extra.py 8.95 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
18

import numpy as np
19
from numpy.testing import assert_
Philipp Arras's avatar
Philipp Arras committed
20

21
from .domain_tuple import DomainTuple
Martin Reinecke's avatar
fix    
Martin Reinecke committed
22
23
from .field import Field
from .linearization import Linearization
24
from .multi_domain import MultiDomain
25
from .multi_field import MultiField
26
from .operators.linear_operator import LinearOperator
Martin Reinecke's avatar
fix    
Martin Reinecke committed
27
from .sugar import from_random
28

Philipp Arras's avatar
Philipp Arras committed
29
30
__all__ = ["consistency_check", "check_jacobian_consistency",
           "assert_allclose"]
31

Philipp Arras's avatar
Philipp Arras committed
32

Philipp Arras's avatar
Philipp Arras committed
33
def assert_allclose(f1, f2, atol, rtol):
Martin Reinecke's avatar
Martin Reinecke committed
34
35
36
37
    if isinstance(f1, Field):
        return np.testing.assert_allclose(f1.local_data, f2.local_data,
                                          atol=atol, rtol=rtol)
    for key, val in f1.items():
Philipp Arras's avatar
Philipp Arras committed
38
        assert_allclose(val, f2[key], atol=atol, rtol=rtol)
Martin Reinecke's avatar
Martin Reinecke committed
39
40


41
42
def _adjoint_implementation(op, domain_dtype, target_dtype, atol, rtol,
                            only_r_linear):
Martin Reinecke's avatar
Martin Reinecke committed
43
44
45
46
47
48
49
    needed_cap = op.TIMES | op.ADJOINT_TIMES
    if (op.capability & needed_cap) != needed_cap:
        return
    f1 = from_random("normal", op.domain, dtype=domain_dtype)
    f2 = from_random("normal", op.target, dtype=target_dtype)
    res1 = f1.vdot(op.adjoint_times(f2))
    res2 = op.times(f1).vdot(f2)
50
51
    if only_r_linear:
        res1, res2 = res1.real, res2.real
Martin Reinecke's avatar
Martin Reinecke committed
52
53
54
55
56
57
58
59
60
    np.testing.assert_allclose(res1, res2, atol=atol, rtol=rtol)


def _inverse_implementation(op, domain_dtype, target_dtype, atol, rtol):
    needed_cap = op.TIMES | op.INVERSE_TIMES
    if (op.capability & needed_cap) != needed_cap:
        return
    foo = from_random("normal", op.target, dtype=target_dtype)
    res = op(op.inverse_times(foo))
Philipp Arras's avatar
Philipp Arras committed
61
    assert_allclose(res, foo, atol=atol, rtol=rtol)
Martin Reinecke's avatar
Martin Reinecke committed
62
63
64

    foo = from_random("normal", op.domain, dtype=domain_dtype)
    res = op.inverse_times(op(foo))
Philipp Arras's avatar
Philipp Arras committed
65
    assert_allclose(res, foo, atol=atol, rtol=rtol)
Martin Reinecke's avatar
Martin Reinecke committed
66
67


68
69
70
71
def _full_implementation(op, domain_dtype, target_dtype, atol, rtol,
                         only_r_linear):
    _adjoint_implementation(op, domain_dtype, target_dtype, atol, rtol,
                            only_r_linear)
Martin Reinecke's avatar
Martin Reinecke committed
72
73
74
    _inverse_implementation(op, domain_dtype, target_dtype, atol, rtol)


75
def _check_linearity(op, domain_dtype, atol, rtol):
Martin Reinecke's avatar
Martin Reinecke committed
76
77
78
    needed_cap = op.TIMES
    if (op.capability & needed_cap) != needed_cap:
        return
79
80
    fld1 = from_random("normal", op.domain, dtype=domain_dtype)
    fld2 = from_random("normal", op.domain, dtype=domain_dtype)
Martin Reinecke's avatar
Martin Reinecke committed
81
    alpha = np.random.random()  # FIXME: this can break badly with MPI!
82
83
    val1 = op(alpha*fld1+fld2)
    val2 = alpha*op(fld1)+op(fld2)
Philipp Arras's avatar
Philipp Arras committed
84
    assert_allclose(val1, val2, atol=atol, rtol=rtol)
85
86


87
88
89
90
91
92
93
94
95
96
97
98
def _actual_domain_check(op, domain_dtype=None, inp=None):
    needed_cap = op.TIMES
    if (op.capability & needed_cap) != needed_cap:
        return
    if domain_dtype is not None:
        inp = from_random("normal", op.domain, dtype=domain_dtype)
    elif inp is None:
        raise ValueError('Need to specify either dtype or inp')
    assert_(inp.domain is op.domain)
    assert_(op(inp).domain is op.target)


Philipp Arras's avatar
Philipp Arras committed
99
def _actual_domain_check_nonlinear(op, loc):
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
    assert isinstance(loc, (Field, MultiField))
    assert_(loc.domain is op.domain)
    lin = Linearization.make_var(loc, False)
    reslin = op(lin)
    assert_(lin.domain is op.domain)
    assert_(lin.target is op.domain)
    assert_(lin.val.domain is lin.domain)

    assert_(reslin.domain is op.domain)
    assert_(reslin.target is op.target)
    assert_(reslin.val.domain is reslin.target)

    assert_(reslin.target is op.target)
    assert_(reslin.jac.domain is reslin.domain)
    assert_(reslin.jac.target is reslin.target)
    _actual_domain_check(reslin.jac, inp=loc)
Philipp Arras's avatar
Philipp Arras committed
116
    _actual_domain_check(reslin.jac.adjoint, inp=reslin.jac(loc))
117
118


119
120
121
def _domain_check(op):
    for dd in [op.domain, op.target]:
        if not isinstance(dd, (DomainTuple, MultiDomain)):
Martin Reinecke's avatar
Martin Reinecke committed
122
123
124
            raise TypeError(
                'The domain and the target of an operator need to',
                'be instances of either DomainTuple or MultiDomain.')
125
126


Martin Reinecke's avatar
Martin Reinecke committed
127
def consistency_check(op, domain_dtype=np.float64, target_dtype=np.float64,
128
                      atol=0, rtol=1e-7, only_r_linear=False):
Reimar H Leike's avatar
Reimar H Leike committed
129
130
131
132
    """
    Checks an operator for algebraic consistency of its capabilities.

    Checks whether times(), adjoint_times(), inverse_times() and
Philipp Arras's avatar
Philipp Arras committed
133
    adjoint_inverse_times() (if in capability list) is implemented
Reimar H Leike's avatar
Reimar H Leike committed
134
    consistently. Additionally, it checks whether the operator is linear.
Philipp Arras's avatar
Philipp Arras committed
135
136
137
138
139

    Parameters
    ----------
    op : LinearOperator
        Operator which shall be checked.
Reimar H Leike's avatar
Reimar H Leike committed
140
    domain_dtype : dtype
Philipp Arras's avatar
Philipp Arras committed
141
142
        The data type of the random vectors in the operator's domain. Default
        is `np.float64`.
Reimar H Leike's avatar
Reimar H Leike committed
143
    target_dtype : dtype
Philipp Arras's avatar
Philipp Arras committed
144
145
146
        The data type of the random vectors in the operator's target. Default
        is `np.float64`.
    atol : float
Martin Reinecke's avatar
Martin Reinecke committed
147
148
        Absolute tolerance for the check. If rtol is specified,
        then satisfying any tolerance will let the check pass.
Reimar H Leike's avatar
Reimar H Leike committed
149
        Default: 0.
Philipp Arras's avatar
Philipp Arras committed
150
    rtol : float
Martin Reinecke's avatar
Martin Reinecke committed
151
152
        Relative tolerance for the check. If atol is specified,
        then satisfying any tolerance will let the check pass.
Reimar H Leike's avatar
Reimar H Leike committed
153
        Default: 0.
154
155
156
    only_r_linear: bool
        set to True if the operator is only R-linear, not C-linear.
        This will relax the adjointness test accordingly.
Philipp Arras's avatar
Philipp Arras committed
157
    """
158
159
    if not isinstance(op, LinearOperator):
        raise TypeError('This test tests only linear operators.')
160
    _domain_check(op)
161
    _actual_domain_check(op, domain_dtype)
Philipp Arras's avatar
Philipp Arras committed
162
163
    _actual_domain_check(op.adjoint, target_dtype)
    _actual_domain_check(op.inverse, target_dtype)
164
    _actual_domain_check(op.adjoint.inverse, domain_dtype)
165
    _check_linearity(op, domain_dtype, atol, rtol)
Martin Reinecke's avatar
Martin Reinecke committed
166
167
168
    _check_linearity(op.adjoint, target_dtype, atol, rtol)
    _check_linearity(op.inverse, target_dtype, atol, rtol)
    _check_linearity(op.adjoint.inverse, domain_dtype, atol, rtol)
169
170
171
172
173
174
    _full_implementation(op, domain_dtype, target_dtype, atol, rtol,
                         only_r_linear)
    _full_implementation(op.adjoint, target_dtype, domain_dtype, atol, rtol,
                         only_r_linear)
    _full_implementation(op.inverse, target_dtype, domain_dtype, atol, rtol,
                         only_r_linear)
Martin Reinecke's avatar
Martin Reinecke committed
175
    _full_implementation(op.adjoint.inverse, domain_dtype, target_dtype, atol,
176
                         rtol, only_r_linear)
Martin Reinecke's avatar
Martin Reinecke committed
177
178


Martin Reinecke's avatar
Martin Reinecke committed
179
def _get_acceptable_location(op, loc, lin):
Martin Reinecke's avatar
Martin Reinecke committed
180
    if not np.isfinite(lin.val.sum()):
Martin Reinecke's avatar
Martin Reinecke committed
181
182
183
184
        raise ValueError('Initial value must be finite')
    dir = from_random("normal", loc.domain)
    dirder = lin.jac(dir)
    if dirder.norm() == 0:
Martin Reinecke's avatar
Martin Reinecke committed
185
        dir = dir * (lin.val.norm()*1e-5)
Martin Reinecke's avatar
Martin Reinecke committed
186
    else:
Martin Reinecke's avatar
Martin Reinecke committed
187
        dir = dir * (lin.val.norm()*1e-5/dirder.norm())
Martin Reinecke's avatar
Martin Reinecke committed
188
189
190
191
    # Find a step length that leads to a "reasonable" location
    for i in range(50):
        try:
            loc2 = loc+dir
192
            lin2 = op(Linearization.make_var(loc2, lin.want_metric))
Martin Reinecke's avatar
Martin Reinecke committed
193
194
195
196
197
198
199
200
201
            if np.isfinite(lin2.val.sum()) and abs(lin2.val.sum()) < 1e20:
                break
        except FloatingPointError:
            pass
        dir = dir*0.5
    else:
        raise ValueError("could not find a reasonable initial step")
    return loc2, lin2

Martin Reinecke's avatar
Martin Reinecke committed
202

Martin Reinecke's avatar
Martin Reinecke committed
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
def check_jacobian_consistency(op, loc, tol=1e-8, ntries=100):
    """
    Checks the Jacobian of an operator against its finite difference
    approximation.

    Computes the Jacobian with finite differences and compares it to the
    implemented Jacobian.

    Parameters
    ----------
    op : Operator
        Operator which shall be checked.
    loc : Field or MultiField
        An Field or MultiField instance which has the same domain
        as op. The location at which the gradient is checked
    tol : float
        Tolerance for the check.
    """
221
    _domain_check(op)
222
    _actual_domain_check_nonlinear(op, loc)
Martin Reinecke's avatar
Martin Reinecke committed
223
    for _ in range(ntries):
224
        lin = op(Linearization.make_var(loc))
Martin Reinecke's avatar
Martin Reinecke committed
225
        loc2, lin2 = _get_acceptable_location(op, loc, lin)
Martin Reinecke's avatar
Martin Reinecke committed
226
        dir = loc2-loc
Martin Reinecke's avatar
Martin Reinecke committed
227
228
229
230
        locnext = loc2
        dirnorm = dir.norm()
        for i in range(50):
            locmid = loc + 0.5*dir
231
            linmid = op(Linearization.make_var(locmid))
Martin Reinecke's avatar
Martin Reinecke committed
232
233
            dirder = linmid.jac(dir)
            numgrad = (lin2.val-lin.val)
Martin Reinecke's avatar
Martin Reinecke committed
234
            xtol = tol * dirder.norm() / np.sqrt(dirder.size)
Martin Reinecke's avatar
Martin Reinecke committed
235
            if (abs(numgrad-dirder) <= xtol).all():
Martin Reinecke's avatar
Martin Reinecke committed
236
237
238
                break
            dir = dir*0.5
            dirnorm *= 0.5
Martin Reinecke's avatar
Martin Reinecke committed
239
            loc2, lin2 = locmid, linmid
Martin Reinecke's avatar
Martin Reinecke committed
240
241
242
        else:
            raise ValueError("gradient and value seem inconsistent")
        loc = locnext