def visibility_first_derivative(self, posix_time):
"""Calculate the derivative of the visibility function of the satellite and the site at a
given time.
Args:
posix_time (float): The UNIX time to evaluate the derivative visibility function at.
Returns:
The value of the visibility function evaluated at the provided time.
"""
# Since most helper functions don't play well with mpmath floats we have to perform a lossy
# conversion.
posix_time = float(posix_time)
sat_pos_vel = np.array(
self.sat_irp.interpolate(posix_time)) * mp.mpf(1.0)
site_pos = np.array(self.site_ecef) * mp.mpf(1.0)
pos_diff = np.subtract(sat_pos_vel[0], site_pos)
vel_diff = sat_pos_vel[1]
site_normal_pos = site_pos / mp.norm(site_pos)
site_normal_vel = [0, 0, 0]
first_term = mp.mpf(
((1.0 / mp.norm(pos_diff)) * (mp.fdot(vel_diff, site_normal_pos) +
mp.fdot(pos_diff, site_normal_vel))))
second_term = mp.mpf(((1.0 / mp.power(
(mp.norm(pos_diff)), 3)) * mp.fdot(pos_diff, vel_diff) *
mp.fdot(pos_diff, site_normal_pos)))
return first_term - second_term
def rotate_mp(pts, x, y):
out = mpm.zeros(pts.rows, pts.cols)
v = x/mpm.norm(x)
cos = mpm.fdot(x,y) / (mpm.norm(x), mpm.norm(y))
sin = mpm.sqrt(1.-cos**2)
u = y - mpm.fdot(v, y) * v
mat = mpm.eye(x.cols) - u.T * u - v.T * v \
+ cos * u.T * u - sin * v.T * u + sin * u.T * v + cos * v.T * v
return mat
def poincare_reflect(a, x, c=1.0, precision=None):
'''
Spherical inversion (or "Poincare reflection") of a point x about a sphere
with center at point "a", and radius = 1/c.
'''
if precision is not None:
mpm.mp.dps = precision
a2 = mpm.fdot(a, a)
x2 = mpm.fdot(x, x)
xa2 = x2 + a2 - 2 * mpm.fdot(x, a)
r2 = a2 - 1. / c
scal = mpm.fdiv(r2, xa2)
return scal * (x - a) + a
def rotate_3D_mp(x, y):
xnorm = mpm.norm(x)
ynorm = mpm.norm(y)
cos = mpm.fdot(x,y)/(xnorm*ynorm)
sin = mpm.sqrt(1.-cos**2)
K = (y.T*x-x.T*y)/(xnorm*ynorm*sin)
return mpm.eye(3) + sin*K + (1.-cos)*(K*K)
def poincare_reflect0(z, x, c=1.0, precision=None):
'''
Spherical inversion (or "Poincare reflection") of a point x
such that point z is mapped to the origin.
'''
if precision is not None:
mpm.mp.dps = precision
# the reflection is poincare_reflect(a, x) where
# a = c * z / |z|**2
z2 = mpm.fdot(z, z)
zscal = c / z2
x2 = mpm.fdot(x, x)
a2 = c * zscal
r2 = a2 - 1. / c
xa2 = x2 + a2 - 2 * zscal * mpm.fdot(z, x)
scal = mpm.fdiv(r2, xa2)
return scal * (x - zscal * z) + zscal * z
def myfunction(M):
"""
sum of matrix elements
"""
if isinstance(M, np.ndarray):
return sum(sum(M))
else:
assert isinstance(M, (mp.iv.matrix)), "type {}".format(type(M))
return mp.fdot(M, mp.iv.ones(len(M)))
def __div__(self, B):
if self.onlyNP == True and (type(B) == int or type(B) == float):
return Matrix(np.divide(self.NP, B).tolist(), onlyNP=True)
elif self.onlyNP == True and (type(B) == int
or isinstance(B, np.float64)):
return Matrix(np.divide(self.NP, B).tolist(), onlyNP=True)
elif self.onlyNP == True and (type(B) == int or type(B) == float):
f = mpmath.fraction(1, B)
return Matrix(mpmath.fdot(self.MP, f).tolist(), onlyMP=True)
def poincare_dist(x, y, c=1.0, precision=None):
'''
The hyperbolic distance between points in the Poincare model with curvature -1/c
Args:
x, y: size 1xD mpmath matrix representing point in the D-dimensional ball |x| < 1
precision (int): bits of precision to use
Returns:
mpmath float object. Can be converted back to regular float
'''
if precision is not None:
mpm.mp.dps = precision
x2 = mpm.fdot(x, x)
y2 = mpm.fdot(y, y)
xy = mpm.fdot(x, y)
sqrt_c = mpm.sqrt(c)
denom = 1 - 2 * c * xy + c**2 * x2 * y2
norm = mpm.norm(
(-(1 - 2 * c * xy + c * y2) * x + (1. - c * x2) * y) / denom)
return 2 / sqrt_c * mpm.atanh(sqrt_c * norm)
def psi(t, eigenvalues, coefficients, f0=mp.mpf("1.0")):
'''The nearly periodic function'''
f = None
if len(eigenvalues) == len(coefficients):
f = [mp.expj(E*t) for E in eigenvalues]
f = mp.fdot(coefficients, f)
f = mp.fabs(f - f0)
return(f)
def point_plane_distance(self, point: Point):
'''
calculates point distance from the plane
:param point: list or numpy array
:return: err, distance
distance = (a*x0 + b*y0 + c*z0 + d)/ sqrt(a**2 + b**2 + c**2)
'''
numerator = mpmath.fdot(self.abcd, HmPoint.from_point(point).xyzw)
denominator = mpmath.sqrt(self.nv.dot(self.nv))
distance = numerator / denominator
return distance
def visibility(self, posix_time):
"""Calculate the visibility function of the satellite and the site at a given time.
Args:
posix_time (float): The time to evaluate the visibility function at
Returns:
The value of the visibility function evaluated at the provided time.
Note:
This function assumes the FOV of the sensors on the satellite are 180 degrees
"""
# Since most helper functions don't play well with mpmath floats we have to perform a lossy
# conversion.
posix_time = float(posix_time)
site_pos = np.array(self.site_ecef) * mp.mpf(1.0)
site_normal_pos = site_pos / mp.norm(site_pos)
sat_pos = self.sat_irp.interpolate(posix_time)[0]
sat_site = np.subtract(sat_pos, site_pos)
return mp.mpf(mp.fdot(sat_site, site_normal_pos) / mp.norm(sat_site))
def remezStep(self, control):
# eval at control points
fxn = mp.matrix([self.evalFunc(c) for c in control])
# create linear system with chebyshev polynomials
size = self.order + 2
system = mp.zeros(size)
for n in range(self.order + 1):
for i in range(self.order + 2):
system[i, n] = mp.chebyt(n, control[i])
# last column is oscillating error
for i in range(size):
sign = -1 if ((i & 1) == 0) else +1
scale = 0.0 if i in [0, size - 1] else 1.0
system[i, size -
1] = sign * scale * mp.fabs(self.evalWeight(control[i]))
#print(system)
# solve the system
solved = system**-1
#print(solved)
# compute polynomial estimate (as Chebyshev weights)
weights = vzeros(size - 1)
for n in range(size - 1):
weights[n] = mp.fdot(solved[n, :], fxn)
#print(f' weights: {weights}')
# estimate error
# self.weights = weights
# est = [self.evalEstimate(x) for x in control]
# print(' est:', est)
# print(' fxn:', fxn.T)
return weights
def __mul__(self, B):
#print(type(B))
if type(B) == float or type(B) == int or type(B) == np.float64 or type(
B) == np.complex128:
if self.onlyNP == True:
return Matrix(np.dot(self.NP, B).tolist(), onlyNP=True)
elif self.Sparse == True:
return Matrix(self.S * B, Sparse=True)
elif self.onlyNP == True and B.onlyNP == True:
if (type(np.dot(self.NP, B.NP).tolist()) == float
or type(np.dot(self.NP, B.NP).tolist()) == int):
return (np.dot(self.NP, B.NP).tolist())
else:
return Matrix(np.dot(self.NP, B.NP).tolist(), onlyNP=True)
elif self.onlyMP == True and B.onlyMP == True:
return Matrix(mpmath.fdot(self.MP, B.MP).tolist(), onlyMP=True)
elif self.Sparse == True and B.Sparse == True:
#print(self.S.shape)
#print(B.S.shape)
M = self.S * B.S
if M.shape == (1, 1):
return float(M.todense())
else:
return Matrix(self.S * B.S, Sparse=True)
def initRemez(self):
#print('Remez.init()')
# constants for domain
(xMin, xMax) = self.domain
self.k1 = (xMax + xMin) * 0.5
self.k2 = (xMax - xMin) * 0.5
# initial estimates for function roots (where error == 0.0)
size = self.order + 1
roots = vzeros(size)
fxn = vzeros(size)
# \todo [petri] use linspace
for i in range(size):
roots[i] = (2.0 * i - self.order) / size
fxn[i] = self.evalFunc(roots[i])
# build matrix of Chebyshev evaluations
system = mp.zeros(size)
for order in range(size):
for i in range(size):
system[i, order] = mp.chebyt(order, roots[i])
# solve system
solved = system**-1
# compute Chebyshev weights of new approximation
weights = vzeros(size)
for n in range(size):
weights[n] = mp.fdot(solved[n, :], fxn)
#print(f' weights: {weights.T}')
# store roots & weights
self.roots = roots
self.weights = weights
self.maxError = 1000.0
def dot(self, other_vector):
return mpmath.fdot(self.abc, other_vector.abc)
def magnitude(self):
p = mpmath.fdot(self.abc, self.abc)
return mpmath.sqrt(p)
def dot(self, other_vector):
return mpmath.fdot(self.xyzw, other_vector.xyzw)