def test_ormqr(self):
mat1 = torch.randn(10, 10)
mat2 = torch.randn(10, 10)
q, r = torch.qr(mat1)
m, tau = torch.geqrf(mat1)
res1 = torch.mm(q, mat2)
res2, _ = torch.ormqr(m, tau, mat2)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q)
res2, _ = torch.ormqr(m, tau, mat2, False)
self.assertEqual(res1, res2)
res1 = torch.mm(q.t(), mat2)
res2, _ = torch.ormqr(m, tau, mat2, True, True)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q.t())
res2, _ = torch.ormqr(m, tau, mat2, False, True)
self.assertEqual(res1, res2)
python类qr()的实例源码
def orthogonal(tensor, gain=1):
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
if rows < cols:
flattened.t_()
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
if rows < cols:
q.t_()
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
def test_ormqr(self):
mat1 = torch.randn(10, 10)
mat2 = torch.randn(10, 10)
q, r = torch.qr(mat1)
m, tau = torch.geqrf(mat1)
res1 = torch.mm(q, mat2)
res2, _ = torch.ormqr(m, tau, mat2)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q)
res2, _ = torch.ormqr(m, tau, mat2, False)
self.assertEqual(res1, res2)
res1 = torch.mm(q.t(), mat2)
res2, _ = torch.ormqr(m, tau, mat2, True, True)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q.t())
res2, _ = torch.ormqr(m, tau, mat2, False, True)
self.assertEqual(res1, res2)
def test_ormqr(self):
mat1 = torch.randn(10, 10)
mat2 = torch.randn(10, 10)
q, r = torch.qr(mat1)
m, tau = torch.geqrf(mat1)
res1 = torch.mm(q, mat2)
res2, _ = torch.ormqr(m, tau, mat2)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q)
res2, _ = torch.ormqr(m, tau, mat2, False)
self.assertEqual(res1, res2)
res1 = torch.mm(q.t(), mat2)
res2, _ = torch.ormqr(m, tau, mat2, True, True)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q.t())
res2, _ = torch.ormqr(m, tau, mat2, False, True)
self.assertEqual(res1, res2)
def test_ormqr(self):
mat1 = torch.randn(10, 10)
mat2 = torch.randn(10, 10)
q, r = torch.qr(mat1)
m, tau = torch.geqrf(mat1)
res1 = torch.mm(q, mat2)
res2, _ = torch.ormqr(m, tau, mat2)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q)
res2, _ = torch.ormqr(m, tau, mat2, False)
self.assertEqual(res1, res2)
res1 = torch.mm(q.t(), mat2)
res2, _ = torch.ormqr(m, tau, mat2, True, True)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q.t())
res2, _ = torch.ormqr(m, tau, mat2, False, True)
self.assertEqual(res1, res2)
def test_ormqr(self):
mat1 = torch.randn(10, 10)
mat2 = torch.randn(10, 10)
q, r = torch.qr(mat1)
m, tau = torch.geqrf(mat1)
res1 = torch.mm(q, mat2)
res2, _ = torch.ormqr(m, tau, mat2)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q)
res2, _ = torch.ormqr(m, tau, mat2, False)
self.assertEqual(res1, res2)
res1 = torch.mm(q.t(), mat2)
res2, _ = torch.ormqr(m, tau, mat2, True, True)
self.assertEqual(res1, res2)
res1 = torch.mm(mat2, q.t())
res2, _ = torch.ormqr(m, tau, mat2, False, True)
self.assertEqual(res1, res2)
def orthogonal(tensor, gain=1):
"""Fills the input Tensor or Variable with a (semi) orthogonal matrix, as described in "Exact solutions to the
nonlinear dynamics of learning in deep linear neural networks" - Saxe, A. et al. (2013). The input tensor must have
at least 2 dimensions, and for tensors with more than 2 dimensions the trailing dimensions are flattened.
Args:
tensor: an n-dimensional torch.Tensor or autograd.Variable, where n >= 2
gain: optional scaling factor
Examples:
>>> w = torch.Tensor(3, 5)
>>> nn.init.orthogonal(w)
"""
if isinstance(tensor, Variable):
orthogonal(tensor.data, gain=gain)
return tensor
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
# Pad zeros to Q (if rows smaller than cols)
if rows < cols:
padding = torch.zeros(rows, cols - rows)
if q.is_cuda:
q = torch.cat([q, padding.cuda()], 1)
else:
q = torch.cat([q, padding], 1)
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
def orthogonal(tensor, gain=1):
"""Fills the input Tensor or Variable with a (semi) orthogonal matrix, as described in "Exact solutions to the
nonlinear dynamics of learning in deep linear neural networks" - Saxe, A. et al. (2013). The input tensor must have
at least 2 dimensions, and for tensors with more than 2 dimensions the trailing dimensions are flattened.
Args:
tensor: an n-dimensional torch.Tensor or autograd.Variable, where n >= 2
gain: optional scaling factor
Examples:
>>> w = torch.Tensor(3, 5)
>>> nn.init.orthogonal(w)
"""
if isinstance(tensor, Variable):
orthogonal(tensor.data, gain=gain)
return tensor
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
# Pad zeros to Q (if rows smaller than cols)
if rows < cols:
padding = torch.zeros(rows, cols - rows)
if q.is_cuda:
q = torch.cat([q, padding.cuda()], 1)
else:
q = torch.cat([q, padding], 1)
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
def qr(mat: T.FloatTensor) -> T.Tuple[T.FloatTensor]:
"""
Compute the QR decomposition of a matrix.
The QR decomposition factorizes a matrix A into a product
A = QR of an orthonormal matrix Q and an upper triangular matrix R.
Provides an orthonormalization of the columns of the matrix.
Args:
mat: A matrix.
Returns:
(Q, R): Tuple of tensors.
"""
return torch.qr(mat)
def orthogonal(tensor, gain=1):
"""Fills the input Tensor or Variable with a (semi) orthogonal matrix, as
described in "Exact solutions to the nonlinear dynamics of learning in deep
linear neural networks" - Saxe, A. et al. (2013). The input tensor must have
at least 2 dimensions, and for tensors with more than 2 dimensions the
trailing dimensions are flattened.
Args:
tensor: an n-dimensional torch.Tensor or autograd.Variable, where n >= 2
gain: optional scaling factor
Examples:
>>> w = torch.Tensor(3, 5)
>>> nn.init.orthogonal(w)
"""
if isinstance(tensor, Variable):
orthogonal(tensor.data, gain=gain)
return tensor
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
if rows < cols:
flattened.t_()
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
if rows < cols:
q.t_()
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
def orthogonal(tensor, gain=1):
"""Fills the input Tensor or Variable with a (semi) orthogonal matrix, as
described in "Exact solutions to the nonlinear dynamics of learning in deep
linear neural networks" - Saxe, A. et al. (2013). The input tensor must have
at least 2 dimensions, and for tensors with more than 2 dimensions the
trailing dimensions are flattened.
Args:
tensor: an n-dimensional torch.Tensor or autograd.Variable, where n >= 2
gain: optional scaling factor
Examples:
>>> w = torch.Tensor(3, 5)
>>> nn.init.orthogonal(w)
"""
if isinstance(tensor, Variable):
orthogonal(tensor.data, gain=gain)
return tensor
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
if rows < cols:
flattened.t_()
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
if rows < cols:
q.t_()
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
def orthogonal(tensor, gain=1):
"""Fills the input Tensor or Variable with a (semi) orthogonal matrix, as
described in "Exact solutions to the nonlinear dynamics of learning in deep
linear neural networks" - Saxe, A. et al. (2013). The input tensor must have
at least 2 dimensions, and for tensors with more than 2 dimensions the
trailing dimensions are flattened.
Args:
tensor: an n-dimensional torch.Tensor or autograd.Variable, where n >= 2
gain: optional scaling factor
Examples:
>>> w = torch.Tensor(3, 5)
>>> nn.init.orthogonal(w)
"""
if isinstance(tensor, Variable):
orthogonal(tensor.data, gain=gain)
return tensor
if tensor.ndimension() < 2:
raise ValueError("Only tensors with 2 or more dimensions are supported")
rows = tensor.size(0)
cols = tensor[0].numel()
flattened = torch.Tensor(rows, cols).normal_(0, 1)
if rows < cols:
flattened.t_()
# Compute the qr factorization
q, r = torch.qr(flattened)
# Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
d = torch.diag(r, 0)
ph = d.sign()
q *= ph.expand_as(q)
if rows < cols:
q.t_()
tensor.view_as(q).copy_(q)
tensor.mul_(gain)
return tensor
