playground.py

type TimeSeries = list[tuple[float, float]]

def normalize_time_series(time_series: TimeSeries, T_min: float, T_max: float) -> TimeSeries:
    min_time = time_series[0][0]
    max_time = time_series[-1][0]

    return [
        (normalize_time(t, min_time, max_time, T_min, T_max), v) for (t, v) in time_series
    ]

type AsOfJoinResult = list[tuple[float, float, float]]

def outer_as_of_join(time_series_a: TimeSeries, time_series_b: TimeSeries) -> AsOfJoinResult:
    merged_time_series = []
    i = 0
    j = 0
    
    while i < len(time_series_a) or j < len(time_series_b):
        if i < len(time_series_a) and (j == len(time_series_b) or time_series_a[i][0] < time_series_b[j][0]):
            timestamp_a, value_a = time_series_a[i]
            closest_value_b = time_series_b[j - 1][1] if j > 0 else 0.0
            merged_time_series.append((timestamp_a, value_a, closest_value_b))
            i += 1
        elif j < len(time_series_b) and (i == len(time_series_a) or time_series_b[j][0] <= time_series_a[i][0]):
            timestamp_b, value_b = time_series_b[j]
            closest_value_a = time_series_a[i - 1][1] if i > 0 else 0.0
            merged_time_series.append((timestamp_b, closest_value_a, value_b))
            j += 1
    
    return merged_time_series

def normalize_time(
    t: float,
    t_min: float,
    t_max: float,
    T_min: float,
    T_max: float
) -> float:
    return (t - t_min) / (t_max - t_min) * (T_max - T_min)

if __name__ == "__main__":
    channel_a_time_series = [
            (0.0, 2.0),
            (1.0, 6.0),
            (4.0, 8.0),
            (7.0, 10.0),
    ]

    channel_b_time_series = [
            (10.0, 1.0),
            (12.0, 2.0),
            (14.0, 3.0),
            (20.0, 0.0),
            (22.0, 0.0),
            (24.0, 1.0),
    ]

    print("----Channel A-----")
    for val in channel_a_time_series:
        print(val)
    print()

    print("----Channel B-----")
    for val in channel_b_time_series:
        print(val)
    print()

    common_time_range_min = 0.0
    common_time_range_max = 100.0

    # Normalize to common time scale for computation
    channel_a_intermediate = normalize_time_series(channel_a_time_series, common_time_range_min, common_time_range_max)
    channel_b_intermediate = normalize_time_series(channel_b_time_series, common_time_range_min, common_time_range_max)

    intermediate = outer_as_of_join(channel_b_intermediate, channel_a_intermediate)

    print("----JOINED AND NORMALIZED-----")
    for v in intermediate:
        print(v)
    print()

    transformed_time_series: TimeSeries = []

    for (t, a, b) in intermediate:
        transformed_time_series.append((t, a + b))

    # Output time range... the "root" time range"
    output_time_range_min = channel_a_time_series[0][0]
    output_time_range_max = channel_a_time_series[-1][0]

    # Normalize to output time scale
    out = normalize_time_series(transformed_time_series, output_time_range_min, output_time_range_max)

    print("----OUT-----")
    for v in out:
        print(v)

# OUTPUT
# ----Channel A-----
# (0.0, 2.0)
# (1.0, 6.0)
# (4.0, 8.0)
# (7.0, 10.0)
# 
# ----Channel B-----
# (10.0, 1.0)
# (12.0, 2.0)
# (14.0, 3.0)
# (20.0, 0.0)
# (22.0, 0.0)
# (24.0, 1.0)
# 
# ----JOINED AND NORMALIZED-----
# (0.0, 0.0, 2.0)
# (0.0, 1.0, 2.0)
# (14.285714285714285, 1.0, 6.0)
# (14.285714285714285, 2.0, 6.0)
# (28.57142857142857, 3.0, 6.0)
# (57.14285714285714, 3.0, 8.0)
# (71.42857142857143, 0.0, 8.0)
# (85.71428571428571, 0.0, 8.0)
# (100.0, 0.0, 10.0)
# (100.0, 1.0, 10.0)
# 
# ----OUT-----
# (0.0, 2.0)
# (0.0, 3.0)
# (1.0, 7.0)
# (1.0, 8.0)
# (2.0, 9.0)
# (4.0, 11.0)
# (5.0, 8.0)
# (6.0, 8.0)
# (7.0, 10.0)
# (7.0, 11.0)