--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/curve_fitting.py	Thu Jul 22 19:34:36 2021 +0000
@@ -0,0 +1,106 @@
+"""
+Copyright 2021 Biomedical Computer Vision Group, Heidelberg University.
+Author: Qi Gao (qi.gao@bioquant.uni-heidelberg.de)
+
+Distributed under the MIT license.
+See file LICENSE for detail or copy at https://opensource.org/licenses/MIT
+
+"""
+
+import argparse
+
+import numpy as np
+import pandas as pd
+from scipy.optimize import least_squares
+
+
+def compute_curve(x, par):
+    assert len(par) in [2, 3], 'The degree of curve must be 1 or 2!'
+    if len(par) == 3:
+        return par[0] * x + par[1] + par[2] * x ** 2
+    elif len(par) == 2:
+        return par[0] * x + par[1]
+
+
+def fitting_err(par, xx, seq, penalty):
+    assert penalty in ['abs', 'quadratic', 'student-t'], 'Unknown penalty function!'
+    curve = compute_curve(xx, par)
+    if penalty == 'abs':
+        err = np.sqrt(np.abs(curve - seq))
+    elif penalty == 'quadratic':
+        err = (curve - seq)
+    elif penalty == 'student-t':
+        a = 1000
+        b = 0.001
+        err = np.sqrt(a * np.log(1 + (b * (curve - seq)) ** 2))
+    return err
+
+
+def curve_fitting(seq, degree=2, penalty='abs'):
+    assert len(seq) > 5, 'Data is too short for curve fitting!'
+    assert degree in [1, 2], 'The degree of curve must be 1 or 2!'
+
+    par0 = [(seq[-1] - seq[0]) / len(seq), np.mean(seq[0:3])]
+    if degree == 2:
+        par0.append(-0.001)
+
+    xx = np.array([i for i in range(len(seq))]) + 1
+    x = np.array(par0, dtype='float64')
+    result = least_squares(fitting_err, x, args=(xx, seq, penalty))
+
+    return compute_curve(xx, result.x)
+
+
+def curve_fitting_io(fn_in, fn_out, degree=2, penalty='abs', alpha=0.01):
+    # read all sheets
+    xl = pd.ExcelFile(fn_in)
+    nSpots = len(xl.sheet_names)
+    data_all = []
+    for i in range(nSpots):
+        df = pd.read_excel(xl, xl.sheet_names[i])
+        data_all.append(np.array(df))
+    col_names = df.columns.tolist()
+    ncols_ori = len(col_names)
+
+    # curve_fitting
+    diff = np.array([], dtype=('float64'))
+    for i in range(nSpots):
+        seq = data_all[i][:, -1]
+        seq_fit = seq.copy()
+        idx_valid = ~np.isnan(seq)
+        seq_fit[idx_valid] = curve_fitting(seq[idx_valid], degree=2, penalty='abs')
+        data_all[i] = np.concatenate((data_all[i], seq_fit.reshape(-1, 1)), axis=1)
+        if alpha > 0:
+            diff = np.concatenate((diff, seq_fit[idx_valid] - seq[idx_valid]))
+
+    # add assistive curve
+    if alpha > 0:
+        sorted_diff = np.sort(diff)
+        fac = 1 - alpha / 2
+        sig3 = sorted_diff[int(diff.size * fac)]
+        for i in range(nSpots):
+            seq_assist = data_all[i][:, -1] + sig3
+            data_all[i] = np.concatenate((data_all[i], seq_assist.reshape(-1, 1)), axis=1)
+
+    # write to file
+    with pd.ExcelWriter(fn_out) as writer:
+        for i in range(nSpots):
+            df = pd.DataFrame()
+            for c in range(ncols_ori):
+                df[col_names[c]] = data_all[i][:, c]
+            df['CURVE'] = data_all[i][:, ncols_ori]
+            if alpha > 0:
+                df['CURVE_A'] = data_all[i][:, ncols_ori + 1]
+            df.to_excel(writer, sheet_name=xl.sheet_names[i], index=False, float_format='%.2f')
+        writer.save()
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description="Fit (1st- or 2nd-degree) polynomial curves to data points")
+    parser.add_argument("fn_in", help="File name of input data points (xlsx)")
+    parser.add_argument("fn_out", help="File name of output fitted curves (xlsx)")
+    parser.add_argument("degree", type=int, help="Degree of the polynomial function")
+    parser.add_argument("penalty", help="Optimization objective for fitting")
+    parser.add_argument("alpha", type=float, help="Significance level for generating assistive curves")
+    args = parser.parse_args()
+    curve_fitting_io(args.fn_in, args.fn_out, args.degree, args.penalty, args.alpha)