Fluctuations at High Q values

xpdtools/pipelines/qoi.py

@@ -1,7 +1,7 @@
 import numpy as np
-
+from streamz import collect
 from toolz import get
-
+from xpdtools.tools import avg_curvature,group_pearson,complete_pearson
 
 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 +29,9 @@
     generate_map_bin,
     generate_binner,
     move_center,
+    avg_curvature,
+    complete_pearson,
+    group_pearson
 )
 from xpdtools.jit_tools import mask_ring_median, mask_ring_mean
 
@@ -131,3 +134,41 @@ 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)
+
+
+def test_complete_pearson():
+    x_dif = []
+    x_same = []
+    t = np.linspace(0, 200)
+    y = np.sin(5 * t)
+    for i in np.arange(20)[1:]:
+        x_dif.append(np.sin(i * t))
+        x_same.append(np.sin(5 * t))
+    dif = complete_pearson(x_dif, y)
+    same = complete_pearson(x_same, y)
+    assert (np.array_equal(same, np.ones(len(x_same)))) \
+        and not (np.array_equal(same, dif))
+
+
+def test_group_pearson():
+    x_dif = []
+    x_same = []
+    t = np.linspace(0, 200)
+    for i in np.arange(20)[1:]:
+        x_dif.append(np.sin(i * t))
+        x_same.append(np.sin(5 * t))
+    dif = group_pearson(x_dif)
+    same = group_pearson(x_same)
+    same = np.asarray(same)
+    assert (np.array_equal(same, np.ones(same.shape))) \
+        and not (np.array_equal(same, dif))

xpdtools/tools.py

@@ -19,6 +19,7 @@
 
 import numpy as np
 from scipy.integrate import simps
+import scipy.stats as stats
 from skbeam.core.accumulators.binned_statistic import BinnedStatistic1D
 from skbeam.core.mask import margin
 from xpdtools.jit_tools import mask_ring_median, mask_ring_mean, ring_zscore
@@ -580,3 +581,81 @@ 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 beyond 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))
+
+
+def complete_pearson(group, y):
+    """ Computes a array of scalars representing the similarity of a given
+    dataset to others in a group. This function returns an array of Pearson
+    Product-Moment Correlation coefficients corresponding to the inputed dataset
+    and every member of the inputed group.
+
+    Parameters
+    ----------
+    y : ndarray
+        data that is to be compared to rest of the group.
+
+    group : ndarray
+        group of data to be compared to.
+    Returns
+    -------
+    ndarray :
+        Array of Pearson's Correlation coefficients, index corresponds to
+        the index of group member.
+
+    """
+    pearsons = []
+    for i in group:
+        r, p = stats.pearsonr(y, i)
+        pearsons.append(r)
+    pearsons = np.asarray(pearsons)
+    return pearsons
+
+
+def group_pearson(group):
+    """ This function returns an array of an array of Pearson Product-Moment
+    Correlation coefficients corresponding the similarity between members in the
+    group.
+
+    Parameters
+    ----------
+    group : ndarray
+        group of data to be compared.
+    Returns
+    -------
+    ndarray :
+       Array of arrays Pearson's Correlation coefficients, index corresponds to
+       index of group member.
+
+        """
+    pearson_list = []
+    for i, x in enumerate(group):
+        pearson_list.append(complete_pearson(group, x))
+    pearson_list = np.asarray(pearson_list)
+    return pearson_list