Rolling and exponentially weighted values

Coral.Window works on a one-dimensional tensor[n, f32] and returns a tensor of the same length n. Take a column out of a frame with get_float_col first.

Function	Signature	Value at position i
rolling_sum	(col: tensor[n, f32], window: i64) -> tensor[n, f32]	Sum of the window values ending at i
rolling_mean	same	That sum divided by window
rolling_std	same	Sample standard deviation (ddof=1) of those values
rolling_min	same	Smallest of those values
rolling_max	same	Largest of those values
ewm	(col: tensor[n, f32], alpha: f32) -> tensor[n, f32]	alpha * col[i] + (1 - alpha) * result[i - 1], with result[0] = col[0]

The rolling functions put NaN at the first window - 1 positions, which come before the first full window. A window longer than the input gives all NaN. ewm is the pandas adjust=False form.

module Coral.BookWindow
import Coral.Window (rolling_mean)
export (main)
def main() -> f32 = {
  values = to_tensor([1.0f32, 2.0f32, 3.0f32, 4.0f32, 5.0f32])
  means = rolling_mean(values, 3i64)
  index(to_list(means), 4i64)
}

main returns 4.0, the mean of 3.0, 4.0, and 5.0.

For the input [1.0, 2.0, 4.0, 8.0, 16.0], these calls return:

Call	Result
rolling_sum(v, 2)	[NaN, 3.0, 6.0, 12.0, 24.0]
rolling_std(v, 2)	[NaN, 0.70710677, 1.4142135, 2.828427, 5.656854]
rolling_min(v, 3)	[NaN, NaN, 1.0, 2.0, 4.0]
ewm(v, 0.5)	[1.0, 1.5, 2.75, 5.375, 10.6875]

Input domain and edge cases

• Window size. Pass window >= 1. A negative window fails with take requires non-negative count. A window of 0 is not rejected but is meaningless: rolling_sum returns zeros, rolling_mean returns NaN, and rolling_min and rolling_max fail with an index error.
• Window of one. rolling_std(v, 1) is NaN everywhere, because the sample divisor window - 1 is zero.
• NaN inputs are not skipped. Every window that contains a NaN gives NaN for all five rolling functions. For [1.0, NaN, 3.0, 4.0, 5.0], rolling_sum(v, 2) is [NaN, NaN, NaN, 7.0, 9.0]. In ewm, a NaN makes that position and every later position NaN. Fill or drop NaNs first; see Missing values.
• alpha. Use a value in (0, 1]; 1 returns the input unchanged. Coral does not check the range: ewm(v, 2.0) runs and returns [1.0, 3.0, 5.0, 11.0, 21.0], which is not a smoothed series.
• Empty input. ewm of an empty tensor returns an empty tensor.