linear_interpolation.py 5.5 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13
# 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/>.
#
14
# Copyright(C) 2013-2019 Max-Planck-Society
15
#
16
# NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik.
17

Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
18
import numpy as np
Philipp Arras's avatar
Cleanup  
Philipp Arras committed
19 20
from scipy.sparse import coo_matrix
from scipy.sparse.linalg import aslinearoperator
21

22
from ..domains.rg_space import RGSpace
Philipp Arras's avatar
Cleanup  
Philipp Arras committed
23 24
from ..domains.unstructured_domain import UnstructuredDomain
from ..field import Field
25
from ..sugar import makeDomain
26 27 28 29 30 31
from .linear_operator import LinearOperator


class LinearInterpolator(LinearOperator):
    def __init__(self, domain, positions):
        """
32
        Multilinear interpolation for points in an RGSpace
33 34

        :param domain:
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
35
            RGSpace
36 37 38
        :param positions:
            positions at which to interpolate
            Field with UnstructuredDomain, shape (dim, ndata)
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
39
            positions that are not within the RGSpace are wrapped
40
            according to periodic boundary conditions
41 42 43 44 45 46 47 48 49
        """
        self._domain = makeDomain(domain)
        N_points = positions.shape[1]
        self._target = makeDomain(UnstructuredDomain(N_points))
        self._capability = self.TIMES | self.ADJOINT_TIMES
        self._build_mat(positions, N_points)

    def _build_mat(self, positions, N_points):
        ndim = positions.shape[0]
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
50 51
        mg = np.mgrid[(slice(0, 2),)*ndim]
        mg = np.array(list(map(np.ravel, mg)))
52 53
        dist = []
        for dom in self.domain:
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
54
            if not isinstance(dom, RGSpace):
55
                raise TypeError
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
56
            dist.append(list(dom.distances))
Philipp Arras's avatar
Tweaks  
Philipp Arras committed
57
        dist = np.array(dist).reshape(-1, 1)
58
        pos = positions/dist
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
59 60 61 62 63 64
        excess = pos-pos.astype(np.int64)
        pos = pos.astype(np.int64)
        max_index = np.array(self.domain.shape).reshape(-1, 1)
        data = np.zeros((len(mg[0]), N_points))
        ii = np.zeros((len(mg[0]), N_points), dtype=np.int64)
        jj = np.zeros((len(mg[0]), N_points), dtype=np.int64)
65
        for i in range(len(mg[0])):
Philipp Arras's avatar
Tweaks  
Philipp Arras committed
66
            factor = np.prod(np.abs(1-mg[:, i].reshape(-1, 1)-excess),
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
67
                             axis=0)
68
            data[i, :] = factor
Philipp Arras's avatar
Tweaks  
Philipp Arras committed
69
            fromi = (pos+mg[:, i].reshape(-1, 1)) % max_index
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
70 71
            ii[i, :] = np.arange(N_points)
            jj[i, :] = np.ravel_multi_index(fromi, self.domain.shape)
72 73
        self._mat = coo_matrix((data.reshape(-1),
                               (ii.reshape(-1), jj.reshape(-1))),
Martin Reinecke's avatar
tweaks  
Martin Reinecke committed
74
                               (N_points, np.prod(self.domain.shape)))
75
        self._mat = aslinearoperator(self._mat)
76

77 78 79 80
    def apply(self, x, mode):
        self._check_input(x, mode)
        x_val = x.to_global_data()
        if mode == self.TIMES:
Philipp Arras's avatar
Tweaks  
Philipp Arras committed
81
            res = self._mat.matvec(x_val.reshape(-1))
82 83 84 85
            return Field.from_global_data(self.target, res)
        res = self._mat.rmatvec(x_val).reshape(self.domain.shape)
        return Field.from_global_data(self.domain, res)

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

# import numpy as np
# from ..domains.rg_space import RGSpace
# import itertools
#
#
# class LinearInterpolator(LinearOperator):
#     def __init__(self, domain, positions):
#         """
#         :param domain:
#             RGSpace
#         :param target:
#             UnstructuredDomain, shape (ndata,)
#         :param positions:
#             positions at which to interpolate
#             Field with UnstructuredDomain, shape (dim, ndata)
#         """
#         if not isinstance(domain, RGSpace):
#             raise TypeError("RGSpace needed")
#         if np.any(domain.shape < 2):
#             raise ValueError("RGSpace shape too small")
#         if positions.ndim != 2:
#             raise ValueError("positions must be a 2D array")
#         ndim = len(domain.shape)
#         if positions.shape[0] != ndim:
#             raise ValueError("shape mismatch")
#         self._domain = makeDomain(domain)
#         N_points = positions.shape[1]
#         dist = np.array(domain.distances).reshape((ndim, -1))
#         self._pos = positions/dist
#         shp = np.array(domain.shape, dtype=int).reshape((ndim, -1))
#         self._idx = np.maximum(0, np.minimum(shp-2, self._pos.astype(int)))
#         self._pos -= self._idx
#         tmp = tuple([0, 1] for i in range(ndim))
#         self._corners = np.array(list(itertools.product(*tmp)))
#         self._target = makeDomain(UnstructuredDomain(N_points))
#         self._capability = self.TIMES | self.ADJOINT_TIMES
#
#     def apply(self, x, mode):
#         self._check_input(x, mode)
#         x = x.to_global_data()
#         ndim = len(self._domain.shape)
#
#         res = np.zeros(self._tgt(mode).shape, dtype=x.dtype)
#         for corner in self._corners:
#             corner = corner.reshape(ndim, -1)
#             idx = self._idx+corner
#             idx2 = tuple(idx[t, :] for t in range(idx.shape[0]))
#             wgt = np.prod(self._pos*corner+(1-self._pos)*(1-corner), axis=0)
#             if mode == self.TIMES:
#                 res += wgt*x[idx2]
#             else:
#                 np.add.at(res, idx2, wgt*x)
#         return Field.from_global_data(self._tgt(mode), res)