def areaint(lats, lons):
assert lats.size == lons.size, 'List of latitudes and longitudes are different sizes.'
if isinstance(lats.iloc[0], u.Quantity):
lat = np.array([lat.value
for lat in lats] + [lats.iloc[0].value]) * u.deg
lon = np.array([lon.value
for lon in lons] + [lons.iloc[0].value]) * u.deg
else:
lat = np.append(lats, lats.iloc[0]) * u.deg
lon = np.append(lons, lons.iloc[0]) * u.deg
if lat.max() > 0:
northern = True
# Get colatitude (a measure of surface distance as an angle) and
# azimuth of each point in segment from the center of mass.
_, center_lat, center_lon = sph_center_of_mass(lat[:-1], lon[:-1])
if np.isnan(center_lat.value):
center_lat = Latitude(0, unit=u.rad)
if np.isnan(center_lon.value):
center_lon = Longitude(0, unit=u.rad)
# force centroid at the N or S pole
# if northern:
# center_lat = 90 * u.deg
# else:
# center_lat = -90 * u.deg
# center_lon = 0 * u.deg
colat = np.array([
distance(center_lon.to(u.deg), center_lat.to(u.deg), longi, latit).to(
u.deg).value for latit, longi in zip(lat, lon)
]) * u.deg
az = np.array([
azimuth(center_lon.to(u.deg), center_lat.to(u.deg), longi, latit).to(
u.deg).value for latit, longi in zip(lat, lon)
]) * u.deg
# Calculate step sizes, taking the complementary angle where needed
daz = np.diff(az).to(u.rad)
daz[np.where(daz > 180 * u.deg)] -= 360. * u.deg
daz[np.where(daz < -180 * u.deg)] += 360. * u.deg
# Determine average surface distance for each step
deltas = np.diff(colat) / 2.
colats = colat[0:-1] + deltas
# Integral over azimuth is 1-cos(colatitudes)
integrands = (1 - np.cos(colats)) * daz
# Integrate and return the answer as a fraction of the unit sphere.
# Note that the sum of the integrands will include a part of 4pi.
return np.abs(
np.nansum(integrands)) / (4 * np.pi * u.rad), center_lat, center_lon
def location(lat, lon, alt):
# Reference location
lon = Longitude(lon.strip(),
u.degree,
wrap_angle=180 * u.degree,
copy=False) # noqa
lat = Latitude(lat.strip(), u.degree, copy=False)
height = u.Quantity(float(alt.strip()), u.m, copy=False)
ref_location = EarthLocation(lat=lat.to(u.deg).value,
lon=lon.to(u.deg).value,
height=height.to(u.m).value) # noqa
return ref_location
def gmst2time(gmst, time):
"""
Converts a Greenwich Mean Sidereal Time to UTC time, for a given date.
Parameters
----------
gmst: ~float
Greenwich Mean Siderial Time (hours)
time : astropy.time.Time
UT date+time
Returns
-------
astropy.time.Time object with closest UT day+time at which
siderial time is correct.
"""
dgmst = Longitude(gmst - time2gmst(time))
return time+TimeDelta(dgmst.to(u.hourangle).value*0.9972695663/24.,
format='jd')
def pixel_to_data(self, x, y, origin=0):
"""
Convert a pixel coordinate to a data (world) coordinate by using
`~astropy.wcs.WCS.wcs_pix2world`.
Parameters
----------
x : float
Pixel coordinate of the CTYPE1 axis. (Normally solar-x).
y : float
Pixel coordinate of the CTYPE2 axis. (Normally solar-y).
origin : int
Origin of the top-left corner. i.e. count from 0 or 1.
Normally, origin should be 0 when passing numpy indices, or 1 if
passing values from FITS header or map attributes.
See `~astropy.wcs.WCS.wcs_pix2world` for more information.
Returns
-------
x : `~astropy.units.Quantity`
Coordinate of the CTYPE1 axis. (Normally solar-x).
y : `~astropy.units.Quantity`
Coordinate of the CTYPE2 axis. (Normally solar-y).
"""
x, y = self.wcs.wcs_pix2world(x, y, origin)
# If the wcs is celestial it is output in degress
if self.wcs.is_celestial:
x *= u.deg
y *= u.deg
else:
x *= self.units.x
y *= self.units.y
x = Longitude(x, wrap_angle=180 * u.deg)
y = Latitude(y)
return x.to(self.units.x), y.to(self.units.y)
def gmst2time(gmst, time):
"""
Converts a Greenwich Mean Sidereal Time to UTC time, for a given date.
Parameters
----------
gmst: ~float
Greenwich Mean Siderial Time (hours)
time : astropy.time.Time
UT date+time
Returns
-------
astropy.time.Time object with closest UT day+time at which
siderial time is correct.
"""
dgmst = Longitude(gmst - time2gmst(time))
return time + TimeDelta(dgmst.to(u.hourangle).value * 0.9972695663 / 24.,
format='jd',
scale='utc')
def rot_hpc(x, y, tstart, tend, frame_time='synodic', rot_type='howard', **kwargs):
"""Given a location on the Sun referred to using the Helioprojective
Cartesian co-ordinate system (typically quoted in the units of arcseconds)
use the solar rotation profile to find that location at some later or
earlier time. Note that this function assumes that the data was observed
from the Earth or near Earth vicinity. Specifically, data from SOHO and
STEREO observatories are not supported. Note also that the function does
NOT use solar B0 and L0 values provided in source FITS files - these
quantities are calculated.
Parameters
----------
x : `~astropy.units.Quantity`
Helio-projective x-co-ordinate in arcseconds (can be an array).
y : `~astropy.units.Quantity`
Helio-projective y-co-ordinate in arcseconds (can be an array).
tstart : `sunpy.time.time`
date/time to which x and y are referred.
tend : `sunpy.time.time`
date/time at which x and y will be rotated to.
rot_type : {'howard' | 'snodgrass' | 'allen'}
| howard: Use values for small magnetic features from Howard et al.
| snodgrass: Use Values from Snodgrass et. al
| allen: Use values from Allen, Astrophysical Quantities, and simpler
equation.
frame_time: {'sidereal' | 'synodic'}
Choose type of day time reference frame.
Returns
-------
x : `~astropy.units.Quantity`
Rotated helio-projective x-co-ordinate in arcseconds (can be an array).
y : `~astropy.units.Quantity`
Rotated helio-projective y-co-ordinate in arcseconds (can be an array).
Examples
--------
>>> import astropy.units as u
>>> from sunpy.physics.transforms.differential_rotation import rot_hpc
>>> rot_hpc( -570 * u.arcsec, 120 * u.arcsec, '2010-09-10 12:34:56', '2010-09-10 13:34:56')
(<Angle -562.9105822671319 arcsec>, <Angle 119.31920621992195 arcsec>)
Notes
-----
SSWIDL code equivalent: http://hesperia.gsfc.nasa.gov/ssw/gen/idl/solar/rot_xy.pro .
The function rot_xy uses arcmin2hel.pro and hel2arcmin.pro to implement the
same functionality as this function. These two functions seem to perform
inverse operations of each other to a high accuracy. The corresponding
equivalent functions here are convert_hpc_hg and convert_hg_hpc
respectively. These two functions seem to perform inverse
operations of each other to a high accuracy. However, the values
returned by arcmin2hel.pro are slightly different from those provided
by convert_hpc_hg. This leads to very slightly different results from
rot_hpc compared to rot_xy.
"""
# must have pairs of co-ordinates
if np.array(x).shape != np.array(y).shape:
raise ValueError('Input co-ordinates must have the same shape.')
# Make sure we have enough time information to perform a solar differential
# rotation
# Start time
dstart = parse_time(tstart)
dend = parse_time(tend)
interval = (dend - dstart).total_seconds() * u.s
# Get the Sun's position from the vantage point at the start time
vstart = kwargs.get("vstart", _calc_P_B0_SD(dstart))
# Compute heliographic co-ordinates - returns (longitude, latitude). Points
# off the limb are returned as nan
longitude, latitude = convert_hpc_hg(x.to(u.arcsec).value,
y.to(u.arcsec).value,
b0_deg=vstart["b0"].to(u.deg).value,
l0_deg=vstart["l0"].to(u.deg).value,
dsun_meters=(constants.au * sun.sunearth_distance(t=dstart)).value,
angle_units='arcsec')
longitude = Longitude(longitude, u.deg)
latitude = Angle(latitude, u.deg)
# Compute the differential rotation
drot = diff_rot(interval, latitude, frame_time=frame_time,
rot_type=rot_type)
# Convert back to heliocentric cartesian in units of arcseconds
vend = kwargs.get("vend", _calc_P_B0_SD(dend))
# It appears that there is a difference in how the SSWIDL function
# hel2arcmin and the sunpy function below performs this co-ordinate
# transform.
newx, newy = convert_hg_hpc(longitude.to(u.deg).value + drot.to(u.deg).value,
latitude.to(u.deg).value,
b0_deg=vend["b0"].to(u.deg).value,
l0_deg=vend["l0"].to(u.deg).value,
dsun_meters=(constants.au * sun.sunearth_distance(t=dend)).value,
occultation=False)
newx = Angle(newx, u.arcsec)
newy = Angle(newy, u.arcsec)
return newx.to(u.arcsec), newy.to(u.arcsec)
