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CADRE_launch.py
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CADRE_launch.py
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import numpy as np
from openmdao.main.api import Assembly, Component
from openmdao.lib.drivers.api import CONMINdriver
from openmdao.lib.drivers.api import SLSQPdriver
from openmdao.main.datatypes.api import Float, Array, Int
from CADRE import Comm_EarthsSpin, Comm_EarthsSpinMtx
from CADRE import Orbit_Initial, Orbit_Dynamics
from scipy.stats import kurtosis, moment
class Uniformity(Component):
def __init__(self, n):
super(Uniformity, self).__init__()
self.n = n
self.add('sample', Array(iotype='in'))
self.add('k', Float(0., iotype='out'))
def execute(self):
self.k = max(self.sample) - min(self.sample)
#def list_deriv_vars(self):
#"""Provide full Jacobian."""
#input_keys = ('sample',)
#output_keys = ('k',)
#return input_keys, output_keys
#def provideJ(self):
#self.J = np.zeros((1,self.n))
#idx_max = np.where(self.sample == max(self.sample))
#idx_min = np.where(self.sample == min(self.sample))
#self.J[0,idx_max] = 1
#self.J[0,idx_min] = -1
#return self.J
class GroundLOC(Component):
""" Gives the lat and lon location of the ground beneath a satellite.
"""
Re = 6378.137
r2d = 180 / np.pi
def __init__(self, n):
super(GroundLOC, self).__init__()
self.n = n
self.add('O_IE', Array(np.zeros((3, 3, self.n)), iotype='in'))
self.add('r_e2b_I', Array(np.zeros((6, self.n)), iotype='in'))
self.add('lats', Array(np.zeros(self.n), iotype='out'))
self.add('lons', Array(np.zeros(self.n), iotype='out'))
def list_deriv_vars(self):
"""Provide full Jacobian."""
input_keys = ('r_e2b_I', 'O_IE')
output_keys = ('lats', 'lons')
return input_keys, output_keys
def provideJ(self):
self.J = np.zeros((self.n, 2, 3))
self.J_O_IE = np.zeros((self.n, 2, 3, 3))
for i in xrange(self.n):
O = self.O_IE[:,:, i].T
r = self.r_e2b_I[:3, i]
d = self.r2d
self.J[i, 0, 0] = self.d_lat(
O[2, 0], O[2, 1], O[2, 2], d, r[0], r[1], r[2])
self.J[i, 0, 1] = self.d_lat(
O[2, 1], O[2, 0], O[2, 2], d, r[1], r[0], r[2])
self.J[i, 0, 2] = self.d_lat(
O[2, 2], O[2, 1], O[2, 0], d, r[2], r[1], r[0])
self.J[i, 1, 0] = self.d_lon(O[1, 0], O[1, 1], O[1, 2], d,
O[0, 0], O[0, 1], O[0, 2], r[0], r[1], r[2])
self.J[i, 1, 1] = self.d_lon(O[1, 1], O[1, 0], O[1, 2], d,
O[0, 1], O[0, 0], O[0, 2], r[1], r[0], r[2])
self.J[i, 1, 2] = self.d_lon(O[1, 2], O[1, 1], O[1, 0], d,
O[0, 2], O[0, 1], O[0, 0], r[2], r[1], r[0])
def apply_deriv(self, arg, result):
if 'r_e2b_I' in arg:
for i in xrange(self.n):
if 'lats' in result:
result['lats'][i] += np.dot(self.J[i, 0,:], arg['r_e2b_I'][:3,i])
if 'lons' in result:
result['lons'][i] += np.dot(self.J[i, 1,:], arg['r_e2b_I'][:3,i])
def apply_derivT(self, arg, result):
if 'lats' in arg:
result['r_e2b_I'][0,:] += arg['lats'] * self.J[:, 0, 0]
result['r_e2b_I'][1,:] += arg['lats'] * self.J[:, 0, 1]
result['r_e2b_I'][2,:] += arg['lats'] * self.J[:, 0, 2]
if 'lons' in arg:
result['r_e2b_I'][0,:] += arg['lons'] * self.J[:, 1, 0]
result['r_e2b_I'][1,:] += arg['lons'] * self.J[:, 1, 1]
result['r_e2b_I'][2,:] += arg['lons'] * self.J[:, 1, 2]
def d_lat(self, a, b, c, d, x, y, z):
return -(d * (-a * (y ** 2 + z ** 2) + b * x * y + c * x * z)) / (np.sqrt((x ** 2 + y ** 2 + z ** 2) ** 3) *
np.sqrt(-((a ** 2 - 1) * x ** 2 + 2 * a * x * (b * y + c * z) + (b ** 2 - 1) * y ** 2 + 2 * b * c * y * z + (c ** 2 - 1) * z ** 2) / (x ** 2 + y ** 2 + z ** 2)))
def d_lon(self, a, b, c, d, e, f, g, x, y, z):
num = -(d * (-a * (f * y + g * z) + b * e * y + c * e * z))
denom = (a ** 2 * x ** 2 + 2 * a * x * (b * y + c * z) + b ** 2 * y ** 2 + 2 * b * c * y * z + c ** 2 *
z ** 2 + e ** 2 * x ** 2 + 2 * e * x * (f * y + g * z) + f ** 2 * y ** 2 + 2 * f * g * y * z + g ** 2 * z ** 2)
if not denom:
return 0.
else:
return num / denom
def d_lat_O_IE(self, a, b, c, d, x, y, z):
return d * a / (np.sqrt(a ** 2 + b ** 2 + c ** 2) * np.sqrt(1 - (a * x + b * y + c * z) ** 2 / (a ** 2 + b ** 2 + c ** 2)))
def d_lon_O_IE(self, a, b, c, d, w, v, u, x, y, z,):
return -d * (a * (a * w + b * v + c * u)) / (a ** 2 * (w ** 2 + x ** 2) + 2 * c * (a * u * w + a * x * z + b * u * v + b * y * z) + 2 * a * b * (v * w + x * y) + b ** 2 * (v ** 2 + y ** 2) + c ** 2 * (u ** 2 + z ** 2))
def execute(self):
self.npos = np.zeros((self.n, 3))
self.g_pos = np.zeros((self.n, 3))
for i in xrange(self.n):
self.pos = self.r_e2b_I[:3, i]
self.npos[i,:] = self.pos / np.linalg.norm(self.pos, 2) * self.Re
self.g_pos[i,:] = np.dot(self.O_IE[:,:, i].T, self.npos[i,:])
self.lats[i] = np.arcsin(self.g_pos[i, 2] / self.Re) * self.r2d
self.lons[i] = np.arctan2(
self.g_pos[i, 1], self.g_pos[i, 0]) * self.r2d
class CADRE_Launch(Assembly):
""" Allows for analysis of the launch parameters of CADRE.
Considers multiple launch parameters and their effects on
coverage of the Earth's thermosphere.
Ultimately, a launch that provides the most uniform sampling is
favorable, which is expected to be given by a polar orbit
(Inclination near 90). Other launch parameters are probably not
very useful in comparison.
"""
def __init__(self, n=200):
super(CADRE_Launch, self).__init__()
# Analysis parameters
self.n = n
self.add('t', Array(np.zeros((n,)), size=(n,),
dtype=np.float, iotype="in"))
self.add('t1', Float(0., iotype='in'))
self.add('t2', Float(43200., iotype='in'))
h = (self.t2 - self.t1) / (self.n - 1)
self.add("h", Float(h, iotype="in", copy=None))
self.t = np.array(range(0, n)) * h
self.add("Orbit_Initial", Orbit_Initial())
self.driver.workflow.add("Orbit_Initial")
self.add("Orbit_Dynamics", Orbit_Dynamics(n))
self.driver.workflow.add("Orbit_Dynamics")
self.add("Comm_EarthsSpin", Comm_EarthsSpin(n))
self.driver.workflow.add("Comm_EarthsSpin")
self.add("Comm_EarthsSpinMtx", Comm_EarthsSpinMtx(n))
self.driver.workflow.add("Comm_EarthsSpinMtx")
self.add("GroundLOC", GroundLOC(n))
self.driver.workflow.add("GroundLOC")
self.add("Lon_uniform", Uniformity(n))
self.driver.workflow.add("Lon_uniform")
self.add("Lat_uniform", Uniformity(n))
self.driver.workflow.add("Lat_uniform")
self.connect("t", "Comm_EarthsSpin.t")
self.connect("h", "Orbit_Dynamics.h")
self.connect("Comm_EarthsSpin.q_E", "Comm_EarthsSpinMtx.q_E")
self.connect("Comm_EarthsSpinMtx.O_IE", "GroundLOC.O_IE")
self.connect("Orbit_Initial.r_e2b_I0", "Orbit_Dynamics.r_e2b_I0")
self.connect("Orbit_Dynamics.r_e2b_I", "GroundLOC.r_e2b_I")
self.connect("GroundLOC.lats", "Lat_uniform.sample")
self.connect("GroundLOC.lons", "Lon_uniform.sample")
#self.driver.add_objective("Lat_uniform.k + Lon_uniform.k")
#self.driver.add_parameter(
#"Orbit_Initial.altPerigee", low=500, high=1000)
#self.driver.add_parameter(
#"Orbit_Initial.altApogee", low=500, high=1000)
#self.driver.add_parameter(
#"Orbit_Initial.RAAN", low=-180, high=180)
#self.driver.add_parameter(
#"Orbit_Initial.Inc", low=0, high=90)
#self.driver.add_parameter(
#"Orbit_Initial.argPerigee", low=0, high=90)
if __name__ == "__main__":
import time
from scipy.optimize import fmin, fmin_slsqp
print 30 * "-"
print "with OpenMDAO optimizer:"
a = CADRE_Launch(10)
a.Orbit_Initial.Inc = 15
#a.add('driver', SLSQPdriver())
a.add('driver', CONMINdriver())
a.driver.conmin_diff = True
a.driver.add_objective("-Lat_uniform.k - Lon_uniform.k")
a.driver.add_parameter(
["Orbit_Initial.altPerigee", "Orbit_Initial.altApogee"],
low=500, high=1000)
a.driver.add_parameter(
"Orbit_Initial.RAAN", low=-180, high=180)
a.driver.add_parameter(
"Orbit_Initial.Inc", low=0, high=90)
a.driver.add_parameter(
"Orbit_Initial.argPerigee", low=0, high=90)
tt = time.time()
a.run()
#outputs = ['Orbit_Dynamics.r_e2b_I']
outputs = None
# hey ken!
# a.driver.workflow.check_gradient(inputs=['Orbit_Dynamics.r_e2b_I0[:3]'], outputs=[ "Orbit_Dynamics.r_e2b_I[:3,:]"])
# exit()
l1, l2 = a.GroundLOC.lats, a.GroundLOC.lons
print "min/max lats:", min(l1), max(l1)
print "min/max lons:", min(l2), max(l2)
print "objective:", a.Lat_uniform.k + a.Lon_uniform.k
print(a.Orbit_Initial.altPerigee,
a.Orbit_Initial.altApogee,
a.Orbit_Initial.RAAN,
a.Orbit_Initial.Inc,
a.Orbit_Initial.argPerigee)
print "Elapsed time: ", time.time() - tt, "seconds"
print 30 * "-"
#print "without OpenMDAO optimizer:"
#a = CADRE_Launch()
#a.Orbit_Initial.Inc = 10.
#tt = time.time()
#def f(orbit):
#a.Orbit_Initial.altPerigee = orbit[0]
#a.Orbit_Initial.altApogee = orbit[0]
#a.Orbit_Initial.RAAN = orbit[1]
#a.Orbit_Initial.Inc = orbit[2]
#a.run()
#return a.Lat_uniform.k + a.Lon_uniform.k
##start_point = [600, 0, 45]
#start_point = [500, 66, 25]
#fmin_slsqp(f, start_point, bounds=[
#(500, 1000), (-180, 180), (0, 90)],
#iprint=1)
#l1, l2 = a.GroundLOC.lats, a.GroundLOC.lons
#print "min/max lats:", min(l1), max(l1)
#print "min/max lons:", min(l2), max(l2)
#print "objective:", a.Lat_uniform.k + a.Lon_uniform.k
#print(a.Orbit_Initial.altPerigee,
#a.Orbit_Initial.altApogee,
#a.Orbit_Initial.RAAN,
#a.Orbit_Initial.Inc,
#a.Orbit_Initial.argPerigee)
#print "Elapsed time: ", time.time() - tt, "seconds"