projection_operator.py 4.93 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# NIFTy
# Copyright (C) 2017  Theo Steininger
#
# Author: Theo Steininger
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <http://www.gnu.org/licenses/>.

Theo Steininger's avatar
Theo Steininger committed
19
20
21
22
23
24
25
26
import numpy as np

from nifty.field import Field

from nifty.operators.endomorphic_operator import EndomorphicOperator


class ProjectionOperator(EndomorphicOperator):
Theo Steininger's avatar
Theo Steininger committed
27
    """ NIFTY class for projection operators.
Theo Steininger's avatar
Theo Steininger committed
28

Theo Steininger's avatar
Theo Steininger committed
29
30
    The NIFTY ProjectionOperator class is a class derived from the
    EndomorphicOperator.
31
32
33

    Parameters
    ----------
Theo Steininger's avatar
Theo Steininger committed
34
    projection_field : Field
35
36
37
38
39
40
41
42
43
        Field on which the operator projects

    Attributes
    ----------

    Raises
    ------
    TypeError
        Raised if
Theo Steininger's avatar
Theo Steininger committed
44
            * if projection_field is not a Field
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65

    Notes
    -----


    Examples
    --------
    >>> x_space = RGSpace(5)
    >>> f1 = Field(x_space, val=3.)
    >>> f2 = Field(x_space, val=5.)
    >>> P = ProjectionOperator(f1)
    >>> res = P.times(f2)
    >>> res.val
    <distributed_data_object>
    array([ 225.,  225.,  225.,  225.,  225.])

    See Also
    --------
    EndomorphicOperator

    """
Theo Steininger's avatar
Theo Steininger committed
66

Theo Steininger's avatar
Theo Steininger committed
67
68
    # ---Overwritten properties and methods---

69
70
71
    def __init__(self, projection_field, default_spaces=None):
        super(ProjectionOperator, self).__init__(default_spaces)

Theo Steininger's avatar
Theo Steininger committed
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
        if not isinstance(projection_field, Field):
            raise TypeError("The projection_field must be a NIFTy-Field"
                            "instance.")
        self._projection_field = projection_field
        self._unitary = None

    def _times(self, x, spaces):
        # if the domain matches directly
        # -> multiply the fields directly
        if x.domain == self.domain:
            # here the actual multiplication takes place
            dotted = (self._projection_field * x).sum()
            return self._projection_field * dotted

        # if the distribution_strategy of self is sub-slice compatible to
        # the one of x, reshape the local data of self and apply it directly
        active_axes = []
        if spaces is None:
            active_axes = range(len(x.shape))
        else:
            for space_index in spaces:
                active_axes += x.domain_axes[space_index]

        axes_local_distribution_strategy = \
            x.val.get_axes_local_distribution_strategy(active_axes)
        if axes_local_distribution_strategy == \
           self._projection_field.distribution_strategy:
            local_projection_vector = \
                self._projection_field.val.get_local_data(copy=False)
        else:
            # create an array that is sub-slice compatible
            self.logger.warn("The input field is not sub-slice compatible to "
                             "the distribution strategy of the operator. "
                             "Performing an probably expensive "
                             "redistribution.")
            redistr_projection_val = self._projection_field.val.copy(
                distribution_strategy=axes_local_distribution_strategy)
            local_projection_vector = \
                redistr_projection_val.get_local_data(copy=False)

        local_x = x.val.get_local_data(copy=False)

        l = len(local_projection_vector.shape)
        sublist_projector = range(l)
        sublist_x = np.arange(len(local_x.shape)) + l

        for i in xrange(l):
            a = active_axes[i]
            sublist_x[a] = i

        dotted = np.einsum(local_projection_vector, sublist_projector,
                           local_x, sublist_x)

        # get those elements from sublist_x that haven't got contracted
        sublist_dotted = sublist_x[sublist_x >= l]

        remultiplied = np.einsum(local_projection_vector, sublist_projector,
                                 dotted, sublist_dotted,
                                 sublist_x)
        result_field = x.copy_empty(dtype=remultiplied.dtype)
        result_field.val.set_local_data(remultiplied, copy=False)
        return result_field

    def _inverse_times(self, x, spaces):
        raise NotImplementedError("The ProjectionOperator is a singular "
                                  "operator and therefore has no inverse.")

    # ---Mandatory properties and methods---

    @property
    def domain(self):
        return self._projection_field.domain

    @property
    def unitary(self):
        if self._unitary is None:
            self._unitary = (self._projection_field.val == 1).all()
        return self._unitary

    @property
Martin Reinecke's avatar
Martin Reinecke committed
152
    def self_adjoint(self):
Theo Steininger's avatar
Theo Steininger committed
153
        return True