summaryrefslogtreecommitdiffstats
path: root/tests/python/test_line2d.py
blob: 30192773195ee5a0109b865ea2dadbb4b7f7982d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
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
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
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
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
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
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
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
import numpy as np
import unittest
import astra
import math
import pylab

# Display sinograms with mismatch on test failure
DISPLAY=False

NONUNITDET=False
OBLIQUE=False
FLEXVOL=False
NONSQUARE=False  # non-square pixels not supported yet by most projectors

# Round interpolation weight to 8 bits to emulate CUDA texture unit precision
CUDA_8BIT_LINEAR=True
CUDA_TOL=2e-2

nloops = 50
seed = 123


# FAILURES:
# fan/cuda with flexible volume
# detweight for fan/cuda
# fan/strip relatively high numerical errors?
# parvec/line+linear for oblique

# INCONSISTENCY:
# effective_detweight vs norm(detu) in line/linear (oblique)



# return length of intersection of the line through points src = (x,y)
# and det (x,y), and the rectangle defined by xmin, ymin, xmax, ymax
def intersect_line_rectangle(src, det, xmin, xmax, ymin, ymax):
  EPS = 1e-5

  if np.abs(src[0] - det[0]) < EPS:
    if src[0] >= xmin and src[0] < xmax:
      return ymax - ymin
    else:
      return 0.0
  if np.abs(src[1] - det[1]) < EPS:
    if src[1] >= ymin and src[1] < ymax:
      return xmax - xmin
    else:
      return 0.0

  n = np.sqrt((det[0] - src[0]) ** 2 + (det[1] - src[1]) ** 2)

  check = [ (-(xmin - src[0]), -(det[0] - src[0]) / n ),
            (xmax - src[0], (det[0] - src[0]) / n ),
            (-(ymin - src[1]), -(det[1] - src[1]) / n ),
            (ymax - src[1], (det[1] - src[1]) / n ) ]

  pre = [ -np.Inf ]
  post = [ np.Inf ]

  for p, q in check:
    r = p / (1.0 * q)
    if q > 0:
      post.append(r)    # exiting half-plane
    else:
      pre.append(r)     # entering half-plane

  end_r = np.min(post)
  start_r = np.max(pre)

  if end_r > start_r:
    return end_r - start_r
  else:
    return 0.0

def intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, feather):
  return intersect_line_rectangle(src, det,
                                  xmin-feather, xmax+feather,
                                  ymin-feather, ymax+feather)

def intersect_line_rectangle_interval(src, det, xmin, xmax, ymin, ymax, f):
  a = intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, -f)
  b = intersect_line_rectangle(src, det, xmin, xmax, ymin, ymax)
  c = intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, f)
  return (a,b,c)


# x-coord of intersection of the line (src, det) with the horizontal line at y
def intersect_line_horizontal(src, det, y):
  EPS = 1e-5

  if np.abs(src[1] - det[1]) < EPS:
    return np.nan

  t = (y - src[1]) / (det[1] - src[1])

  return src[0] + t * (det[0] - src[0])

# y-coord of intersection of the line (src, det) with the vertical line at x
def intersect_line_vertical(src, det, x):
  src = ( src[1], src[0] )
  det = ( det[1], det[0] )
  return intersect_line_horizontal(src, det, x)

# length of the intersection of the strip with boundaries edge1, edge2 with the horizontal
# segment at y, with horizontal extent x_seg
def intersect_ray_horizontal_segment(edge1, edge2, y, x_seg):
  e1 = intersect_line_horizontal(edge1[0], edge1[1], y)
  e2 = intersect_line_horizontal(edge2[0], edge2[1], y)

  if not (np.isfinite(e1) and np.isfinite(e2)):
    return np.nan

  (e1, e2) = np.sort([e1, e2])
  (x1, x2) = np.sort(x_seg)
  l = np.max([e1, x1])
  r = np.min([e2, x2])
  return np.max([r-l, 0.0])

def intersect_ray_vertical_segment(edge1, edge2, x, y_seg):
  # mirror edge1 and edge2
  edge1 = [ (a[1], a[0]) for a in edge1 ]
  edge2 = [ (a[1], a[0]) for a in edge2 ]
  return intersect_ray_horizontal_segment(edge1, edge2, x, y_seg)

# weight of the intersection of line with the horizontal segment at y, with horizontal extent x_seg
# using linear interpolation
def intersect_line_horizontal_segment_linear(src, det, y, x_seg, inter_width):
  EPS = 1e-5
  x = intersect_line_horizontal(src, det, y)

  assert(x_seg[1] - x_seg[0] + EPS >= inter_width)
  if x < x_seg[0] - 0.5*inter_width:
    return 0.0
  elif x < x_seg[0] + 0.5*inter_width:
    return (x - (x_seg[0] - 0.5*inter_width)) / inter_width
  elif x < x_seg[1] - 0.5*inter_width:
    return 1.0
  elif x < x_seg[1] + 0.5*inter_width:
    return (x_seg[1] + 0.5*inter_width - x) / inter_width
  else:
    return 0.0

def intersect_line_vertical_segment_linear(src, det, x, y_seg, inter_height):
  src = ( src[1], src[0] )
  det = ( det[1], det[0] )
  return intersect_line_horizontal_segment_linear(src, det, x, y_seg, inter_height)



def area_signed(a, b):
  return a[0] * b[1] - a[1] * b[0]

# is c to the left of ab
def is_left_of(a, b, c):
  EPS = 1e-5
  return area_signed( (b[0] - a[0], b[1] - a[1]), (c[0] - a[0], c[1] - a[1]) ) > EPS

# compute area of rect on left side of line
def halfarea_rect_line(src, det, xmin, xmax, ymin, ymax):
  pts = ( (xmin,ymin), (xmin,ymax), (xmax,ymin), (xmax,ymax) )
  pts_left = list(filter( lambda p: is_left_of(src, det, p), pts ))
  npts_left = len(pts_left)
  if npts_left == 0:
    return 0.0
  elif npts_left == 1:
    # triangle
    p = pts_left[0]
    xd = intersect_line_horizontal(src, det, p[1]) - p[0]
    yd = intersect_line_vertical(src, det, p[0]) - p[1]
    ret = 0.5 * abs(xd) * abs(yd)
    return ret
  elif npts_left == 2:
    p = pts_left[0]
    q = pts_left[1]
    if p[0] == q[0]:
      # vertical intersection
      x1 = intersect_line_horizontal(src, det, p[1]) - p[0]
      x2 = intersect_line_horizontal(src, det, q[1]) - q[0]
      ret = 0.5 * (ymax - ymin) * (abs(x1) + abs(x2))
      return ret
    else:
      assert(p[1] == q[1])
      # horizontal intersection
      y1 = intersect_line_vertical(src, det, p[0]) - p[1]
      y2 = intersect_line_vertical(src, det, q[0]) - q[1]
      ret = 0.5 * (xmax - xmin) * (abs(y1) + abs(y2))
      return ret
  else:
    # mirror and invert
    ret = ((xmax - xmin) * (ymax - ymin)) - halfarea_rect_line(det, src, xmin, xmax, ymin, ymax)
    return ret

# area of intersection of the strip with boundaries edge1, edge2 with rectangle
def intersect_ray_rect(edge1, edge2, xmin, xmax, ymin, ymax):
  s1 = halfarea_rect_line(edge1[0], edge1[1], xmin, xmax, ymin, ymax)
  s2 = halfarea_rect_line(edge2[0], edge2[1], xmin, xmax, ymin, ymax)
  return abs(s1 - s2)


# width of projection of detector orthogonal to ray direction
# i.e., effective detector width
def effective_detweight(src, det, u):
  ray = np.array(det) - np.array(src)
  ray = ray / np.linalg.norm(ray, ord=2)
  return abs(area_signed(ray, u))


# LINE GENERATORS
# ---------------
#
# Per ray these yield three lines, at respectively the center and two edges of the detector pixel.
# Each line is given by two points on the line.
# ( ( (p0x, p0y), (q0x, q0y) ), ( (p1x, p1y), (q1x, q1y) ), ( (p2x, p2y), (q2x, q2y) ) )

def gen_lines_fanflat(proj_geom):
  angles = proj_geom['ProjectionAngles']
  for theta in angles:
    #theta = -theta
    src = ( math.sin(theta) * proj_geom['DistanceOriginSource'],
           -math.cos(theta) * proj_geom['DistanceOriginSource'] )
    detc= (-math.sin(theta) * proj_geom['DistanceOriginDetector'],
            math.cos(theta) * proj_geom['DistanceOriginDetector'] )
    detu= ( math.cos(theta) * proj_geom['DetectorWidth'],
            math.sin(theta) * proj_geom['DetectorWidth'] )

    src = np.array(src, dtype=np.float64)
    detc= np.array(detc, dtype=np.float64)
    detu= np.array(detu, dtype=np.float64)

    detb= detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu

    for i in range(proj_geom['DetectorCount']):
      yield ((src, detb + i * detu),
             (src, detb + (i - 0.5) * detu),
             (src, detb + (i + 0.5) * detu))

def gen_lines_fanflat_vec(proj_geom):
  v = proj_geom['Vectors']
  for i in range(v.shape[0]):
    src = v[i,0:2]
    detc = v[i,2:4]
    detu = v[i,4:6]

    detb = detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu
    for i in range(proj_geom['DetectorCount']):
      yield ((src, detb + i * detu),
             (src, detb + (i - 0.5) * detu),
             (src, detb + (i + 0.5) * detu))

def gen_lines_parallel(proj_geom):
  angles = proj_geom['ProjectionAngles']
  for theta in angles:
    ray = ( math.sin(theta),
           -math.cos(theta) )
    detc= (0, 0 )
    detu= ( math.cos(theta) * proj_geom['DetectorWidth'],
            math.sin(theta) * proj_geom['DetectorWidth'] )

    ray = np.array(ray, dtype=np.float64)
    detc= np.array(detc, dtype=np.float64)
    detu= np.array(detu, dtype=np.float64)


    detb= detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu

    for i in range(proj_geom['DetectorCount']):
      yield ((detb + i * detu - ray, detb + i * detu),
             (detb + (i - 0.5) * detu - ray, detb + (i - 0.5) * detu),
             (detb + (i + 0.5) * detu - ray, detb + (i + 0.5) * detu))


def gen_lines_parallel_vec(proj_geom):
  v = proj_geom['Vectors']
  for i in range(v.shape[0]):
    ray = v[i,0:2]
    detc = v[i,2:4]
    detu = v[i,4:6]

    detb = detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu

    for i in range(proj_geom['DetectorCount']):
      yield ((detb + i * detu - ray, detb + i * detu),
             (detb + (i - 0.5) * detu - ray, detb + (i - 0.5) * detu),
             (detb + (i + 0.5) * detu - ray, detb + (i + 0.5) * detu))


def gen_lines(proj_geom):
  g = { 'fanflat': gen_lines_fanflat,
        'fanflat_vec': gen_lines_fanflat_vec,
        'parallel': gen_lines_parallel,
        'parallel_vec': gen_lines_parallel_vec }
  for l in g[proj_geom['type']](proj_geom):
    yield l

range2d = ( 8, 64 )


def gen_random_geometry_fanflat():
  if not NONUNITDET:
    w = 1.0
  else:
    w = 0.6 + 0.8 * np.random.random()
  pg = astra.create_proj_geom('fanflat', w, np.random.randint(*range2d), np.linspace(0, 2*np.pi, np.random.randint(*range2d), endpoint=False), 256 * (0.5 + np.random.random()), 256 * np.random.random())
  return pg

def gen_random_geometry_parallel():
  if not NONUNITDET:
    w = 1.0
  else:
    w = 0.8 + 0.4 * np.random.random()
  pg = astra.create_proj_geom('parallel', w, np.random.randint(*range2d), np.linspace(0, 2*np.pi, np.random.randint(*range2d), endpoint=False))
  return pg

def gen_random_geometry_fanflat_vec():
  Vectors = np.zeros([16,6])
  # We assume constant detector width in these tests
  if not NONUNITDET:
    w = 1.0
  else:
    w = 0.6 + 0.8 * np.random.random()
  for i in range(Vectors.shape[0]):
    angle1 = 2*np.pi*np.random.random()
    if OBLIQUE:
      angle2 = angle1 + 0.5 * np.random.random()
    else:
      angle2 = angle1
    dist1 = 256 * (0.5 + np.random.random())
    detc = 10 * np.random.random(size=2)
    detu = [ math.cos(angle1) * w, math.sin(angle1) * w ]
    src = [ math.sin(angle2) * dist1, -math.cos(angle2) * dist1 ]
    Vectors[i, :] = [ src[0], src[1], detc[0], detc[1], detu[0], detu[1] ]
  pg = astra.create_proj_geom('fanflat_vec', np.random.randint(*range2d), Vectors)
  return pg

def gen_random_geometry_parallel_vec():
  Vectors = np.zeros([16,6])
  # We assume constant detector width in these tests
  if not NONUNITDET:
    w = 1.0
  else:
    w = 0.6 + 0.8 * np.random.random()
  for i in range(Vectors.shape[0]):
    l = 0.6 + 0.8 * np.random.random()
    angle1 = 2*np.pi*np.random.random()
    if OBLIQUE:
      angle2 = angle1 + 0.5 * np.random.random()
    else:
      angle2 = angle1
    detc = 10 * np.random.random(size=2)
    detu = [ math.cos(angle1) * w, math.sin(angle1) * w ]
    ray = [ math.sin(angle2) * l, -math.cos(angle2) * l ]
    Vectors[i, :] = [ ray[0], ray[1], detc[0], detc[1], detu[0], detu[1] ]
  pg = astra.create_proj_geom('parallel_vec', np.random.randint(*range2d), Vectors)
  return pg




def proj_type_to_fan(t):
  if t == 'cuda':
    return t
  else:
    return t + '_fanflat'

def display_mismatch(data, sinogram, a):
  pylab.gray()
  pylab.imshow(data)
  pylab.figure()
  pylab.imshow(sinogram)
  pylab.figure()
  pylab.imshow(a)
  pylab.figure()
  pylab.imshow(sinogram-a)
  pylab.show()

def display_mismatch_triple(data, sinogram, a, b, c):
  pylab.gray()
  pylab.imshow(data)
  pylab.figure()
  pylab.imshow(sinogram)
  pylab.figure()
  pylab.imshow(b)
  pylab.figure()
  pylab.imshow(a)
  pylab.figure()
  pylab.imshow(c)
  pylab.figure()
  pylab.imshow(sinogram-a)
  pylab.figure()
  pylab.imshow(c-sinogram)
  pylab.show()

class Test2DKernel(unittest.TestCase):
  def single_test(self, type, proj_type):
      shape = np.random.randint(*range2d, size=2)
      # these rectangles are biased, but that shouldn't matter
      rect_min = [ np.random.randint(0, a) for a in shape ]
      rect_max = [ np.random.randint(rect_min[i]+1, shape[i]+1) for i in range(len(shape))]
      if FLEXVOL:
          if not NONSQUARE:
            pixsize = np.array([0.5, 0.5]) + np.random.random()
          else:
            pixsize = 0.5 + np.random.random(size=2)
          origin = 10 * np.random.random(size=2)
      else:
          pixsize = (1.,1.)
          origin = (0.,0.)
      vg = astra.create_vol_geom(shape[1], shape[0],
                                 origin[0] - 0.5 * shape[0] * pixsize[0],
                                 origin[0] + 0.5 * shape[0] * pixsize[0],
                                 origin[1] - 0.5 * shape[1] * pixsize[1],
                                 origin[1] + 0.5 * shape[1] * pixsize[1])

      if type == 'parallel':
        pg = gen_random_geometry_parallel()
        projector_id = astra.create_projector(proj_type, pg, vg)
      elif type == 'parallel_vec':
        pg = gen_random_geometry_parallel_vec()
        projector_id = astra.create_projector(proj_type, pg, vg)
      elif type == 'fanflat':
        pg = gen_random_geometry_fanflat()
        projector_id = astra.create_projector(proj_type_to_fan(proj_type), pg, vg)
      elif type == 'fanflat_vec':
        pg = gen_random_geometry_fanflat_vec()
        projector_id = astra.create_projector(proj_type_to_fan(proj_type), pg, vg)


      data = np.zeros((shape[1], shape[0]), dtype=np.float32)
      data[rect_min[1]:rect_max[1],rect_min[0]:rect_max[0]] = 1

      sinogram_id, sinogram = astra.create_sino(data, projector_id)

      self.assertTrue(np.all(np.isfinite(sinogram)))

      #print(pg)
      #print(vg)

      astra.data2d.delete(sinogram_id)

      astra.projector.delete(projector_id)

      # NB: Flipped y-axis here, since that is how astra interprets 2D volumes
      xmin = origin[0] + (-0.5 * shape[0] + rect_min[0]) * pixsize[0]
      xmax = origin[0] + (-0.5 * shape[0] + rect_max[0]) * pixsize[0]
      ymin = origin[1] + (+0.5 * shape[1] - rect_max[1]) * pixsize[1]
      ymax = origin[1] + (+0.5 * shape[1] - rect_min[1]) * pixsize[1]

      if proj_type == 'line':

        a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        b = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        c = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)

        for i, (center, edge1, edge2) in enumerate(gen_lines(pg)):
          (src, det) = center

          # We compute line intersections with slightly bigger (cw) and
          # smaller (aw) rectangles, and see if the kernel falls
          # between these two values.
          (aw,bw,cw) = intersect_line_rectangle_interval(src, det,
                        xmin, xmax, ymin, ymax,
                        1e-3)
          a[i] = aw
          b[i] = bw
          c[i] = cw
        a = a.reshape(astra.functions.geom_size(pg))
        b = b.reshape(astra.functions.geom_size(pg))
        c = c.reshape(astra.functions.geom_size(pg))

        if not np.all(np.isfinite(a)):
          raise RuntimeError("Invalid value in reference sinogram")
        if not np.all(np.isfinite(b)):
          raise RuntimeError("Invalid value in reference sinogram")
        if not np.all(np.isfinite(c)):
          raise RuntimeError("Invalid value in reference sinogram")
        self.assertTrue(np.all(np.isfinite(sinogram)))

        # Check if sinogram lies between a and c
        y = np.min(sinogram-a)
        z = np.min(c-sinogram)
        if DISPLAY and (z < 0 or y < 0):
          display_mismatch_triple(data, sinogram, a, b, c)
        self.assertFalse(z < 0 or y < 0)
      elif proj_type == 'linear' or proj_type == 'cuda':
        a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        for i, (center, edge1, edge2) in enumerate(gen_lines(pg)):
          (src, det) = center
          (xd, yd) = det - src
          l = 0.0
          if np.abs(xd) > np.abs(yd): # horizontal ray
            length = math.sqrt(1.0 + abs(yd/xd)**2) * pixsize[0]
            y_seg = (ymin, ymax)
            for j in range(rect_min[0], rect_max[0]):
              x = origin[0] + (-0.5 * shape[0] + j + 0.5) * pixsize[0]
              w = intersect_line_vertical_segment_linear(center[0], center[1], x, y_seg, pixsize[1])
              # limited interpolation precision with cuda
              if CUDA_8BIT_LINEAR and proj_type == 'cuda':
                w = np.round(w * 256.0) / 256.0
              l += w * length
          else:
            length = math.sqrt(1.0 + abs(xd/yd)**2) * pixsize[1]
            x_seg = (xmin, xmax)
            for j in range(rect_min[1], rect_max[1]):
              y = origin[1] + (+0.5 * shape[1] - j - 0.5) * pixsize[1]
              w = intersect_line_horizontal_segment_linear(center[0], center[1], y, x_seg, pixsize[0])
              # limited interpolation precision with cuda
              if CUDA_8BIT_LINEAR and proj_type == 'cuda':
                w = np.round(w * 256.0) / 256.0
              l += w * length
          a[i] = l
        a = a.reshape(astra.functions.geom_size(pg))
        if not np.all(np.isfinite(a)):
          raise RuntimeError("Invalid value in reference sinogram")
        x = np.max(np.abs(sinogram-a))
        TOL = 2e-3 if proj_type != 'cuda' else CUDA_TOL
        if DISPLAY and x > TOL:
          display_mismatch(data, sinogram, a)
        self.assertFalse(x > TOL)
      elif proj_type == 'distance_driven' and 'par' in type:
        a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        for i, (center, edge1, edge2) in enumerate(gen_lines(pg)):
          (src, det) = center
          try:
            detweight = pg['DetectorWidth']
          except KeyError:
            detweight = effective_detweight(src, det, pg['Vectors'][i//pg['DetectorCount'],4:6])
          (xd, yd) = det - src
          l = 0.0
          if np.abs(xd) > np.abs(yd): # horizontal ray
            y_seg = (ymin, ymax)
            for j in range(rect_min[0], rect_max[0]):
              x = origin[0] + (-0.5 * shape[0] + j + 0.5) * pixsize[0]
              l += intersect_ray_vertical_segment(edge1, edge2, x, y_seg) * pixsize[0] / detweight
          else:
            x_seg = (xmin, xmax)
            for j in range(rect_min[1], rect_max[1]):
              y = origin[1] + (+0.5 * shape[1] - j - 0.5) * pixsize[1]
              l += intersect_ray_horizontal_segment(edge1, edge2, y, x_seg) * pixsize[1] / detweight
          a[i] = l
        a = a.reshape(astra.functions.geom_size(pg))
        if not np.all(np.isfinite(a)):
          raise RuntimeError("Invalid value in reference sinogram")
        x = np.max(np.abs(sinogram-a))
        TOL = 2e-3
        if DISPLAY and x > TOL:
          display_mismatch(data, sinogram, a)
        self.assertFalse(x > TOL)
      elif proj_type == 'strip' and 'fan' in type:
        a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        for i, (center, edge1, edge2) in enumerate(gen_lines(pg)):
          (src, det) = center
          det_dist = np.linalg.norm(src-det, ord=2)
          l = 0.0
          for j in range(rect_min[0], rect_max[0]):
            xmin = origin[0] + (-0.5 * shape[0] + j) * pixsize[0]
            xmax = origin[0] + (-0.5 * shape[0] + j + 1) * pixsize[0]
            xcen = 0.5 * (xmin + xmax)
            for k in range(rect_min[1], rect_max[1]):
              ymin = origin[1] + (+0.5 * shape[1] - k - 1) * pixsize[1]
              ymax = origin[1] + (+0.5 * shape[1] - k) * pixsize[1]
              ycen = 0.5 * (ymin + ymax)
              scale = det_dist / np.linalg.norm( src - np.array((xcen,ycen)), ord=2 )
              w = intersect_ray_rect(edge1, edge2, xmin, xmax, ymin, ymax)
              l += w * scale
          a[i] = l
        a = a.reshape(astra.functions.geom_size(pg))
        if not np.all(np.isfinite(a)):
          raise RuntimeError("Invalid value in reference sinogram")
        x = np.max(np.abs(sinogram-a))
        TOL = 8e-3
        if DISPLAY and x > TOL:
          display_mismatch(data, sinogram, a)
        self.assertFalse(x > TOL)
      elif proj_type == 'strip':
        a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
        for i, (center, edge1, edge2) in enumerate(gen_lines(pg)):
          a[i] = intersect_ray_rect(edge1, edge2, xmin, xmax, ymin, ymax)
        a = a.reshape(astra.functions.geom_size(pg))
        if not np.all(np.isfinite(a)):
          raise RuntimeError("Invalid value in reference sinogram")
        x = np.max(np.abs(sinogram-a))
        TOL = 8e-3
        if DISPLAY and x > TOL:
          display_mismatch(data, sinogram, a)
        self.assertFalse(x > TOL)
      else:
        raise RuntimeError("Unsupported projector")

  def multi_test(self, type, proj_type):
    np.random.seed(seed)
    for _ in range(nloops):
      self.single_test(type, proj_type)

  def test_par(self):
    self.multi_test('parallel', 'line')
  def test_par_linear(self):
    self.multi_test('parallel', 'linear')
  def test_par_cuda(self):
    self.multi_test('parallel', 'cuda')
  def test_par_dd(self):
    self.multi_test('parallel', 'distance_driven')
  def test_par_strip(self):
    self.multi_test('parallel', 'strip')
  def test_fan(self):
    self.multi_test('fanflat', 'line')
  def test_fan_strip(self):
    self.multi_test('fanflat', 'strip')
  def test_fan_cuda(self):
    self.multi_test('fanflat', 'cuda')
  def test_parvec(self):
    self.multi_test('parallel_vec', 'line')
  def test_parvec_linear(self):
    self.multi_test('parallel_vec', 'linear')
  def test_parvec_dd(self):
    self.multi_test('parallel_vec', 'distance_driven')
  def test_parvec_strip(self):
    self.multi_test('parallel_vec', 'strip')
  def test_parvec_cuda(self):
    self.multi_test('parallel_vec', 'cuda')
  def test_fanvec(self):
    self.multi_test('fanflat_vec', 'line')
  def test_fanvec_cuda(self):
    self.multi_test('fanflat_vec', 'cuda')





if __name__ == '__main__':
  unittest.main()