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Commit9602112

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1 parenta2ddfc0 commit9602112

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  • lib/matplotlib/projections

1 file changed

+47
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‎lib/matplotlib/projections/geo.py

Lines changed: 47 additions & 37 deletions
Original file line numberDiff line numberDiff line change
@@ -1,3 +1,4 @@
1+
importmath
12
importnumpyasnp
23

34
frommatplotlibimport_api,rcParams
@@ -52,8 +53,8 @@ def cla(self):
5253

5354
self.grid(rcParams['axes.grid'])
5455

55-
Axes.set_xlim(self,-np.pi,np.pi)
56-
Axes.set_ylim(self,-np.pi/2.0,np.pi/2.0)
56+
Axes.set_xlim(self,-math.pi,math.pi)
57+
Axes.set_ylim(self,-math.pi/2.0,math.pi/2.0)
5758

5859
def_set_lim_and_transforms(self):
5960
# A (possibly non-linear) projection on the (already scaled) data
@@ -88,7 +89,7 @@ def _set_lim_and_transforms(self):
8889
Affine2D().translate(0,-4)
8990

9091
# This is the transform for latitude ticks.
91-
yaxis_stretch=Affine2D().scale(np.pi*2,1).translate(-np.pi,0)
92+
yaxis_stretch=Affine2D().scale(math.pi*2,1).translate(-math.pi,0)
9293
yaxis_space=Affine2D().scale(1,1.1)
9394
self._yaxis_transform= \
9495
yaxis_stretch+ \
@@ -108,8 +109,8 @@ def _set_lim_and_transforms(self):
108109

109110
def_get_affine_transform(self):
110111
transform=self._get_core_transform(1)
111-
xscale,_=transform.transform((np.pi,0))
112-
_,yscale=transform.transform((0,np.pi/2))
112+
xscale,_=transform.transform((math.pi,0))
113+
_,yscale=transform.transform((0,math.pi/2))
113114
returnAffine2D() \
114115
.scale(0.5/xscale,0.5/yscale) \
115116
.translate(0.5,0.5)
@@ -261,14 +262,17 @@ def transform_non_affine(self, ll):
261262
longitude,latitude=ll.T
262263

263264
# Pre-compute some values
264-
half_long=longitude/2.0
265-
cos_latitude=np.cos(latitude)
265+
half_long=longitude/2
266+
cos_half=np.cos(half_long)
267+
sin_half=np.cos(half_long)
268+
cos_latitude=cos_half*cos_half-sin_half*sin_half
266269

267-
alpha=np.arccos(cos_latitude*np.cos(half_long))
268-
sinc_alpha=np.sinc(alpha/np.pi)# np.sinc is sin(pi*x)/(pi*x).
270+
alpha=np.arccos(cos_latitude*cos_half)
271+
# np.sinc is sin(pi*x)/(pi*x).
272+
sinc_alpha=np.sinc(alpha/math.pi)
269273

270-
x= (cos_latitude*np.sin(half_long))/sinc_alpha
271-
y=np.sin(latitude)/sinc_alpha
274+
x= (cos_latitude*sin_half)/sinc_alpha
275+
y=2.0*sin_half*cos_half/sinc_alpha#sin(lat) / sinc_alpha
272276
returnnp.column_stack([x,y])
273277

274278
definverted(self):
@@ -287,7 +291,7 @@ def inverted(self):
287291
returnAitoffAxes.AitoffTransform(self._resolution)
288292

289293
def__init__(self,*args,**kwargs):
290-
self._longitude_cap=np.pi/2.0
294+
self._longitude_cap=math.pi/2
291295
super().__init__(*args,**kwargs)
292296
self.set_aspect(0.5,adjustable='box',anchor='C')
293297
self.cla()
@@ -305,12 +309,14 @@ class HammerTransform(_GeoTransform):
305309
deftransform_non_affine(self,ll):
306310
# docstring inherited
307311
longitude,latitude=ll.T
308-
half_long=longitude/2.0
309-
cos_latitude=np.cos(latitude)
310-
sqrt2=np.sqrt(2.0)
311-
alpha=np.sqrt(1.0+cos_latitude*np.cos(half_long))
312-
x= (2.0*sqrt2)* (cos_latitude*np.sin(half_long))/alpha
313-
y= (sqrt2*np.sin(latitude))/alpha
312+
half_long=longitude/2
313+
cos_half=np.cos(half_long)
314+
sin_half=np.cos(half_long)
315+
cos_latitude=cos_half*cos_half-sin_half*sin_half
316+
sqrt8=8** (1/2)
317+
alpha=np.sqrt(1.0+cos_latitude*cos_half)
318+
x= (sqrt8*cos_latitude*sin_half)/alpha
319+
y= (sqrt8*cos_half*sin_half)/alpha# sin(lat)
314320
returnnp.column_stack([x,y])
315321

316322
definverted(self):
@@ -324,15 +330,15 @@ def transform_non_affine(self, xy):
324330
x,y=xy.T
325331
z=np.sqrt(1- (x/4)**2- (y/2)**2)
326332
longitude=2*np.arctan((z*x)/ (2* (2*z**2-1)))
327-
latitude=np.arcsin(y*z)
333+
latitude=np.arcsin(y*z)
328334
returnnp.column_stack([longitude,latitude])
329335

330336
definverted(self):
331337
# docstring inherited
332338
returnHammerAxes.HammerTransform(self._resolution)
333339

334340
def__init__(self,*args,**kwargs):
335-
self._longitude_cap=np.pi/2.0
341+
self._longitude_cap=math.pi/2
336342
super().__init__(*args,**kwargs)
337343
self.set_aspect(0.5,adjustable='box',anchor='C')
338344
self.cla()
@@ -351,18 +357,18 @@ def transform_non_affine(self, ll):
351357
# docstring inherited
352358
defd(theta):
353359
delta= (-(theta+np.sin(theta)-pi_sin_l)
354-
/ (1+np.cos(theta)))
360+
/ (1.0+np.cos(theta)))
355361
returndelta,np.abs(delta)>0.001
356362

357363
longitude,latitude=ll.T
358-
359-
clat=np.pi/2-np.abs(latitude)
364+
pi_half=math.pi/2
365+
clat=pi_half-np.abs(latitude)
360366
ihigh=clat<0.087# within 5 degrees of the poles
361367
ilow=~ihigh
362368
aux=np.empty(latitude.shape,dtype=float)
363369

364370
ifilow.any():# Newton-Raphson iteration
365-
pi_sin_l=np.pi*np.sin(latitude[ilow])
371+
pi_sin_l=math.pi*np.sin(latitude[ilow])
366372
theta=2.0*latitude[ilow]
367373
delta,large_delta=d(theta)
368374
whilenp.any(large_delta):
@@ -372,12 +378,13 @@ def d(theta):
372378

373379
ifihigh.any():# Taylor series-based approx. solution
374380
e=clat[ihigh]
375-
d=0.5* (3*np.pi*e**2)** (1.0/3)
376-
aux[ihigh]= (np.pi/2-d)*np.sign(latitude[ihigh])
381+
d=np.cbrt(3.0*math.pi*e**2)/2
382+
aux[ihigh]= (pi_half-d)*np.sign(latitude[ihigh])
377383

378384
xy=np.empty(ll.shape,dtype=float)
379-
xy[:,0]= (2.0*np.sqrt(2.0)/np.pi)*longitude*np.cos(aux)
380-
xy[:,1]=np.sqrt(2.0)*np.sin(aux)
385+
sqrt2=2** (1/2)
386+
xy[:,0]= (sqrt2/pi_half)*longitude*np.cos(aux)
387+
xy[:,1]=sqrt2*np.sin(aux)
381388

382389
returnxy
383390

@@ -392,17 +399,18 @@ def transform_non_affine(self, xy):
392399
x,y=xy.T
393400
# from Equations (7, 8) of
394401
# https://mathworld.wolfram.com/MollweideProjection.html
395-
theta=np.arcsin(y/np.sqrt(2))
396-
longitude= (np.pi/ (2*np.sqrt(2)))*x/np.cos(theta)
397-
latitude=np.arcsin((2*theta+np.sin(2*theta))/np.pi)
402+
sqrt2=2** (1/2)
403+
theta=np.arcsin(y/sqrt2)
404+
longitude= (math.pi/ (2.0*sqrt2))*x/np.cos(theta)
405+
latitude=np.arcsin((2.0*theta+np.sin(2.0*theta))/math.pi)
398406
returnnp.column_stack([longitude,latitude])
399407

400408
definverted(self):
401409
# docstring inherited
402410
returnMollweideAxes.MollweideTransform(self._resolution)
403411

404412
def__init__(self,*args,**kwargs):
405-
self._longitude_cap=np.pi/2.0
413+
self._longitude_cap=math.pi/2.0
406414
super().__init__(*args,**kwargs)
407415
self.set_aspect(0.5,adjustable='box',anchor='C')
408416
self.cla()
@@ -434,15 +442,17 @@ def transform_non_affine(self, ll):
434442
clat=self._center_latitude
435443
cos_lat=np.cos(latitude)
436444
sin_lat=np.sin(latitude)
445+
cos_clat=np.cos(clat)
446+
sin_clat=np.sin(clat)
437447
diff_long=longitude-clong
438448
cos_diff_long=np.cos(diff_long)
439449

440450
inner_k=np.maximum(# Prevent divide-by-zero problems
441-
1+np.sin(clat)*sin_lat+np.cos(clat)*cos_lat*cos_diff_long,
451+
1.0+sin_clat*sin_lat+cos_clat*cos_lat*cos_diff_long,
442452
1e-15)
443-
k=np.sqrt(2/inner_k)
453+
k=np.sqrt(2.0/inner_k)
444454
x=k*cos_lat*np.sin(diff_long)
445-
y=k* (np.cos(clat)*sin_lat-np.sin(clat)*cos_lat*cos_diff_long)
455+
y=k* (cos_clat*sin_lat-sin_clat*cos_lat*cos_diff_long)
446456

447457
returnnp.column_stack([x,y])
448458

@@ -466,7 +476,7 @@ def transform_non_affine(self, xy):
466476
clong=self._center_longitude
467477
clat=self._center_latitude
468478
p=np.maximum(np.hypot(x,y),1e-9)
469-
c=2*np.arcsin(0.5*p)
479+
c=2.0*np.arcsin(0.5*p)
470480
sin_c=np.sin(c)
471481
cos_c=np.cos(c)
472482

@@ -485,7 +495,7 @@ def inverted(self):
485495
self._resolution)
486496

487497
def__init__(self,*args,center_longitude=0,center_latitude=0,**kwargs):
488-
self._longitude_cap=np.pi/2
498+
self._longitude_cap=math.pi/2
489499
self._center_longitude=center_longitude
490500
self._center_latitude=center_latitude
491501
super().__init__(*args,**kwargs)

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