Replace CSVs with chi2.ppf for GLRT test (#456)

* Replace CSVs with `chi2.ppf` for GLRT test

* default 0.001

* test smaller alphas

* specify log in temp dir

src/dolphin/shp/_glrt.py

@@ -1,14 +1,12 @@
 from __future__ import annotations
 
-import csv
-from functools import lru_cache
 from math import log
-from pathlib import Path
 from typing import Optional
 
 import numba
 import numpy as np
 from numpy.typing import ArrayLike
+from scipy import stats
 
 from dolphin._types import Strides
 from dolphin.utils import _get_slices, compute_out_shape
@@ -78,7 +76,8 @@ def estimate_neighbors(
     half_row, half_col = halfwin_rowcol
     rows, cols = mean.shape
 
-    threshold = get_cutoff(alpha=alpha, N=nslc)
+    # 1 Degree of freedom, regardless of N
+    threshold = stats.chi2.ppf(1 - alpha, df=1)
 
     strides_rowcol = (strides["y"], strides["x"])
     out_rows, out_cols = compute_out_shape((rows, cols), Strides(*strides_rowcol))
@@ -88,6 +87,7 @@ def estimate_neighbors(
     return _loop_over_pixels(
         mean,
         var,
+        nslc,
         halfwin_rowcol,
         strides_rowcol,
         threshold,
@@ -96,47 +96,18 @@ def estimate_neighbors(
     )
 
 
-def get_cutoff(alpha: float, N: int) -> float:
-    r"""Compute the upper cutoff for the GLRT test statistic.
-
-    Statistic is
-
-    \[
-    2\log(\sigma_{pooled}) - \log(\sigma_{p}) -\log(\sigma_{q})
-    \]
-
-    Parameters
-    ----------
-    alpha: float
-        Significance level (0 < alpha < 1).
-    N: int
-        Number of samples.
-
-    Returns
-    -------
-    float
-        Cutoff value for the GLRT test statistic.
-
-    """
-    n_alpha_to_cutoff = _read_cutoff_csv()
-    try:
-        return n_alpha_to_cutoff[(N, alpha)]
-    except KeyError as e:
-        msg = f"Not implemented for {N = }, {alpha = }"
-        raise NotImplementedError(msg) from e
-
-
 @numba.njit(nogil=True)
-def _compute_glrt_test_stat(scale_1, scale_2):
+def _compute_glrt_test_stat(scale_sq_1, scale_sq_2, N):
     """Compute the GLRT test statistic."""
-    scale_pooled = (scale_1 + scale_2) / 2
-    return 2 * log(scale_pooled) - log(scale_1) - log(scale_2)
+    scale_pooled = (scale_sq_1 + scale_sq_2) / 2
+    return N * (2 * log(scale_pooled) - log(scale_sq_1) - log(scale_sq_2))
 
 
 @numba.njit(nogil=True, parallel=True)
 def _loop_over_pixels(
     mean: ArrayLike,
     var: ArrayLike,
+    N: int,
     halfwin_rowcol: tuple[int, int],
     strides_rowcol: tuple[int, int],
     threshold: float,
@@ -180,27 +151,11 @@ def _loop_over_pixels(
                         continue
                     scale_2 = scale_squared[in_r2, in_c2]
 
-                    T = _compute_glrt_test_stat(scale_1, scale_2)
+                    T = _compute_glrt_test_stat(scale_1, scale_2, N)
 
                     is_shp[out_r, out_c, r_off, c_off] = threshold > T
             if prune_disconnected:
                 # For this pixel, prune the groups not connected to the center
                 remove_unconnected(is_shp[out_r, out_c], inplace=True)
 
     return is_shp
-
-
-@lru_cache
-def _read_cutoff_csv():
-    filename = Path(__file__).parent / "glrt_cutoffs.csv"
-
-    result = {}
-    with open(filename) as file:
-        reader = csv.DictReader(file)
-        for row in reader:
-            n = int(row["N"])
-            alpha = float(row["alpha"])
-            cutoff = float(row["cutoff"])
-            result[(n, alpha)] = cutoff
-
-    return result