I am trying to create a transition matric using this code:
transition_matrix[0:720,:] = (1 / np.sqrt(2 * np.pi * sigma_n2)) * np.exp(-( np.abs(eventspace_psi_i_min_1 - eventspace_psi_i) )**2 / (2 * sigma_n2))
where the formula after it is just the Gaussian distribution.
The eventspaces are arrays of 720 elements, all of which are supposed to angles starting from 0,0.5,...,359.5. Knowing how close 0° and 359.5° are, a non-zero value should appear in the transition matrix for this calculation. But, because of Eucidean distance, it returns 0.
I tried switching up the eventspaces and making them: 0, 0.5,...,180,179.5,...,0,5 but it doesn't work because again of Eukidean distance, since it will give a non-zero when considering 90° and the equivalent for 270° (which is 90 in this case).
In order for this to perform properly, I need to have the angle values in a circle as they would usually appear in a diagram.
Can anyone help me understand how this can be done?
I'm a bit puzzled because you're using degrees, not radians, however if you want an angular distance with the property 0 ≤ δ ≤ 180 you can go like this
def distance(φ, θ):
from numpy import abs
δ = abs(φ-θ) # 0 ≤ δ < 360
δ[δ>=180] -= 360 # -180 ≤ δ < 180
return abs(δ) # 0 ≤ δ ≤ 180
edit
Your angles are in the [0, 360) interval, but this is not always the case, so it's better to normalize them, moreover if the arguments are both scalars a TypeError is raised, so it's better to envelope the 360 decrement into a try except clause.
def distance(φ, θ):
from numpy import abs
δ = abs(φ%360 - θ%360) # 0 ≤ δ < 360
try:
δ[δ>=180] -= 360 # -180 ≤ δ < 180
except TypeError:
if δ >= 180 : δ -= 360
return abs(δ) # 0 ≤ δ ≤ 180