"""
Convert between different components and coordinate systems used by
the geomagnetic community.
We use three coordinate systems.
Geo: Based on Geographic North. X, Y, Z
X is north, Y is east
Obs: Based on the observatories orientaion. H, E, Z [d]
Mag: Based on Magnetic North. H, D, Z [E]
d0: Declination baseline in radians
Notes: We use numpy functions instead of standard python arithmetic funtions
for 2 reasons. 1) so that either array's can be passed in, or individual
values. 2) Because they are more flexible/robust then the standard python
functions.
"""
import numpy
M2R = numpy.pi / 180 / 60 # Minutes to Radians
R2M = 180.0 / numpy.pi * 60 # Radians to Minutes
M2D = 1.0 / 60.0 # Minutes to Degrees
D2M = 60.0 # Degrees to Minutes
# ###
# get geographic coordinates from....
# ###
def get_geo_from_obs(h, e, d0=0):
"""gets the geographical components given the observatory components.
Parameters
__________
h: array_like
the h component from the observatory
e: array_like
the e component from the observatory
d0: float
the declination baseline angle in radians
Returns
_______
tuple of array_like
[0]: x component as a float
[1]: y component as a float
"""
mag_h, mag_d = get_mag_from_obs(h, e, d0)
return get_geo_from_mag(mag_h, mag_d)
def get_geo_from_mag(h, d):
"""gets the geographical components given the magnetic components
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
Returns
_______
tuple of array_like
geo_x: x component as a float
geo_y: y component as a float
"""
geo_x = get_geo_x_from_mag(h, d)
geo_y = get_geo_y_from_mag(h, d)
return (geo_x, geo_y)
# inividual get geo from calls
def get_geo_x_from_mag(h, d):
"""gets the geographical x component given magnetic north components
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
Returns
_______
array_like
x component
"""
return numpy.multiply(h, numpy.cos(d))
def get_geo_y_from_mag(h, d):
"""gets the geographical y component given magnetic north components
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
Returns
_______
array_like
y component
"""
return numpy.multiply(h, numpy.sin(d))
# ###
# get magnetic north coordinates from....
# ###
def get_mag_from_obs(h, e, d0=0):
"""gets the magnetic north components given the observatory components.
Parameters
__________
h: array_like
the h component from the observatory
e: array_like
the e component from the observatory
d0: float
the declination baseline angle in radians
Returns
_______
tuple of array_like
[0]: total h component as a float
[1]: total d declination as a float
"""
mag_h = get_mag_h_from_obs(h, e)
mag_d = get_mag_d_from_obs(h, e, d0)
return (mag_h, mag_d)
def get_mag_from_geo(x, y):
"""gets the magnetic north components given the geographic components.
Parameters
__________
x: array_like
the geographic x component
y: array_like
the geographic y component
Returns
_______
tuple of array_like
[0]: total h component as a float
[1]: total d declination as a float
"""
mag_h = get_mag_h_from_geo(x, y)
mag_d = get_mag_d_from_geo(x, y)
return (mag_h, mag_d)
def get_mag_d_from_obs(h, e, d0=0):
"""gets the magnetic d component given the observatory components.
Parameters
__________
h: array_like
the h component from the observatory
e: array_like
the e component from the observatory
d0: float
the declination baseline angle in radians
Returns
_______
array_like
the total magnetic declination
"""
return numpy.add(d0, get_obs_d_from_obs(h, e))
def get_mag_d_from_geo(x, y):
"""gets the magnetic d component given the geographic components.
Parameters
__________
x: array_like
the geographic x component
y: array_like
the geographic y component
Returns
_______
array_like
the total magnetic declination
"""
return numpy.arctan2(y, x)
def get_mag_h_from_obs(h, e):
"""gets the magnetic h component given the observatory components.
Parameters
__________
h: array_like
the h component from the observatory
e: array_like
the e component from the observatory
Returns
_______
array_like
the total magnetic h component
"""
return numpy.hypot(h, e)
def get_mag_h_from_geo(x, y):
"""gets the magnetic h component given the geographic components.
Parameters
__________
x: array_like
the geographic x component
y: array_like
the geographic y component
Returns
_______
array_like
the total magnetic h component
"""
return numpy.hypot(x, y)
# ###
# get observatory coordinates from....
# ###
def get_obs_from_geo(x, y, d0=0):
"""gets the observatory components given the geographic components.
Parameters
__________
x: array_like
the geographic x component
y: array_like
the geographic y component
d0: float
the declination baseline angle in radians
Returns
_______
tuple of array_like
[0]: observatory h component
[1]: observatory e component
[2]: observatory d declination
"""
mag_h, mag_d = get_mag_from_geo(x, y)
return get_obs_from_mag(mag_h, mag_d, d0)
def get_obs_from_mag(h, d, d0=0):
"""gets the observatory components given the magnetic north components.
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
d0: float
the declination baseline angle in radians
Returns
_______
tuple of array_like
[0]: observatory h component
[1]: observatory e component
[2]: observatory d declination
"""
obs_h = get_obs_h_from_mag(h, d, d0)
obs_e = get_obs_e_from_mag(h, d, d0)
return (obs_h, obs_e)
# inividual get obs from calls
def get_obs_d_from_obs(h, e):
"""gets the observatory d declination given the observatory components.
Parameters
__________
h: array_like
the h component from the observatory
e: array_like
the e component from the observatory
Returns
_______
array_like
the observatory d declination
"""
return numpy.arctan2(e, h)
def get_obs_d_from_mag_d(d, d0=0):
"""gets the observatory d declination given the magnetic north
declination.
Parameters
__________
d: array_like
the total declination d to magnetic north
d0: float
the declination baseline angle in radians
Returns
_______
array_like
the observatory d declination
"""
return numpy.subtract(d, d0)
def get_obs_e_from_mag(h, d, d0=0):
"""gets the observatory e component given the magnetic components.
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
d0: float
the declination baseline angle in radians
Returns
_______
array_like
the observatory e component
"""
obs_d = get_obs_d_from_mag_d(d, d0)
return numpy.multiply(h, numpy.sin(obs_d))
def get_obs_e_from_obs(h, d):
"""gets the observatory e component given the observatory components.
Parameters
__________
h: array_like
the observatory h component.
d: array_like
the observatory d declination.
Returns
_______
array_like
the observatory e component
"""
return numpy.multiply(h, numpy.tan(d))
def get_obs_h_from_mag(h, d, d0=0):
"""gets the observatory h component given the magnetic north components
Parameters
__________
h: array_like
the total h component in the magnetic north direction.
d: array_like
the total d declination for the magnetic north direction.
d0: float
the declination baseline angle in radians
Returns
_______
array_like
the observatory h component
"""
obs_d = get_obs_d_from_mag_d(d, d0)
return numpy.multiply(h, numpy.cos(obs_d))
def get_deltaf(fv, fs):
"""gets the deltaf value given the scalar F and computed F values.
Parameters
----------
fv: array_like
the F vector computed from the observatory instruments
fs: array_like
the measured F value
"""
return numpy.subtract(fv, fs)
def get_computed_f_using_squares(x, y, z):
"""gets the computed f value
Parameters
----------
x: array_like
the x component from the observatory
y: array_like
the y component from the observatory
z: array_like
the z component from the observatory
Notes
-----
This works for geographic coordinates, or observatory coordinates.
ie x, y, z or h, e, z
We're using variables x,y,z to represent generic cartisian coordinates.
"""
x2 = numpy.square(x)
y2 = numpy.square(y)
z2 = numpy.square(z)
fv = numpy.add(x2, y2)
fv = numpy.add(fv, z2)
return numpy.sqrt(fv)
def get_radians_from_minutes(m):
"""gets the radian value given the decimal value
Parameters
__________
d: array_like
the decimal value to be converted
"""
return numpy.multiply(m, M2R)
def get_minutes_from_radians(r):
"""gets the decimal value given the radian value
Parameters
__________
r: float
the radian value to be converted
"""
return numpy.multiply(r, R2M)
def get_degrees_from_minutes(m):
"""
Converts angular minutes to degrees.
Parameters
----------
m : float or array_like
The angular minutes to be converted.
Returns
-------
float or array_like
The corresponding degrees.
"""
return numpy.multiply(m, M2D)
def get_minutes_from_degrees(d):
"""
Converts degrees to angular minutes.
Parameters
----------
d : float or array_like
The degrees to be converted.
Returns
-------
float or array_like
The corresponding angular minutes.
"""
return numpy.multiply(d, D2M)