def testBackwardGrayscaleAnalysisMode(self, datatype, nchs, nrows, ncols,
mus):
rtol, atol = 1e-3, 1e-6
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=False)
# Parameters
nSamples = 8
nChsTotal = sum(nchs)
nAngles = int((nChsTotal - 2) * nChsTotal / 8)
angles = torch.randn(nAngles, dtype=datatype)
# nSamples x nRows x nCols x nChsTotal
X = torch.randn(nSamples,
nrows,
ncols,
nChsTotal,
dtype=datatype,
requires_grad=True)
dLdZ = torch.randn(nSamples, nrows, ncols, nChsTotal, dtype=datatype)
# Expected values
ps, pa = nchs
UnT = omgs(angles, mus).T
# dLdX = dZdX x dLdZ
expctddLdX = dLdZ.clone()
Ya = dLdZ[:, :, :, ps:].view(nSamples * nrows * ncols, pa).T # pa * n
Za = UnT @ Ya
expctddLdX[:, :, :, ps:] = Za.T.view(nSamples, nrows, ncols, pa)
# dLdWi = <dLdZ,(dVdWi)X>
expctddLdW_U = torch.zeros(nAngles, dtype=datatype)
omgs.partial_difference = True
for iAngle in range(nAngles):
dUn = omgs(angles, mus, index_pd_angle=iAngle)
Xa = X[:, :, :, ps:].view(-1, pa).T
Za = dUn @ Xa # pa x n
expctddLdW_U[iAngle] = torch.sum(Ya * Za)
# Instantiation of target class
layer = NsoltIntermediateRotation2dLayer(number_of_channels=nchs,
mode='Analysis',
name='Vn')
layer.orthTransUn.angles.data = angles
layer.orthTransUn.mus = mus
# Actual values
torch.autograd.set_detect_anomaly(True)
Z = layer.forward(X)
layer.zero_grad()
Z.backward(dLdZ)
actualdLdX = X.grad
actualdLdW_U = layer.orthTransUn.angles.grad
# Evaluation
self.assertEqual(actualdLdX.dtype, datatype)
self.assertEqual(actualdLdW_U.dtype, datatype)
self.assertTrue(
torch.allclose(actualdLdX, expctddLdX, rtol=rtol, atol=atol))
self.assertTrue(
torch.allclose(actualdLdW_U, expctddLdW_U, rtol=rtol, atol=atol))
self.assertTrue(Z.requires_grad)
def testSetAngles(self, datatype):
rtol, atol = 1e-5, 1e-8
# Expected values
expctdM = torch.eye(2, dtype=datatype)
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Actual values
actualM = omgs(angles=0, mus=1)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
# Expected values
expctdM = torch.tensor(
[[math.cos(math.pi / 4), -math.sin(math.pi / 4)],
[math.sin(math.pi / 4),
math.cos(math.pi / 4)]],
dtype=datatype)
actualM = omgs(angles=math.pi / 4, mus=1)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testPartialDifferenceSetAngles(self, datatype):
rtol, atol = 1e-4, 1e-7
# Expected values
expctdM = torch.tensor([[0., -1.], [1., 0.]], dtype=datatype)
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=True)
# Actual values
actualM = omgs(angles=0, mus=1, index_pd_angle=0)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
# Expected values
expctdM = torch.tensor([[
math.cos(math.pi / 4 + math.pi / 2),
-math.sin(math.pi / 4 + math.pi / 2)
],
[
math.sin(math.pi / 4 + math.pi / 2),
math.cos(math.pi / 4 + math.pi / 2)
]],
dtype=datatype)
# Actual values
actualM = omgs(angles=math.pi / 4, mus=1, index_pd_angle=0)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testPartialDifference4x4RandAngPdAng1(self, datatype):
rtol, atol = 1e-1, 1e-3
# Expcted values
mus = [-1, -1, -1, -1]
angs = 2 * math.pi * torch.rand(6)
pdAng = 1
delta = 1e-3
expctdM = torch.as_tensor(
(1/delta)*torch.tensor(mus).view(-1,1) * \
torch.tensor(
[ [1, 0, 0, 0. ],
[0, 1, 0., 0. ],
[0, 0, math.cos(angs[5]), -math.sin(angs[5]) ],
[0., 0, math.sin(angs[5]), math.cos(angs[5]) ] ]
) @ torch.tensor(
[ [1, 0, 0, 0 ],
[0, math.cos(angs[4]), 0, -math.sin(angs[4]) ],
[0, 0, 1, 0 ],
[0, math.sin(angs[4]), 0, math.cos(angs[4]) ] ]
) @ torch.tensor(
[ [1, 0, 0, 0 ],
[0, math.cos(angs[3]), -math.sin(angs[3]), 0 ],
[0, math.sin(angs[3]), math.cos(angs[3]), 0 ],
[0, 0, 0, 1 ] ]
) @ torch.tensor(
[ [ math.cos(angs[2]), 0, 0, -math.sin(angs[2]) ],
[0, 1, 0, 0 ],
[0, 0, 1, 0 ],
[ math.sin(angs[2]), 0, 0, math.cos(angs[2]) ] ]
) @ (
torch.tensor(
[ [math.cos(angs[1]+delta/2), 0, -math.sin(angs[1]+delta/2), 0 ],
[0, 1, 0, 0 ],
[math.sin(angs[1]+delta/2), 0, math.cos(angs[1]+delta/2), 0 ],
[0, 0, 0, 1 ] ] ) - \
torch.tensor(
[ [math.cos(angs[1]-delta/2), 0, -math.sin(angs[1]-delta/2), 0 ],
[0, 1, 0, 0 ],
[math.sin(angs[1]-delta/2), 0, math.cos(angs[1]-delta/2), 0 ],
[0, 0, 0, 1 ] ] )
) @ torch.tensor(
[ [ math.cos(angs[0]), -math.sin(angs[0]), 0, 0 ],
[ math.sin(angs[0]), math.cos(angs[0]), 0, 0 ],
[ 0, 0, 1, 0 ],
[ 0, 0, 0, 1 ] ]
),dtype=datatype)
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=True)
# Actual values
actualM = omgs(angles=angs, mus=mus, index_pd_angle=pdAng)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testPredictGrayscaleWithRandomAnglesNoDcLeackage(self,
nchs, stride, nrows, ncols, datatype,mus):
rtol,atol=1e-5,1e-8
gen = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Parameters
nSamples = 8
nDecs = stride[0]*stride[1] # math.prod(stride)
nChsTotal = sum(nchs)
# nSamples x nRows x nCols x nDecs
X = torch.randn(nSamples,nrows,ncols,nDecs,dtype=datatype)
angles = torch.randn(int((nChsTotal-2)*nChsTotal/4),dtype=datatype)
# Expected values
# nSamples x nRows x nCols x nChs
ps,pa = nchs
nAngsW = int(len(angles)/2)
angsW,angsU = angles[:nAngsW],angles[nAngsW:]
angsWNoDcLeak = angsW.clone()
angsWNoDcLeak[:ps-1] = torch.zeros(ps-1,dtype=angles.dtype)
musW,musU = mus*torch.ones(ps,dtype=datatype),mus*torch.ones(pa,dtype=datatype)
musW[0] = 1
W0,U0 = gen(angsWNoDcLeak,musW),gen(angsU,musU)
ms,ma = int(math.ceil(nDecs/2.)), int(math.floor(nDecs/2.))
Zsa = torch.zeros(nChsTotal,nrows*ncols*nSamples,dtype=datatype)
Ys = X[:,:,:,:ms].view(-1,ms).T
Zsa[:ps,:] = W0[:,:ms] @ Ys
if ma > 0:
Ya = X[:,:,:,ms:].view(-1,ma).T
Zsa[ps:,:] = U0[:,:ma] @ Ya
expctdZ = Zsa.T.view(nSamples,nrows,ncols,nChsTotal)
# Instantiation of target class
layer = NsoltInitialRotation2dLayer(
number_of_channels=nchs,
decimation_factor=stride,
no_dc_leakage=True,
name='V0')
layer.orthTransW0.angles.data = angsW
layer.orthTransW0.mus = musW
layer.orthTransU0.angles.data = angsU
layer.orthTransU0.mus = musU
# Actual values
with torch.no_grad():
actualZ = layer.forward(X)
# Evaluation
self.assertEqual(actualZ.dtype,datatype)
self.assertTrue(torch.allclose(actualZ,expctdZ,rtol=rtol,atol=atol))
self.assertFalse(actualZ.requires_grad)
def testBackward8x8RandAngMusPdAng13(self, mode, ncols):
datatype = torch.double
rtol, atol = 1e-4, 1e-7
# Configuration
#mode = 'Synthesis'
nPoints = 8
#ncols = 2
mus = [1, 1, 1, 1, -1, -1, -1, -1]
angs0 = 2 * math.pi * torch.rand(28, dtype=datatype)
angs1 = angs0.clone()
angs2 = angs0.clone()
pdAng = 13
delta = 1e-4
angs1[pdAng] = angs0[pdAng] - delta / 2.
angs2[pdAng] = angs0[pdAng] + delta / 2.
# Expcted values
X = torch.randn(nPoints, ncols, dtype=datatype, requires_grad=True)
dLdZ = torch.randn(nPoints, ncols, dtype=datatype)
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=False)
R = omgs(angles=angs0, mus=mus)
dRdW = (omgs(angles=angs2, mus=mus) -
omgs(angles=angs1, mus=mus)) / delta
if mode != 'Synthesis':
expctddLdX = R.T @ dLdZ # = dZdX @ dLdZ
expctddLdW = torch.sum(dLdZ * (dRdW @ X))
else:
expctddLdX = R @ dLdZ # = dZdX @ dLdZ
expctddLdW = torch.sum(dLdZ * (dRdW.T @ X))
# Instantiation of target class
target = OrthonormalTransform(n=nPoints, dtype=datatype, mode=mode)
target.angles.data = angs0
target.mus = mus
# Actual values
torch.autograd.set_detect_anomaly(True)
Z = target.forward(X)
target.zero_grad()
Z.backward(dLdZ)
actualdLdX = X.grad
actualdLdW = target.angles.grad[pdAng]
# Evaluation
self.assertTrue(
torch.allclose(actualdLdX, expctddLdX, rtol=rtol, atol=atol))
self.assertTrue(
torch.allclose(actualdLdW, expctddLdW, rtol=rtol, atol=atol))
def test4x4RandAngs(self, datatype):
rtol, atol = 1e-4, 1e-7
# Expcted values
mus = [-1, 1, -1, 1]
angs = 2 * math.pi * torch.rand(6)
expctdM = torch.as_tensor(
torch.tensor(mus).view(-1,1) * \
torch.tensor(
[ [1, 0, 0, 0. ],
[0, 1, 0, 0. ],
[0, 0, math.cos(angs[5]), -math.sin(angs[5]) ],
[0, 0, math.sin(angs[5]), math.cos(angs[5]) ] ]
) @ torch.tensor(
[ [1, 0, 0, 0 ],
[0, math.cos(angs[4]), 0, -math.sin(angs[4]) ],
[0, 0, 1, 0 ],
[0, math.sin(angs[4]), 0, math.cos(angs[4]) ] ]
) @ torch.tensor(
[ [1, 0, 0, 0 ],
[0, math.cos(angs[3]), -math.sin(angs[3]), 0 ],
[0, math.sin(angs[3]), math.cos(angs[3]), 0 ],
[0, 0, 0, 1 ] ]
) @ torch.tensor(
[ [ math.cos(angs[2]), 0, 0, -math.sin(angs[2]) ],
[0, 1, 0, 0 ],
[0, 0, 1, 0 ],
[ math.sin(angs[2]), 0, 0, math.cos(angs[2]) ] ]
) @ torch.tensor(
[ [math.cos(angs[1]), 0, -math.sin(angs[1]), 0 ],
[0, 1, 0, 0 ],
[math.sin(angs[1]), 0, math.cos(angs[1]), 0 ],
[0, 0, 0, 1 ] ]
) @ torch.tensor(
[ [ math.cos(angs[0]), -math.sin(angs[0]), 0, 0 ],
[ math.sin(angs[0]), math.cos(angs[0]), 0, 0 ],
[ 0, 0, 1, 0 ],
[ 0, 0, 0, 1 ] ]
),dtype=datatype)
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Actual values
actualM = omgs(angles=angs, mus=mus)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testPartialDifference8x8RandAngPdAng13(self, datatype):
rtol, atol = 1e-1, 1e-3
# Expcted values
pdAng = 13
delta = 1e-3
angs0 = 2 * math.pi * torch.rand(28)
angs1 = angs0.clone()
angs2 = angs0.clone()
angs1[pdAng] = angs0[pdAng] - delta / 2
angs2[pdAng] = angs0[pdAng] + delta / 2
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=False)
expctdM = (omgs(angles=angs2, mus=1) -
omgs(angles=angs1, mus=1)) / delta
# Instantiation of target class
omgs.partial_difference = True
actualM = omgs(angles=angs0, mus=1, index_pd_angle=pdAng)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testConstructor(self, datatype):
rtol, atol = 1e-5, 1e-8
# Expected values
expctdM = torch.eye(2, dtype=datatype)
# Instantiation of target class
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Actual values
angles = 0
mus = 1
actualM = omgs(angles=angles, mus=mus)
# Evaluation
self.assertTrue(torch.allclose(actualM, expctdM, rtol=rtol, atol=atol))
def testPredictGrayscaleWithRandomAngles(self, datatype, nchs, stride,
nrows, ncols):
rtol, atol = 1e-3, 1e-6
gen = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Parameters
nSamples = 8
nDecs = stride[0] * stride[1] # math.prod(stride)
nChsTotal = sum(nchs)
# nSamples x nRows x nCols x nChs
X = torch.randn(nSamples, nrows, ncols, nChsTotal, dtype=datatype)
angles = torch.randn(int((nChsTotal - 2) * nChsTotal / 4),
dtype=datatype)
# Expected values
# nSamples x nRows x nCols x nDecs
ps, pa = nchs
nAngsW = int(len(angles) / 2)
angsW, angsU = angles[:nAngsW], angles[nAngsW:]
W0T, U0T = gen(angsW).T, gen(angsU).T
Ys = X[:, :, :, :ps].view(-1, ps).T
Ya = X[:, :, :, ps:].view(-1, pa).T
ms, ma = int(math.ceil(nDecs / 2.)), int(math.floor(nDecs / 2.))
Zsa = torch.cat((W0T[:ms, :] @ Ys, U0T[:ma, :] @ Ya), dim=0)
expctdZ = Zsa.T.view(nSamples, nrows, ncols, nDecs)
# Instantiation of target class
layer = NsoltFinalRotation2dLayer(number_of_channels=nchs,
decimation_factor=stride,
name='V0~')
layer.orthTransW0T.angles.data = angsW
layer.orthTransW0T.mus = 1
layer.orthTransU0T.angles.data = angsU
layer.orthTransU0T.mus = 1
# Actual values
with torch.no_grad():
actualZ = layer.forward(X)
# Evaluation
self.assertEqual(actualZ.dtype, datatype)
self.assertTrue(torch.allclose(actualZ, expctdZ, rtol=rtol, atol=atol))
self.assertFalse(actualZ.requires_grad)
def testPredictGrayscaleAnalysisMode(self, nchs, stride, nrows, ncols, mus,
datatype):
rtol, atol = 1e-5, 1e-8
gen = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Parameters
nSamples = 8
nChsTotal = sum(nchs)
# nSamples x nRows x nCols x nChsTotal
X = torch.randn(nSamples,
nrows,
ncols,
nChsTotal,
dtype=datatype,
requires_grad=True)
angles = torch.randn(int((nChsTotal - 2) * nChsTotal / 8),
dtype=datatype)
# Expected values
# nSamples x nRows x nCols x nChsTotal
ps, pa = nchs
Un = gen(angles, mus)
expctdZ = X.clone()
Ya = X[:, :, :, ps:].view(-1, pa).T
Za = Un @ Ya
expctdZ[:, :, :, ps:] = Za.T.view(nSamples, nrows, ncols, pa)
# Instantiation of target class
layer = NsoltIntermediateRotation2dLayer(number_of_channels=nchs,
name='Vn',
mode='Analysis')
layer.orthTransUn.angles.data = angles
layer.orthTransUn.mus = mus
# Actual values
with torch.no_grad():
actualZ = layer.forward(X)
# Evaluation
self.assertEqual(actualZ.dtype, datatype)
self.assertTrue(torch.allclose(actualZ, expctdZ, rtol=rtol, atol=atol))
self.assertFalse(actualZ.requires_grad)
def test8x8(self, datatype):
rtol, atol = 1e-5, 1e-8
# Expected values
expctdNorm = torch.tensor(1., dtype=datatype)
# Instantiation of target class
ang = 2 * math.pi * torch.rand(28)
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Actual values
unitvec = torch.randn(8, dtype=datatype)
unitvec /= unitvec.norm()
actualNorm = omgs(angles=ang, mus=1).mv(unitvec).norm() #.numpy()
# Evaluation
message = "actualNorm=%s differs from %s" % (str(actualNorm),
str(expctdNorm))
self.assertTrue(
torch.isclose(actualNorm, expctdNorm, rtol=rtol, atol=atol),
message)
def test8x8red(self, datatype):
rtol, atol = 1e-5, 1e-8
# Expected values
expctdLeftTop = torch.tensor(1., dtype=datatype)
# Instantiation of target class
ang = 2 * math.pi * torch.rand(28)
nSize = 8
ang[:nSize - 1] = torch.zeros(nSize - 1)
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype)
# Actual values
matrix = omgs(angles=ang, mus=1)
actualLeftTop = matrix[0, 0]
# Evaluation
message = "actualLeftTop=%s differs from %s" % (str(actualLeftTop),
str(expctdLeftTop))
self.assertTrue(
torch.isclose(actualLeftTop, expctdLeftTop, rtol=rtol, atol=atol),
message)
def testBackwardWithRandomAnglesNoDcLeackage(self, datatype, nchs, stride,
nrows, ncols, mus):
rtol, atol = 1e-2, 1e-5
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,
partial_difference=False)
# Parameters
nSamples = 8
nDecs = stride[0] * stride[1] # math.prod(stride)
nChsTotal = sum(nchs)
nAnglesH = int((nChsTotal - 2) * nChsTotal / 8)
anglesW = torch.randn(nAnglesH, dtype=datatype)
anglesU = torch.randn(nAnglesH, dtype=datatype)
# nSamples x nRows x nCols x nChs
X = torch.randn(nSamples,
nrows,
ncols,
nChsTotal,
dtype=datatype,
requires_grad=True)
dLdZ = torch.randn(nSamples, nrows, ncols, nDecs, dtype=datatype)
# Expected values
ps, pa = nchs
anglesWNoDcLeak = anglesW.clone()
anglesWNoDcLeak[:ps - 1] = torch.zeros(ps - 1, dtype=datatype)
musW, musU = mus * torch.ones(ps, dtype=datatype), mus * torch.ones(
pa, dtype=datatype)
musW[0] = 1
W0 = omgs(anglesWNoDcLeak, musW)
U0 = omgs(anglesU, musU)
# dLdX = dZdX x dLdZ
ms, ma = int(math.ceil(nDecs / 2.)), int(math.floor(nDecs / 2.))
Ys = dLdZ[:, :, :, :ms].view(nSamples * nrows * ncols, ms).T # ms x n
Ya = dLdZ[:, :, :, ms:].view(nSamples * nrows * ncols, ma).T # ma x n
Y = torch.cat(
(
W0[:, :ms] @ Ys, # ps x ms @ ms x n
U0[:, :ma] @ Ya),
dim=0) # pa x ma @ ma x n
expctddLdX = Y.T.view(nSamples, nrows, ncols,
nChsTotal) # n x (ps+pa) -> N x R x C X P
# dLdWi = <dLdZ,(dVdWi)X>
expctddLdW_W = torch.zeros(nAnglesH, dtype=datatype)
expctddLdW_U = torch.zeros(nAnglesH, dtype=datatype)
omgs.partial_difference = True
for iAngle in range(nAnglesH):
dW0_T = omgs(anglesWNoDcLeak, musW, index_pd_angle=iAngle).T
dU0_T = omgs(anglesU, musU, index_pd_angle=iAngle).T
Xs = X[:, :, :, :ps].view(-1, ps).T
Xa = X[:, :, :, ps:].view(-1, pa).T
Zs = dW0_T[:ms, :] @ Xs # ms x n
Za = dU0_T[:ma, :] @ Xa # ma x n
expctddLdW_W[iAngle] = torch.sum(Ys[:ms, :] * Zs)
expctddLdW_U[iAngle] = torch.sum(Ya[:ma, :] * Za)
# Instantiation of target class
layer = NsoltFinalRotation2dLayer(number_of_channels=nchs,
decimation_factor=stride,
no_dc_leakage=True,
name='V0~')
layer.orthTransW0T.angles.data = anglesW
layer.orthTransW0T.mus = mus
layer.orthTransU0T.angles.data = anglesU
layer.orthTransU0T.mus = mus
# Actual values
torch.autograd.set_detect_anomaly(True)
Z = layer.forward(X)
layer.zero_grad()
Z.backward(dLdZ)
actualdLdX = X.grad
actualdLdW_W = layer.orthTransW0T.angles.grad
actualdLdW_U = layer.orthTransU0T.angles.grad
# Evaluation
self.assertEqual(actualdLdX.dtype, datatype)
self.assertEqual(actualdLdW_W.dtype, datatype)
self.assertEqual(actualdLdW_U.dtype, datatype)
self.assertTrue(
torch.allclose(actualdLdX, expctddLdX, rtol=rtol, atol=atol))
self.assertTrue(
torch.allclose(actualdLdW_W, expctddLdW_W, rtol=rtol, atol=atol))
self.assertTrue(
torch.allclose(actualdLdW_U, expctddLdW_U, rtol=rtol, atol=atol))
self.assertTrue(Z.requires_grad)
def testBackwardGrayscaleWithRandomAngles(self,
nchs, stride, nrows, ncols, datatype):
rtol,atol=1e-3,1e-6
omgs = OrthonormalMatrixGenerationSystem(dtype=datatype,partial_difference=False)
# Parameters
nSamples = 8
nDecs = stride[0]*stride[1] # math.prod(stride)
nChsTotal = sum(nchs)
nAnglesH = int((nChsTotal-2)*nChsTotal/8)
anglesW = torch.randn(nAnglesH,dtype=datatype)
anglesU = torch.randn(nAnglesH,dtype=datatype)
mus = 1
# nSamples x nRows x nCols x nDecs
X = torch.randn(nSamples,nrows,ncols,nDecs,dtype=datatype,requires_grad=True)
dLdZ = torch.randn(nSamples,nrows,ncols,nChsTotal,dtype=datatype)
# Expected values
ps,pa = nchs
W0T = omgs(anglesW,mus).T
U0T = omgs(anglesU,mus).T
# dLdX = dZdX x dLdZ
ms,ma = int(math.ceil(nDecs/2.)),int(math.floor(nDecs/2.))
Ys = dLdZ[:,:,:,:ps].view(nSamples*nrows*ncols,ps).T # ps * n
Ya = dLdZ[:,:,:,ps:].view(nSamples*nrows*ncols,pa).T # pa * n
Y = torch.cat(
( W0T[:ms,:] @ Ys, # ms x ps @ ps x n
U0T[:ma,:] @ Ya ), dim=0) # ma x pa @ pa x n
expctddLdX = Y.T.view(nSamples,nrows,ncols,nDecs) # n x (ms+ma)
# dLdWi = <dLdZ,(dVdWi)X>
expctddLdW_W = torch.zeros(nAnglesH,dtype=datatype)
expctddLdW_U = torch.zeros(nAnglesH,dtype=datatype)
omgs.partial_difference = True
for iAngle in range(nAnglesH):
dW0 = omgs(anglesW,mus,index_pd_angle=iAngle)
Xs = X[:,:,:,:ms].view(-1,ms).T
Zs = dW0[:,:ms] @ Xs # ps x n
expctddLdW_W[iAngle] = torch.sum(Ys * Zs) # ps x n
if ma>0:
dU0 = omgs(anglesU,mus,index_pd_angle=iAngle)
Xa = X[:,:,:,ms:].view(-1,ma).T
Za = dU0[:,:ma] @ Xa # pa x n
expctddLdW_U[iAngle] = torch.sum(Ya * Za) # pa x n
# Instantiation of target class
layer = NsoltInitialRotation2dLayer(
number_of_channels=nchs,
decimation_factor=stride,
name='V0')
layer.orthTransW0.angles.data = anglesW
layer.orthTransW0.mus = mus
layer.orthTransU0.angles.data = anglesU
layer.orthTransU0.mus = mus
# Actual values
torch.autograd.set_detect_anomaly(True)
Z = layer.forward(X)
layer.zero_grad()
Z.backward(dLdZ)
actualdLdX = X.grad
actualdLdW_W = layer.orthTransW0.angles.grad
actualdLdW_U = layer.orthTransU0.angles.grad
# Evaluation
self.assertEqual(actualdLdX.dtype,datatype)
self.assertEqual(actualdLdW_W.dtype,datatype)
self.assertEqual(actualdLdW_U.dtype,datatype)
self.assertTrue(torch.allclose(actualdLdX,expctddLdX,rtol=rtol,atol=atol))
self.assertTrue(torch.allclose(actualdLdW_W,expctddLdW_W,rtol=rtol,atol=atol))
self.assertTrue(torch.allclose(actualdLdW_U,expctddLdW_U,rtol=rtol,atol=atol))
self.assertTrue(Z.requires_grad)