Fluctuations at High Q values

xpdtools/pipelines/qoi.py

@@ -1,7 +1,7 @@
 import numpy as np
 
 from toolz import get
-
+from xpdtools.tools import avg_curvature
 
 def max_intensity_mean(mean, q, **kwargs):
     q_at_mean_max = (
@@ -21,6 +21,13 @@ def max_gr_mean(pdf, **kwargs):
     return locals()
 
 
+def fluc_high_q(iq_comp, high_q_val=45, **kwargs):
+    q = iq_comp.pluck(0)
+    iq = iq_comp.pluck(1)
+    high_q_fluc = avg_curvature(iq, q, high_q_val)
+    return locals()
+
+
 """
 r = pdf.pluck(0)
 true_pdf = pdf.pluck(1)

xpdtools/tests/test_tools.py

@@ -29,6 +29,7 @@
     generate_map_bin,
     generate_binner,
     move_center,
+    avg_curvature,
 )
 from xpdtools.jit_tools import mask_ring_median, mask_ring_mean
 
@@ -131,3 +132,13 @@ def test_move_center():
     g2 = move_center(m, geo)
     for mm, n in zip(m, ["poni1", "poni2"]):
         assert getattr(g2, n) == getattr(geo, n) + mm
+
+
+def test_avg_curvature():
+    t = np.linspace(0,20*np.pi, 100)
+
+    def damp_sin(t, damp_coef):
+        return 5 * np.sin(t)*np.e**(-damp_coef*t)
+
+    assert avg_curvature(damp_sin(t, .05), t, 40) \
+        < avg_curvature(damp_sin(t, .03), t, 40)

xpdtools/tools.py

@@ -580,3 +580,30 @@ def inner(x, *args, **kwargs):
         return func(*args, **kwargs)
 
     return inner
+
+
+def avg_curvature(y, x, high_val):
+    """Computes the average of the curvature of a given signal past a
+    (currently) user provided high Q value, this will be used as the scalar
+     representation for fluctuations at high Q values.
+
+    Parameters
+    ----------
+    y : ndarray
+        Dependent variable of a given signal
+    x  : ndarray
+        Independent variable of a given signal
+    high_val : float
+        User-defined value start point of analysis. This should remain constant
+        over a scan.
+
+    Returns
+    -------
+    float :
+        The average of curvature beyond a given high_val
+
+    """
+    idx = np.abs(x - high_val).argmin()
+    first_der = np.gradient(y[idx:], x[idx:])
+    sec_der = np.gradient(first_der, x[idx:])
+    return np.average(np.abs(sec_der)/(1+first_der**2)**(3/2))