"""
Different symbolic regularization and sparsity functions.
"""

import theano
import theano.tensor as T

from tags import tags

__authors__   = "Frederic Bastien, Nicolas Boulanger-Lewandowski, .."
__copyright__ = "(c) 2010, Universite de Montreal"
__license__   = "3-clause BSD License"
__contact__   = "theano-user <theano-users@googlegroups.com>"

@tags('regularization', 'L1')
def l1(x, target = 0, axis_sum = -1, axis_mean = 0):
    """ Construct the L1 regularization penalty :math:`\sum|x-target|`

    :type x: Theano variable
    :param x: Weights or other variable to regularize
    :type target: Theano variable
    :param target: Target of x
    :type axis_sum: Scalar
    :param axis_sum: Axis along which the penalty terms will be summed (e.g. output units)
    :type axis_mean: Scalar
    :param axis_mean: Axis along which the penalty terms will be averaged (e.g. minibatches)    

    :note: no stabilization required
    """
    return T.mean(T.sum(T.abs_(x - target), axis_sum), axis_mean)

@tags('regularization', 'L2')
def l2(x, target = 0, axis_sum = -1, axis_mean = 0):
    """ Construct the L2 regularization penalty :math:`\sum(x-target)^2`

    :type x: Theano variable
    :param x: Weights or other variable to regularize
    :type target: Theano variable
    :param target: Target of x
    :type axis_sum: Scalar
    :param axis_sum: Axis along which the penalty terms will be summed (e.g. output units)
    :type axis_mean: Scalar
    :param axis_mean: Axis along which the penalty terms will be averaged (e.g. minibatches)    

    :note: no stabilization required
    """
    return T.mean(T.sum((x - target)**2, axis_sum), axis_mean)