Source code for TransportMaps.Maps.IdentityTransportMapBase

#
# This file is part of TransportMaps.
#
# TransportMaps is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# TransportMaps is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with TransportMaps.  If not, see <http://www.gnu.org/licenses/>.
#
# Transport Maps Library
# Copyright (C) 2015-2018 Massachusetts Institute of Technology
# Uncertainty Quantification group
# Department of Aeronautics and Astronautics
#
# Authors: Transport Map Team
# Website: transportmaps.mit.edu
# Support: transportmaps.mit.edu/qa/
#

import numpy as np

from ..Misc import counted

from .TransportMapBase import TransportMap

__all__ = [
    'IdentityTransportMap',
]


class IdentityTransportMap(TransportMap): 
    r""" Map :math:`T({\bf x})={\bf x}`.
    """
    def __init__(self, dim):
        super(IdentityTransportMap, self).__init__(
            dim=dim
        )

    @counted
    def evaluate(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return x

    @counted
    def grad_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        gx = np.zeros((1, self.dim, self.dim))
        gxdiag = np.einsum('...ii->...i', gx)
        gxdiag[:] = 1.
        return gx

    @counted
    def hess_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return np.zeros((1, self.dim, self.dim, self.dim))

    @counted
    def inverse(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return x

    @counted
    def grad_x_inverse(self, x, *args, **kwargs):
        return self.grad_x(x, *args, **kwargs)
        
    @counted
    def hess_x_inverse(self, x, *args, **kwargs):
        return self.hess_x(x, *args, **kwargs)

    @counted
    def log_det_grad_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return np.zeros(1)

    @counted
    def grad_x_log_det_grad_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return np.zeros((1, self.dim))

    @counted
    def hess_x_log_det_grad_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return np.zeros((1, self.dim, self.dim))

    @counted
    def det_grad_x(self, x, *args, **kwargs):
        if x.shape[1] != self.dim:
            raise ValueError("dimension mismatch")
        return np.ones(1)

    @counted
    def log_det_grad_x_inverse(self, x, *args, **kwargs):
        return self.log_det_grad_x(x, *args, **kwargs)

    @counted
    def det_grad_x_inverse(self, x, *args, **kwargs):
        return self.det_grad_x(x, *args, **kwargs)

    @counted
    def grad_x_log_det_grad_x_inverse(self, x, *args, **kwargs):
        return self.grad_x_log_det_grad_x(x, *args, **kwargs)

    @counted
    def hess_x_log_det_grad_x_inverse(self, x, *args, **kwargs):
        return self.hess_x_log_det_grad_x(x, *args, **kwargs)