def Br_for_ml(r, th, ph, g, h, m, l, a=6371.2):
"""
Calculates the Br contribution for one set of m,l, using the potential field.
Inputs
------
r:
radius location (km)
th:
latitude location (radians)
ph:
longitude location (radians)
g:
Gauss coefficient (cos term)
h:
Gauss coefficient (sin term)
m:
Order of calculation
l:
Degree of calculation
a:
Radius (km) at which Gauss coefficients are calculated
Returns
-------
Br contribution in Tesla at a particular point from a particular degree and order.
"""
return (l + 1.) * a**(l + 2.) / abs(r)**(l + 2.) * (
g * _cos(m * ph) + h * _sin(m * ph)) * Pml(_cos(th), l, m)
def Br_for_ml(r,th,ph,g,h,m,l, a=6371.2):
"""
Calculates the Br contribution for one set of m,l, using the potential field.
Inputs
------
r:
radius location (km)
th:
latitude location (radians)
ph:
longitude location (radians)
g:
Gauss coefficient (cos term)
h:
Gauss coefficient (sin term)
m:
Order of calculation
l:
Degree of calculation
a:
Radius (km) at which Gauss coefficients are calculated
Returns
-------
Br contribution in Tesla at a particular point from a particular degree and order.
"""
return (l+1.)*a**(l+2.)/abs(r)**(l+2.)*(g*_cos(m*ph) + h*_sin(m*ph))*Pml(_cos(th), l, m)
def _dphi_Br_for_ml_complex(self, r, th, ph, c, m, l, a=6371.2):
"""
Calculates the d_phi(Br)/(R*sin(th)) contribution for one set of m,l, using the potential field.
Inputs
------
r:
radius location (km)
th:
latitude location (radians)
ph:
longitude location (radians)
c:
complex gauss coefficient
m:
Order of calculation
l:
Degree of calculation
a:
Radius (km) at which Gauss coefficients are calculated
Returns
-------
d_phi(Br)/(R*sin(th)) in Tesla/m at a particular point from a particular degree and order.
"""
return 1j*m/(r*_sin(th))*self._Br_for_ml_complex(r, th, ph, c, m, l, a=a)
def rcosfir(beta, sps, span=None):
"""Generates a raised cosine FIR filter.
:param beta: shape of the raised cosine filter (0-1)
:param sps: number of samples per symbol
:param span: length of the filter in symbols (None => automatic selection)
>>> import arlpy
>>> rc = arlpy.comms.rcosfir(0.25, 6)
>>> bb = arlpy.comms.modulate(arlpy.comms.random_data(100), arlpy.comms.psk())
>>> pb = arlpy.comms.upconvert(bb, 6, 27000, 18000, rc)
"""
if beta < 0 or beta > 1:
raise ValueError('Beta must be between 0 and 1')
if span is None:
# from http://www.commsys.isy.liu.se/TSKS04/lectures/3/MichaelZoltowski_SquareRootRaisedCosine.pdf
# since this recommendation is for root raised cosine filter, it is conservative for a raised cosine filter
span = 33 - int(44 * beta) if beta < 0.68 else 4
delay = int(span * sps / 2)
t = _np.arange(-delay, delay + 1, dtype=_np.float) / sps
denom = 1 - (2 * beta * t)**2
eps = _np.finfo(float).eps
idx1 = _np.nonzero(_np.abs(denom) > _sqrt(eps))
b = _np.full_like(t, beta * _sin(_pi / (2 * beta)) / (2 * sps))
b[idx1] = _np.sinc(t[idx1]) * _cos(
_pi * beta * t[idx1]) / denom[idx1] / sps
b /= _sqrt(_np.sum(b**2))
return b
def rrcosfir(beta, sps, span=None):
"""Generates a root raised cosine FIR filter.
:param beta: shape of the root raised cosine filter (0-1)
:param sps: number of samples per symbol
:param span: length of the filter in symbols (None => automatic selection)
>>> import arlpy
>>> rrc = arlpy.comms.rrcosfir(0.25, 6)
>>> bb = arlpy.comms.modulate(arlpy.comms.random_data(100), arlpy.comms.psk())
>>> pb = arlpy.comms.upconvert(bb, 6, 27000, 18000, rrc)
"""
if beta < 0 or beta > 1:
raise ValueError('Beta must be between 0 and 1')
if span is None:
# from http://www.commsys.isy.liu.se/TSKS04/lectures/3/MichaelZoltowski_SquareRootRaisedCosine.pdf
span = 33 - int(44 * beta) if beta < 0.68 else 4
delay = int(span * sps / 2)
t = _np.arange(-delay, delay + 1, dtype=_np.float) / sps
b = _np.empty_like(t)
b[delay] = -1 / (_pi * sps) * (_pi * (beta - 1) - 4 * beta)
eps = _np.finfo(float).eps
idx2 = _np.nonzero(_np.abs(_np.abs(4 * beta * t) - 1) < _sqrt(eps))
if len(idx2) > 0:
b[idx2] = (_pi * (beta + 1) * _sin(_pi * (beta + 1) / (4 * beta)) -
4 * beta * _sin(_pi * (beta - 1) / (4 * beta)) + _pi *
(beta - 1) * _cos(_pi * (beta - 1) /
(4 * beta))) / (2 * _pi * sps)
ind = _np.arange(len(t))
ind = _np.delete(ind, _np.append(idx2, delay))
nind = t[ind]
b[ind] = -4 * beta / sps * (_cos((1 + beta) * _pi * nind) + _sin(
(1 - beta) * _pi * nind) / (4 * beta * nind)) / (_pi * (
(4 * beta * nind)**2 - 1))
b /= _sqrt(_np.sum(b**2))
return b
def _do_dispersal(spp,
parent_midpoint_x,
parent_midpoint_y,
dispersal_distance_distr_param1,
dispersal_distance_distr_param2,
mu_dir=0,
kappa_dir=0):
within_landscape = False
while not within_landscape:
# choose direction using movement surface, if applicable
if spp._disp_surf:
# and use those choices to draw movement directions
direction = spp._disp_surf._draw_directions(
[int(parent_midpoint_x)], [int(parent_midpoint_y)])[0]
# else, choose direction using a random walk with a uniform vonmises
elif not spp._disp_surf:
direction = _r_vonmises(mu_dir, kappa_dir)
if spp.dispersal_distance_distr == 'levy':
distance = _s_levy.rvs(loc=spp.dispersal_distance_distr_param1,
scale=spp.dispersal_distance_distr_param2)
elif spp.dispersal_distance_distr == 'wald':
distance = _wald(mean=dispersal_distance_distr_param1,
scale=dispersal_distance_distr_param2)
elif spp.dispersal_distance_distr == 'lognormal':
distance = _lognormal(mean=spp.dispersal_distance_distr_param1,
sigma=spp.dispersal_distance_distr_param2)
# decompose distance into x and y components
dist_x = _cos(direction) * distance
dist_y = _sin(direction) * distance
# multiply the x and y distances by the land's resolution-ratios,
# if they're not 1 and 1 (e.g. using a non-square-resolution raster)
if spp._land_res_ratio[0] != 1:
dist_x *= spp._land_res_ratio[0]
if spp._land_res_ratio[1] != 1:
dist_y *= spp._land_res_ratio[1]
offspring_x = parent_midpoint_x + dist_x
offspring_y = parent_midpoint_y + dist_y
offspring_x = np.clip(offspring_x,
a_min=0,
a_max=spp._land_dim[0] - 0.001)
offspring_y = np.clip(offspring_y,
a_min=0,
a_max=spp._land_dim[1] - 0.001)
within_landscape = (
(offspring_x > 0 and offspring_x < spp._land_dim[0])
and (offspring_y > 0 and offspring_y < spp._land_dim[1]))
return (offspring_x, offspring_y)
def _do_movement(spp):
# get individuals' coordinates (soon to be their old coords, so
# 'old_x' and 'old_y')
old_x, old_y = [
a.flatten() for a in np.split(spp._get_coords(), 2, axis=1)
]
# and get their cells (by rounding down to the int)
old_x_cells, old_y_cells = [
a.flatten() for a in np.split(spp._get_cells(), 2, axis=1)
]
# choose direction using movement surface, if applicable
if spp._move_surf:
# and use those choices to draw movement directions
direction = spp._move_surf._draw_directions(old_x_cells, old_y_cells)
# NOTE: Pretty sure that I don't need to constrain values output
# for the Gaussian KDE that is approximating the von Mises mixture
# distribution to 0<=val<=2*pi, because e.g. cos(2*pi + 1) = cos(1),
# etc...
# NOTE: indexed out of move_surf as y then x because becuase the
# list of lists (like a numpy array structure) is indexed i then j,
# i.e. vertical, then horizontal
# else, choose direction using a random walk with a uniform vonmises
elif not spp._move_surf:
direction = _r_vonmises(spp.direction_distr_mu,
spp.direction_distr_kappa,
size=len(old_x))
# choose distance
# NOTE: Instead of lognormal, could use something with long right tail
# for Levy-flight type movement, same as below
if spp.movement_distance_distr == 'levy':
distance = _s_levy.rvs(loc=spp.movement_distance_distr_param1,
scale=spp.movement_distance_distr_param2,
size=len(old_x))
elif spp.movement_distance_distr == 'wald':
distance = _wald(mean=spp.movement_distance_distr_param1,
scale=spp.movement_distance_distr_param2,
size=len(old_x))
elif spp.movement_distance_distr == 'lognormal':
distance = _lognormal(mean=spp.movement_distance_distr_param1,
sigma=spp.movement_distance_distr_param2,
size=len(old_x))
# decompose distance into x and y components
dist_x = _cos(direction) * distance
dist_y = _sin(direction) * distance
# multiply the x and y distances by the land's resolution-ratios,
# if they're not 1 and 1 (e.g. a non-square-resolution raster was read in)
if spp._land_res_ratio[0] != 1:
dist_x *= spp._land_res_ratio[0]
if spp._land_res_ratio[1] != 1:
dist_y *= spp._land_res_ratio[1]
# create the new locations by adding x- and y-dim line segments to their
# current positions, using trig then clip the values to be within the
# landscape dimensions
# NOTE: subtract a small value to avoid having the dimension itself set
# as a coordinate, when the coordinates are converted to np.float32
new_x = old_x + dist_x
new_x = np.clip(new_x, a_min=0, a_max=spp._land_dim[0] - 0.001)
new_y = old_y + dist_y
new_y = np.clip(new_y, a_min=0, a_max=spp._land_dim[1] - 0.001)
# then feed the new locations into each individual's set_pos method
[ind._set_pos(x, y) for ind, x, y in zip(spp.values(), new_x, new_y)]
def sin(x, unit='rad'):
if unit == 'rad':
return _sin(x)
elif unit == 'deg':
return _sin(deg_to_rad(x))
