computer_vision.gramian
=======================

.. py:module:: computer_vision.gramian

.. autoapi-nested-parse::

   Image style reconstruction with Gram matrices.

   https://en.wikipedia.org/wiki/Gram_matrix
   https://en.wikipedia.org/wiki/Neural_style_transfer
   https://arxiv.org/pdf/1603.08155#page=7&zoom=auto,-294,3



Functions
---------

.. autoapisummary::

   computer_vision.gramian.gram_loss
   computer_vision.gramian.gram_matrix


Module Contents
---------------

.. py:function:: gram_loss(input_features: numpy.ndarray, reference_features: numpy.ndarray) -> numpy.float64

   Calculates the squared Frobenius norm of the difference between
   the Gram matrices of the input and reference image.

   :param input_features: Feature map of shape (C, H, W)
   :type input_features: np.ndarray
   :param reference_features: Feature map of shape (C, H, W)
   :type reference_features: np.ndarray
   :return: Gram loss between the two feature maps.
   :rtype: float64

   Examples
   --------
   >>> a = np.random.randn(3,5,5)
   >>> gram_loss(a, a)
   np.float64(0.0)
   >>> a = np.zeros((3,5,5))
   >>> b = np.ones((3,5,5))
   >>> gram_loss(a, b)
   np.float64(1.0)


.. py:function:: gram_matrix(mat: numpy.ndarray) -> numpy.ndarray

   Returns the Gram (Gramian) matrix of an image.

   :param mat: matrix of shape (C, H, W); C = color channels, H = height, W = width.
   :type mat: np.ndarray
   :return: matrix of shape (C, C).
   :rtype: np.ndarray

   Examples
   --------
   >>> gram_matrix(np.ones((2,5,5)))
   array([[0.5, 0.5],
          [0.5, 0.5]])
   >>> gram_matrix(np.ones((3,5,5)))
   array([[0.33333333, 0.33333333, 0.33333333],
          [0.33333333, 0.33333333, 0.33333333],
          [0.33333333, 0.33333333, 0.33333333]])
   >>> gram_matrix(np.ones((3,5,5))).shape
   (3, 3)