Add intensity_map_predict_gap with corrected 3-parameter fit

Undulator gap predictor for cSAXS, regenerated from plot_intensity_map.py.
Calibrated on the operating locus (per-energy lowest-gap odd/even flux
maxima, harmonics labelled from the global resonance fit): 3-parameter
pure-exponential field model, gap-residual RMS ~14 um.

Supersedes the earlier 4-parameter (quadratic) constants: c2 was
insignificant (0.2 sigma) and left E_inf degenerate (+/-11 keV).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

csaxs_bec/bec_ipython_client/plugins/cSAXS/intensity_map_predict_gap.py

@@ -0,0 +1,26 @@
+"""Undulator gap predictor emitted by plot_intensity_map.py.
+Edit the fitted constants in the signature to retune."""
+
+import numpy as np
+
+
+def predict_gap(energy, n=3, gap_min=5.0,
+                E_inf=3.2878, c0=2.46086, c1=-0.468091, c2=0.0):
+    """Undulator gap [mm] to place `energy` [keV] on harmonic `n`.
+    Fitted constants are the defaults below; edit them to retune.
+    Returns NaN where the energy is unreachable on that harmonic."""
+    energy = np.asarray(energy, float)
+    arg = E_inf * n / energy - 1.0          # required K^2/2; must be > 0
+    with np.errstate(invalid="ignore", divide="ignore"):
+        y = np.log(arg)
+    if abs(c2) < 1e-12:
+        g = (y - c0) / c1
+    else:
+        disc = c1 * c1 - 4.0 * c2 * (c0 - y)
+        sq = np.sqrt(np.where(disc >= 0, disc, np.nan))
+        r1 = (-c1 + sq) / (2.0 * c2)
+        r2 = (-c1 - sq) / (2.0 * c2)
+        g = np.where(c1 + 2.0 * c2 * r1 < 0, r1, r2)
+    g = np.where(arg > 0, g, np.nan)         # above harmonic cutoff
+    g = np.where(g >= gap_min, g, np.nan)    # below mechanical minimum
+    return g