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_stats/schmidt_test.py

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+from bisect import bisect_left
+
+import numpy as np
+import scipy as scp
+import pandas as pd
+
+def schmidt_test(decay_times):
+    """
+    Calculates σ_Θ_exp following the original Schmidt test.
+
+    Keyword arguments:
+        decay_times         1D array of decay times to be tested.
+
+    Returns:
+        sigma_theta_exp     The σ_Θ_exp value for the given data.
+        confidence_interval The upper and lower limit to the confidence interval.
+
+    """
+    
+    sigma_theta_exp = np.nanstd(np.log(decay_times))
+
+    if len(decay_times) <= 100: # Schmidt (2000) has tabulated values for n <= 100 events
+        dat = pd.read_pickle("_stats/st_sigma_theta_exp_properties.pkl") # load tabulated values
+        i = bisect_left(dat.loc[:,'n'], len(decay_times)) # find the closest value in tabulated values
+        lim_l = dat.loc[i,'lower limit of σ_Θ_exp']
+        lim_h = dat.loc[i,'upper limit of σ_Θ_exp']
+    else: # if n > 100, calculate limits based on analytical formula
+        lim_l = 1.28-2.15/np.sqrt(len(decay_times))
+        lim_h = 1.28+2.15/np.sqrt(len(decay_times))
+
+    confidence_interval = (lim_l, lim_h)
+    return sigma_theta_exp, confidence_interval
+
+def g_nan_mean(data):
+    """
+    Code written by Anton
+    """
+
+    if len(np.shape(data)) == 1:
+        return data
+    ret = np.empty(np.shape(data)[0])
+    for i in range(np.shape(data)[0]):
+        temp = 1
+        steps = 0
+        for j in range(np.shape(data)[1]):
+            if isinstance(data, pd.DataFrame) and ~np.isnan(data.iloc[i,j]):
+                temp *= data.iloc[i,j]
+            elif not isinstance(data, pd.DataFrame) and ~np.isnan(data[i,j]):
+                temp *= data[i,j]
+            else:
+                break
+            steps += 1
+        ret[i] = temp**(1./steps)
+    return ret
+
+def generalised_schmidt_test(df):
+    """
+    Generalised Schmidt Test
+
+    Keyword arguments:
+        df    DataFrame containing simulated chain event times  
+    """
+
+    if any(df.iloc[:,-1].str.contains('SF')):
+        df = df.iloc[:,:-1]
+
+    theta = np.log(df)
+    theta_var = np.square(theta - np.nanmean(theta, axis=0))
+    gen_Schmidt_temp = g_nan_mean(theta_var)
+    sigma_theta_exp = np.sqrt(np.mean(gen_Schmidt_temp))
+
+    if len(df) <= 100: # Schmidt (2000) has tabulated values for n <= 100 events
+        dat = pd.read_pickle("_stats/st_sigma_theta_exp_properties.pkl") # load tabulated values
+        i = bisect_left(dat.loc[:,'n'], len(df)) # find the closest value in tabulated values
+        lim_l = dat.loc[i,'lower limit of σ_Θ_exp']
+        lim_h = dat.loc[i,'upper limit of σ_Θ_exp']
+    else: # if n > 100, calculate limits based on analytical formula
+        lim_l = 1.28-2.15/np.sqrt(len(df))
+        lim_h = 1.28+2.15/np.sqrt(len(df))
+
+    confidence_interval = (lim_l, lim_h)
+
+    return sigma_theta_exp, confidence_interval