpadf(a, 2))
a = array([1.0, 2, 3, 4])
za = array([1, 2, 1.5, 0, 1.5, 4])
self.assertArraysClose(za, mm.zpadf(a, 2))
a = array([1.0, 2, 3, 4])
za = array([1, 2, 1.5, 0, 0, 1.5, 4])
self.assertArraysClose(za, mm.zpadf(a, 3))
def test_1d(self):
a = array([1.0, 1.0])
za = array([1.0, 0.5, 0, 0.5])
self.assertArraysClose(za, mm.zpadf(a, 2))
self.assertArraysClose(za, mm.zpadf(a, (2,)))
a = array([1.0, 2, 3])
za = array([1, 2, 0, 0, 3])
self.assertArraysClose(za, mm.zpadf(a, 2))
a = array([1.0, 2, 3, 4])
za = array([1, 2, 1.5, 0, 1.5, 4])
self.assertArraysClose(za, mm.zpadf(a, 2))
a = array([1.0, 2, 3, 4])
za = array([1, 2, 1.5, 0, 0, 1.5, 4])
self.assertArraysClose(za, mm.zpadf(a, 3))
def test_full_array(self):
nx = self.nx
ny = self.ny
upsample = self.upsample
aa = rand(ny, nx)
aa[:-5, :-5] += 1
aa[:-2, :] += 2
a = fft2(aa)
aa, a = self.remove_nyquist(aa, a)
## calculate the slow way
extra_zeros = ((upsample - 1) * ny, (upsample - 1) * nx)
padded = mm.zpadf(a, extra_zeros)
b_slow_big = ifft2(padded)
# calculate the fast way
b_fast_big = mm.upsampled_idft2(a, upsample, upsample * ny,
upsample * nx, 0, 0)
b_slow_big = b_slow_big / mean(abs(b_slow_big))
b_fast_big = b_fast_big / mean(abs(b_fast_big))
if PLOTTING:
subplot(131)
imshow(abs(b_fast_big - b_slow_big))
colorbar()
subplot(132)
imshow(angle(b_fast_big))
colorbar()
subplot(133)
imshow(angle(b_slow_big))
colorbar()
show()
self.assertArraysClose(abs(b_fast_big), abs(b_slow_big), rtol=1e-2)
def test_equivalence(self):
"""
The dft_upsample function should be equivalent to:
1. Embedding the array "a" in an array that is "upsample" times larger
in each dimension. ifftshift to bring the center of the image to
(0, 0).
2. Take the IFFT of the larger array
3. Extract an [height, width] region of the result. Starting with the
[top, left] element.
"""
aa = self.aa
a = self.a
nx = self.nx
ny = self.ny
height = self.height
width = self.width
top = self.top
left = self.left
upsample = self.upsample
## calculate the slow way
extra_zeros = ((upsample - 1)*ny, (upsample - 1)*nx)
padded = mm.zpadf(a, extra_zeros)
b_slow_big = ifft2(padded)
b_slow = b_slow_big[
top:top + height,
left:left + width,
]
# calculate the fast way
b_fast = mm.upsampled_idft2(a, upsample, height, width, top, left)
b_fast_big = mm.upsampled_idft2(a, upsample, upsample*ny, upsample*nx, 0, 0)
if PLOTTING:
subplot(411)
imshow(abs(b_fast_big))
subplot(412)
imshow(abs(b_slow_big))
subplot(413)
imshow(abs(b_fast))
subplot(414)
imshow(abs(b_slow))
title('{}x{} starting at {}x{}'.format(height, width, top, left))
figure()
imshow(aa)
show()
if PLOTTING:
subplot(221)
imshow(abs(b_slow))
title('slow abs')
subplot(222)
imshow(abs(b_fast))
title('fast abs')
subplot(223)
imshow(unwrap(angle(b_slow)))
title('slow angle')
subplot(224)
imshow(unwrap(angle(b_fast)))
title('fast angle')
show()
# are they the same (within a multiplier)
b_slow = b_slow/mean(abs(b_slow))
b_fast = b_fast/mean(abs(b_fast))
self.assertArraysClose(b_slow, b_fast, rtol=1e-2)
def test_equivalence(self):
"""
The dft_upsample function should be equivalent to:
1. Embedding the array "a" in an array that is "upsample" times larger
in each dimension. ifftshift to bring the center of the image to
(0, 0).
2. Take the IFFT of the larger array
3. Extract an [height, width] region of the result. Starting with the
[top, left] element.
"""
aa = self.aa
a = self.a
nx = self.nx
ny = self.ny
height = self.height
width = self.width
top = self.top
left = self.left
upsample = self.upsample
## calculate the slow way
extra_zeros = ((upsample - 1) * ny, (upsample - 1) * nx)
padded = mm.zpadf(a, extra_zeros)
b_slow_big = ifft2(padded)
b_slow = b_slow_big[top:top + height, left:left + width, ]
# calculate the fast way
b_fast = mm.upsampled_idft2(a, upsample, height, width, top, left)
b_fast_big = mm.upsampled_idft2(a, upsample, upsample * ny,
upsample * nx, 0, 0)
if PLOTTING:
subplot(411)
imshow(abs(b_fast_big))
subplot(412)
imshow(abs(b_slow_big))
subplot(413)
imshow(abs(b_fast))
subplot(414)
imshow(abs(b_slow))
title('{}x{} starting at {}x{}'.format(height, width, top, left))
figure()
imshow(aa)
show()
if PLOTTING:
subplot(221)
imshow(abs(b_slow))
title('slow abs')
subplot(222)
imshow(abs(b_fast))
title('fast abs')
subplot(223)
imshow(unwrap(angle(b_slow)))
title('slow angle')
subplot(224)
imshow(unwrap(angle(b_fast)))
title('fast angle')
show()
# are they the same (within a multiplier)
b_slow = b_slow / mean(abs(b_slow))
b_fast = b_fast / mean(abs(b_fast))
self.assertArraysClose(b_slow, b_fast, rtol=1e-2)
