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2import numpy as np
3from scipy.optimize import least_squares
4from scipy.spatial import cKDTree
5from scipy.stats import sigmaclip
7import lsst.pipe.base as pipeBase
10def _rotation_matrix_chi_sq(flattened_rot_matrix,
11 pattern_a,
12 pattern_b,
13 max_dist_rad):
14 """Compute the squared differences for least squares fitting.
16 Given a flattened rotation matrix, one N point pattern and another N point
17 pattern to transform into to, compute the squared differences between the
18 points in the two patterns after the rotation.
20 Parameters
21 ----------
22 flattened_rot_matrix : `numpy.ndarray`, (9, )
23 A flattened array representing a 3x3 rotation matrix. The array is
24 flattened to comply with the API of scipy.optimize.least_squares.
25 Flattened elements are [[0, 0], [0, 1], [0, 2], [1, 0]...]
26 pattern_a : `numpy.ndarray`, (N, 3)
27 A array containing N, 3 vectors representing the objects we would like
28 to transform into the frame of pattern_b.
29 pattern_b : `numpy.ndarray`, (N, 3)
30 A array containing N, 3 vectors representing the reference frame we
31 would like to transform pattern_a into.
32 max_dist_rad : `float`
33 The maximum distance allowed from the pattern matching. This value is
34 used as the standard error for the resultant chi values.
36 Returns
37 -------
38 noralized_diff : `numpy.ndarray`, (9,)
39 Array of differences between the vectors representing of the source
40 pattern rotated into the reference frame and the converse. This is
41 used to minimize in a least squares fitter.
42 """
43 # Unflatten the rotation matrix
44 rot_matrix = flattened_rot_matrix.reshape((3, 3))
45 # Compare the rotated source pattern to the references.
46 rot_pattern_a = np.dot(rot_matrix, pattern_a.transpose()).transpose()
47 diff_pattern_a_to_b = rot_pattern_a - pattern_b
48 # Return the flattened differences and length tolerances for use in a least
49 # squares fitter.
50 return diff_pattern_a_to_b.flatten() / max_dist_rad
53class PessimisticPatternMatcherB:
54 """Class implementing a pessimistic version of Optimistic Pattern Matcher
55 B (OPMb) from Tabur 2007. See `DMTN-031 <http://ls.st/DMTN-031`_
57 Parameters
58 ----------
59 reference_array : `numpy.ndarray`, (N, 3)
60 spherical points x, y, z of to use as reference objects for
61 pattern matching.
62 log : `lsst.log.Log`
63 Logger for outputting debug info.
65 Notes
66 -----
67 The class loads and stores the reference object
68 in a convenient data structure for matching any set of source objects that
69 are assumed to contain each other. The pessimistic nature of the algorithm
70 comes from requiring that it discovers at least two patterns that agree on
71 the correct shift and rotation for matching before exiting. The original
72 behavior of OPMb can be recovered simply. Patterns matched between the
73 input datasets are n-spoked pinwheels created from n+1 points. Refer to
74 DMTN #031 for more details. http://github.com/lsst-dm/dmtn-031
75 """
77 def __init__(self, reference_array, log):
78 self._reference_array = reference_array
79 self._n_reference = len(self._reference_array)
80 self.log = log
82 if self._n_reference > 0:
83 self._build_distances_and_angles()
84 else:
85 raise ValueError("No reference objects supplied")
87 def _build_distances_and_angles(self):
88 """Create the data structures we will use to search for our pattern
89 match in.
91 Throughout this function and the rest of the class we use id to
92 reference the position in the input reference catalog and index to
93 'index' into the arrays sorted on distance.
94 """
95 # Create empty lists to temporarily store our pair information per
96 # reference object. These will be concatenated into our final arrays.
97 sub_id_array_list = []
98 sub_dist_array_list = []
100 # Loop over reference objects storing pair distances and ids.
101 for ref_id, ref_obj in enumerate(self._reference_array):
103 # Reserve and fill the ids of each reference object pair.
104 # 16 bit is safe for the id array as the catalog input from
105 # MatchPessimisticB is limited to a max length of 2 ** 16.
106 sub_id_array = np.empty((self._n_reference - 1 - ref_id, 2),
107 dtype="uint16")
108 sub_id_array[:, 0] = ref_id
109 sub_id_array[:, 1] = np.arange(ref_id + 1, self._n_reference,
110 dtype="uint16")
112 # Compute the vector deltas for each pair of reference objects.
113 # Compute and store the distances.
114 sub_dist_array = np.sqrt(
115 ((self._reference_array[ref_id + 1:, :]
116 - ref_obj) ** 2).sum(axis=1)).astype("float32")
118 # Append to our arrays to the output lists for later
119 # concatenation.
120 sub_id_array_list.append(sub_id_array)
121 sub_dist_array_list.append(sub_dist_array)
123 # Concatenate our arrays together.
124 unsorted_id_array = np.concatenate(sub_id_array_list)
125 unsorted_dist_array = np.concatenate(sub_dist_array_list)
127 # Sort each array on the pair distances for the initial
128 # optimistic pattern matcher lookup.
129 sorted_dist_args = unsorted_dist_array.argsort()
130 self._dist_array = unsorted_dist_array[sorted_dist_args]
131 self._id_array = unsorted_id_array[sorted_dist_args]
133 def match(self, source_array, n_check, n_match, n_agree,
134 max_n_patterns, max_shift, max_rotation, max_dist,
135 min_matches, pattern_skip_array=None):
136 """Match a given source catalog into the loaded reference catalog.
138 Given array of points on the unit sphere and tolerances, we
139 attempt to match a pinwheel like pattern between these input sources
140 and the reference objects this class was created with. This pattern
141 informs of the shift and rotation needed to align the input source
142 objects into the frame of the references.
144 Parameters
145 ----------
146 source_array : `numpy.ndarray`, (N, 3)
147 An array of spherical x,y,z coordinates and a magnitude in units
148 of objects having a lower value for sorting. The array should be
149 of shape (N, 4).
150 n_check : `int`
151 Number of sources to create a pattern from. Not all objects may be
152 checked if n_match criteria is before looping through all n_check
153 objects.
154 n_match : `int`
155 Number of objects to use in constructing a pattern to match.
156 n_agree : `int`
157 Number of found patterns that must agree on their shift and
158 rotation before exiting. Set this value to 1 to recover the
159 expected behavior of Optimistic Pattern Matcher B.
160 max_n_patters : `int`
161 Number of patterns to create from the input source objects to
162 attempt to match into the reference objects.
163 max_shift : `float`
164 Maximum allowed shift to match patterns in arcseconds.
165 max_rotation : `float`
166 Maximum allowed rotation between patterns in degrees.
167 max_dist : `float`
168 Maximum distance in arcseconds allowed between candidate spokes in
169 the source and reference objects. Also sets that maximum distance
170 in the intermediate verify, pattern shift/rotation agreement, and
171 final verify steps.
172 pattern_skip_array : `int`
173 Patterns we would like to skip. This could be due to the pattern
174 being matched on a previous iteration that we now consider invalid.
175 This assumes the ordering of the source objects is the same
176 between different runs of the matcher which, assuming no object
177 has been inserted or the magnitudes have changed, it should be.
179 Returns
180 -------
181 output_struct : `lsst.pipe.base.Struct`
182 Result struct with components
184 - ``matches`` : (N, 2) array of matched ids for pairs. Empty list if no
185 match found (`numpy.ndarray`, (N, 2) or `list`)
186 - ``distances_rad`` : Radian distances between the matched objects.
187 Empty list if no match found (`numpy.ndarray`, (N,))
188 - ``pattern_idx``: Index of matched pattern. None if no match found
189 (`int`).
190 - ``shift`` : Magnitude for the shift between the source and reference
191 objects in arcseconds. None if no match found (`float`).
192 """
194 # Given our input source_array we sort on magnitude.
195 sorted_source_array = source_array[source_array[:, -1].argsort(), :3]
196 n_source = len(sorted_source_array)
198 # Initialize output struct.
199 output_match_struct = pipeBase.Struct(
200 match_ids=[],
201 distances_rad=[],
202 pattern_idx=None,
203 shift=None,
204 max_dist_rad=None,)
206 if n_source <= 0:
207 self.log.warn("Source object array is empty. Unable to match. "
208 "Exiting matcher.")
209 return None
211 # To test if the shifts and rotations we find agree with each other,
212 # we first create two test points situated at the top and bottom of
213 # where the z axis on the sphere bisects the source catalog.
214 test_vectors = self._compute_test_vectors(source_array[:, :3])
216 # We now create an empty list of our resultant rotated vectors to
217 # compare the different rotations we find.
218 rot_vect_list = []
220 # Convert the tolerances to values we will use in the code.
221 max_cos_shift = np.cos(np.radians(max_shift / 3600.))
222 max_cos_rot_sq = np.cos(np.radians(max_rotation)) ** 2
223 max_dist_rad = np.radians(max_dist / 3600.)
225 # Loop through the sources from brightest to faintest, grabbing a
226 # chunk of n_check each time.
227 for pattern_idx in range(np.min((max_n_patterns,
228 n_source - n_match))):
230 # If this pattern is one that we matched on the past but we
231 # now want to skip, we do so here.
232 if pattern_skip_array is not None and \
233 np.any(pattern_skip_array == pattern_idx):
234 self.log.debug(
235 "Skipping previously matched bad pattern %i..." %
236 pattern_idx)
237 continue
238 # Grab the sources to attempt to create this pattern.
239 pattern = sorted_source_array[
240 pattern_idx: np.min((pattern_idx + n_check, n_source)), :3]
242 # Construct a pattern given the number of points defining the
243 # pattern complexity. This is the start of the primary tests to
244 # match our source pattern into the reference objects.
245 construct_return_struct = \
246 self._construct_pattern_and_shift_rot_matrix(
247 pattern, n_match, max_cos_shift, max_cos_rot_sq,
248 max_dist_rad)
250 # Our struct is None if we could not match the pattern.
251 if construct_return_struct.ref_candidates is None or \
252 construct_return_struct.shift_rot_matrix is None or \
253 construct_return_struct.cos_shift is None or \
254 construct_return_struct.sin_rot is None:
255 continue
257 # Grab the output data from the Struct object.
258 ref_candidates = construct_return_struct.ref_candidates
259 shift_rot_matrix = construct_return_struct.shift_rot_matrix
260 cos_shift = construct_return_struct.cos_shift
261 sin_rot = construct_return_struct.sin_rot
263 # If we didn't match enough candidates we continue to the next
264 # pattern.
265 if len(ref_candidates) < n_match:
266 continue
268 # Now that we know our pattern and shift/rotation are valid we
269 # store the the rotated versions of our test points for later
270 # use.
271 tmp_rot_vect_list = []
272 for test_vect in test_vectors:
273 tmp_rot_vect_list.append(np.dot(shift_rot_matrix, test_vect))
274 # Since our test point are in the source frame, we can test if
275 # their lengths are mostly preserved under the transform.
276 if not self._test_pattern_lengths(np.array(tmp_rot_vect_list),
277 max_dist_rad):
278 continue
280 tmp_rot_vect_list.append(pattern_idx)
281 rot_vect_list.append(tmp_rot_vect_list)
283 # Test if we have enough rotations, which agree, or if we
284 # are in optimistic mode.
285 if self._test_rotation_agreement(rot_vect_list, max_dist_rad) < \
286 n_agree - 1:
287 continue
289 # Run the final verify step.
290 match_struct = self._final_verify(source_array[:, :3],
291 shift_rot_matrix,
292 max_dist_rad,
293 min_matches)
294 if match_struct.match_ids is None or \
295 match_struct.distances_rad is None or \
296 match_struct.max_dist_rad is None:
297 continue
299 # Convert the observed shift to arcseconds
300 shift = np.degrees(np.arccos(cos_shift)) * 3600.
301 # Print information to the logger.
302 self.log.debug("Succeeded after %i patterns." % pattern_idx)
303 self.log.debug("\tShift %.4f arcsec" % shift)
304 self.log.debug("\tRotation: %.4f deg" %
305 np.degrees(np.arcsin(sin_rot)))
307 # Fill the struct and return.
308 output_match_struct.match_ids = \
309 match_struct.match_ids
310 output_match_struct.distances_rad = \
311 match_struct.distances_rad
312 output_match_struct.pattern_idx = pattern_idx
313 output_match_struct.shift = shift
314 output_match_struct.max_dist_rad = match_struct.max_dist_rad
315 return output_match_struct
317 self.log.debug("Failed after %i patterns." % (pattern_idx + 1))
318 return output_match_struct
320 def _compute_test_vectors(self, source_array):
321 """Compute spherical 3 vectors at the edges of the x, y, z extent
322 of the input source catalog.
324 Parameters
325 ----------
326 source_array : `numpy.ndarray`, (N, 3)
327 array of 3 vectors representing positions on the unit
328 sphere.
330 Returns
331 -------
332 test_vectors : `numpy.ndarray`, (N, 3)
333 Array of vectors representing the maximum extents in x, y, z
334 of the input source array. These are used with the rotations
335 the code finds to test for agreement from different patterns
336 when the code is running in pessimistic mode.
337 """
339 # Get the center of source_array.
340 if np.any(np.logical_not(np.isfinite(source_array))):
341 self.log.warn("Input source objects contain non-finite values. "
342 "This could end badly.")
343 center_vect = np.nanmean(source_array, axis=0)
345 # So that our rotation test works over the full sky we compute
346 # the max extent in each Cartesian direction x,y,z.
347 xbtm_vect = np.array([np.min(source_array[:, 0]), center_vect[1],
348 center_vect[2]], dtype=np.float64)
349 xtop_vect = np.array([np.max(source_array[:, 0]), center_vect[1],
350 center_vect[2]], dtype=np.float64)
351 xbtm_vect /= np.sqrt(np.dot(xbtm_vect, xbtm_vect))
352 xtop_vect /= np.sqrt(np.dot(xtop_vect, xtop_vect))
354 ybtm_vect = np.array([center_vect[0], np.min(source_array[:, 1]),
355 center_vect[2]], dtype=np.float64)
356 ytop_vect = np.array([center_vect[0], np.max(source_array[:, 1]),
357 center_vect[2]], dtype=np.float64)
358 ybtm_vect /= np.sqrt(np.dot(ybtm_vect, ybtm_vect))
359 ytop_vect /= np.sqrt(np.dot(ytop_vect, ytop_vect))
361 zbtm_vect = np.array([center_vect[0], center_vect[1],
362 np.min(source_array[:, 2])], dtype=np.float64)
363 ztop_vect = np.array([center_vect[0], center_vect[1],
364 np.max(source_array[:, 2])], dtype=np.float64)
365 zbtm_vect /= np.sqrt(np.dot(zbtm_vect, zbtm_vect))
366 ztop_vect /= np.sqrt(np.dot(ztop_vect, ztop_vect))
368 # Return our list of vectors for later rotation testing.
369 return np.array([xbtm_vect, xtop_vect, ybtm_vect, ytop_vect,
370 zbtm_vect, ztop_vect])
372 def _construct_pattern_and_shift_rot_matrix(self, src_pattern_array,
373 n_match, max_cos_theta_shift,
374 max_cos_rot_sq, max_dist_rad):
375 """Test an input source pattern against the reference catalog.
377 Returns the candidate matched patterns and their
378 implied rotation matrices or None.
380 Parameters
381 ----------
382 src_pattern_array : `numpy.ndarray`, (N, 3)
383 Sub selection of source 3 vectors to create a pattern from
384 n_match : `int`
385 Number of points to attempt to create a pattern from. Must be
386 >= len(src_pattern_array)
387 max_cos_theta_shift : `float`
388 Maximum shift allowed between two patterns' centers.
389 max_cos_rot_sq : `float`
390 Maximum rotation between two patterns that have been shifted
391 to have their centers on top of each other.
392 max_dist_rad : `float`
393 Maximum delta distance allowed between the source and reference
394 pair distances to consider the reference pair a candidate for
395 the source pair. Also sets the tolerance between the opening
396 angles of the spokes when compared to the reference.
398 Return
399 -------
400 output_matched_pattern : `lsst.pipe.base.Struct`
401 Result struct with components:
403 - ``ref_candidates`` : ids of the matched pattern in the internal
404 reference_array object (`list` of `int`).
405 - ``src_candidates`` : Pattern ids of the sources matched
406 (`list` of `int`).
407 - ``shift_rot_matrix_src_to_ref`` : 3x3 matrix specifying the full
408 shift and rotation between the reference and source objects.
409 Rotates source into reference frame. `None` if match is not
410 found. (`numpy.ndarray`, (3, 3))
411 - ``shift_rot_matrix_ref_to_src`` : 3x3 matrix specifying the full
412 shift and rotation of the reference and source objects. Rotates
413 reference into source frame. None if match is not found
414 (`numpy.ndarray`, (3, 3)).
415 - ``cos_shift`` : Magnitude of the shift found between the two
416 patten centers. `None` if match is not found (`float`).
417 - ``sin_rot`` : float value of the rotation to align the already
418 shifted source pattern to the reference pattern. `None` if no match
419 found (`float`).
420 """
422 # Create our place holder variables for the matched sources and
423 # references. The source list starts with the 0th and first indexed
424 # objects as we are guaranteed to use those and these define both
425 # the shift and rotation of the final pattern.
426 output_matched_pattern = pipeBase.Struct(
427 ref_candidates=[],
428 src_candidates=[],
429 shift_rot_matrix=None,
430 cos_shift=None,
431 sin_rot=None)
433 # Create the delta vectors and distances we will need to assemble the
434 # spokes of the pattern.
435 src_delta_array = np.empty((len(src_pattern_array) - 1, 3))
436 src_delta_array[:, 0] = (src_pattern_array[1:, 0]
437 - src_pattern_array[0, 0])
438 src_delta_array[:, 1] = (src_pattern_array[1:, 1]
439 - src_pattern_array[0, 1])
440 src_delta_array[:, 2] = (src_pattern_array[1:, 2]
441 - src_pattern_array[0, 2])
442 src_dist_array = np.sqrt(src_delta_array[:, 0]**2
443 + src_delta_array[:, 1]**2
444 + src_delta_array[:, 2]**2)
446 # Our first test. We search the reference dataset for pairs
447 # that have the same length as our first source pairs to with
448 # plus/minus the max_dist tolerance.
449 ref_dist_index_array = self._find_candidate_reference_pairs(
450 src_dist_array[0], self._dist_array, max_dist_rad)
452 # Start our loop over the candidate reference objects.
453 for ref_dist_idx in ref_dist_index_array:
454 # We have two candidates for which reference object corresponds
455 # with the source at the center of our pattern. As such we loop
456 # over and test both possibilities.
457 tmp_ref_pair_list = self._id_array[ref_dist_idx]
458 for pair_idx, ref_id in enumerate(tmp_ref_pair_list):
459 src_candidates = [0, 1]
460 ref_candidates = []
461 shift_rot_matrix = None
462 cos_shift = None
463 sin_rot = None
464 # Test the angle between our candidate ref center and the
465 # source center of our pattern. This angular distance also
466 # defines the shift we will later use.
467 ref_center = self._reference_array[ref_id]
468 cos_shift = np.dot(src_pattern_array[0], ref_center)
469 if cos_shift < max_cos_theta_shift:
470 continue
472 # We can now append this one as a candidate.
473 ref_candidates.append(ref_id)
474 # Test to see which reference object to use in the pair.
475 if pair_idx == 0:
476 ref_candidates.append(
477 tmp_ref_pair_list[1])
478 ref_delta = (self._reference_array[tmp_ref_pair_list[1]]
479 - ref_center)
480 else:
481 ref_candidates.append(
482 tmp_ref_pair_list[0])
483 ref_delta = (self._reference_array[tmp_ref_pair_list[0]]
484 - ref_center)
486 # For dense fields it will be faster to compute the absolute
487 # rotation this pair suggests first rather than saving it
488 # after all the spokes are found. We then compute the cos^2
489 # of the rotation and first part of the rotation matrix from
490 # source to reference frame.
491 test_rot_struct = self._test_rotation(
492 src_pattern_array[0], ref_center, src_delta_array[0],
493 ref_delta, cos_shift, max_cos_rot_sq)
494 if test_rot_struct.cos_rot_sq is None or \
495 test_rot_struct.proj_ref_ctr_delta is None or \
496 test_rot_struct.shift_matrix is None:
497 continue
499 # Get the data from the return struct.
500 cos_rot_sq = test_rot_struct.cos_rot_sq
501 proj_ref_ctr_delta = test_rot_struct.proj_ref_ctr_delta
502 shift_matrix = test_rot_struct.shift_matrix
504 # Now that we have a candidate first spoke and reference
505 # pattern center, we mask our future search to only those
506 # pairs that contain our candidate reference center.
507 tmp_ref_id_array = np.arange(len(self._reference_array),
508 dtype="uint16")
509 tmp_ref_dist_array = np.sqrt(
510 ((self._reference_array
511 - self._reference_array[ref_id])
512 ** 2).sum(axis=1)).astype("float32")
513 tmp_sorted_args = np.argsort(tmp_ref_dist_array)
514 tmp_ref_id_array = tmp_ref_id_array[tmp_sorted_args]
515 tmp_ref_dist_array = tmp_ref_dist_array[tmp_sorted_args]
517 # Now we feed this sub data to match the spokes of
518 # our pattern.
519 pattern_spoke_struct = self._create_pattern_spokes(
520 src_pattern_array[0], src_delta_array, src_dist_array,
521 self._reference_array[ref_id], ref_id, proj_ref_ctr_delta,
522 tmp_ref_dist_array, tmp_ref_id_array, max_dist_rad,
523 n_match)
525 # If we don't find enough candidates we can continue to the
526 # next reference center pair.
527 if len(pattern_spoke_struct.ref_spoke_list) < n_match - 2 or \
528 len(pattern_spoke_struct.src_spoke_list) < n_match - 2:
529 continue
531 # If we have the right number of matched ids we store these.
532 ref_candidates.extend(pattern_spoke_struct.ref_spoke_list)
533 src_candidates.extend(pattern_spoke_struct.src_spoke_list)
535 # We can now create our full rotation matrix for both the
536 # shift and rotation. Reminder shift, aligns the pattern
537 # centers, rotation rotates the spokes on top of each other.
538 shift_rot_struct = self._create_shift_rot_matrix(
539 cos_rot_sq, shift_matrix, src_delta_array[0],
540 self._reference_array[ref_id], ref_delta)
541 # If we fail to create the rotation matrix, continue to the
542 # next objects.
543 if shift_rot_struct.sin_rot is None or \
544 shift_rot_struct.shift_rot_matrix is None:
545 continue
547 # Get the data from the return struct.
548 sin_rot = shift_rot_struct.sin_rot
549 shift_rot_matrix = shift_rot_struct.shift_rot_matrix
551 # Now that we have enough candidates we test to see if it
552 # passes intermediate verify. This shifts and rotates the
553 # source pattern into the reference frame and then tests that
554 # each source/reference object pair is within max_dist. It also
555 # tests the opposite rotation that is reference to source
556 # frame.
557 fit_shift_rot_matrix = self._intermediate_verify(
558 src_pattern_array[src_candidates],
559 self._reference_array[ref_candidates],
560 shift_rot_matrix, max_dist_rad)
562 if fit_shift_rot_matrix is not None:
563 # Fill the struct and return.
564 output_matched_pattern.ref_candidates = ref_candidates
565 output_matched_pattern.src_candidates = src_candidates
566 output_matched_pattern.shift_rot_matrix = \
567 fit_shift_rot_matrix
568 output_matched_pattern.cos_shift = cos_shift
569 output_matched_pattern.sin_rot = sin_rot
570 return output_matched_pattern
572 return output_matched_pattern
574 def _find_candidate_reference_pairs(self, src_dist, ref_dist_array,
575 max_dist_rad):
576 """Wrap numpy.searchsorted to find the range of reference spokes
577 within a spoke distance tolerance of our source spoke.
579 Returns an array sorted from the smallest absolute delta distance
580 between source and reference spoke length. This sorting increases the
581 speed for the pattern search greatly.
583 Parameters
584 ----------
585 src_dist : `float`
586 float value of the distance we would like to search for in
587 the reference array in radians.
588 ref_dist_array : `numpy.ndarray`, (N,)
589 sorted array of distances in radians.
590 max_dist_rad : `float`
591 maximum plus/minus search to find in the reference array in
592 radians.
594 Return
595 ------
596 tmp_diff_array : `numpy.ndarray`, (N,)
597 indices lookup into the input ref_dist_array sorted by the
598 difference in value to the src_dist from absolute value
599 smallest to largest.
600 """
601 # Find the index of the minimum and maximum values that satisfy
602 # the tolerance.
603 start_idx = np.searchsorted(ref_dist_array, src_dist - max_dist_rad)
604 end_idx = np.searchsorted(ref_dist_array, src_dist + max_dist_rad,
605 side='right')
607 # If these are equal there are no candidates and we exit.
608 if start_idx == end_idx:
609 return []
611 # Make sure the endpoints of the input array are respected.
612 if start_idx < 0:
613 start_idx = 0
614 if end_idx > ref_dist_array.shape[0]:
615 end_idx = ref_dist_array.shape[0]
617 # Now we sort the indices from smallest absolute delta dist difference
618 # to the largest and return the vector. This step greatly increases
619 # the speed of the algorithm.
620 tmp_diff_array = np.fabs(ref_dist_array[start_idx:end_idx] - src_dist)
621 return tmp_diff_array.argsort() + start_idx
623 def _test_rotation(self, src_center, ref_center, src_delta, ref_delta,
624 cos_shift, max_cos_rot_sq):
625 """ Test if the rotation implied between the source
626 pattern and reference pattern is within tolerance. To test this
627 we need to create the first part of our spherical rotation matrix
628 which we also return for use later.
630 Parameters
631 ----------
632 src_center : `numpy.ndarray`, (N, 3)
633 pattern.
634 ref_center : `numpy.ndarray`, (N, 3)
635 3 vector defining the center of the candidate reference pinwheel
636 pattern.
637 src_delta : `numpy.ndarray`, (N, 3)
638 3 vector delta between the source pattern center and the end of
639 the pinwheel spoke.
640 ref_delta : `numpy.ndarray`, (N, 3)
641 3 vector delta of the candidate matched reference pair
642 cos_shift : `float`
643 Cosine of the angle between the source and reference candidate
644 centers.
645 max_cos_rot_sq : `float`
646 candidate reference pair after shifting the centers on top of each
647 other. The function will return None if the rotation implied is
648 greater than max_cos_rot_sq.
650 Returns
651 -------
652 result : `lsst.pipe.base.Struct`
653 Result struct with components:
655 - ``cos_rot_sq`` : magnitude of the rotation needed to align the
656 two patterns after their centers are shifted on top of each
657 other. `None` if rotation test fails (`float`).
658 - ``shift_matrix`` : 3x3 rotation matrix describing the shift needed to
659 align the source and candidate reference center. `None` if rotation
660 test fails (`numpy.ndarray`, (N, 3)).
661 """
663 # Make sure the sine is a real number.
664 if cos_shift > 1.0:
665 cos_shift = 1.
666 elif cos_shift < -1.0:
667 cos_shift = -1.
668 sin_shift = np.sqrt(1 - cos_shift ** 2)
670 # If the sine of our shift is zero we only need to use the identity
671 # matrix for the shift. Else we construct the rotation matrix for
672 # shift.
673 if sin_shift > 0:
674 rot_axis = np.cross(src_center, ref_center)
675 rot_axis /= sin_shift
676 shift_matrix = self._create_spherical_rotation_matrix(
677 rot_axis, cos_shift, sin_shift)
678 else:
679 shift_matrix = np.identity(3)
681 # Now that we have our shift we apply it to the src delta vector
682 # and check the rotation.
683 rot_src_delta = np.dot(shift_matrix, src_delta)
684 proj_src_delta = (rot_src_delta
685 - np.dot(rot_src_delta, ref_center) * ref_center)
686 proj_ref_delta = (ref_delta
687 - np.dot(ref_delta, ref_center) * ref_center)
688 cos_rot_sq = (np.dot(proj_src_delta, proj_ref_delta) ** 2
689 / (np.dot(proj_src_delta, proj_src_delta)
690 * np.dot(proj_ref_delta, proj_ref_delta)))
691 # If the rotation isn't in tolerance return None.
692 if cos_rot_sq < max_cos_rot_sq:
693 return pipeBase.Struct(
694 cos_rot_sq=None,
695 proj_ref_ctr_delta=None,
696 shift_matrix=None,)
697 # Return the rotation angle, the plane projected reference vector,
698 # and the first half of the full shift and rotation matrix.
699 return pipeBase.Struct(
700 cos_rot_sq=cos_rot_sq,
701 proj_ref_ctr_delta=proj_ref_delta,
702 shift_matrix=shift_matrix,)
704 def _create_spherical_rotation_matrix(self, rot_axis, cos_rotation,
705 sin_rotion):
706 """Construct a generalized 3D rotation matrix about a given
707 axis.
709 Parameters
710 ----------
711 rot_axis : `numpy.ndarray`, (3,)
712 3 vector defining the axis to rotate about.
713 cos_rotation : `float`
714 cosine of the rotation angle.
715 sin_rotation : `float`
716 sine of the rotation angle.
718 Return
719 ------
720 shift_matrix : `numpy.ndarray`, (3, 3)
721 3x3 spherical, rotation matrix.
722 """
724 rot_cross_matrix = np.array(
725 [[0., -rot_axis[2], rot_axis[1]],
726 [rot_axis[2], 0., -rot_axis[0]],
727 [-rot_axis[1], rot_axis[0], 0.]], dtype=np.float64)
728 shift_matrix = (cos_rotation*np.identity(3)
729 + sin_rotion*rot_cross_matrix
730 + (1. - cos_rotation)*np.outer(rot_axis, rot_axis))
732 return shift_matrix
734 def _create_pattern_spokes(self, src_ctr, src_delta_array, src_dist_array,
735 ref_ctr, ref_ctr_id, proj_ref_ctr_delta,
736 ref_dist_array, ref_id_array, max_dist_rad,
737 n_match):
738 """ Create the individual spokes that make up the pattern now that the
739 shift and rotation are within tolerance.
741 If we can't create a valid pattern we exit early.
743 Parameters
744 ----------
745 src_ctr : `numpy.ndarray`, (3,)
746 3 vector of the source pinwheel center
747 src_delta_array : `numpy.ndarray`, (N, 3)
748 Array of 3 vector deltas between the source center and the pairs
749 that make up the remaining spokes of the pinwheel
750 src_dist_array : `numpy.ndarray`, (N, 3)
751 Array of the distances of each src_delta in the pinwheel
752 ref_ctr : `numpy.ndarray`, (3,)
753 3 vector of the candidate reference center
754 ref_ctr_id : `int`
755 id of the ref_ctr in the master reference array
756 proj_ref_ctr_delta : `numpy.ndarray`, (3,)
757 Plane projected 3 vector formed from the center point of the
758 candidate pin-wheel and the second point in the pattern to create
759 the first spoke pair. This is the candidate pair that was matched
760 in the main _construct_pattern_and_shift_rot_matrix loop
761 ref_dist_array : `numpy.ndarray`, (N,)
762 Array of vector distances for each of the reference pairs
763 ref_id_array : `numpy.ndarray`, (N,)
764 Array of id lookups into the master reference array that our
765 center id object is paired with.
766 max_dist_rad : `float`
767 Maximum search distance
768 n_match : `int`
769 Number of source deltas that must be matched into the reference
770 deltas in order to consider this a successful pattern match.
772 Returns
773 -------
774 output_spokes : `lsst.pipe.base.Struct`
775 Result struct with components:
777 - ``ref_spoke_list`` : list of ints specifying ids into the master
778 reference array (`list` of `int`).
779 - ``src_spoke_list`` : list of ints specifying indices into the
780 current source pattern that is being tested (`list` of `int`).
781 """
782 # Struct where we will be putting our results.
783 output_spokes = pipeBase.Struct(
784 ref_spoke_list=[],
785 src_spoke_list=[],)
787 # Counter for number of spokes we failed to find a reference
788 # candidate for. We break the loop if we haven't found enough.
789 n_fail = 0
790 ref_spoke_list = []
791 src_spoke_list = []
793 # Plane project the center/first spoke of the source pattern using
794 # the center vector of the pattern as normal.
795 proj_src_ctr_delta = (src_delta_array[0]
796 - np.dot(src_delta_array[0], src_ctr) * src_ctr)
797 proj_src_ctr_dist_sq = np.dot(proj_src_ctr_delta, proj_src_ctr_delta)
799 # Pre-compute the squared length of the projected reference vector.
800 proj_ref_ctr_dist_sq = np.dot(proj_ref_ctr_delta, proj_ref_ctr_delta)
802 # Loop over the source pairs.
803 for src_idx in range(1, len(src_dist_array)):
804 if n_fail > len(src_dist_array) - (n_match - 1):
805 break
807 # Given our length tolerance we can use it to compute a tolerance
808 # on the angle between our spoke.
809 src_sin_tol = (max_dist_rad
810 / (src_dist_array[src_idx] + max_dist_rad))
812 # Test if the small angle approximation will still hold. This is
813 # defined as when sin(theta) ~= theta to within 0.1% of each
814 # other. If the implied opening angle is too large we set it to
815 # the 0.1% threshold.
816 max_sin_tol = 0.0447
817 if src_sin_tol > max_sin_tol:
818 src_sin_tol = max_sin_tol
820 # Plane project the candidate source spoke and compute the cosine
821 # and sine of the opening angle.
822 proj_src_delta = (
823 src_delta_array[src_idx]
824 - np.dot(src_delta_array[src_idx], src_ctr) * src_ctr)
825 geom_dist_src = np.sqrt(
826 np.dot(proj_src_delta, proj_src_delta)
827 * proj_src_ctr_dist_sq)
829 # Compute cosine and sine of the delta vector opening angle.
830 cos_theta_src = (np.dot(proj_src_delta, proj_src_ctr_delta)
831 / geom_dist_src)
832 cross_src = (np.cross(proj_src_delta, proj_src_ctr_delta)
833 / geom_dist_src)
834 sin_theta_src = np.dot(cross_src, src_ctr)
836 # Find the reference pairs that include our candidate pattern
837 # center and sort them in increasing delta
838 ref_dist_idx_array = self._find_candidate_reference_pairs(
839 src_dist_array[src_idx], ref_dist_array, max_dist_rad)
841 # Test the spokes and return the id of the reference object.
842 # Return None if no match is found.
843 ref_id = self._test_spoke(
844 cos_theta_src,
845 sin_theta_src,
846 ref_ctr,
847 ref_ctr_id,
848 proj_ref_ctr_delta,
849 proj_ref_ctr_dist_sq,
850 ref_dist_idx_array,
851 ref_id_array,
852 src_sin_tol)
853 if ref_id is None:
854 n_fail += 1
855 continue
857 # Append the successful indices to our list. The src_idx needs
858 # an extra iteration to skip the first and second source objects.
859 ref_spoke_list.append(ref_id)
860 src_spoke_list.append(src_idx + 1)
861 # If we found enough reference objects we can return early. This is
862 # n_match - 2 as we already have 2 source objects matched into the
863 # reference data.
864 if len(ref_spoke_list) >= n_match - 2:
865 # Set the struct data and return the struct.
866 output_spokes.ref_spoke_list = ref_spoke_list
867 output_spokes.src_spoke_list = src_spoke_list
868 return output_spokes
870 return output_spokes
872 def _test_spoke(self, cos_theta_src, sin_theta_src, ref_ctr, ref_ctr_id,
873 proj_ref_ctr_delta, proj_ref_ctr_dist_sq,
874 ref_dist_idx_array, ref_id_array, src_sin_tol):
875 """Test the opening angle between the first spoke of our pattern
876 for the source object against the reference object.
878 This method makes heavy use of the small angle approximation to perform
879 the comparison.
881 Parameters
882 ----------
883 cos_theta_src : `float`
884 Cosine of the angle between the current candidate source spoke and
885 the first spoke.
886 sin_theta_src : `float`
887 Sine of the angle between the current candidate source spoke and
888 the first spoke.
889 ref_ctr : `numpy.ndarray`, (3,)
890 3 vector of the candidate reference center
891 ref_ctr_id : `int`
892 id lookup of the ref_ctr into the master reference array
893 proj_ref_ctr_delta : `float`
894 Plane projected first spoke in the reference pattern using the
895 pattern center as normal.
896 proj_ref_ctr_dist_sq : `float`
897 Squared length of the projected vector.
898 ref_dist_idx_array : `numpy.ndarray`, (N,)
899 Indices sorted by the delta distance between the source
900 spoke we are trying to test and the candidate reference
901 spokes.
902 ref_id_array : `numpy.ndarray`, (N,)
903 Array of id lookups into the master reference array that our
904 center id object is paired with.
905 src_sin_tol : `float`
906 Sine of tolerance allowed between source and reference spoke
907 opening angles.
909 Returns
910 -------
911 id : `int`
912 If we can not find a candidate spoke we return `None` else we
913 return an int id into the master reference array.
914 """
916 # Loop over our candidate reference objects.
917 for ref_dist_idx in ref_dist_idx_array:
918 # Compute the delta vector from the pattern center.
919 ref_delta = (self._reference_array[ref_id_array[ref_dist_idx]]
920 - ref_ctr)
921 # Compute the cos between our "center" reference vector and the
922 # current reference candidate.
923 proj_ref_delta = ref_delta - np.dot(ref_delta, ref_ctr) * ref_ctr
924 geom_dist_ref = np.sqrt(proj_ref_ctr_dist_sq
925 * np.dot(proj_ref_delta, proj_ref_delta))
926 cos_theta_ref = (np.dot(proj_ref_delta, proj_ref_ctr_delta)
927 / geom_dist_ref)
929 # Make sure we can safely make the comparison in case
930 # our "center" and candidate vectors are mostly aligned.
931 if cos_theta_ref ** 2 < (1 - src_sin_tol ** 2):
932 cos_sq_comparison = ((cos_theta_src - cos_theta_ref) ** 2
933 / (1 - cos_theta_ref ** 2))
934 else:
935 cos_sq_comparison = ((cos_theta_src - cos_theta_ref) ** 2
936 / src_sin_tol ** 2)
937 # Test the difference of the cosine of the reference angle against
938 # the source angle. Assumes that the delta between the two is
939 # small.
940 if cos_sq_comparison > src_sin_tol ** 2:
941 continue
943 # The cosine tests the magnitude of the angle but not
944 # its direction. To do that we need to know the sine as well.
945 # This cross product calculation does that.
946 cross_ref = (np.cross(proj_ref_delta, proj_ref_ctr_delta)
947 / geom_dist_ref)
948 sin_theta_ref = np.dot(cross_ref, ref_ctr)
950 # Check the value of the cos again to make sure that it is not
951 # near zero.
952 if abs(cos_theta_src) < src_sin_tol:
953 sin_comparison = (sin_theta_src - sin_theta_ref) / src_sin_tol
954 else:
955 sin_comparison = \
956 (sin_theta_src - sin_theta_ref) / cos_theta_ref
958 if abs(sin_comparison) > src_sin_tol:
959 continue
961 # Return the correct id of the candidate we found.
962 return ref_id_array[ref_dist_idx]
964 return None
966 def _create_shift_rot_matrix(self, cos_rot_sq, shift_matrix, src_delta,
967 ref_ctr, ref_delta):
968 """ Create the final part of our spherical rotation matrix.
970 Parameters
971 ----------
972 cos_rot_sq : `float`
973 cosine of the rotation needed to align our source and reference
974 candidate patterns.
975 shift_matrix : `numpy.ndarray`, (3, 3)
976 3x3 rotation matrix for shifting the source pattern center on top
977 of the candidate reference pattern center.
978 src_delta : `numpy.ndarray`, (3,)
979 3 vector delta of representing the first spoke of the source
980 pattern
981 ref_ctr : `numpy.ndarray`, (3,)
982 3 vector on the unit-sphere representing the center of our
983 reference pattern.
984 ref_delta : `numpy.ndarray`, (3,)
985 3 vector delta made by the first pair of the reference pattern.
987 Returns
988 -------
989 result : `lsst.pipe.base.Struct`
990 Result struct with components:
992 - ``sin_rot`` : float sine of the amount of rotation between the
993 source and reference pattern. We use sine here as it is
994 signed and tells us the chirality of the rotation (`float`).
995 - ``shift_rot_matrix`` : float array representing the 3x3 rotation
996 matrix that takes the source pattern and shifts and rotates
997 it to align with the reference pattern (`numpy.ndarray`, (3,3)).
998 """
999 cos_rot = np.sqrt(cos_rot_sq)
1000 rot_src_delta = np.dot(shift_matrix, src_delta)
1001 delta_dot_cross = np.dot(np.cross(rot_src_delta, ref_delta), ref_ctr)
1003 sin_rot = np.sign(delta_dot_cross) * np.sqrt(1 - cos_rot_sq)
1004 rot_matrix = self._create_spherical_rotation_matrix(
1005 ref_ctr, cos_rot, sin_rot)
1007 shift_rot_matrix = np.dot(rot_matrix, shift_matrix)
1009 return pipeBase.Struct(
1010 sin_rot=sin_rot,
1011 shift_rot_matrix=shift_rot_matrix,)
1013 def _intermediate_verify(self, src_pattern, ref_pattern, shift_rot_matrix,
1014 max_dist_rad):
1015 """ Perform an intermediate verify step.
1017 Rotate the matches references into the source frame and test their
1018 distances against tolerance. Only return true if all points are within
1019 tolerance.
1021 Parameters
1022 ----------
1023 src_pattern : `numpy.ndarray`, (N,3)
1024 Array of 3 vectors representing the points that make up our source
1025 pinwheel pattern.
1026 ref_pattern : `numpy.ndarray`, (N,3)
1027 Array of 3 vectors representing our candidate reference pinwheel
1028 pattern.
1029 shift_rot_matrix : `numpy.ndarray`, (3,3)
1030 3x3 rotation matrix that takes the source objects and rotates them
1031 onto the frame of the reference objects
1032 max_dist_rad : `float`
1033 Maximum distance allowed to consider two objects the same.
1035 Returns
1036 -------
1037 fit_shift_rot_matrix : `numpy.ndarray`, (3,3)
1038 Return the fitted shift/rotation matrix if all of the points in our
1039 source pattern are within max_dist_rad of their matched reference
1040 objects. Returns None if this criteria is not satisfied.
1041 """
1042 if len(src_pattern) != len(ref_pattern):
1043 raise ValueError(
1044 "Source pattern length does not match ref pattern.\n"
1045 "\t source pattern len=%i, reference pattern len=%i" %
1046 (len(src_pattern), len(ref_pattern)))
1048 if self._intermediate_verify_comparison(
1049 src_pattern, ref_pattern, shift_rot_matrix, max_dist_rad):
1050 # Now that we know our initial shift and rot matrix is valid we
1051 # want to fit the implied transform using all points from
1052 # our pattern. This is a more robust rotation matrix as our
1053 # initial matrix only used the first 2 points from the source
1054 # pattern to estimate the shift and rotation. The matrix we fit
1055 # are allowed to be non unitary but need to preserve the length of
1056 # the rotated vectors to within the match tolerance.
1057 fit_shift_rot_matrix = least_squares(
1058 _rotation_matrix_chi_sq,
1059 x0=shift_rot_matrix.flatten(),
1060 args=(src_pattern, ref_pattern, max_dist_rad)
1061 ).x.reshape((3, 3))
1062 # Do another verify in case the fits have wondered off.
1063 if self._intermediate_verify_comparison(
1064 src_pattern, ref_pattern, fit_shift_rot_matrix,
1065 max_dist_rad):
1066 return fit_shift_rot_matrix
1068 return None
1070 def _intermediate_verify_comparison(self, pattern_a, pattern_b,
1071 shift_rot_matrix, max_dist_rad):
1072 """Test the input rotation matrix against one input pattern and
1073 a second one.
1075 If every point in the pattern after rotation is within a distance of
1076 max_dist_rad to its candidate point in the other pattern, we return
1077 True.
1079 Parameters
1080 ----------
1081 pattern_a : `numpy.ndarray`, (N,3)
1082 Array of 3 vectors representing the points that make up our source
1083 pinwheel pattern.
1084 pattern_b : `numpy.ndarray`, (N,3)
1085 Array of 3 vectors representing our candidate reference pinwheel
1086 pattern.
1087 shift_rot_matrix : `numpy.ndarray`, (3,3)
1088 3x3 rotation matrix that takes the source objects and rotates them
1089 onto the frame of the reference objects
1090 max_dist_rad : `float`
1091 Maximum distance allowed to consider two objects the same.
1094 Returns
1095 -------
1096 bool
1097 True if all rotated source points are within max_dist_rad of
1098 the candidate references matches.
1099 """
1100 shifted_pattern_a = np.dot(shift_rot_matrix,
1101 pattern_a.transpose()).transpose()
1102 tmp_delta_array = shifted_pattern_a - pattern_b
1103 tmp_dist_array = (tmp_delta_array[:, 0] ** 2
1104 + tmp_delta_array[:, 1] ** 2
1105 + tmp_delta_array[:, 2] ** 2)
1106 return np.all(tmp_dist_array < max_dist_rad ** 2)
1108 def _test_pattern_lengths(self, test_pattern, max_dist_rad):
1109 """ Test that the all vectors in a pattern are unit length within
1110 tolerance.
1112 This is useful for assuring the non unitary transforms do not contain
1113 too much distortion.
1115 Parameters
1116 ----------
1117 test_pattern : `numpy.ndarray`, (N, 3)
1118 Test vectors at the maximum and minimum x, y, z extents.
1119 max_dist_rad : `float`
1120 maximum distance in radians to consider two points "agreeing" on
1121 a rotation
1123 Returns
1124 -------
1125 test : `bool`
1126 Length tests pass.
1127 """
1128 dists = (test_pattern[:, 0] ** 2
1129 + test_pattern[:, 1] ** 2
1130 + test_pattern[:, 2] ** 2)
1131 return np.all(
1132 np.logical_and((1 - max_dist_rad) ** 2 < dists,
1133 dists < (1 + max_dist_rad) ** 2))
1135 def _test_rotation_agreement(self, rot_vects, max_dist_rad):
1136 """ Test this rotation against the previous N found and return
1137 the number that a agree within tolerance to where our test
1138 points are.
1140 Parameters
1141 ----------
1142 rot_vects : `numpy.ndarray`, (N, 3)
1143 Arrays of rotated 3 vectors representing the maximum x, y,
1144 z extent on the unit sphere of the input source objects rotated by
1145 the candidate rotations into the reference frame.
1146 max_dist_rad : `float`
1147 maximum distance in radians to consider two points "agreeing" on
1148 a rotation
1150 Returns
1151 -------
1152 tot_consent : `int`
1153 Number of candidate rotations that agree for all of the rotated
1154 test 3 vectors.
1155 """
1157 self.log.debug("Comparing pattern %i to previous %i rotations..." %
1158 (rot_vects[-1][-1], len(rot_vects) - 1))
1160 tot_consent = 0
1161 for rot_idx in range(max((len(rot_vects) - 1), 0)):
1162 tmp_dist_list = []
1163 for vect_idx in range(len(rot_vects[rot_idx]) - 1):
1164 tmp_delta_vect = (rot_vects[rot_idx][vect_idx]
1165 - rot_vects[-1][vect_idx])
1166 tmp_dist_list.append(
1167 np.dot(tmp_delta_vect, tmp_delta_vect))
1168 if np.all(np.array(tmp_dist_list) < max_dist_rad ** 2):
1169 tot_consent += 1
1170 return tot_consent
1172 def _final_verify(self,
1173 source_array,
1174 shift_rot_matrix,
1175 max_dist_rad,
1176 min_matches):
1177 """Match the all sources into the reference catalog using the shift/rot
1178 matrix.
1180 After the initial shift/rot matrix is found, we refit the shift/rot
1181 matrix using the matches the initial matrix produces to find a more
1182 stable solution.
1184 Parameters
1185 ----------
1186 source_array : `numpy.ndarray` (N, 3)
1187 3-vector positions on the unit-sphere representing the sources to
1188 match
1189 shift_rot_matrix : `numpy.ndarray` (3, 3)
1190 Rotation matrix representing inferred shift/rotation of the
1191 sources onto the reference catalog. Matrix need not be unitary.
1192 max_dist_rad : `float`
1193 Maximum distance allowed for a match.
1194 min_matches : `int`
1195 Minimum number of matched objects required to consider the
1196 match good.
1198 Returns
1199 -------
1200 output_struct : `lsst.pipe.base.Struct`
1201 Result struct with components:
1203 - ``match_ids`` : Pairs of indexes into the source and reference
1204 data respectively defining a match (`numpy.ndarray`, (N, 2)).
1205 - ``distances_rad`` : distances to between the matched objects in
1206 the shift/rotated frame. (`numpy.ndarray`, (N,)).
1207 - ``max_dist_rad`` : Value of the max matched distance. Either
1208 returning the input value of the 2 sigma clipped value of the
1209 shift/rotated distances. (`float`).
1210 """
1211 output_struct = pipeBase.Struct(
1212 match_ids=None,
1213 distances_rad=None,
1214 max_dist_rad=None,
1215 )
1217 # Perform an iterative final verify.
1218 match_sources_struct = self._match_sources(source_array,
1219 shift_rot_matrix)
1220 cut_ids = match_sources_struct.match_ids[
1221 match_sources_struct.distances_rad < max_dist_rad]
1223 n_matched = len(cut_ids)
1224 clipped_struct = self._clip_distances(
1225 match_sources_struct.distances_rad)
1226 n_matched_clipped = clipped_struct.n_matched_clipped
1228 if n_matched < min_matches or n_matched_clipped < min_matches:
1229 return output_struct
1231 # The shift/rotation matrix returned by
1232 # ``_construct_pattern_and_shift_rot_matrix``, above, was
1233 # based on only six points. Here, we refine that result by
1234 # using all of the good matches from the “final verification”
1235 # step, above. This will produce a more consistent result.
1236 fit_shift_rot_matrix = least_squares(
1237 _rotation_matrix_chi_sq,
1238 x0=shift_rot_matrix.flatten(),
1239 args=(source_array[cut_ids[:, 0], :3],
1240 self._reference_array[cut_ids[:, 1], :3],
1241 max_dist_rad)
1242 ).x.reshape((3, 3))
1244 # Redo the matching using the newly fit shift/rotation matrix.
1245 match_sources_struct = self._match_sources(
1246 source_array, fit_shift_rot_matrix)
1248 # Double check the match distances to make sure enough matches
1249 # survive still. We'll just overwrite the previously used variables.
1250 n_matched = np.sum(
1251 match_sources_struct.distances_rad < max_dist_rad)
1252 clipped_struct = self._clip_distances(
1253 match_sources_struct.distances_rad)
1254 n_matched_clipped = clipped_struct.n_matched_clipped
1255 clipped_max_dist = clipped_struct.clipped_max_dist
1257 if n_matched < min_matches or n_matched_clipped < min_matches:
1258 return output_struct
1260 # Store our matches in the output struct. Decide between the clipped
1261 # distance and the input max dist based on which is smaller.
1262 output_struct.match_ids = match_sources_struct.match_ids
1263 output_struct.distances_rad = match_sources_struct.distances_rad
1264 if clipped_max_dist < max_dist_rad:
1265 output_struct.max_dist_rad = clipped_max_dist
1266 else:
1267 output_struct.max_dist_rad = max_dist_rad
1269 return output_struct
1271 def _clip_distances(self, distances_rad):
1272 """Compute a clipped max distance and calculate the number of pairs
1273 that pass the clipped dist.
1275 Parameters
1276 ----------
1277 distances_rad : `numpy.ndarray`, (N,)
1278 Distances between pairs.
1280 Returns
1281 -------
1282 output_struct : `lsst.pipe.base.Struct`
1283 Result struct with components:
1285 - ``n_matched_clipped`` : Number of pairs that survive the
1286 clipping on distance. (`float`)
1287 - ``clipped_max_dist`` : Maximum distance after clipping.
1288 (`float`).
1289 """
1290 clipped_dists, _, clipped_max_dist = sigmaclip(
1291 distances_rad,
1292 low=100,
1293 high=2)
1294 # Check clipped distances. The minimum value here
1295 # prevents over convergence on perfect test data.
1296 if clipped_max_dist < 1e-16:
1297 clipped_max_dist = 1e-16
1298 n_matched_clipped = np.sum(distances_rad < clipped_max_dist)
1299 else:
1300 n_matched_clipped = len(clipped_dists)
1302 return pipeBase.Struct(n_matched_clipped=n_matched_clipped,
1303 clipped_max_dist=clipped_max_dist)
1305 def _match_sources(self,
1306 source_array,
1307 shift_rot_matrix):
1308 """ Shift both the reference and source catalog to the the respective
1309 frames and find their nearest neighbor using a kdTree.
1311 Removes all matches who do not agree when either the reference or
1312 source catalog is rotated. Cuts on a maximum distance are left to an
1313 external function.
1315 Parameters
1316 ----------
1317 source_array : `numpy.ndarray`, (N, 3)
1318 array of 3 vectors representing the source objects we are trying
1319 to match into the source catalog.
1320 shift_rot_matrix : `numpy.ndarray`, (3, 3)
1321 3x3 rotation matrix that performs the spherical rotation from the
1322 source frame into the reference frame.
1324 Returns
1325 -------
1326 results : `lsst.pipe.base.Struct`
1327 Result struct with components:
1329 - ``matches`` : array of integer ids into the source and
1330 reference arrays. Matches are only returned for those that
1331 satisfy the distance and handshake criteria
1332 (`numpy.ndarray`, (N, 2)).
1333 - ``distances`` : Distances between each match in radians after
1334 the shift and rotation is applied (`numpy.ndarray`, (N)).
1335 """
1336 shifted_references = np.dot(
1337 np.linalg.inv(shift_rot_matrix),
1338 self._reference_array.transpose()).transpose()
1339 shifted_sources = np.dot(
1340 shift_rot_matrix,
1341 source_array.transpose()).transpose()
1343 ref_matches = np.empty((len(shifted_references), 2),
1344 dtype="uint16")
1345 src_matches = np.empty((len(shifted_sources), 2),
1346 dtype="uint16")
1348 ref_matches[:, 1] = np.arange(len(shifted_references),
1349 dtype="uint16")
1350 src_matches[:, 0] = np.arange(len(shifted_sources),
1351 dtype="uint16")
1353 ref_kdtree = cKDTree(self._reference_array)
1354 src_kdtree = cKDTree(source_array)
1356 ref_to_src_dist, tmp_ref_to_src_idx = \
1357 src_kdtree.query(shifted_references)
1358 src_to_ref_dist, tmp_src_to_ref_idx = \
1359 ref_kdtree.query(shifted_sources)
1361 ref_matches[:, 0] = tmp_ref_to_src_idx
1362 src_matches[:, 1] = tmp_src_to_ref_idx
1364 handshake_mask = self._handshake_match(src_matches, ref_matches)
1365 return pipeBase.Struct(
1366 match_ids=src_matches[handshake_mask],
1367 distances_rad=src_to_ref_dist[handshake_mask],)
1369 def _handshake_match(self, matches_src, matches_ref):
1370 """Return only those matches where both the source
1371 and reference objects agree they they are each others'
1372 nearest neighbor.
1374 Parameters
1375 ----------
1376 matches_src : `numpy.ndarray`, (N, 2)
1377 int array of nearest neighbor matches between shifted and
1378 rotated reference objects matched into the sources.
1379 matches_ref : `numpy.ndarray`, (N, 2)
1380 int array of nearest neighbor matches between shifted and
1381 rotated source objects matched into the references.
1382 Return
1383 ------
1384 handshake_mask_array : `numpy.ndarray`, (N,)
1385 Return the array positions where the two match catalogs agree.
1386 """
1387 handshake_mask_array = np.zeros(len(matches_src), dtype=bool)
1389 for src_match_idx, match in enumerate(matches_src):
1390 ref_match_idx = np.searchsorted(matches_ref[:, 1], match[1])
1391 if match[0] == matches_ref[ref_match_idx, 0]:
1392 handshake_mask_array[src_match_idx] = True
1393 return handshake_mask_array