Statistics

Scripts to generate statistics out of orbit data 
from orbit_generation.data import get_example_orbit_data
orbit_data = get_example_orbit_data()
orbit_data.shape
(400, 7, 100)

Simple statistics

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calculate_overall_spatial_statistics

 calculate_overall_spatial_statistics (orbits:numpy.ndarray)

Calculate the overall min, mean, max, and percentile statistics for each scalar (position and velocity in X, Y, Z) across all time instants and orbits.

Type Details
orbits ndarray Array of shape (number_of_orbits, 6 or 7, number_of_time_instants) containing orbit data
Returns ndarray 
orbits = np.array([
    [[1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 6], [5, 6, 7], [6, 7, 8]],  # Orbit 1
    [[4, 4, 4], [3, 4, 5], [4, 5, 6], [5, 6, 7], [6, 7, 8], [7, 8, 9]]   # Orbit 2
])

# Call the function to calculate statistics
stats = calculate_overall_spatial_statistics(orbits)

# Define the expected values for each statistic
expected_stats = np.array([
    [1, 3, 4, 2.25, 3.5, 4],    # posx
    [2, 3.5, 5, 3, 3.5, 4],     # posy
    [3, 4.5, 6, 4, 4.5, 5],     # posz
    [4, 5.5, 7, 5, 5.5, 6],     # velx
    [5, 6.5, 8, 6, 6.5, 7],     # vely
    [6, 7.5, 9, 7, 7.5, 8]      # velz
])

# Test each statistic for each scalar
for i, scalar_name in enumerate(['posx', 'posy', 'posz', 'velx', 'vely', 'velz']):
    test_eq(stats[i, 0], expected_stats[i, 0])
    test_eq(stats[i, 1], expected_stats[i, 1])
    test_eq(stats[i, 2], expected_stats[i, 2])
    test_eq(stats[i, 3], expected_stats[i, 3])
    test_eq(stats[i, 4], expected_stats[i, 4])
    test_eq(stats[i, 5], expected_stats[i, 5])

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calculate_per_orbit_spatial_statistics

 calculate_per_orbit_spatial_statistics (orbits:numpy.ndarray)

Calculate per-orbit min, mean, max, and percentile statistics for each scalar (position and velocity in X, Y, Z) across all time instants.

Type Details
orbits ndarray A numpy array of shape (number_of_orbits, 6 or 7, number_of_time_instants) containing orbit data
Returns ndarray

Plot Time

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plot_time_increments

 plot_time_increments (orbit_dataset:numpy.ndarray,
                       orbits_to_plot:Optional[List[int]]=None,
                       show_legend:bool=True)

Plots the time as a function to visualize how it increments for each orbit.

Type Default Details
orbit_dataset ndarray The 3D numpy array representing the orbits
orbits_to_plot Optional None Optional list of integers referring to the orbits to plot
show_legend bool True Boolean to control the display of the legend
Returns None

Plot Histograms

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plot_orbit_data_lengths

 plot_orbit_data_lengths (orbit_data:Dict[int,numpy.ndarray],
                          key_range:Tuple[int,int]=(1, 36072),
                          dimension:int=0, bins:int=30, color:str='blue',
                          plot:bool=True, title:str='Histogram of Orbits
                          Time Steps')

Analyzes and optionally plots the distribution of time steps across multiple orbits. Returns the list of lengths if plot=False, otherwise displays histogram and returns None.

Type Default Details
orbit_data Dict Dictionary mapping orbit IDs to orbit data arrays
key_range Tuple (1, 36072) Range of orbit IDs to analyze (start, end)
dimension int 0 Dimension of the orbit data to measure length
bins int 30 Number of bins for histogram
color str blue Color of histogram bars
plot bool True Whether to plot the histogram
title str Histogram of Orbits Time Steps Title of the plot
Returns Optional

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plot_histograms_position

 plot_histograms_position (data:numpy.ndarray,
                           save_path:Optional[str]=None,
                           last_time_elements:bool=True)

Plots histograms for the scalar values (position and velocity in X, Y, Z, and optionally time) across all orbits and time points. Handles arrays with 6 or 7 scalar dimensions, with the 7th being ‘time’.

Type Default Details
data ndarray The orbit data array of shape (num_orbits, num_scalars, num_time_points)
save_path Optional None Optional path to save the plot image
last_time_elements bool True Whether to plot only the last elements of the time vectors
Returns None 
plot_histograms_position(orbit_data)

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plot_histograms_comparison

 plot_histograms_comparison (data1:numpy.ndarray, data2:numpy.ndarray,
                             label1:str='Dataset 1', label2:str='Dataset
                             2', save_path:str=None, normalize:bool=False)

Plots histograms for scalar values (position, velocity in X, Y, Z, and optionally time) from two datasets on the same chart with different colors. Supports both 6 and 7 scalar dimensions, with the 7th being ‘time’. Optionally saves the plot to a specified file path and can normalize histograms for relative comparison.

Type Default Details
data1 ndarray First orbit data array of shape (num_orbits, num_scalars, num_time_points).
data2 ndarray Second orbit data array of shape (num_orbits, num_scalars, num_time_points).
label1 str Dataset 1 Label for the first dataset.
label2 str Dataset 2 Label for the second dataset.
save_path str None Optional path to save the plot image.
normalize bool False Normalize histograms to show relative frequencies.
Returns None 
orbit_data1 = orbit_data[:100]
orbit_data2 = orbit_data[100:]

plot_histograms_comparison(orbit_data1, orbit_data2)

orbit_data3 = orbit_data2[:5]

plot_histograms_comparison(orbit_data1, orbit_data3, normalize=True)