From fa6433815206f16cb56e18fe97fa6a38e5ee10fe Mon Sep 17 00:00:00 2001
From: Jan Grewe <jan.grewe@g-node.org>
Date: Fri, 3 Feb 2017 09:33:39 +0100
Subject: [PATCH] solution (python) for eod fit problem

---
 projects/project_eod/solution/fit_eod.py | 80 ++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 projects/project_eod/solution/fit_eod.py

diff --git a/projects/project_eod/solution/fit_eod.py b/projects/project_eod/solution/fit_eod.py
new file mode 100644
index 0000000..3af725e
--- /dev/null
+++ b/projects/project_eod/solution/fit_eod.py
@@ -0,0 +1,80 @@
+import matplotlib.pyplot as plt
+import numpy as np
+from IPython import embed
+import scipy.io as scio
+
+def load_data(filename):
+    data = scio.loadmat(filename)
+    t = data['t']
+    eod = data['eod']
+    return t[0], eod[0]
+    
+
+def eod_model(p, t):
+    b_0 = p[0]
+    omega_0 = p[1]
+    
+    params = p[2:]
+    n = len(params)/2
+    eod = np.zeros(t.shape)
+    for i in range(n):
+        eod += params[i*2]  * np.sin(2 * np.pi * t * (i+1) * omega_0 + params[i*2+1]) 
+    eod += b_0
+    return eod
+
+
+def fit_error(p, t, y):
+    y_dash = eod_model(p,t)
+    err = np.mean((y - y_dash)**2)
+    return err
+
+
+def gradient(p, t, y, scale=None):
+    if scale is None:
+        scale = np.ones(len(p))
+    grad = np.zeros(len(p))
+    h = 0.002
+    for i in range(len(p)):
+        p_temp = list(p)
+        p_temp[i] =  p[i] + scale[i] * h
+        grad[i] = (fit_error(p_temp, t, y) - fit_error(p, t, y)) / h
+    return grad
+
+
+def gradient_descent(t, y):
+    count = 80
+    b_0 = np.mean(y)
+    omega_0 = 650
+    params = [b_0, omega_0, np.min(y) +  np.max(y), np.pi/2, (np.min(y) +  np.max(y))/2,  np.pi/3, (np.min(y) +  np.max(y))/4,  np.pi/4, (np.min(y) +  np.max(y))/5,  np.pi]
+    scale = np.ones(len(params))
+    scale[1] = 1000
+    eps = 0.01
+    grad = None
+    errors = []
+    plt.axis([0, t[count], -3, 3.5])
+    plt.ion()
+    plt.plot(t[:count], y[:count])
+    l = None
+    while (grad is None) or (np.linalg.norm(grad) > 0.01):
+        errors.append(fit_error(params, t[:count], y[:count]))
+        
+        grad = gradient(params, t[:count], y[:count])        
+        params -= eps * scale * grad 
+        if l is None:
+            l = plt.plot(t[:count], eod_model(params, t[:count]))
+        else:
+            l[0].set_data(t[:count], eod_model(params, t[:count]))
+        plt.title("norm: %.2f, freq: %.2f" % (np.linalg.norm(grad), params[1]))
+        plt.pause(0.005)
+    embed()
+    exit()
+    
+
+
+if __name__ == "__main__":
+    datafile = '../data/EOD_data.mat'
+    t, eod = load_data(datafile)
+    # eod = eod_model([0.0, 600, 1.0, 0.0], t[:100])
+    gradient_descent(t, eod)
+    embed()
+    exit()