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LSST Data Management Base Package
_hpxUtils.py
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1# This file is part of afw.
2#
3# Developed for the LSST Data Management System.
4# This product includes software developed by the LSST Project
5# (https://www.lsst.org).
6# See the COPYRIGHT file at the top-level directory of this distribution
7# for details of code ownership.
8#
9# This program is free software: you can redistribute it and/or modify
10# it under the terms of the GNU General Public License as published by
11# the Free Software Foundation, either version 3 of the License, or
12# (at your option) any later version.
13#
14# This program is distributed in the hope that it will be useful,
15# but WITHOUT ANY WARRANTY; without even the implied warranty of
16# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17# GNU General Public License for more details.
18#
19# You should have received a copy of the GNU General Public License
20# along with this program. If not, see <https://www.gnu.org/licenses/>.
21#
22# This code is partly based on AladinSrc.jar version 11.024.
23# AladinSrc.jar is licensed with GPLv3, see http://aladin.u-strasbg.fr/COPYING
24import numpy as np
25
26from lsst.daf.base import PropertySet
27
28from ._geom import makeSkyWcs
29
30
31def makeHpxWcs(hips_order, pixel, shift_order=9):
32 """
33 Make a SkyWcs object with HEALPix grid projection (HPX).
34
35 The SkyWcs generated by this function is suitable to be used with a
36 Hierarchical Progressive Survey (HiPS) FITS image as described in
37 https://www.ivoa.net/documents/HiPS/20170519/REC-HIPS-1.0-20170519.pdf
38
39 A HiPS image covers one HEALPix cell, with the HEALPix nside equal to
40 2**hips_order. Each cell is 'shift_order' orders deeper than the HEALPix
41 cell, with 2**shift_order x 2**shift_order sub-pixels on a side, which
42 defines the target resolution of the HiPS image. The IVOA recommends
43 shift_order=9, for 2**9=512 pixels on a side. See Notes below to
44 convert from hips_order to image resolution.
45
46 Parameters
47 ----------
48 hips_order : `int`
49 HiPS order, such that HEALPix nside=2**hips_order.
50 Must be a positive integer.
51 pixel : `int`
52 Pixel number in the nest ordering scheme.
53 shift_order : `int`, optional
54 Shift order for subpixels, such that there are 2**shift_order
55 sub-pixels on a side of the HiPS cell.
56 Must be a positive integer.
57
58 Returns
59 -------
60 wcs : `lsst.geom.SkyWcs`
61
62 Raises
63 ------
64 `ValueError`: Raise if hips_order is <=0, or if shift_order is <=0, or
65 if pixel number is out of range for the given hips_order
66 (0 <= pixel < 12*nside*nside).
67
68 Notes
69 -----
70 Table 5 from
71 https://www.ivoa.net/documents/HiPS/20170519/REC-HIPS-1.0-20170519.pdf
72 shows the relationship between hips_order, number of tiles (full
73 sky coverage), cell size, and sub-pixel size/image resolution (with
74 the default shift_order=9):
75
76 +------------+-----------------+--------------+------------------+
77 | hips_order | Number of Tiles | Cell Size | Image Resolution |
78 +============+=================+==============+==================+
79 | 0 | 12 | 58.63 deg | 6.871 arcmin |
80 | 1 | 48 | 29.32 deg | 3.435 arcmin |
81 | 2 | 192 | 14.66 deg | 1.718 arcmin |
82 | 3 | 768 | 7.329 deg | 51.53 arcsec |
83 | 4 | 3072 | 3.665 deg | 25.77 arcsec |
84 | 5 | 12288 | 1.832 deg | 12.88 arcsec |
85 | 6 | 49152 | 54.97 arcmin | 6.442 arcsec |
86 | 7 | 196608 | 27.48 arcmin | 3.221 arcsec |
87 | 8 | 786432 | 13.74 arcmin | 1.61 arcsec |
88 | 9 | 3145728 | 6.871 arcmin | 805.2mas |
89 | 10 | 12582912 | 3.435 arcmin | 402.6mas |
90 | 11 | 50331648 | 1.718 arcmin | 201.3mas |
91 | 12 | 201326592 | 51.53 arcsec | 100.6mas |
92 | 13 | 805306368 | 25.77 arcsec | 50.32mas |
93 +------------+-----------------+--------------+------------------+
94 """
95 if shift_order <= 0:
96 raise ValueError(f"shift_order {shift_order} must be positive.")
97 hips_tilepix = 2**shift_order
98
99 if hips_order <= 0:
100 raise ValueError(f"order {hips_order} must be positive.")
101 nside_cell = 2**hips_order
102
103 if pixel < 0 or pixel >= 12*nside_cell*nside_cell:
104 raise ValueError(f"pixel value {pixel} out of range.")
105
106 # The HEALPix grid projection (HPX) is defined in the FITS standard
107 # https://fits.gsfc.nasa.gov/standard40/fits_standard40aa-le.pdf
108 # from Calabretta & Roukema (2007)
109 # https://ui.adsabs.harvard.edu/abs/2007MNRAS.381..865C/abstract
110 # which defines the standard H = 4, K = 3 pixelization parameters
111 # encoded in PV2_1 = H, PV2_2 = K.
112 # The CRVAL1, CRVAL2 values should always be 0, 0 according to
113 # the FITS standard.
114 # The CD matrix is defined in wcslib HPXcvt.c.
115 # The Calabretta & Roukema (2007) paper and wcslib HPXcvt.c only
116 # define full-sky HPX projections. For single pixels we
117 # use the code from AladinSrc.jar Tile2HPX.java to compute
118 # CRPIX1, CRPIX2.
119
120 # The nside of the sub-pixels is the product of the tile nside
121 # and the number of sub-pixels on a side.
122 nside_pix = nside_cell*hips_tilepix
123 # All tiles are rotated 45 degrees.
124 cos45 = np.sqrt(2.0)/2.0
125 # This defines the pixel scale.
126 scale = 90.0/nside_pix/np.sqrt(2.0)
127 cos45_scale = cos45*scale
128 # The projected center of the pixel used for the HPX header is
129 # a non-trivial computation, and typically is outside of the
130 # tile pixel itself. Therefore, these values are not the same
131 # as the values computed from healpy.pix2ang().
132 cent_ra_proj, cent_dec_proj = _hpx_projected_center(hips_order, pixel)
133
134 md = PropertySet()
135 md['CD1_1'] = -cos45_scale
136 md['CD1_2'] = -cos45_scale
137 md['CD2_1'] = cos45_scale
138 md['CD2_2'] = -cos45_scale
139 md['CTYPE1'] = 'RA---HPX'
140 md['CTYPE2'] = 'DEC--HPX'
141 md['CRVAL1'] = 0.0
142 md['CRVAL2'] = 0.0
143 md['PV2_1'] = 4
144 md['PV2_2'] = 3
145 md['CRPIX1'] = ((hips_tilepix + 1)/2.0) - 0.5*(-cent_ra_proj/cos45_scale + cent_dec_proj/cos45_scale)
146 md['CRPIX2'] = ((hips_tilepix + 1)/2.0) - 0.5*(-cent_ra_proj/cos45_scale - cent_dec_proj/cos45_scale)
147
148 return makeSkyWcs(md)
149
150
151def _hpx_projected_center(hips_order, pixel):
152 """
153 Compute the projected center for use in HPX WCS headers.
154
155 The values of cent_ra_proj, cent_dec_proj computed by this function are
156 typically outside of the cell pixel itself, and are not the same as
157 the values computed from 'healpy.pix2ang()'.
158
159 Code is adapted from AladinSrc.jar version 11.024, Tile2HPX.java.
160 AladinSrc.jar is licensed with GPLv3, see
161 http://aladin.u-strasbg.fr/COPYING
162
163 Parameters
164 ----------
165 hips_order : `int`
166 HiPS order, such that HEALPix nside=2**hips_order.
167 pixel : `int`
168 Pixel number in the nest ordering scheme.
169
170 Returns
171 -------
172 cent_ra_proj, cent_dec_proj : `float`
173 Projected center ra/dec in degrees.
174
175 Raises
176 ------
177 `ValueError`: Raised if hips_order is <=0, or if pixel number is out of
178 range for the given order (0 < 12*nside*nside).
179 """
180 if hips_order <= 0:
181 raise ValueError(f"hips_order {hips_order} must be positive.")
182 nside_cell = 2**hips_order
183
184 if pixel < 0 or pixel >= 12*nside_cell*nside_cell:
185 raise ValueError(f"pixel value {pixel} out of range.")
186
187 twice_depth = np.left_shift(hips_order, 1)
188 xy_mask = np.left_shift(1, twice_depth) - 1
189 fc = _ZOrderCurve2DInt()
190
191 d0h = np.int32(np.right_shift(pixel, twice_depth))
192 _hash = fc.hash2ij(pixel & xy_mask)
193 i_in_d0h = fc.ij2i(_hash)
194 j_in_d0h = fc.ij2j(_hash)
195 # Compute coordinates from the center of the base pixel
196 # with x-axis = W-->E, y-axis = S-->N
197 l_in_d0h = i_in_d0h - j_in_d0h
198 h_in_d0h = i_in_d0h + j_in_d0h - (nside_cell - 1)
199 # Compute coordinates of the base pixel in the projection plane
200 d0h_by_4_quotient = np.right_shift(d0h, 2)
201 d0h_mod_4 = d0h - np.left_shift(d0h_by_4_quotient, 2)
202 h_d0h = 1 - d0h_by_4_quotient
203 l_d0h = np.left_shift(d0h_mod_4, 1)
204 if ((h_d0h == 0) and ((l_d0h == 6) or ((l_d0h == 4) and (l_in_d0h > 0)))):
205 # Equatorial region
206 l_d0h -= 8
207 elif (h_d0h != 0):
208 # Polar caps regions
209 l_d0h += 1
210 if (l_d0h > 3):
211 l_d0h -= 8
212 # Finalize
213 return (np.rad2deg((np.pi/4.)*(l_d0h + l_in_d0h/float(nside_cell))),
214 np.rad2deg((np.pi/4.)*(h_d0h + h_in_d0h/float(nside_cell))))
215
216
218 """
219 Z-Order 2D curve for 32-bit integer values.
220
221 Code is ported from AladinSrc.jar version 11.024,
222 ZOrderCurve2DImpls.java.
223 AladinSrc.jar is licensed with GPLv3, see
224 http://aladin.u-strasbg.fr/COPYING
225
226 From the original documentation:
227 "Z-Order Curve (ZOC) implementation in which the vertical coordinate
228 carry the most significant bit (VMSB). This implementation is based
229 on a lookup table (LOOKUP). We assume that each discritized
230 coordinates is coded on maximum 32 bits (INT)."
231 """
232 LUPT_TO_HASH = np.array([
233 0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015, 0x0040, 0x0041, 0x0044,
234 0x0045, 0x0050, 0x0051, 0x0054, 0x0055, 0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111,
235 0x0114, 0x0115, 0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155, 0x0400,
236 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415, 0x0440, 0x0441, 0x0444, 0x0445,
237 0x0450, 0x0451, 0x0454, 0x0455, 0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514,
238 0x0515, 0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555, 0x1000, 0x1001,
239 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015, 0x1040, 0x1041, 0x1044, 0x1045, 0x1050,
240 0x1051, 0x1054, 0x1055, 0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115,
241 0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155, 0x1400, 0x1401, 0x1404,
242 0x1405, 0x1410, 0x1411, 0x1414, 0x1415, 0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451,
243 0x1454, 0x1455, 0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515, 0x1540,
244 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555, 0x4000, 0x4001, 0x4004, 0x4005,
245 0x4010, 0x4011, 0x4014, 0x4015, 0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054,
246 0x4055, 0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115, 0x4140, 0x4141,
247 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155, 0x4400, 0x4401, 0x4404, 0x4405, 0x4410,
248 0x4411, 0x4414, 0x4415, 0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455,
249 0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515, 0x4540, 0x4541, 0x4544,
250 0x4545, 0x4550, 0x4551, 0x4554, 0x4555, 0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011,
251 0x5014, 0x5015, 0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055, 0x5100,
252 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115, 0x5140, 0x5141, 0x5144, 0x5145,
253 0x5150, 0x5151, 0x5154, 0x5155, 0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414,
254 0x5415, 0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455, 0x5500, 0x5501,
255 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515, 0x5540, 0x5541, 0x5544, 0x5545, 0x5550,
256 0x5551, 0x5554, 0x5555], dtype=np.int16)
257
258 LUPT_TO_IJ_INT = np.array([
259 0x000000000, 0x000000001, 0x100000000, 0x100000001, 0x000000002, 0x000000003,
260 0x100000002, 0x100000003, 0x200000000, 0x200000001, 0x300000000, 0x300000001,
261 0x200000002, 0x200000003, 0x300000002, 0x300000003, 0x000000004, 0x000000005,
262 0x100000004, 0x100000005, 0x000000006, 0x000000007, 0x100000006, 0x100000007,
263 0x200000004, 0x200000005, 0x300000004, 0x300000005, 0x200000006, 0x200000007,
264 0x300000006, 0x300000007, 0x400000000, 0x400000001, 0x500000000, 0x500000001,
265 0x400000002, 0x400000003, 0x500000002, 0x500000003, 0x600000000, 0x600000001,
266 0x700000000, 0x700000001, 0x600000002, 0x600000003, 0x700000002, 0x700000003,
267 0x400000004, 0x400000005, 0x500000004, 0x500000005, 0x400000006, 0x400000007,
268 0x500000006, 0x500000007, 0x600000004, 0x600000005, 0x700000004, 0x700000005,
269 0x600000006, 0x600000007, 0x700000006, 0x700000007, 0x000000008, 0x000000009,
270 0x100000008, 0x100000009, 0x00000000A, 0x00000000B, 0x10000000A, 0x10000000B,
271 0x200000008, 0x200000009, 0x300000008, 0x300000009, 0x20000000A, 0x20000000B,
272 0x30000000A, 0x30000000B, 0x00000000C, 0x00000000D, 0x10000000C, 0x10000000D,
273 0x00000000E, 0x00000000F, 0x10000000E, 0x10000000F, 0x20000000C, 0x20000000D,
274 0x30000000C, 0x30000000D, 0x20000000E, 0x20000000F, 0x30000000E, 0x30000000F,
275 0x400000008, 0x400000009, 0x500000008, 0x500000009, 0x40000000A, 0x40000000B,
276 0x50000000A, 0x50000000B, 0x600000008, 0x600000009, 0x700000008, 0x700000009,
277 0x60000000A, 0x60000000B, 0x70000000A, 0x70000000B, 0x40000000C, 0x40000000D,
278 0x50000000C, 0x50000000D, 0x40000000E, 0x40000000F, 0x50000000E, 0x50000000F,
279 0x60000000C, 0x60000000D, 0x70000000C, 0x70000000D, 0x60000000E, 0x60000000F,
280 0x70000000E, 0x70000000F, 0x800000000, 0x800000001, 0x900000000, 0x900000001,
281 0x800000002, 0x800000003, 0x900000002, 0x900000003, 0xA00000000, 0xA00000001,
282 0xB00000000, 0xB00000001, 0xA00000002, 0xA00000003, 0xB00000002, 0xB00000003,
283 0x800000004, 0x800000005, 0x900000004, 0x900000005, 0x800000006, 0x800000007,
284 0x900000006, 0x900000007, 0xA00000004, 0xA00000005, 0xB00000004, 0xB00000005,
285 0xA00000006, 0xA00000007, 0xB00000006, 0xB00000007, 0xC00000000, 0xC00000001,
286 0xD00000000, 0xD00000001, 0xC00000002, 0xC00000003, 0xD00000002, 0xD00000003,
287 0xE00000000, 0xE00000001, 0xF00000000, 0xF00000001, 0xE00000002, 0xE00000003,
288 0xF00000002, 0xF00000003, 0xC00000004, 0xC00000005, 0xD00000004, 0xD00000005,
289 0xC00000006, 0xC00000007, 0xD00000006, 0xD00000007, 0xE00000004, 0xE00000005,
290 0xF00000004, 0xF00000005, 0xE00000006, 0xE00000007, 0xF00000006, 0xF00000007,
291 0x800000008, 0x800000009, 0x900000008, 0x900000009, 0x80000000A, 0x80000000B,
292 0x90000000A, 0x90000000B, 0xA00000008, 0xA00000009, 0xB00000008, 0xB00000009,
293 0xA0000000A, 0xA0000000B, 0xB0000000A, 0xB0000000B, 0x80000000C, 0x80000000D,
294 0x90000000C, 0x90000000D, 0x80000000E, 0x80000000F, 0x90000000E, 0x90000000F,
295 0xA0000000C, 0xA0000000D, 0xB0000000C, 0xB0000000D, 0xA0000000E, 0xA0000000F,
296 0xB0000000E, 0xB0000000F, 0xC00000008, 0xC00000009, 0xD00000008, 0xD00000009,
297 0xC0000000A, 0xC0000000B, 0xD0000000A, 0xD0000000B, 0xE00000008, 0xE00000009,
298 0xF00000008, 0xF00000009, 0xE0000000A, 0xE0000000B, 0xF0000000A, 0xF0000000B,
299 0xC0000000C, 0xC0000000D, 0xD0000000C, 0xD0000000D, 0xC0000000E, 0xC0000000F,
300 0xD0000000E, 0xD0000000F, 0xE0000000C, 0xE0000000D, 0xF0000000C, 0xF0000000D,
301 0xE0000000E, 0xE0000000F, 0xF0000000E, 0xF0000000F], dtype=np.int64)
302
303 def __init__(self):
304 pass
305
306 def xy2hash(self, x, y):
307 """
308 Compute the hash value from x/y.
309
310 Parameters
311 ----------
312 x : `float`
313 x coordinate along the horizontal axis.
314 Must fit within the 32-bit integer range.
315 y : `float`
316 y coordinate along the vertical axis.
317 Must fit within the 32-bit integer range.
318
319 Returns
320 -------
321 hash : `numpy.int64`
322 The space-filling hash value associated with the
323 given coordinates.
324 """
325 return self.ij2hash(np.int32(x), np.int32(y))
326
327 def ij2hash(self, i, j):
328 """
329 Compute the hash value from discretized i, j.
330
331 Parameters
332 ----------
333 i : `int`
334 i discretized coordinate along the horizontal axis.
335 Must fit within the 32-bit integer range.
336 j : `int`
337 j discretized coordinate along the vertical axis.
338 Must fit within the 32-bit integer range.
339
340 Returns
341 -------
342 hash : `numpy.int64`
343 The space-filling hash value associated with the
344 given coordinates.
345 """
346 return (self.i02hashi02hash(np.int32(j)) << 1) | self.i02hashi02hash(np.int32(i))
347
348 def i02hash(self, i):
349 """
350 Special case of ij2hash in which the discretized coordinate along
351 the vertical axis equals zero.
352
353 Parameters
354 ----------
355 i : `int`
356 i discretized coordinate along the horizontal axis.
357 Must fit within the 32-bit integer range.
358
359 Returns
360 -------
361 hash : `numpy.int64`
362 The space-filling hash value associated with the
363 given coordinate.
364 """
365 val1 = np.int64(self.LUPT_TO_HASHLUPT_TO_HASH[np.uint32(i) >> np.uint32(24)] << np.int64(48))
366 val2 = np.int64(self.LUPT_TO_HASHLUPT_TO_HASH[(np.uint32(i) & 0x00FF0000) >> np.uint32(16)] << np.uint64(32))
367 val3 = np.int64(self.LUPT_TO_HASHLUPT_TO_HASH[(np.uint32(i) & 0x0000FF00) >> np.uint32(8)] << np.uint64(16))
368 val4 = np.int64(self.LUPT_TO_HASHLUPT_TO_HASH[np.uint32(i) & 0x000000FF])
369 return val1 | val2 | val3 | val4
370
371 def hash2ij(self, h):
372 """
373 Transforms the given space-filling hash value into a single value
374 from which the 2d coordinates can be extracted using ij2i and ij2j.
375
376 Parameters
377 ----------
378 h : `int`
379 Space-filling hash value
380
381 Returns
382 -------
383 ij : `np.int64`
384 Single value from which 2d coordinates can be extracted.
385 """
386 val1 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
387 np.int32((np.uint64(h)
388 & np.uint64(0xFF00000000000000)) >> np.uint64(56))] << np.int64(28)
389 val2 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
390 np.int32((np.uint64(h)
391 & np.uint64(0x00FF000000000000)) >> np.uint64(48))] << np.int64(24)
392 val3 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
393 np.int32((np.uint64(h)
394 & np.uint64(0x0000FF0000000000)) >> np.uint64(40))] << np.int64(20)
395 val4 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
396 np.int32((np.uint64(h)
397 & np.uint64(0x000000FF00000000)) >> np.uint64(32))] << np.int64(16)
398 val5 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
399 np.int32((np.uint64(h)
400 & np.uint64(0x00000000FF000000)) >> np.uint64(24))] << np.int64(12)
401 val6 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
402 np.int32((np.uint64(h)
403 & np.uint64(0x0000000000FF0000)) >> np.uint64(16))] << np.int64(8)
404 val7 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
405 np.int32((np.uint64(h)
406 & np.uint64(0x000000000000FF00)) >> np.uint64(8))] << np.int64(4)
407 val8 = self.LUPT_TO_IJ_INTLUPT_TO_IJ_INT[
408 np.int32((np.uint64(h)
409 & np.uint64(0x00000000000000FF)))]
410 return val1 | val2 | val3 | val4 | val5 | val6 | val7 | val8
411
412 def hash2i0(self, _hash):
413 """
414 Special case of hash2ij in which the discretized coordinate along
415 the vertical axis is zero.
416
417 Parameters
418 ----------
419 _hash : `int`
420 Space-filling hash value.
421
422 Returns
423 -------
424 ij : `np.int64`
425 Single value from which 2d coordinates can be extracted.
426 """
427 assert((0xFFFFFFFF33333333 & np.int64(_hash)) == 0)
428 return self.hash2ijhash2ij(_hash)
429
430 def ij2i(self, ij):
431 """
432 Extract the discretized horizontal coordinate from hash2ij.
433
434 Parameters
435 ----------
436 ij : `int`
437 The ij result of hash2ij.
438
439 Returns
440 -------
441 i : `np.int32`
442 Discretized horizontal coordinate stored in ij.
443 """
444 return np.int32(ij)
445
446 def ij2j(self, ij):
447 """
448 Extract the discretized vertical coordinate from hash2ij.
449
450 Parameters
451 ----------
452 ij : `int`
453 The ij result of hash2ij.
454
455 Returns
456 -------
457 j : `np.int32`
458 Discretized vertical coordinate stored in ij.
459 """
460 return np.int32(np.uint64(ij) >> np.uint64(32))
Class for storing generic metadata.
Definition: PropertySet.h:66
def makeHpxWcs(hips_order, pixel, shift_order=9)
Definition: _hpxUtils.py:31
std::shared_ptr< SkyWcs > makeSkyWcs(daf::base::PropertySet &metadata, bool strip=false)
Construct a SkyWcs from FITS keywords.
Definition: SkyWcs.cc:521