# **a_i** is a 4D Tensor of shape ``(7, 3, 1000, 1)`` and **not**
# a 3D Tensor of shape ``(7, 3, 1000)``.
#
#############################################################################
# Supported formulas
# ------------------------------------
#
# The full range of mathematical operations supported by
# :class:`LazyTensors<pykeops.torch.LazyTensor>` is described
# in our API documentation.
# Let's just mention that the lines below define valid computations:
#
x_i = LazyTensor(torch.randn(A, B, M, 1, D))
l_i = LazyTensor(torch.randn(1, 1, M, 1, D))
y_j = LazyTensor(torch.randn(1, B, 1, N, D))
s = LazyTensor(torch.rand(A, 1, 1, 1, 1))
F_ij = (x_i**1.5 + y_j / l_i).cos() - (x_i | y_j) + (x_i[:, :, :, :, 2] *
s.relu() * y_j)
print(F_ij)
a_j = F_ij.sum(dim=2)
print("a_j is now a {} of shape {}.".format(type(a_j), a_j.shape))
#############################################################################
# Enjoy! And feel free to check the next tutorial for a discussion
# of the varied reduction operations that can be applied to
# KeOps :class:`LazyTensors<pykeops.torch.LazyTensor>`.
# **a_i** is a 4D Tensor of shape ``(7, 3, 1000, 1)`` and **not**
# a 3D Tensor of shape ``(7, 3, 1000)``.
#
#############################################################################
# Supported formulas
# ------------------------------------
#
# The full range of mathematical operations supported by
# :class:`LazyTensors<pykeops.torch.LazyTensor>` is described
# in our API documentation.
# Let's just mention that the lines below define valid computations:
#
x_i = LazyTensor(torch.randn(A, B, M, 1, D))
l_i = LazyTensor(torch.randn(1, 1, M, 1, D))
y_j = LazyTensor(torch.randn(1, B, 1, N, D))
s = LazyTensor(torch.rand(A, 1, 1, 1, 1))
F_ij = (x_i ** 1.5 + y_j / l_i).cos() - (x_i | y_j) + (x_i[:, :, :, :, 2] * s.relu() * y_j)
print(F_ij)
a_j = F_ij.sum(dim=2)
print("a_j is now a {} of shape {}.".format(type(a_j), a_j.shape))
#############################################################################
# Enjoy! And feel free to check the next tutorial for a discussion
# of the varied reduction operations that can be applied to
# KeOps :class:`LazyTensors<pykeops.torch.LazyTensor>`.
# **a_i** is a 4D Tensor of shape ``(7, 3, 1000, 1)`` and **not**
# a 3D Tensor of shape ``(7, 3, 1000)``.
#
#############################################################################
# Supported formulas
# ------------------------------------
#
# The full range of mathematical operations supported by
# :class:`LazyTensors<pykeops.torch.LazyTensor>` is described
# in our API documentation.
# Let's just mention that the lines below define valid computations:
#
x_i = LazyTensor(torch.randn(A, B, M, 1, D))
l_i = LazyTensor(torch.randn(1, 1, M, 1, D))
y_j = LazyTensor(torch.randn(1, B, 1, N, D))
s = LazyTensor(torch.rand(A, 1, 1, 1, 1))
F_ij = ((x_i**1.5 + y_j / l_i).cos() - (x_i | y_j) +
(x_i[:, :, :, :, 2] * s.relu() * y_j))
print(F_ij)
a_j = F_ij.sum(dim=2)
print("a_j is now a {} of shape {}.".format(type(a_j), a_j.shape))
#############################################################################
# Enjoy! And feel free to check the next tutorial for a discussion
# of the varied reduction operations that can be applied to
# KeOps :class:`LazyTensors<pykeops.torch.LazyTensor>`.