Norms

Module containing various norms.

breze.arch.component.norm.l2(arr, axis=None)

Return the L2 norm of a tensor.

Parameters:

arr : Theano variable.

The variable to calculate the norm of.

axis : integer, optional [default: None]

The sum will be performed along this axis. This makes it possible to calculate the norm of many tensors in parallel, given they are organized along some axis. If not given, the norm will be computed for the whole tensor.

Returns:

res : Theano variable.

If axis is None, this will be a scalar. Otherwise it will be a tensor with one dimension less, where the missing dimension corresponds to axis.

Examples

>>> v = T.vector()
>>> this_norm = l2(v)

>>> m = T.matrix()
>>> this_norm = l2(m, axis=1)

>>> m = T.matrix()
>>> this_norm = l2(m)

breze.arch.component.norm.l1(arr, axis=None)

Return the L1 norm of a tensor.

Parameters:

arr : Theano variable.

The variable to calculate the norm of.

axis : integer, optional [default: None]

The sum will be performed along this axis. This makes it possible to calculate the norm of many tensors in parallel, given they are organized along some axis. If not given, the norm will be computed for the whole tensor.

Returns:

res : Theano variable.

If axis is None, this will be a scalar. Otherwise it will be a tensor with one dimension less, where the missing dimension corresponds to axis.

Examples

>>> v = T.vector()
>>> this_norm = l1(v)

>>> m = T.matrix()
>>> this_norm = l1(m, axis=1)

>>> m = T.matrix()
>>> this_norm = l1(m)

breze.arch.component.norm.soft_l1(inpt, eps=1e-08, axis=None)

Return a “soft” L1 norm of a tensor.

The term “soft” is used because we are using \(\sqrt{x^2 + \epsilon}\) in favor of \(|x|\) which is not smooth at \(x=0\).

Parameters:

arr : Theano variable.

The variable to calculate the norm of.

eps : float, optional [default: 1e-8]

Small offset to make the function more smooth.

axis : integer, optional [default: None]

The sum will be performed along this axis. This makes it possible to calculate the norm of many tensors in parallel, given they are organized along some axis. If not given, the norm will be computed for the whole tensor.

Returns:

res : Theano variable.

If axis is None, this will be a scalar. Otherwise it will be a tensor with one dimension less, where the missing dimension corresponds to axis.

Examples

>>> v = T.vector()
>>> this_norm = soft_l1(v)

>>> m = T.matrix()
>>> this_norm = soft_l1(m, axis=1)

>>> m = T.matrix()
>>> this_norm = soft_l1(m)

breze.arch.component.norm.lp(inpt, p, axis=None)

Return the Lp norm of a tensor.

Parameters:

arr : Theano variable.

The variable to calculate the norm of.

p : Theano variable or float.

Order of the norm.

axis : integer, optional [default: None]

The sum will be performed along this axis. This makes it possible to calculate the norm of many tensors in parallel, given they are organized along some axis. If not given, the norm will be computed for the whole tensor.

Returns:

res : Theano variable.

If axis is None, this will be a scalar. Otherwise it will be a tensor with one dimension less, where the missing dimension corresponds to axis.

Examples

>>> v = T.vector()
>>> this_norm = lp(v, .5)

>>> m = T.matrix()
>>> this_norm = lp(m, 3, axis=1)

>>> m = T.matrix()
>>> this_norm = lp(m, 4)