nifty_operators.py 142 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
# NIFTY (Numerical Information Field Theory) has been developed at the
# Max-Planck-Institute for Astrophysics.
#
# Copyright (C) 2015 Max-Planck-Society
#
# Author: Marco Selig
# Project homepage: <http://www.mpa-garching.mpg.de/ift/nifty/>
#
# 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/>.
Ultimanet's avatar
Ultimanet committed
21
22
23

from __future__ import division
import numpy as np
24
from nifty.keepers import about
Ultimanet's avatar
Ultimanet committed
25
from nifty.nifty_core import space, \
26
27
    point_space, \
    field
28
from nifty_minimization import conjugate_gradient
Ultima's avatar
Ultima committed
29
from nifty_probing import trace_prober,\
30
31
32
33
    inverse_trace_prober,\
    diagonal_prober,\
    inverse_diagonal_prober
import nifty.nifty_utilities as utilities
Ultima's avatar
Ultima committed
34
import nifty.nifty_simple_math as nifty_simple_math
Ultima's avatar
Ultima committed
35

Ultimanet's avatar
Ultimanet committed
36

37
# =============================================================================
Ultimanet's avatar
Ultimanet committed
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
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

class operator(object):
    """
        ..                                                      __
        ..                                                    /  /_
        ..    ______    ______    _______   _____   ____ __  /   _/  ______    _____
        ..  /   _   | /   _   | /   __  / /   __/ /   _   / /  /   /   _   | /   __/
        .. /  /_/  / /  /_/  / /  /____/ /  /    /  /_/  / /  /_  /  /_/  / /  /
        .. \______/ /   ____/  \______/ /__/     \______|  \___/  \______/ /__/     class
        ..         /__/

        NIFTY base class for (linear) operators

        The base NIFTY operator class is an abstract class from which other
        specific operator subclasses, including those preimplemented in NIFTY
        (e.g. the diagonal operator class) must be derived.

        Parameters
        ----------
        domain : space
            The space wherein valid arguments live.
        sym : bool, *optional*
            Indicates whether the operator is self-adjoint or not
            (default: False)
        uni : bool, *optional*
            Indicates whether the operator is unitary or not
            (default: False)
        imp : bool, *optional*
            Indicates whether the incorporation of volume weights in
            multiplications is already implemented in the `multiply`
            instance methods or not (default: False)
        target : space, *optional*
            The space wherein the operator output lives (default: domain)
        para : {single object, list of objects}, *optional*
            This is a freeform list of parameters that derivatives of the
            operator class can use. Not used in the base operators.
            (default: None)

        See Also
        --------
        diagonal_operator :  An operator class for handling purely diagonal
            operators.
        power_operator : Similar to diagonal_operator but with handy features
            for dealing with diagonal operators whose diagonal
            consists of a power spectrum.
        vecvec_operator : Operators constructed from the outer product of two
            fields
        response_operator : Implements a modeled instrument response which
            translates a signal into data space.
        projection_operator : An operator that projects out one or more
            components in a basis, e.g. a spectral band
            of Fourier components.

        Attributes
        ----------
        domain : space
            The space wherein valid arguments live.
        sym : bool
            Indicates whether the operator is self-adjoint or not
        uni : bool
            Indicates whether the operator is unitary or not
        imp : bool
            Indicates whether the incorporation of volume weights in
            multiplications is already implemented in the `multiply`
            instance methods or not
        target : space
            The space wherein the operator output lives
        para : {single object, list of objects}
            This is a freeform list of parameters that derivatives of the
            operator class can use. Not used in the base operators.
    """
109
110

    def __init__(self, domain, codomain=None, sym=False, uni=False,
Ultima's avatar
Ultima committed
111
                 imp=False, target=None, cotarget=None, bare=False):
Ultimanet's avatar
Ultimanet committed
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
        """
            Sets the attributes for an operator class instance.

            Parameters
            ----------
            domain : space
                The space wherein valid arguments live.
            sym : bool, *optional*
                Indicates whether the operator is self-adjoint or not
                (default: False)
            uni : bool, *optional*
                Indicates whether the operator is unitary or not
                (default: False)
            imp : bool, *optional*
                Indicates whether the incorporation of volume weights in
                multiplications is already implemented in the `multiply`
                instance methods or not (default: False)
            target : space, *optional*
                The space wherein the operator output lives (default: domain)
            para : {object, list of objects}, *optional*
                This is a freeform list of parameters that derivatives of the
                operator class can use. Not used in the base operators.
                (default: None)

            Returns
            -------
            None
        """
140
        # Check if the domain is realy a space
141
        if not isinstance(domain, space):
142
143
            raise TypeError(about._errors.cstring(
                "ERROR: invalid input. domain is not a space."))
Ultimanet's avatar
Ultimanet committed
144
        self.domain = domain
145
146
        # Parse codomain
        if self.domain.check_codomain(codomain) == True:
147
148
149
            self.codomain = codomain
        else:
            self.codomain = self.domain.get_codomain()
150
151

        # Cast the symmetric and unitary input
Ultimanet's avatar
Ultimanet committed
152
153
        self.sym = bool(sym)
        self.uni = bool(uni)
Ultima's avatar
Ultima committed
154
        self.bare = bool(bare)
Ultimanet's avatar
Ultimanet committed
155

156
157
158
        # If no target is supplied, we assume that the operator is square
        # If the operator is symmetric or unitary, we know that the operator
        # must be square
159

Ultima's avatar
Ultima committed
160
        if self.sym or self.uni:
161
            target = self.domain
162
            cotarget = self.codomain
163
164
            if target is not None:
                about.warnings.cprint("WARNING: Ignoring target.")
165

166
        elif target is None:
Ultimanet's avatar
Ultimanet committed
167
            target = self.domain
168
            cotarget = self.codomain
169

170
        elif isinstance(target, space):
171
172
173
            self.target = target
            # Parse cotarget
            if self.target.check_codomain(cotarget) == True:
174
175
176
                self.codomain = codomain
            else:
                self.codomain = self.domain.get_codomain()
177
        else:
178
            raise TypeError(about._errors.cstring(
179
                "ERROR: invalid input. Target is not a space."))
Ultimanet's avatar
Ultimanet committed
180

181
        if self.domain.discrete and self.target.discrete:
Ultimanet's avatar
Ultimanet committed
182
183
184
185
            self.imp = True
        else:
            self.imp = bool(imp)

Ultima's avatar
Ultima committed
186
187
188
189
190
191
192
193
194
195
    def set_val(self, new_val):
        """
            Resets the field values.

            Parameters
            ----------
            new_val : {scalar, ndarray}
                New field values either as a constant or an arbitrary array.

        """
Ultima's avatar
Ultima committed
196
        self.val = new_val
Ultima's avatar
Ultima committed
197
        return self.val
198

Ultima's avatar
Ultima committed
199
200
201
    def get_val(self):
        return self.val

202
203
    def _multiply(self, x, **kwargs):
        # > applies the operator to a given field
204
205
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'multiply'."))
Ultimanet's avatar
Ultimanet committed
206

207
208
    def _adjoint_multiply(self, x, **kwargs):
        # > applies the adjoint operator to a given field
209
210
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'adjoint_multiply'."))
Ultimanet's avatar
Ultimanet committed
211

212
213
    def _inverse_multiply(self, x, **kwargs):
        # > applies the inverse operator to a given field
214
215
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'inverse_multiply'."))
Ultimanet's avatar
Ultimanet committed
216

217
218
    def _adjoint_inverse_multiply(self, x, **kwargs):
        # > applies the inverse adjoint operator to a given field
219
220
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'adjoint_inverse_multiply'."))
Ultimanet's avatar
Ultimanet committed
221

222
223
    def _inverse_adjoint_multiply(self, x, **kwargs):
        # > applies the adjoint inverse operator to a given field
224
225
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'inverse_adjoint_multiply'."))
Ultimanet's avatar
Ultimanet committed
226

227
    def _briefing(self, x, domain, codomain, inverse):
Ultima's avatar
Ultima committed
228
229
230
231
        # make sure, that the result_field of the briefing lives in the
        # given domain and codomain
        result_field = field(domain=domain, val=x, codomain=codomain,
                             copy=False)
232

Ultima's avatar
Ultima committed
233
        # weight if necessary
234
        if (not self.imp) and (not domain.discrete) and (not inverse):
Ultima's avatar
Ultima committed
235
236
            result_field = result_field.weight(power=1)
        return result_field
Ultimanet's avatar
Ultimanet committed
237

238
    def _debriefing(self, x, y, target, cotarget, inverse):
Ultima's avatar
Ultima committed
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
        # The debriefing takes care that the result field lives in the same
        # fourier-type domain as the input field
        assert(isinstance(y, field))

        # weight if necessary
        if (not self.imp) and (not target.discrete) and inverse:
            y = y.weight(power=-1)

        # if the operators domain as well as the target have the harmonic
        # attribute, try to match the result_field to the input_field
        if hasattr(self.domain, 'harmonic') and \
                hasattr(self.target, 'harmonic'):
            if x.domain.harmonic != y.domain.harmonic:
                y = y.transform()

        return y
Ultimanet's avatar
Ultimanet committed
255

256
    def times(self, x, **kwargs):
Ultimanet's avatar
Ultimanet committed
257
258
259
260
261
262
263
264
265
266
267
268
269
270
        """
            Applies the operator to a given object

            Parameters
            ----------
            x : {scalar, ndarray, field}
                Scalars are interpreted as constant arrays, and an array will
                be interpreted as a field on the domain of the operator.

            Returns
            -------
            Ox : field
                Mapped field on the target domain of the operator.
        """
271
        # prepare
272
        y = self._briefing(x, self.domain, self.codomain, inverse=False)
273
        # apply operator
274
        y = self._multiply(y, **kwargs)
275
        # evaluate
276
        return self._debriefing(x, y, self.target, self.cotarget,
277
                                inverse=False)
Ultimanet's avatar
Ultimanet committed
278

279
280
    def __call__(self, x, **kwargs):
        return self.times(x, **kwargs)
Ultimanet's avatar
Ultimanet committed
281

282
    def adjoint_times(self, x, **kwargs):
Ultimanet's avatar
Ultimanet committed
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
        """
            Applies the adjoint operator to a given object.

            Parameters
            ----------
            x : {scalar, ndarray, field}
                Scalars are interpreted as constant arrays, and an array will
                be interpreted as a field on the target space of the operator.

            Returns
            -------
            OAx : field
                Mapped field on the domain of the operator.

        """
298
        # check whether self-adjoint
299
        if self.sym:
300
            return self.times(x, **kwargs)
301
        # check whether unitary
302
        if self.uni:
303
            return self.inverse_times(x, **kwargs)
Ultimanet's avatar
Ultimanet committed
304

305
        # prepare
306
        y = self._briefing(x, self.target, self.cotarget, inverse=False)
307
        # apply operator
308
        y = self._adjoint_multiply(y, **kwargs)
309
        # evaluate
310
        return self._debriefing(x, y, self.domain, self.codomain,
311
                                inverse=False)
Ultimanet's avatar
Ultimanet committed
312

313
    def inverse_times(self, x, **kwargs):
Ultimanet's avatar
Ultimanet committed
314
315
316
317
318
319
320
321
322
323
324
325
326
327
        """
            Applies the inverse operator to a given object.

            Parameters
            ----------
            x : {scalar, ndarray, field}
                Scalars are interpreted as constant arrays, and an array will
                be interpreted as a field on the domain space of the operator.

            Returns
            -------
            OIx : field
                Mapped field on the target space of the operator.
        """
328
        # check whether self-inverse
329
        if self.sym and self.uni:
330
            return self.times(x, **kwargs)
Ultimanet's avatar
Ultimanet committed
331

332
        # prepare
333
        y = self._briefing(x, self.target, self.cotarget, inverse=True)
334
        # apply operator
335
        y = self._inverse_multiply(y, **kwargs)
336
        # evaluate
337
        return self._debriefing(x, y, self.domain, self.codomain,
338
                                inverse=True)
Ultimanet's avatar
Ultimanet committed
339

340
    def adjoint_inverse_times(self, x, **kwargs):
Ultimanet's avatar
Ultimanet committed
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
        """
            Applies the inverse adjoint operator to a given object.

            Parameters
            ----------
            x : {scalar, ndarray, field}
                Scalars are interpreted as constant arrays, and an array will
                be interpreted as a field on the target space of the operator.

            Returns
            -------
            OAIx : field
                Mapped field on the domain of the operator.

        """
356
        # check whether self-adjoint
357
        if self.sym:
358
            return self.inverse_times(x, **kwargs)
359
        # check whether unitary
360
        if self.uni:
361
            return self.times(x, **kwargs)
Ultimanet's avatar
Ultimanet committed
362

363
        # prepare
364
        y = self._briefing(x, self.domain, self.codomain, inverse=True)
365
        # apply operator
366
        y = self._adjoint_inverse_multiply(y, **kwargs)
367
        # evaluate
368
        return self._debriefing(x, y, self.target, self.cotarget,
369
                                inverse=True)
Ultimanet's avatar
Ultimanet committed
370

371
    def inverse_adjoint_times(self, x, **kwargs):
Ultimanet's avatar
Ultimanet committed
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
        """
            Applies the adjoint inverse operator to a given object.

            Parameters
            ----------
            x : {scalar, ndarray, field}
                Scalars are interpreted as constant arrays, and an array will
                be interpreted as a field on the target space of the operator.

            Returns
            -------
            OIAx : field
                Mapped field on the domain of the operator.

        """
387
        # check whether self-adjoint
388
        if self.sym:
389
            return self.inverse_times(x, **kwargs)
390
        # check whether unitary
391
        if self.uni:
392
            return self.times(x, **kwargs)
Ultimanet's avatar
Ultimanet committed
393

394
        # prepare
395
        y = self._briefing(x, self.domain, self.codomain, inverse=True)
396
        # apply operator
397
        y = self._inverse_adjoint_multiply(y, **kwargs)
398
        # evaluate
399
        return self._debriefing(x, y, self.target, self.cotarget,
400
                                inverse=True)
Ultimanet's avatar
Ultimanet committed
401

Ultima's avatar
Ultima committed
402
    def tr(self, domain=None, codomain=None, random="pm1", nrun=8,
403
           varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
        """
            Computes the trace of the operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            tr : float
                Trace of the operator
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

            See Also
            --------
            probing : The class used to perform probing operations
        """
445
446
447
448
449
450
451

        return trace_prober(operator=self,
                            domain=domain,
                            codomain=codomain,
                            random=random,
                            nrun=nrun,
                            varQ=varQ,
Ultima's avatar
Ultima committed
452
453
                            **kwargs
                            )()
454

Ultima's avatar
Ultima committed
455
    def inverse_tr(self, domain=None, codomain=None, random="pm1", nrun=8,
456
                   varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
        """
            Computes the trace of the inverse operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            nrun : int, *optional*
                total number of probes (default: 8)
Ultima's avatar
Ultima committed
475
            varQ : bool, *optional*
Ultimanet's avatar
Ultimanet committed
476
477
                Indicates whether to additionally return the probing variance
                or not (default: False).
Ultima's avatar
Ultima committed
478

Ultimanet's avatar
Ultimanet committed
479
480
481
482
483
484
485
486
487
488
489
490
491

            Returns
            -------
            tr : float
                Trace of the inverse operator
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

            See Also
            --------
            probing : The class used to perform probing operations
        """
492
493
494
495
496
497
498
499
        return inverse_trace_prober(operator=self,
                                    domain=domain,
                                    codomain=codomain,
                                    random=random,
                                    nrun=nrun,
                                    varQ=varQ,
                                    **kwargs
                                    )()
Ultimanet's avatar
Ultimanet committed
500

Ultima's avatar
Ultima committed
501
    def diag(self, domain=None, codomain=None, random="pm1", nrun=8,
502
             varQ=False, bare=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
        """
            Computes the diagonal of the operator via probing.

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            diag : ndarray
                The matrix diagonal
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
Ultima's avatar
Ultima committed
567

568
569
570
571
572
573
574
575
        diag = diagonal_prober(operator=self,
                               domain=domain,
                               codomain=codomain,
                               random=random,
                               nrun=nrun,
                               varQ=varQ,
                               **kwargs
                               )()
576
        if diag is None:
Ultima's avatar
Ultima committed
577
            about.warnings.cprint("WARNING: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
578
            return None
579

Ultima's avatar
Ultima committed
580
        if domain is None:
581
            domain = diag.domain
582
        # weight if ...
583
        if (not domain.discrete) and bare:
584
            if(isinstance(diag, tuple)):  # diag == (diag,variance)
Ultima's avatar
Ultima committed
585
586
                return (diag[0].weight(power=-1),
                        diag[1].weight(power=-1))
Ultimanet's avatar
Ultimanet committed
587
            else:
Ultima's avatar
Ultima committed
588
                return diag.weight(power=-1)
Ultimanet's avatar
Ultimanet committed
589
590
591
        else:
            return diag

592
593
    def inverse_diag(self, domain=None, codomain=None, random="pm1",
                     nrun=8, varQ=False, bare=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
        """
            Computes the diagonal of the inverse operator via probing.

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            diag : ndarray
                The diagonal of the inverse matrix
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
        if(domain is None):
            domain = self.target
660
661
662
663
664
665
666
667
        diag = inverse_diagonal_prober(operator=self,
                                       domain=domain,
                                       codomain=codomain,
                                       random=random,
                                       nrun=nrun,
                                       varQ=varQ,
                                       **kwargs
                                       )()
Ultimanet's avatar
Ultimanet committed
668
        if(diag is None):
669
            about.infos.cprint("INFO: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
670
            return None
671

Ultima's avatar
Ultima committed
672
        if domain is None:
673
            domain = diag.codomain
674
        # weight if ...
675
        if not domain.discrete and bare:
676
            if(isinstance(diag, tuple)):  # diag == (diag,variance)
Ultima's avatar
Ultima committed
677
678
                return (diag[0].weight(power=-1),
                        diag[1].weight(power=-1))
Ultimanet's avatar
Ultimanet committed
679
            else:
Ultima's avatar
Ultima committed
680
                return diag.weight(power=-1)
Ultimanet's avatar
Ultimanet committed
681
682
        else:
            return diag
683

Ultimanet's avatar
Ultimanet committed
684
685
686
687
688
689
690
691
692
693
    def det(self):
        """
            Computes the determinant of the operator.

            Returns
            -------
            det : float
                The determinant

        """
694
695
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'det'."))
Ultimanet's avatar
Ultimanet committed
696
697
698
699
700
701
702
703
704
705
706

    def inverse_det(self):
        """
            Computes the determinant of the inverse operator.

            Returns
            -------
            det : float
                The determinant

        """
707
708
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'inverse_det'."))
Ultimanet's avatar
Ultimanet committed
709
710
711

    def log_det(self):
        """
712
713
            Computes the logarithm of the determinant of the operator
            (if applicable).
Ultimanet's avatar
Ultimanet committed
714
715
716
717
718
719
720

            Returns
            -------
            logdet : float
                The logarithm of the determinant

        """
721
722
        raise NotImplementedError(about._errors.cstring(
            "ERROR: no generic instance method 'log_det'."))
Ultimanet's avatar
Ultimanet committed
723
724
725

    def tr_log(self):
        """
726
727
            Computes the trace of the logarithm of the operator
            (if applicable).
Ultimanet's avatar
Ultimanet committed
728
729
730
731
732
733
734
735
736

            Returns
            -------
            logdet : float
                The trace of the logarithm

        """
        return self.log_det()

737
    def hat(self, bare=False, domain=None, codomain=None, **kwargs):
Ultimanet's avatar
Ultimanet committed
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
        """
            Translates the operator's diagonal into a field

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            x : field
                The matrix diagonal as a field living on the operator
                domain space

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
797
        if domain is None:
Ultimanet's avatar
Ultimanet committed
798
            domain = self.domain
799
800
801
        if codomain is None:
            codomain = self.codomain

802
        diag = self.diag(bare=bare, domain=domain, codomain=codomain,
803
804
                         var=False, **kwargs)
        if diag is None:
805
            about.infos.cprint("WARNING: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
806
            return None
807
808
        return diag

809
    def inverse_hat(self, bare=False, domain=None, codomain=None, **kwargs):
Ultimanet's avatar
Ultimanet committed
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
        """
            Translates the inverse operator's diagonal into a field

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            x : field
                The matrix diagonal as a field living on the operator
                domain space

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
869
        if domain is None:
Ultimanet's avatar
Ultimanet committed
870
            domain = self.target
871
872
        if codomain is None:
            codomain = self.cotarget
873
        diag = self.inverse_diag(bare=bare, domain=domain, codomain=codomain,
874
875
                                 var=False, **kwargs)
        if diag is None:
876
            about.infos.cprint("WARNING: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
877
            return None
878
879
        return diag

880
    def hathat(self, domain=None, codomain=None, **kwargs):
Ultimanet's avatar
Ultimanet committed
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
        """
            Translates the operator's diagonal into a diagonal operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            D : diagonal_operator
                The matrix diagonal as an operator

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
935
        if domain is None:
Ultimanet's avatar
Ultimanet committed
936
            domain = self.domain
937
938
        if codomain is None:
            codomain = self.codomain
939
940

        diag = self.diag(bare=False, domain=domain, codomain=codomain,
941
                         var=False, **kwargs)
942
        if diag is None:
943
            about.infos.cprint("WARNING: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
944
            return None
945
946
        return diagonal_operator(domain=domain, codomain=codomain,
                                 diag=diag, bare=False)
Ultimanet's avatar
Ultimanet committed
947

948
    def inverse_hathat(self, domain=None, codomain=None, **kwargs):
Ultimanet's avatar
Ultimanet committed
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
        """
            Translates the inverse operator's diagonal into a diagonal
            operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            D : diagonal_operator
                The diagonal of the inverse matrix as an operator

            See Also
            --------
            probing : The class used to perform probing operations

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
1004
        if domain is None:
Ultimanet's avatar
Ultimanet committed
1005
            domain = self.target
1006
1007
        if codomain is None:
            codomain = self.cotarget
1008

1009
        diag = self.inverse_diag(bare=False, domain=domain, codomain=codomain,
1010
1011
                                 var=False, **kwargs)
        if diag is None:
1012
            about.infos.cprint("WARNING: forwarding 'NoneType'.")
Ultimanet's avatar
Ultimanet committed
1013
            return None
1014
        return diagonal_operator(domain=domain, codomain=codomain,
1015
                                 diag=diag, bare=False)
Ultimanet's avatar
Ultimanet committed
1016
1017
1018
1019

    def __repr__(self):
        return "<nifty_core.operator>"

1020
# =============================================================================
Ultimanet's avatar
Ultimanet committed
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081


class diagonal_operator(operator):
    """
        ..           __   __                                                     __
        ..         /  / /__/                                                   /  /
        ..    ____/  /  __   ____ __   ____ __   ______    __ ___    ____ __  /  /
        ..  /   _   / /  / /   _   / /   _   / /   _   | /   _   | /   _   / /  /
        .. /  /_/  / /  / /  /_/  / /  /_/  / /  /_/  / /  / /  / /  /_/  / /  /_
        .. \______| /__/  \______|  \___   /  \______/ /__/ /__/  \______|  \___/  operator class
        ..                         /______/

        NIFTY subclass for diagonal operators

        Parameters
        ----------
        domain : space, *optional*
            The space wherein valid arguments live. If no domain is given
            then the diag parameter *must* be a field and the domain
            of that field is assumed. (default: None)
        diag : {scalar, ndarray, field}
            The diagonal entries of the operator. For a scalar, a constant
            diagonal is defined having the value provided. If no domain
            is given, diag must be a field. (default: 1)
        bare : bool, *optional*
            whether the diagonal entries are `bare` or not
            (mandatory for the correct incorporation of volume weights)
            (default: False)

        Notes
        -----
        The ambiguity of `bare` or non-bare diagonal entries is based
        on the choice of a matrix representation of the operator in
        question. The naive choice of absorbing the volume weights
        into the matrix leads to a matrix-vector calculus with the
        non-bare entries which seems intuitive, though. The choice of
        keeping matrix entries and volume weights separate deals with the
        bare entries that allow for correct interpretation of the matrix
        entries; e.g., as variance in case of an covariance operator.

        The inverse applications of the diagonal operator feature a ``pseudo``
        flag indicating if zero divison shall be ignored and return zero
        instead of causing an error.

        Attributes
        ----------
        domain : space
            The space wherein valid arguments live.
        val : ndarray
            A field containing the diagonal entries of the matrix.
        sym : bool
            Indicates whether the operator is self-adjoint or not
        uni : bool
            Indicates whether the operator is unitary or not
        imp : bool
            Indicates whether the incorporation of volume weights in
            multiplications is already implemented in the `multiply`
            instance methods or not
        target : space
            The space wherein the operator output lives
    """
1082

1083
    def __init__(self, domain=None, codomain=None, diag=1, bare=False):
Ultimanet's avatar
Ultimanet committed
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
        """
            Sets the standard operator properties and `values`.

            Parameters
            ----------
            domain : space, *optional*
                The space wherein valid arguments live. If no domain is given
                then the diag parameter *must* be a field and the domain
                of that field is assumed. (default: None)
            diag : {scalar, ndarray, field}, *optional*
                The diagonal entries of the operator. For a scalar, a constant
                diagonal is defined having the value provided. If no domain
                is given, diag must be a field. (default: 1)
            bare : bool, *optional*
                whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)

            Returns
            -------
            None

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

1117
        """
1118
        # Set the domain
1119
1120
1121
1122
1123
        if domain is None:
            try:
                self.domain = diag.domain
            except(AttributeError):
                raise TypeError(about._errors.cstring(
1124
1125
                    "ERROR: Explicit or implicit, i.e. via diag domain " +
                    "inupt needed!"))
1126

1127
1128
1129
        else:
            self.domain = domain

1130
        if self.domain.check_codomain(codomain):
1131
1132
1133
            self.codomain = codomain
        else:
            self.codomain = self.domain.get_codomain()
Ultima's avatar
Ultima committed
1134

1135
        self.target = self.domain
1136
        self.cotarget = self.codomain
1137
        self.imp = True
Ultima's avatar
Ultima committed
1138
        self.set_diag(new_diag=diag, bare=bare)
Ultima's avatar
Ultima committed
1139
1140

    def set_diag(self, new_diag, bare=False):
Ultimanet's avatar
Ultimanet committed
1141
1142
1143
1144
1145
        """
            Sets the diagonal of the diagonal operator

            Parameters
            ----------
Ultima's avatar
Ultima committed
1146
            new_diag : {scalar, ndarray, field}
Ultimanet's avatar
Ultimanet committed
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
                The new diagonal entries of the operator. For a scalar, a
                constant diagonal is defined having the value provided. If
                no domain is given, diag must be a field.

            bare : bool, *optional*
                whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)

            Returns
            -------
            None
        """
Ultima's avatar
Ultima committed
1160

1161
        # Set the diag-val
Ultima's avatar
Ultima committed
1162
1163
        self.val = self.domain.cast(new_diag)

1164
1165
1166
        # Set the bare-val #TODO Check with Theo
        self.bare = bare

1167
        # Weight if necessary
1168
        if not self.domain.discrete and bare:
1169
1170
1171
            self.val = self.domain.calc_weight(self.val, power=1)

        # Check complexity attributes
Ultima's avatar
Ultima committed
1172
1173
1174
1175
        if self.domain.calc_real_Q(self.val) == True:
            self.sym = True
        else:
            self.sym = False
1176
1177

        # Check if unitary, i.e. identity
Ultima's avatar
Ultima committed
1178
1179
1180
        if (self.val == 1).all() == True:
            self.uni = True
        else:
1181
1182
1183
            self.uni = False

    def _multiply(self, x, **kwargs):
1184
        # applies the operator to a given field
1185
        y = x.copy(domain=self.target, codomain=self.cotarget)
Ultima's avatar
Ultima committed
1186
        y *= self.get_val()
1187
1188
1189
        return y

    def _adjoint_multiply(self, x, **kwargs):
1190
        # applies the adjoint operator to a given field
1191
        y = x.copy(domain=self.domain, codomain=self.codomain)
Ultima's avatar
Ultima committed
1192
        y *= self.get_val().conjugate()
1193
        return y
Ultima's avatar
Ultima committed
1194

1195
    def _inverse_multiply(self, x, pseudo=False, **kwargs):
1196
        # applies the inverse operator to a given field
1197
        y = x.copy(domain=self.domain, codomain=self.codomain)
Ultima's avatar
Ultima committed
1198
        if (self.get_val() == 0).any():
1199
            if not pseudo:
Ultima's avatar
Ultima committed
1200
1201
1202
                raise AttributeError(about._errors.cstring(
                    "ERROR: singular operator."))
            else:
1203
1204
#                raise NotImplementedError(
#                    "ERROR: function not yet implemented!")
Ultima's avatar
Ultima committed
1205
                y /= self.get_val()
1206
1207
1208
1209
1210
                # TODO: implement this
                # the following code does not work. np.isnan is needed,
                # but on a level of fields
#                y[y == np.nan] = 0
#                y[y == np.inf] = 0
Ultima's avatar
Ultima committed
1211
1212
1213
1214
        else:
            y /= self.get_val()
        return y

1215
1216
1217
    def _adjoint_inverse_multiply(self, x, pseudo=False, **kwargs):
        # > applies the inverse adjoint operator to a given field
        y = x.copy(domain=self.target, codomain=self.cotarget)
Ultima's avatar
Ultima committed
1218
        if (self.get_val() == 0).any():
1219
            if not pseudo:
Ultima's avatar
Ultima committed
1220
1221
1222
                raise AttributeError(about._errors.cstring(
                    "ERROR: singular operator."))
            else:
1223
1224
1225
1226
1227
                raise NotImplementedError(
                    "ERROR: function not yet implemented!")
                # TODO: implement this
                # the following code does not work. np.isnan is needed,
                # but on a level of fields
Ultima's avatar
Ultima committed
1228
1229
1230
1231
1232
                y /= self.get_val().conjugate()
                y[y == np.nan] = 0
                y[y == np.inf] = 0
        else:
            y /= self.get_val().conjugate()
1233
1234
1235
1236
1237
        return y

    def _inverse_adjoint_multiply(self, x, pseudo=False, **kwargs):
        # > applies the adjoint inverse operator to a given field
        return self._adjoint_inverse_multiply(x, pseudo=pseudo, **kwargs)
Ultimanet's avatar
Ultimanet committed
1238

Ultima's avatar
Ultima committed
1239
    def tr(self, varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
        """
            Computes the trace of the operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            tr : float
                Trace of the operator
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

Ultima's avatar
Ultima committed
1277
        """
1278

Ultima's avatar
Ultima committed
1279
1280
        tr = self.domain.unary_operation(self.val, 'sum')

1281
        if varQ:
1282
            return (tr, 1)
Ultima's avatar
Ultima committed
1283
1284
        else:
            return tr
1285

Ultima's avatar
Ultima committed
1286
    def inverse_tr(self, varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
        """
            Computes the trace of the inverse operator

            Parameters
            ----------
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            tr : float
                Trace of the inverse operator
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

        """
Ultima's avatar
Ultima committed
1325
1326
1327
1328
        if (self.get_val() == 0).any():
            raise AttributeError(about._errors.cstring(
                "ERROR: singular operator."))
        inverse_tr = self.domain.unary_operation(
1329
1330
1331
            self.domain.binary_operation(self.val, 1, 'rdiv', cast=0),
            'sum')

1332
        if varQ:
1333
            return (inverse_tr, 1)
Ultima's avatar
Ultima committed
1334
1335
        else:
            return inverse_tr
1336
1337

    def diag(self, bare=False, domain=None, codomain=None,
1338
             varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
        """
            Computes the diagonal of the operator.

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)

            Returns
            -------
            diag : ndarray
                The matrix diagonal
            delta : float, *optional*
                Probing variance of the trace. Returned if `var` is True in
                of probing case.

            Notes
            -----
            The ambiguity of `bare` or non-bare diagonal entries is based
            on the choice of a matrix representation of the operator in
            question. The naive choice of absorbing the volume weights
            into the matrix leads to a matrix-vector calculus with the
            non-bare entries which seems intuitive, though. The choice of
            keeping matrix entries and volume weights separate deals with the
            bare entries that allow for correct interpretation of the matrix
            entries; e.g., as variance in case of an covariance operator.

        """
1399

1400
        if (domain is None) or (domain == self.domain):
1401
            if not self.domain.discrete and bare:
1402
                diag_val = self.domain.calc_weight(self.val, power=-1)
1403
            else:
1404
                diag_val = self.val
1405
            diag = field(self.domain, codomain=self.codomain, val=diag_val)
1406
        else:
1407
1408
1409
            diag = super(diagonal_operator, self).diag(bare=bare,
                                                       domain=domain,
                                                       codomain=codomain,
1410
1411
1412
                                                       nrun=1,
                                                       random='pm1',
                                                       varQ=False,
1413
                                                       **kwargs)
1414
        if varQ:
1415
            return (diag, diag.domain.cast(1))
Ultima's avatar
Ultima committed
1416
1417
        else:
            return diag
1418
1419

    def inverse_diag(self, bare=False, domain=None, codomain=None,
1420
                     varQ=False, **kwargs):
Ultimanet's avatar
Ultimanet committed
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
        """
            Computes the diagonal of the inverse operator.

            Parameters
            ----------
            bare : bool, *optional*
                Indicatese whether the diagonal entries are `bare` or not
                (mandatory for the correct incorporation of volume weights)
                (default: False)
            domain : space, *optional*
                space wherein the probes live (default: self.domain)
            target : space, *optional*
                space wherein the transform of the probes live
                (default: None, applies target of the domain)
            random : string, *optional*
                Specifies the pseudo random number generator. Valid
                options are "pm1" for a random vector of +/-1, or "gau"
                for a random vector with entries drawn from a Gaussian
                distribution with zero mean and unit variance.
                (default: "pm1")
            ncpu : int, *optional*
                number of used CPUs to use. (default: 2)
            nrun : int, *optional*
                total number of probes (default: 8)
            nper : int, *optional*
                number of tasks performed by one process (default: 1)
            var : bool, *optional*
                Indicates whether to additionally return the probing variance
                or not (default: False).
            save : bool, *optional*
                whether all individual probing results are saved or not
                (default: False)
            path : string, *optional*
                path wherein the results are saved (default: "tmp")
            prefix : string, *optional*
                prefix for all saved files (default: "")
            loop : bool, *optional*
                Indicates whether or not to perform a loop i.e., to
                parallelise (default: False)