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创建一个新的坐标类（针对人马座流）#
本文档详细介绍了如何划分子类并定义自定义球面坐标框架，如中所述 定义新框架 和的文档字符串 BaseCoordinateFrame 。在这个例子中，我们将定义一个由人马座矮星系的轨道平面定义的坐标系(以下简称SGR；正如Majewski等人所定义的。2003年)。SGR坐标系通常指的是两个角坐标， \(\Lambda,B\) 。
为此，我们需要定义 BaseCoordinateFrame 它知道每个支持的表示中坐标系角度的名称和单位。在这种情况下，我们支持 SphericalRepresentation 有“Lambda”和“Beta”。然后我们要定义从这个坐标系到其他内置系统的转换。这里我们将使用银河系的坐标，用 Galactic 班级。
也见#
这个 gala package ，它为恒星流坐标系定义了许多天文坐标系。
Majewski等人。2003年，“人马座矮星系的两微米全天空观测图。一、 人马座核心和潮汐臂的形态“，https://arxiv.org/abs/astro-ph/0304198
Law&Majewski 2010，“人马座矮星系：三轴星系晕演化模型”，https://arxiv.org/abs/1003.1132
大卫·劳的Sgr信息页面https://www.stsci.edu/~dlaw/Sgr/
By: Adrian Price-Whelan, Erik Tollerud
许可证：BSD
制作 print 在所有版本的Python中都一样，设置numpy、matplotlib，并使用一组更好的绘图参数：
import matplotlib.pyplot as plt
import numpy as np
from astropy.visualization import astropy_mpl_style
plt.style.use(astropy_mpl_style)
导入坐标所需的包
import astropy.coordinates as coord
import astropy.units as u
from astropy.coordinates import frame_transform_graph
from astropy.coordinates.matrix_utilities import matrix_transpose, rotation_matrix
我们称之为创建新类的第一步 Sagittarius 并使其成为 BaseCoordinateFrame ：
class Sagittarius(coord.BaseCoordinateFrame):
"""
A Heliocentric spherical coordinate system defined by the orbit
of the Sagittarius dwarf galaxy, as described in
https://ui.adsabs.harvard.edu/abs/2003ApJ...599.1082M
and further explained in
https://www.stsci.edu/~dlaw/Sgr/.
Parameters
----------
representation : `~astropy.coordinates.BaseRepresentation` or None
A representation object or None to have no data (or use the other keywords)
Lambda : `~astropy.coordinates.Angle`, optional, must be keyword
The longitude-like angle corresponding to Sagittarius' orbit.
Beta : `~astropy.coordinates.Angle`, optional, must be keyword
The latitude-like angle corresponding to Sagittarius' orbit.
distance : `~astropy.units.Quantity`, optional, must be keyword
The Distance for this object along the line-of-sight.
pm_Lambda_cosBeta : `~astropy.units.Quantity`, optional, must be keyword
The proper motion along the stream in ``Lambda`` (including the
``cos(Beta)`` factor) for this object (``pm_Beta`` must also be given).
pm_Beta : `~astropy.units.Quantity`, optional, must be keyword
The proper motion in Declination for this object (``pm_ra_cosdec`` must
also be given).
radial_velocity : `~astropy.units.Quantity`, optional, keyword-only
The radial velocity of this object.
"""
default_representation = coord.SphericalRepresentation
default_differential = coord.SphericalCosLatDifferential
frame_specific_representation_info = {
coord.SphericalRepresentation: [
coord.RepresentationMapping("lon", "Lambda"),
coord.RepresentationMapping("lat", "Beta"),
coord.RepresentationMapping("distance", "distance"),
]
}
逐行分解，我们将类定义为 BaseCoordinateFrame . 然后我们包括一个描述性docstring。最后几行是类级别的属性，这些属性指定数据的默认表示形式、速度信息的默认差分，以及从表示对象使用的属性名称到将由 Sagittarius 框架。在本例中，我们重写了球形表示中的名称，但对其他表示（如笛卡尔表示或圆柱形表示）不做任何操作。
下一步我们要定义从这个坐标系到其他内置坐标系的转换；我们将使用银河系坐标系。我们可以通过定义返回转换矩阵的函数，或者简单地定义一个接受坐标并在新系统中返回新坐标的函数。因为到人马座坐标系的转换只是银河系坐标系的一个球面旋转，所以我们定义一个函数来返回这个矩阵。我们将从使用预先确定的欧拉角和 rotation_matrix 帮助程序函数：
SGR_PHI = (180 + 3.75) * u.degree # Euler angles (from Law & Majewski 2010)
SGR_THETA = (90 - 13.46) * u.degree
SGR_PSI = (180 + 14.111534) * u.degree
# Generate the rotation matrix using the x-convention (see Goldstein)
SGR_MATRIX = (
np.diag([1.0, 1.0, -1.0])
@ rotation_matrix(SGR_PSI, "z")
@ rotation_matrix(SGR_THETA, "x")
@ rotation_matrix(SGR_PHI, "z")
)
由于我们已经在上面构造了变换（旋转）矩阵，而旋转矩阵的逆矩阵只是它的转置，所以所需的变换函数非常简单：
@frame_transform_graph.transform(
coord.StaticMatrixTransform, coord.Galactic, Sagittarius
)
def galactic_to_sgr():
"""Compute the Galactic spherical to heliocentric Sgr transformation matrix."""
return SGR_MATRIX
装饰工 @frame_transform_graph.transform(coord.StaticMatrixTransform, coord.Galactic, Sagittarius) 在上注册此函数 frame_transform_graph 作为坐标变换。在函数内部，我们只返回先前定义的旋转矩阵。
然后，我们使用旋转矩阵的转置来注册逆变换（这比求逆更快）：
@frame_transform_graph.transform(
coord.StaticMatrixTransform, Sagittarius, coord.Galactic
)
def sgr_to_galactic():
"""Compute the heliocentric Sgr to spherical Galactic transformation matrix."""
return matrix_transpose(SGR_MATRIX)
现在我们已经在 Sagittarius 和 Galactic ，我们可以在 any 坐标系和 Sagittarius （只要另一个系统有转换的路径 Galactic ). 例如，将ICRS坐标转换为 Sagittarius ，我们会：
icrs = coord.SkyCoord(280.161732 * u.degree, 11.91934 * u.degree, frame="icrs")
sgr = icrs.transform_to(Sagittarius)
print(sgr)
<SkyCoord (Sagittarius): (Lambda, Beta) in deg
(346.81830652, -39.28360407)>
或者，从 Sagittarius 帧到ICRS坐标（在本例中，是沿着 Sagittarius x-y平面）：
sgr = coord.SkyCoord(
Lambda=np.linspace(0, 2 * np.pi, 128) * u.radian,
Beta=np.zeros(128) * u.radian,
frame="sagittarius",
)
icrs = sgr.transform_to(coord.ICRS)
print(icrs)
<SkyCoord (ICRS): (ra, dec) in deg
[(284.03876751, -29.00408353), (287.24685769, -29.44848352),
(290.48068369, -29.81535572), (293.7357366 , -30.1029631 ),
(297.00711066, -30.30991693), (300.28958688, -30.43520293),
(303.57772919, -30.47820084), (306.86598944, -30.43869669),
(310.14881715, -30.31688708), (313.42076929, -30.11337526),
(316.67661568, -29.82915917), (319.91143548, -29.46561215),
(323.12070147, -29.02445708), (326.30034928, -28.50773532),
(329.44683007, -27.9177717 ), (332.55714589, -27.257137 ),
(335.62886847, -26.52860943), (338.66014233, -25.73513624),
(341.64967439, -24.87979679), (344.59671212, -23.96576781),
(347.50101283, -22.99629167), (350.36280652, -21.97464811),
(353.18275454, -20.90412969), (355.96190618, -19.78802107),
(358.70165491, -18.62958199), ( 1.40369557, -17.43203397),
( 4.06998374, -16.19855028), ( 6.70269788, -14.93224899),
( 9.30420479, -13.63618882), ( 11.87702861, -12.31336727),
( 14.42382347, -10.96672102), ( 16.94734952, -9.59912794),
( 19.45045241, -8.21341071), ( 21.93604568, -6.81234162),
( 24.40709589, -5.39864845), ( 26.86661004, -3.97502106),
( 29.31762493, -2.54411871), ( 31.76319801, -1.10857781),
( 34.20639942, 0.32898001), ( 36.65030466, 1.76593955),
( 39.09798768, 3.19968374), ( 41.55251374, 4.6275852 ),
( 44.01693189, 6.04699804), ( 46.49426651, 7.45524993),
( 48.98750752, 8.84963453), ( 51.4995989 , 10.22740448),
( 54.03342512, 11.58576509), ( 56.59179508, 12.92186896),
( 59.17742314, 14.23281165), ( 61.79290712, 15.51562883),
( 64.44070278, 16.76729487), ( 67.12309478, 17.98472356),
( 69.84216409, 19.16477088), ( 72.59975183, 20.30424045),
( 75.39742013, 21.3998918 ), ( 78.23641033, 22.44845192),
( 81.11759966, 23.44663022), ( 84.04145735, 24.39113719),
( 87.00800203, 25.27870692), ( 90.01676196, 26.10612335),
( 93.06674057, 26.87025019), ( 96.15638947, 27.56806406),
( 99.28359159, 28.19669038), (102.44565666, 28.75344107),
(105.63933131, 29.23585315), (108.86082534, 29.64172698),
(112.105855 , 29.96916281), (115.36970341, 30.21659414),
(118.64729687, 30.38281659), (121.93329519, 30.46701088),
(125.22219273, 30.46875885), (128.50842634, 30.38805179),
(131.78648572, 30.22529063), (135.05102157, 29.98127794),
(138.29694697, 29.6572022 ), (141.51952827, 29.2546151 ),
(144.71446203, 28.77540295), (147.87793614, 28.22175338),
(151.00667382, 27.59611901), (154.09796066, 26.90117914),
(157.14965528, 26.13980125), (160.16018547, 25.31500315),
(163.12853176, 24.42991703), (166.05420084, 23.48775622),
(168.93719133, 22.49178507), (171.77795423, 21.44529257),
(174.57735037, 20.35156967), (177.33660656, 19.21389046),
(180.05727218, 18.03549704), (182.74117737, 16.81958784),
(185.39039367, 15.56930924), (188.00719783, 14.28774998),
(190.59403895, 12.97793826), (193.15350938, 11.64284103),
(195.68831902, 10.28536518), (198.20127316, 8.90836046),
(200.69525342, 7.51462369), (203.17320154, 6.10690412),
(205.63810576, 4.6879097 ), (208.09298919, 3.26031403),
(210.54090002, 1.82676397), (212.984903 , 0.38988751),
(215.42807182, -1.04769799), (217.87348209, -2.48337744),
(220.32420429, -3.91452965), (222.7832966 , -5.338519 ),
(225.25379684, -6.75268736), (227.73871349, -8.15434631),
(230.24101506, -9.54076983), (232.76361762, -10.90918763),
(235.30937003, -12.25677927), (237.88103647, -13.58066929),
(240.48127601, -14.87792359), (243.11261883, -16.14554723),
(245.777439 , -17.38048408), (248.47792364, -18.57961852),
(251.2160385 , -19.7397795 ), (253.9934903 , -20.85774736),
(256.81168612, -21.93026371), (259.67169071, -22.95404466),
(262.57418275, -23.92579758), (265.51941137, -24.84224172),
(268.50715471, -25.70013256), (271.53668252, -26.49628998),
(274.6067251 , -27.22762983), (277.71545113, -27.89119849),
(280.86045662, -28.48420985), (284.03876751, -29.00408353)]>
例如，我们现在将在两个坐标系中绘制点：
fig, axes = plt.subplots(2, 1, figsize=(8, 10), subplot_kw={"projection": "aitoff"})
axes[0].set_title("Sagittarius")
axes[0].plot(
sgr.Lambda.wrap_at(180 * u.deg).radian,
sgr.Beta.radian,
linestyle="none",
marker=".",
)
axes[1].set_title("ICRS")
axes[1].plot(
icrs.ra.wrap_at(180 * u.deg).radian, icrs.dec.radian, linestyle="none", marker="."
)
plt.show()
这个特殊的变换只是一个球面旋转，这是没有向量偏移的仿射变换的一个特例。因此，速度分量的转换也得到了本机支持：
sgr = coord.SkyCoord(
Lambda=np.linspace(0, 2 * np.pi, 128) * u.radian,
Beta=np.zeros(128) * u.radian,
pm_Lambda_cosBeta=np.random.uniform(-5, 5, 128) * u.mas / u.yr,
pm_Beta=np.zeros(128) * u.mas / u.yr,
frame="sagittarius",
)
icrs = sgr.transform_to(coord.ICRS)
print(icrs)
fig, axes = plt.subplots(3, 1, figsize=(8, 10), sharex=True)
axes[0].set_title("Sagittarius")
axes[0].plot(
sgr.Lambda.degree, sgr.pm_Lambda_cosBeta.value, linestyle="none", marker="."
)
axes[0].set_xlabel(r"$\Lambda$ [deg]")
axes[0].set_ylabel(
rf"$\mu_\Lambda \, \cos B$ [{sgr.pm_Lambda_cosBeta.unit.to_string('latex_inline')}]"
)
axes[1].set_title("ICRS")
axes[1].plot(icrs.ra.degree, icrs.pm_ra_cosdec.value, linestyle="none", marker=".")
axes[1].set_ylabel(
rf"$\mu_\alpha \, \cos\delta$ [{icrs.pm_ra_cosdec.unit.to_string('latex_inline')}]"
)
axes[2].set_title("ICRS")
axes[2].plot(icrs.ra.degree, icrs.pm_dec.value, linestyle="none", marker=".")
axes[2].set_xlabel("RA [deg]")
axes[2].set_ylabel(rf"$\mu_\delta$ [{icrs.pm_dec.unit.to_string('latex_inline')}]")
plt.show()
<SkyCoord (ICRS): (ra, dec) in deg
[(284.03876751, -29.00408353), (287.24685769, -29.44848352),
(290.48068369, -29.81535572), (293.7357366 , -30.1029631 ),
(297.00711066, -30.30991693), (300.28958688, -30.43520293),
(303.57772919, -30.47820084), (306.86598944, -30.43869669),
(310.14881715, -30.31688708), (313.42076929, -30.11337526),
(316.67661568, -29.82915917), (319.91143548, -29.46561215),
(323.12070147, -29.02445708), (326.30034928, -28.50773532),
(329.44683007, -27.9177717 ), (332.55714589, -27.257137 ),
(335.62886847, -26.52860943), (338.66014233, -25.73513624),
(341.64967439, -24.87979679), (344.59671212, -23.96576781),
(347.50101283, -22.99629167), (350.36280652, -21.97464811),
(353.18275454, -20.90412969), (355.96190618, -19.78802107),
(358.70165491, -18.62958199), ( 1.40369557, -17.43203397),
( 4.06998374, -16.19855028), ( 6.70269788, -14.93224899),
( 9.30420479, -13.63618882), ( 11.87702861, -12.31336727),
( 14.42382347, -10.96672102), ( 16.94734952, -9.59912794),
( 19.45045241, -8.21341071), ( 21.93604568, -6.81234162),
( 24.40709589, -5.39864845), ( 26.86661004, -3.97502106),
( 29.31762493, -2.54411871), ( 31.76319801, -1.10857781),
( 34.20639942, 0.32898001), ( 36.65030466, 1.76593955),
( 39.09798768, 3.19968374), ( 41.55251374, 4.6275852 ),
( 44.01693189, 6.04699804), ( 46.49426651, 7.45524993),
( 48.98750752, 8.84963453), ( 51.4995989 , 10.22740448),
( 54.03342512, 11.58576509), ( 56.59179508, 12.92186896),
( 59.17742314, 14.23281165), ( 61.79290712, 15.51562883),
( 64.44070278, 16.76729487), ( 67.12309478, 17.98472356),
( 69.84216409, 19.16477088), ( 72.59975183, 20.30424045),
( 75.39742013, 21.3998918 ), ( 78.23641033, 22.44845192),
( 81.11759966, 23.44663022), ( 84.04145735, 24.39113719),
( 87.00800203, 25.27870692), ( 90.01676196, 26.10612335),
( 93.06674057, 26.87025019), ( 96.15638947, 27.56806406),
( 99.28359159, 28.19669038), (102.44565666, 28.75344107),
(105.63933131, 29.23585315), (108.86082534, 29.64172698),
(112.105855 , 29.96916281), (115.36970341, 30.21659414),
(118.64729687, 30.38281659), (121.93329519, 30.46701088),
(125.22219273, 30.46875885), (128.50842634, 30.38805179),
(131.78648572, 30.22529063), (135.05102157, 29.98127794),
(138.29694697, 29.6572022 ), (141.51952827, 29.2546151 ),
(144.71446203, 28.77540295), (147.87793614, 28.22175338),
(151.00667382, 27.59611901), (154.09796066, 26.90117914),
(157.14965528, 26.13980125), (160.16018547, 25.31500315),
(163.12853176, 24.42991703), (166.05420084, 23.48775622),
(168.93719133, 22.49178507), (171.77795423, 21.44529257),
(174.57735037, 20.35156967), (177.33660656, 19.21389046),
(180.05727218, 18.03549704), (182.74117737, 16.81958784),
(185.39039367, 15.56930924), (188.00719783, 14.28774998),
(190.59403895, 12.97793826), (193.15350938, 11.64284103),
(195.68831902, 10.28536518), (198.20127316, 8.90836046),
(200.69525342, 7.51462369), (203.17320154, 6.10690412),
(205.63810576, 4.6879097 ), (208.09298919, 3.26031403),
(210.54090002, 1.82676397), (212.984903 , 0.38988751),
(215.42807182, -1.04769799), (217.87348209, -2.48337744),
(220.32420429, -3.91452965), (222.7832966 , -5.338519 ),
(225.25379684, -6.75268736), (227.73871349, -8.15434631),
(230.24101506, -9.54076983), (232.76361762, -10.90918763),
(235.30937003, -12.25677927), (237.88103647, -13.58066929),
(240.48127601, -14.87792359), (243.11261883, -16.14554723),
(245.777439 , -17.38048408), (248.47792364, -18.57961852),
(251.2160385 , -19.7397795 ), (253.9934903 , -20.85774736),
(256.81168612, -21.93026371), (259.67169071, -22.95404466),
(262.57418275, -23.92579758), (265.51941137, -24.84224172),
(268.50715471, -25.70013256), (271.53668252, -26.49628998),
(274.6067251 , -27.22762983), (277.71545113, -27.89119849),
(280.86045662, -28.48420985), (284.03876751, -29.00408353)]
(pm_ra_cosdec, pm_dec) in mas / yr
[(-3.84553112, 6.64267318e-01), (-1.90437617, 2.75568611e-01),
(-1.57629479, 1.83345258e-01), ( 1.27433938, -1.11683956e-01),
(-4.37130997, 2.56826700e-01), ( 3.38024554, -1.00464794e-01),
(-2.50681782, 1.54613720e-03), ( 0.03757461, 1.07046752e-03),
( 4.55986067, 2.62307298e-01), (-1.85184122, -1.60037387e-01),
(-3.66320127, -4.21651305e-01), ( 4.39046434, 6.30061612e-01),
(-2.90742531, -4.98791706e-01), ( 2.09439131, 4.17179899e-01),
(-2.22920076, -5.04541373e-01), (-3.01718347, -7.63114332e-01),
(-0.30457643, -8.49444465e-02), ( 4.6530665 , 1.41537974e+00),
(-3.12968507, -1.02880950e+00), (-0.49190279, -1.73378919e-01),
(-3.53905294, -1.32835837e+00), ( 2.49991254, 9.93218845e-01),
(-0.48728238, -2.03824234e-01), (-0.91497502, -4.00988149e-01),
( 0.01429669, 6.53559925e-03), (-1.00449793, -4.77048180e-01),
(-1.21720634, -5.98282918e-01), ( 4.10522314, 2.08105185e+00),
( 2.76066111, 1.43856326e+00), (-4.22542615, -2.25631198e+00),
( 3.95183221, 2.15599499e+00), (-4.15449863, -2.30914235e+00),
( 1.27191276, 7.18256808e-01), (-3.42995761, -1.96266565e+00),
( 3.21111326, 1.85704867e+00), (-3.52944583, -2.05770396e+00),
( 0.38116508, 2.23467554e-01), (-1.98781256, -1.16904207e+00),
( 3.85286413, 2.26739272e+00), (-3.20252372, -1.88130919e+00),
( 0.14334117, 8.38486614e-02), ( 0.20721822, 1.20402087e-01),
( 1.25442301, 7.22170763e-01), ( 0.89745517, 5.10607295e-01),
( 4.28063376, 2.40061589e+00), ( 0.49726114, 2.74137310e-01),
(-0.99053255, -5.35314773e-01), (-2.87227577, -1.51726697e+00),
( 1.78238091, 9.17511175e-01), ( 1.55002055, 7.75055289e-01),
(-4.09178142, -1.98069741e+00), (-0.94439179, -4.40956248e-01),
( 0.17507806, 7.85455968e-02), (-2.01573442, -8.65243883e-01),
( 2.59408667, 1.06048250e+00), ( 2.29372273, 8.88519180e-01),
( 3.82081221, 1.39453614e+00), ( 3.74344386, 1.27915473e+00),
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Total running time of the script: (0分0.472秒)