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float precision check in rational quadratic spline discriminant #71

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float precision check in rational quadratic spline discriminant #71

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d8b0858
float precision check
francesco-vaselli Mar 15, 2023
4934a85
comments and torch.where
francesco-vaselli Sep 30, 2023
4bcc21d
comments 1
francesco-vaselli Sep 30, 2023
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10 changes: 10 additions & 0 deletions nflows/transforms/splines/rational_quadratic.py
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Original file line number Diff line number Diff line change
Expand Up @@ -139,6 +139,16 @@ def rational_quadratic_spline(
c = -input_delta * (inputs - input_cumheights)

discriminant = b.pow(2) - 4 * a * c

# Correcting for floating-point errors in the discriminant calculation.
# The float_precision_mask identifies elements where the discriminant is essentially zero,
# compared to the magnitude of b.pow(2),
# but appears nonzero due to machine precision limitations.
# Threshold values (1e-8 and 1e-6) are heuristic-based to manage numerical stability.
float_precision_mask = (torch.abs(discriminant) / (b.pow(2) + 1e-8)) < 1e-6
discriminant = torch.where(float_precision_mask,
torch.zeros_like(discriminant), discriminant)

assert (discriminant >= 0).all()

root = (2 * c) / (-b - torch.sqrt(discriminant))
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