-
-
Notifications
You must be signed in to change notification settings - Fork 7.5k
/
quiver.py
1182 lines (984 loc) · 45.1 KB
/
quiver.py
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
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
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
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
797
798
799
800
801
802
803
804
805
806
807
808
809
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
869
870
871
872
873
874
875
876
877
878
879
880
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
935
936
937
938
939
940
941
942
943
944
945
946
947
948
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
"""
Support for plotting vector fields.
Presently this contains Quiver and Barb. Quiver plots an arrow in the
direction of the vector, with the size of the arrow related to the
magnitude of the vector.
Barbs are like quiver in that they point along a vector, but
the magnitude of the vector is given schematically by the presence of barbs
or flags on the barb.
This will also become a home for things such as standard
deviation ellipses, which can and will be derived very easily from
the Quiver code.
"""
import math
import numpy as np
from numpy import ma
from matplotlib import _api, cbook, _docstring
import matplotlib.artist as martist
import matplotlib.collections as mcollections
from matplotlib.patches import CirclePolygon
import matplotlib.text as mtext
import matplotlib.transforms as transforms
_quiver_doc = """
Plot a 2D field of arrows.
Call signature::
quiver([X, Y], U, V, [C], **kwargs)
*X*, *Y* define the arrow locations, *U*, *V* define the arrow directions, and
*C* optionally sets the color.
**Arrow length**
The default settings auto-scales the length of the arrows to a reasonable size.
To change this behavior see the *scale* and *scale_units* parameters.
**Arrow shape**
The arrow shape is determined by *width*, *headwidth*, *headlength* and
*headaxislength*. See the notes below.
**Arrow styling**
Each arrow is internally represented by a filled polygon with a default edge
linewidth of 0. As a result, an arrow is rather a filled area, not a line with
a head, and `.PolyCollection` properties like *linewidth*, *edgecolor*,
*facecolor*, etc. act accordingly.
Parameters
----------
X, Y : 1D or 2D array-like, optional
The x and y coordinates of the arrow locations.
If not given, they will be generated as a uniform integer meshgrid based
on the dimensions of *U* and *V*.
If *X* and *Y* are 1D but *U*, *V* are 2D, *X*, *Y* are expanded to 2D
using ``X, Y = np.meshgrid(X, Y)``. In this case ``len(X)`` and ``len(Y)``
must match the column and row dimensions of *U* and *V*.
U, V : 1D or 2D array-like
The x and y direction components of the arrow vectors. The interpretation
of these components (in data or in screen space) depends on *angles*.
*U* and *V* must have the same number of elements, matching the number of
arrow locations in *X*, *Y*. *U* and *V* may be masked. Locations masked
in any of *U*, *V*, and *C* will not be drawn.
C : 1D or 2D array-like, optional
Numeric data that defines the arrow colors by colormapping via *norm* and
*cmap*.
This does not support explicit colors. If you want to set colors directly,
use *color* instead. The size of *C* must match the number of arrow
locations.
angles : {'uv', 'xy'} or array-like, default: 'uv'
Method for determining the angle of the arrows.
- 'uv': Arrow direction in screen coordinates. Use this if the arrows
symbolize a quantity that is not based on *X*, *Y* data coordinates.
If *U* == *V* the orientation of the arrow on the plot is 45 degrees
counter-clockwise from the horizontal axis (positive to the right).
- 'xy': Arrow direction in data coordinates, i.e. the arrows point from
(x, y) to (x+u, y+v). Use this e.g. for plotting a gradient field.
- Arbitrary angles may be specified explicitly as an array of values
in degrees, counter-clockwise from the horizontal axis.
In this case *U*, *V* is only used to determine the length of the
arrows.
Note: inverting a data axis will correspondingly invert the
arrows only with ``angles='xy'``.
pivot : {'tail', 'mid', 'middle', 'tip'}, default: 'tail'
The part of the arrow that is anchored to the *X*, *Y* grid. The arrow
rotates about this point.
'mid' is a synonym for 'middle'.
scale : float, optional
Scales the length of the arrow inversely.
Number of data units per arrow length unit, e.g., m/s per plot width; a
smaller scale parameter makes the arrow longer. Default is *None*.
If *None*, a simple autoscaling algorithm is used, based on the average
vector length and the number of vectors. The arrow length unit is given by
the *scale_units* parameter.
scale_units : {'width', 'height', 'dots', 'inches', 'x', 'y', 'xy'}, optional
If the *scale* kwarg is *None*, the arrow length unit. Default is *None*.
e.g. *scale_units* is 'inches', *scale* is 2.0, and ``(u, v) = (1, 0)``,
then the vector will be 0.5 inches long.
If *scale_units* is 'width' or 'height', then the vector will be half the
width/height of the axes.
If *scale_units* is 'x' then the vector will be 0.5 x-axis
units. To plot vectors in the x-y plane, with u and v having
the same units as x and y, use
``angles='xy', scale_units='xy', scale=1``.
units : {'width', 'height', 'dots', 'inches', 'x', 'y', 'xy'}, default: 'width'
Affects the arrow size (except for the length). In particular, the shaft
*width* is measured in multiples of this unit.
Supported values are:
- 'width', 'height': The width or height of the Axes.
- 'dots', 'inches': Pixels or inches based on the figure dpi.
- 'x', 'y', 'xy': *X*, *Y* or :math:`\\sqrt{X^2 + Y^2}` in data units.
The following table summarizes how these values affect the visible arrow
size under zooming and figure size changes:
================= ================= ==================
units zoom figure size change
================= ================= ==================
'x', 'y', 'xy' arrow size scales —
'width', 'height' — arrow size scales
'dots', 'inches' — —
================= ================= ==================
width : float, optional
Shaft width in arrow units. All head parameters are relative to *width*.
The default depends on choice of *units* above, and number of vectors;
a typical starting value is about 0.005 times the width of the plot.
headwidth : float, default: 3
Head width as multiple of shaft *width*. See the notes below.
headlength : float, default: 5
Head length as multiple of shaft *width*. See the notes below.
headaxislength : float, default: 4.5
Head length at shaft intersection as multiple of shaft *width*.
See the notes below.
minshaft : float, default: 1
Length below which arrow scales, in units of head length. Do not
set this to less than 1, or small arrows will look terrible!
minlength : float, default: 1
Minimum length as a multiple of shaft width; if an arrow length
is less than this, plot a dot (hexagon) of this diameter instead.
color : color or color sequence, optional
Explicit color(s) for the arrows. If *C* has been set, *color* has no
effect.
This is a synonym for the `.PolyCollection` *facecolor* parameter.
Other Parameters
----------------
data : indexable object, optional
DATA_PARAMETER_PLACEHOLDER
**kwargs : `~matplotlib.collections.PolyCollection` properties, optional
All other keyword arguments are passed on to `.PolyCollection`:
%(PolyCollection:kwdoc)s
Returns
-------
`~matplotlib.quiver.Quiver`
See Also
--------
.Axes.quiverkey : Add a key to a quiver plot.
Notes
-----
**Arrow shape**
The arrow is drawn as a polygon using the nodes as shown below. The values
*headwidth*, *headlength*, and *headaxislength* are in units of *width*.
.. image:: /_static/quiver_sizes.svg
:width: 500px
The defaults give a slightly swept-back arrow. Here are some guidelines how to
get other head shapes:
- To make the head a triangle, make *headaxislength* the same as *headlength*.
- To make the arrow more pointed, reduce *headwidth* or increase *headlength*
and *headaxislength*.
- To make the head smaller relative to the shaft, scale down all the head
parameters proportionally.
- To remove the head completely, set all *head* parameters to 0.
- To get a diamond-shaped head, make *headaxislength* larger than *headlength*.
- Warning: For *headaxislength* < (*headlength* / *headwidth*), the "headaxis"
nodes (i.e. the ones connecting the head with the shaft) will protrude out
of the head in forward direction so that the arrow head looks broken.
""" % _docstring.interpd.params
_docstring.interpd.update(quiver_doc=_quiver_doc)
class QuiverKey(martist.Artist):
"""Labelled arrow for use as a quiver plot scale key."""
halign = {'N': 'center', 'S': 'center', 'E': 'left', 'W': 'right'}
valign = {'N': 'bottom', 'S': 'top', 'E': 'center', 'W': 'center'}
pivot = {'N': 'middle', 'S': 'middle', 'E': 'tip', 'W': 'tail'}
def __init__(self, Q, X, Y, U, label,
*, angle=0, coordinates='axes', color=None, labelsep=0.1,
labelpos='N', labelcolor=None, fontproperties=None, **kwargs):
"""
Add a key to a quiver plot.
The positioning of the key depends on *X*, *Y*, *coordinates*, and
*labelpos*. If *labelpos* is 'N' or 'S', *X*, *Y* give the position of
the middle of the key arrow. If *labelpos* is 'E', *X*, *Y* positions
the head, and if *labelpos* is 'W', *X*, *Y* positions the tail; in
either of these two cases, *X*, *Y* is somewhere in the middle of the
arrow+label key object.
Parameters
----------
Q : `~matplotlib.quiver.Quiver`
A `.Quiver` object as returned by a call to `~.Axes.quiver()`.
X, Y : float
The location of the key.
U : float
The length of the key.
label : str
The key label (e.g., length and units of the key).
angle : float, default: 0
The angle of the key arrow, in degrees anti-clockwise from the
x-axis.
coordinates : {'axes', 'figure', 'data', 'inches'}, default: 'axes'
Coordinate system and units for *X*, *Y*: 'axes' and 'figure' are
normalized coordinate systems with (0, 0) in the lower left and
(1, 1) in the upper right; 'data' are the axes data coordinates
(used for the locations of the vectors in the quiver plot itself);
'inches' is position in the figure in inches, with (0, 0) at the
lower left corner.
color : color
Overrides face and edge colors from *Q*.
labelpos : {'N', 'S', 'E', 'W'}
Position the label above, below, to the right, to the left of the
arrow, respectively.
labelsep : float, default: 0.1
Distance in inches between the arrow and the label.
labelcolor : color, default: :rc:`text.color`
Label color.
fontproperties : dict, optional
A dictionary with keyword arguments accepted by the
`~matplotlib.font_manager.FontProperties` initializer:
*family*, *style*, *variant*, *size*, *weight*.
**kwargs
Any additional keyword arguments are used to override vector
properties taken from *Q*.
"""
super().__init__()
self.Q = Q
self.X = X
self.Y = Y
self.U = U
self.angle = angle
self.coord = coordinates
self.color = color
self.label = label
self._labelsep_inches = labelsep
self.labelpos = labelpos
self.labelcolor = labelcolor
self.fontproperties = fontproperties or dict()
self.kw = kwargs
self.text = mtext.Text(
text=label,
horizontalalignment=self.halign[self.labelpos],
verticalalignment=self.valign[self.labelpos],
fontproperties=self.fontproperties)
if self.labelcolor is not None:
self.text.set_color(self.labelcolor)
self._dpi_at_last_init = None
self.zorder = Q.zorder + 0.1
@property
def labelsep(self):
return self._labelsep_inches * self.Q.axes.figure.dpi
def _init(self):
if True: # self._dpi_at_last_init != self.axes.figure.dpi
if self.Q._dpi_at_last_init != self.Q.axes.figure.dpi:
self.Q._init()
self._set_transform()
with cbook._setattr_cm(self.Q, pivot=self.pivot[self.labelpos],
# Hack: save and restore the Umask
Umask=ma.nomask):
u = self.U * np.cos(np.radians(self.angle))
v = self.U * np.sin(np.radians(self.angle))
angle = (self.Q.angles if isinstance(self.Q.angles, str)
else 'uv')
self.verts = self.Q._make_verts(
np.array([u]), np.array([v]), angle)
kwargs = self.Q.polykw
kwargs.update(self.kw)
self.vector = mcollections.PolyCollection(
self.verts,
offsets=[(self.X, self.Y)],
offset_transform=self.get_transform(),
**kwargs)
if self.color is not None:
self.vector.set_color(self.color)
self.vector.set_transform(self.Q.get_transform())
self.vector.set_figure(self.get_figure())
self._dpi_at_last_init = self.Q.axes.figure.dpi
def _text_shift(self):
return {
"N": (0, +self.labelsep),
"S": (0, -self.labelsep),
"E": (+self.labelsep, 0),
"W": (-self.labelsep, 0),
}[self.labelpos]
@martist.allow_rasterization
def draw(self, renderer):
self._init()
self.vector.draw(renderer)
pos = self.get_transform().transform((self.X, self.Y))
self.text.set_position(pos + self._text_shift())
self.text.draw(renderer)
self.stale = False
def _set_transform(self):
self.set_transform(_api.check_getitem({
"data": self.Q.axes.transData,
"axes": self.Q.axes.transAxes,
"figure": self.Q.axes.figure.transFigure,
"inches": self.Q.axes.figure.dpi_scale_trans,
}, coordinates=self.coord))
def set_figure(self, fig):
super().set_figure(fig)
self.text.set_figure(fig)
def contains(self, mouseevent):
inside, info = self._default_contains(mouseevent)
if inside is not None:
return inside, info
# Maybe the dictionary should allow one to
# distinguish between a text hit and a vector hit.
if (self.text.contains(mouseevent)[0] or
self.vector.contains(mouseevent)[0]):
return True, {}
return False, {}
def _parse_args(*args, caller_name='function'):
"""
Helper function to parse positional parameters for colored vector plots.
This is currently used for Quiver and Barbs.
Parameters
----------
*args : list
list of 2-5 arguments. Depending on their number they are parsed to::
U, V
U, V, C
X, Y, U, V
X, Y, U, V, C
caller_name : str
Name of the calling method (used in error messages).
"""
X = Y = C = None
nargs = len(args)
if nargs == 2:
# The use of atleast_1d allows for handling scalar arguments while also
# keeping masked arrays
U, V = np.atleast_1d(*args)
elif nargs == 3:
U, V, C = np.atleast_1d(*args)
elif nargs == 4:
X, Y, U, V = np.atleast_1d(*args)
elif nargs == 5:
X, Y, U, V, C = np.atleast_1d(*args)
else:
raise _api.nargs_error(caller_name, takes="from 2 to 5", given=nargs)
nr, nc = (1, U.shape[0]) if U.ndim == 1 else U.shape
if X is not None:
X = X.ravel()
Y = Y.ravel()
if len(X) == nc and len(Y) == nr:
X, Y = [a.ravel() for a in np.meshgrid(X, Y)]
elif len(X) != len(Y):
raise ValueError('X and Y must be the same size, but '
f'X.size is {X.size} and Y.size is {Y.size}.')
else:
indexgrid = np.meshgrid(np.arange(nc), np.arange(nr))
X, Y = [np.ravel(a) for a in indexgrid]
# Size validation for U, V, C is left to the set_UVC method.
return X, Y, U, V, C
def _check_consistent_shapes(*arrays):
all_shapes = {a.shape for a in arrays}
if len(all_shapes) != 1:
raise ValueError('The shapes of the passed in arrays do not match')
class Quiver(mcollections.PolyCollection):
"""
Specialized PolyCollection for arrows.
The only API method is set_UVC(), which can be used
to change the size, orientation, and color of the
arrows; their locations are fixed when the class is
instantiated. Possibly this method will be useful
in animations.
Much of the work in this class is done in the draw()
method so that as much information as possible is available
about the plot. In subsequent draw() calls, recalculation
is limited to things that might have changed, so there
should be no performance penalty from putting the calculations
in the draw() method.
"""
_PIVOT_VALS = ('tail', 'middle', 'tip')
@_docstring.Substitution(_quiver_doc)
def __init__(self, ax, *args,
scale=None, headwidth=3, headlength=5, headaxislength=4.5,
minshaft=1, minlength=1, units='width', scale_units=None,
angles='uv', width=None, color='k', pivot='tail', **kwargs):
"""
The constructor takes one required argument, an Axes
instance, followed by the args and kwargs described
by the following pyplot interface documentation:
%s
"""
self._axes = ax # The attr actually set by the Artist.axes property.
X, Y, U, V, C = _parse_args(*args, caller_name='quiver')
self.X = X
self.Y = Y
self.XY = np.column_stack((X, Y))
self.N = len(X)
self.scale = scale
self.headwidth = headwidth
self.headlength = float(headlength)
self.headaxislength = headaxislength
self.minshaft = minshaft
self.minlength = minlength
self.units = units
self.scale_units = scale_units
self.angles = angles
self.width = width
if pivot.lower() == 'mid':
pivot = 'middle'
self.pivot = pivot.lower()
_api.check_in_list(self._PIVOT_VALS, pivot=self.pivot)
self.transform = kwargs.pop('transform', ax.transData)
kwargs.setdefault('facecolors', color)
kwargs.setdefault('linewidths', (0,))
super().__init__([], offsets=self.XY, offset_transform=self.transform,
closed=False, **kwargs)
self.polykw = kwargs
self.set_UVC(U, V, C)
self._dpi_at_last_init = None
def _init(self):
"""
Initialization delayed until first draw;
allow time for axes setup.
"""
# It seems that there are not enough event notifications
# available to have this work on an as-needed basis at present.
if True: # self._dpi_at_last_init != self.axes.figure.dpi
trans = self._set_transform()
self.span = trans.inverted().transform_bbox(self.axes.bbox).width
if self.width is None:
sn = np.clip(math.sqrt(self.N), 8, 25)
self.width = 0.06 * self.span / sn
# _make_verts sets self.scale if not already specified
if (self._dpi_at_last_init != self.axes.figure.dpi
and self.scale is None):
self._make_verts(self.U, self.V, self.angles)
self._dpi_at_last_init = self.axes.figure.dpi
def get_datalim(self, transData):
trans = self.get_transform()
offset_trf = self.get_offset_transform()
full_transform = (trans - transData) + (offset_trf - transData)
XY = full_transform.transform(self.XY)
bbox = transforms.Bbox.null()
bbox.update_from_data_xy(XY, ignore=True)
return bbox
@martist.allow_rasterization
def draw(self, renderer):
self._init()
verts = self._make_verts(self.U, self.V, self.angles)
self.set_verts(verts, closed=False)
super().draw(renderer)
self.stale = False
def set_UVC(self, U, V, C=None):
# We need to ensure we have a copy, not a reference
# to an array that might change before draw().
U = ma.masked_invalid(U, copy=True).ravel()
V = ma.masked_invalid(V, copy=True).ravel()
if C is not None:
C = ma.masked_invalid(C, copy=True).ravel()
for name, var in zip(('U', 'V', 'C'), (U, V, C)):
if not (var is None or var.size == self.N or var.size == 1):
raise ValueError(f'Argument {name} has a size {var.size}'
f' which does not match {self.N},'
' the number of arrow positions')
mask = ma.mask_or(U.mask, V.mask, copy=False, shrink=True)
if C is not None:
mask = ma.mask_or(mask, C.mask, copy=False, shrink=True)
if mask is ma.nomask:
C = C.filled()
else:
C = ma.array(C, mask=mask, copy=False)
self.U = U.filled(1)
self.V = V.filled(1)
self.Umask = mask
if C is not None:
self.set_array(C)
self.stale = True
def _dots_per_unit(self, units):
"""Return a scale factor for converting from units to pixels."""
bb = self.axes.bbox
vl = self.axes.viewLim
return _api.check_getitem({
'x': bb.width / vl.width,
'y': bb.height / vl.height,
'xy': np.hypot(*bb.size) / np.hypot(*vl.size),
'width': bb.width,
'height': bb.height,
'dots': 1.,
'inches': self.axes.figure.dpi,
}, units=units)
def _set_transform(self):
"""
Set the PolyCollection transform to go
from arrow width units to pixels.
"""
dx = self._dots_per_unit(self.units)
self._trans_scale = dx # pixels per arrow width unit
trans = transforms.Affine2D().scale(dx)
self.set_transform(trans)
return trans
def _angles_lengths(self, U, V, eps=1):
xy = self.axes.transData.transform(self.XY)
uv = np.column_stack((U, V))
xyp = self.axes.transData.transform(self.XY + eps * uv)
dxy = xyp - xy
angles = np.arctan2(dxy[:, 1], dxy[:, 0])
lengths = np.hypot(*dxy.T) / eps
return angles, lengths
def _make_verts(self, U, V, angles):
uv = (U + V * 1j)
str_angles = angles if isinstance(angles, str) else ''
if str_angles == 'xy' and self.scale_units == 'xy':
# Here eps is 1 so that if we get U, V by diffing
# the X, Y arrays, the vectors will connect the
# points, regardless of the axis scaling (including log).
angles, lengths = self._angles_lengths(U, V, eps=1)
elif str_angles == 'xy' or self.scale_units == 'xy':
# Calculate eps based on the extents of the plot
# so that we don't end up with roundoff error from
# adding a small number to a large.
eps = np.abs(self.axes.dataLim.extents).max() * 0.001
angles, lengths = self._angles_lengths(U, V, eps=eps)
if str_angles and self.scale_units == 'xy':
a = lengths
else:
a = np.abs(uv)
if self.scale is None:
sn = max(10, math.sqrt(self.N))
if self.Umask is not ma.nomask:
amean = a[~self.Umask].mean()
else:
amean = a.mean()
# crude auto-scaling
# scale is typical arrow length as a multiple of the arrow width
scale = 1.8 * amean * sn / self.span
if self.scale_units is None:
if self.scale is None:
self.scale = scale
widthu_per_lenu = 1.0
else:
if self.scale_units == 'xy':
dx = 1
else:
dx = self._dots_per_unit(self.scale_units)
widthu_per_lenu = dx / self._trans_scale
if self.scale is None:
self.scale = scale * widthu_per_lenu
length = a * (widthu_per_lenu / (self.scale * self.width))
X, Y = self._h_arrows(length)
if str_angles == 'xy':
theta = angles
elif str_angles == 'uv':
theta = np.angle(uv)
else:
theta = ma.masked_invalid(np.deg2rad(angles)).filled(0)
theta = theta.reshape((-1, 1)) # for broadcasting
xy = (X + Y * 1j) * np.exp(1j * theta) * self.width
XY = np.stack((xy.real, xy.imag), axis=2)
if self.Umask is not ma.nomask:
XY = ma.array(XY)
XY[self.Umask] = ma.masked
# This might be handled more efficiently with nans, given
# that nans will end up in the paths anyway.
return XY
def _h_arrows(self, length):
"""Length is in arrow width units."""
# It might be possible to streamline the code
# and speed it up a bit by using complex (x, y)
# instead of separate arrays; but any gain would be slight.
minsh = self.minshaft * self.headlength
N = len(length)
length = length.reshape(N, 1)
# This number is chosen based on when pixel values overflow in Agg
# causing rendering errors
# length = np.minimum(length, 2 ** 16)
np.clip(length, 0, 2 ** 16, out=length)
# x, y: normal horizontal arrow
x = np.array([0, -self.headaxislength,
-self.headlength, 0],
np.float64)
x = x + np.array([0, 1, 1, 1]) * length
y = 0.5 * np.array([1, 1, self.headwidth, 0], np.float64)
y = np.repeat(y[np.newaxis, :], N, axis=0)
# x0, y0: arrow without shaft, for short vectors
x0 = np.array([0, minsh - self.headaxislength,
minsh - self.headlength, minsh], np.float64)
y0 = 0.5 * np.array([1, 1, self.headwidth, 0], np.float64)
ii = [0, 1, 2, 3, 2, 1, 0, 0]
X = x[:, ii]
Y = y[:, ii]
Y[:, 3:-1] *= -1
X0 = x0[ii]
Y0 = y0[ii]
Y0[3:-1] *= -1
shrink = length / minsh if minsh != 0. else 0.
X0 = shrink * X0[np.newaxis, :]
Y0 = shrink * Y0[np.newaxis, :]
short = np.repeat(length < minsh, 8, axis=1)
# Now select X0, Y0 if short, otherwise X, Y
np.copyto(X, X0, where=short)
np.copyto(Y, Y0, where=short)
if self.pivot == 'middle':
X -= 0.5 * X[:, 3, np.newaxis]
elif self.pivot == 'tip':
# numpy bug? using -= does not work here unless we multiply by a
# float first, as with 'mid'.
X = X - X[:, 3, np.newaxis]
elif self.pivot != 'tail':
_api.check_in_list(["middle", "tip", "tail"], pivot=self.pivot)
tooshort = length < self.minlength
if tooshort.any():
# Use a heptagonal dot:
th = np.arange(0, 8, 1, np.float64) * (np.pi / 3.0)
x1 = np.cos(th) * self.minlength * 0.5
y1 = np.sin(th) * self.minlength * 0.5
X1 = np.repeat(x1[np.newaxis, :], N, axis=0)
Y1 = np.repeat(y1[np.newaxis, :], N, axis=0)
tooshort = np.repeat(tooshort, 8, 1)
np.copyto(X, X1, where=tooshort)
np.copyto(Y, Y1, where=tooshort)
# Mask handling is deferred to the caller, _make_verts.
return X, Y
quiver_doc = _api.deprecated("3.7")(property(lambda self: _quiver_doc))
_barbs_doc = r"""
Plot a 2D field of barbs.
Call signature::
barbs([X, Y], U, V, [C], **kwargs)
Where *X*, *Y* define the barb locations, *U*, *V* define the barb
directions, and *C* optionally sets the color.
All arguments may be 1D or 2D. *U*, *V*, *C* may be masked arrays, but masked
*X*, *Y* are not supported at present.
Barbs are traditionally used in meteorology as a way to plot the speed
and direction of wind observations, but can technically be used to
plot any two dimensional vector quantity. As opposed to arrows, which
give vector magnitude by the length of the arrow, the barbs give more
quantitative information about the vector magnitude by putting slanted
lines or a triangle for various increments in magnitude, as show
schematically below::
: /\ \
: / \ \
: / \ \ \
: / \ \ \
: ------------------------------
The largest increment is given by a triangle (or "flag"). After those
come full lines (barbs). The smallest increment is a half line. There
is only, of course, ever at most 1 half line. If the magnitude is
small and only needs a single half-line and no full lines or
triangles, the half-line is offset from the end of the barb so that it
can be easily distinguished from barbs with a single full line. The
magnitude for the barb shown above would nominally be 65, using the
standard increments of 50, 10, and 5.
See also https://en.wikipedia.org/wiki/Wind_barb.
Parameters
----------
X, Y : 1D or 2D array-like, optional
The x and y coordinates of the barb locations. See *pivot* for how the
barbs are drawn to the x, y positions.
If not given, they will be generated as a uniform integer meshgrid based
on the dimensions of *U* and *V*.
If *X* and *Y* are 1D but *U*, *V* are 2D, *X*, *Y* are expanded to 2D
using ``X, Y = np.meshgrid(X, Y)``. In this case ``len(X)`` and ``len(Y)``
must match the column and row dimensions of *U* and *V*.
U, V : 1D or 2D array-like
The x and y components of the barb shaft.
C : 1D or 2D array-like, optional
Numeric data that defines the barb colors by colormapping via *norm* and
*cmap*.
This does not support explicit colors. If you want to set colors directly,
use *barbcolor* instead.
length : float, default: 7
Length of the barb in points; the other parts of the barb
are scaled against this.
pivot : {'tip', 'middle'} or float, default: 'tip'
The part of the arrow that is anchored to the *X*, *Y* grid. The barb
rotates about this point. This can also be a number, which shifts the
start of the barb that many points away from grid point.
barbcolor : color or color sequence
The color of all parts of the barb except for the flags. This parameter
is analogous to the *edgecolor* parameter for polygons, which can be used
instead. However this parameter will override facecolor.
flagcolor : color or color sequence
The color of any flags on the barb. This parameter is analogous to the
*facecolor* parameter for polygons, which can be used instead. However,
this parameter will override facecolor. If this is not set (and *C* has
not either) then *flagcolor* will be set to match *barbcolor* so that the
barb has a uniform color. If *C* has been set, *flagcolor* has no effect.
sizes : dict, optional
A dictionary of coefficients specifying the ratio of a given
feature to the length of the barb. Only those values one wishes to
override need to be included. These features include:
- 'spacing' - space between features (flags, full/half barbs)
- 'height' - height (distance from shaft to top) of a flag or full barb
- 'width' - width of a flag, twice the width of a full barb
- 'emptybarb' - radius of the circle used for low magnitudes
fill_empty : bool, default: False
Whether the empty barbs (circles) that are drawn should be filled with
the flag color. If they are not filled, the center is transparent.
rounding : bool, default: True
Whether the vector magnitude should be rounded when allocating barb
components. If True, the magnitude is rounded to the nearest multiple
of the half-barb increment. If False, the magnitude is simply truncated
to the next lowest multiple.
barb_increments : dict, optional
A dictionary of increments specifying values to associate with
different parts of the barb. Only those values one wishes to
override need to be included.
- 'half' - half barbs (Default is 5)
- 'full' - full barbs (Default is 10)
- 'flag' - flags (default is 50)
flip_barb : bool or array-like of bool, default: False
Whether the lines and flags should point opposite to normal.
Normal behavior is for the barbs and lines to point right (comes from wind
barbs having these features point towards low pressure in the Northern
Hemisphere).
A single value is applied to all barbs. Individual barbs can be flipped by
passing a bool array of the same size as *U* and *V*.
Returns
-------
barbs : `~matplotlib.quiver.Barbs`
Other Parameters
----------------
data : indexable object, optional
DATA_PARAMETER_PLACEHOLDER
**kwargs
The barbs can further be customized using `.PolyCollection` keyword
arguments:
%(PolyCollection:kwdoc)s
""" % _docstring.interpd.params
_docstring.interpd.update(barbs_doc=_barbs_doc)
class Barbs(mcollections.PolyCollection):
"""
Specialized PolyCollection for barbs.
The only API method is :meth:`set_UVC`, which can be used to
change the size, orientation, and color of the arrows. Locations
are changed using the :meth:`set_offsets` collection method.
Possibly this method will be useful in animations.
There is one internal function :meth:`_find_tails` which finds
exactly what should be put on the barb given the vector magnitude.
From there :meth:`_make_barbs` is used to find the vertices of the
polygon to represent the barb based on this information.
"""
# This may be an abuse of polygons here to render what is essentially maybe
# 1 triangle and a series of lines. It works fine as far as I can tell
# however.
@_docstring.interpd
def __init__(self, ax, *args,
pivot='tip', length=7, barbcolor=None, flagcolor=None,
sizes=None, fill_empty=False, barb_increments=None,
rounding=True, flip_barb=False, **kwargs):
"""
The constructor takes one required argument, an Axes
instance, followed by the args and kwargs described
by the following pyplot interface documentation:
%(barbs_doc)s
"""
self.sizes = sizes or dict()
self.fill_empty = fill_empty
self.barb_increments = barb_increments or dict()
self.rounding = rounding
self.flip = np.atleast_1d(flip_barb)
transform = kwargs.pop('transform', ax.transData)
self._pivot = pivot
self._length = length
# Flagcolor and barbcolor provide convenience parameters for
# setting the facecolor and edgecolor, respectively, of the barb
# polygon. We also work here to make the flag the same color as the
# rest of the barb by default
if None in (barbcolor, flagcolor):
kwargs['edgecolors'] = 'face'
if flagcolor:
kwargs['facecolors'] = flagcolor
elif barbcolor:
kwargs['facecolors'] = barbcolor
else:
# Set to facecolor passed in or default to black
kwargs.setdefault('facecolors', 'k')
else:
kwargs['edgecolors'] = barbcolor
kwargs['facecolors'] = flagcolor
# Explicitly set a line width if we're not given one, otherwise
# polygons are not outlined and we get no barbs
if 'linewidth' not in kwargs and 'lw' not in kwargs:
kwargs['linewidth'] = 1
# Parse out the data arrays from the various configurations supported
x, y, u, v, c = _parse_args(*args, caller_name='barbs')
self.x = x
self.y = y
xy = np.column_stack((x, y))
# Make a collection
barb_size = self._length ** 2 / 4 # Empirically determined
super().__init__(
[], (barb_size,), offsets=xy, offset_transform=transform, **kwargs)
self.set_transform(transforms.IdentityTransform())
self.set_UVC(u, v, c)
def _find_tails(self, mag, rounding=True, half=5, full=10, flag=50):
"""
Find how many of each of the tail pieces is necessary.
Parameters
----------
mag : `~numpy.ndarray`
Vector magnitudes; must be non-negative (and an actual ndarray).
rounding : bool, default: True
Whether to round or to truncate to the nearest half-barb.
half, full, flag : float, defaults: 5, 10, 50
Increments for a half-barb, a barb, and a flag.
Returns
-------
n_flags, n_barbs : int array
For each entry in *mag*, the number of flags and barbs.
half_flag : bool array
For each entry in *mag*, whether a half-barb is needed.
empty_flag : bool array
For each entry in *mag*, whether nothing is drawn.
"""
# If rounding, round to the nearest multiple of half, the smallest
# increment
if rounding:
mag = half * np.around(mag / half)
n_flags, mag = divmod(mag, flag)
n_barb, mag = divmod(mag, full)
half_flag = mag >= half
empty_flag = ~(half_flag | (n_flags > 0) | (n_barb > 0))
return n_flags.astype(int), n_barb.astype(int), half_flag, empty_flag
def _make_barbs(self, u, v, nflags, nbarbs, half_barb, empty_flag, length,
pivot, sizes, fill_empty, flip):
"""
Create the wind barbs.
Parameters
----------
u, v
Components of the vector in the x and y directions, respectively.
nflags, nbarbs, half_barb, empty_flag
Respectively, the number of flags, number of barbs, flag for
half a barb, and flag for empty barb, ostensibly obtained from
:meth:`_find_tails`.
length
The length of the barb staff in points.
pivot : {"tip", "middle"} or number
The point on the barb around which the entire barb should be
rotated. If a number, the start of the barb is shifted by that
many points from the origin.
sizes : dict
Coefficients specifying the ratio of a given feature to the length
of the barb. These features include: