Create rossler.md

docs/examples/rossler.md

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+# Rossler Attractor
+Firstly, we will define functions for simulating Rossler attractor
+
+
+```python
+def rossler(t, X, a, b, c):
+    """The Rössler equations."""
+    x, y, z = X
+    xp = -y - z
+    yp = x + a*y
+    zp = b + z*(x - c)
+    return xp, yp, zp
+
+def rossler_time_series(tmax,n, Xi, a, b, c):
+    x, y, z = Xi
+    X=[x]
+    Y=[y]
+    Z=[z]
+    dt=0.0001
+    for i in range(1, tmax):
+      #print('Xi:', Xi)
+      x, y, z = Xi
+      xp, yp, zp=rossler(t, Xi, a, b, c)
+      x_next=x+dt*xp
+      y_next=y+dt*yp
+      z_next=z+dt*zp
+      X.append(x_next)
+      Y.append(y_next)
+      Z.append(z_next)
+      Xi=(x+dt*xp,y+dt*yp,z+dt*zp)
+
+    X=np.array(X)
+    Y=np.array(Y)
+    Z=np.array(Z)
+
+    step=int(tmax/n)
+    indices = np.arange(0,tmax, step)
+    #print('IS NAN X:',np.sum(np.isnan(X[indices])))
+    #print('IS NAN Y:',np.sum(np.isnan(Y[indices])))
+    #print('IS NAN Z:',np.sum(np.isnan(Z[indices])))
+
+    return X[indices], Y[indices], Z[indices]
+```
+Now, define the parameter values. We are mainly varying a, while keeping b and c the same for getting transition from periodic to chaotic attractor. 
+```python
+b = 0.2
+c = 5.7
+a_array = [0.1,0.15,0.2,0.25,0.3]
+SNR = [0.125,0.25,0.5,0.75,1.0,1.25,1.5,1.75,2.0]
+```
+
+Now we will simulate the data for different nose levels, and will save it to a directory
+
+
+```python
+for snr in tqdm(SNR):                                                                             # Looping over SNR values
+  for j in tqdm(range(len(a_array)):                                                              # Looping over values of parameter a
+    a=a_array[j]
+    random.seed(1)
+    np.random.seed(seed=301)
+    rp_sizes = random.sample(range(150, 251), 10)                                                 # selecting a length for time series
+    for k in tqdm(range(5)):                                                                      # Repeats
+
+          u0, v0, w0 = 0+(1*np.random.randn()), 0+(1*np.random.randn()), 10+(1*np.random.randn()) # Setting initial conditions
+
+
+          for k2 in tqdm(range(len(rp_sizes))):                                                   # Looping over different RP sizes(time series length)
+            tmax, n = int(1000000*(rp_sizes[k2]/250)), rp_sizes[k2]
+            print('started model')
+            Xi=(u0, v0, w0)
+            t = np.linspace(0, tmax, n)
+            x, y, z=rossler_time_series(tmax,n, Xi, a, b, c)
+
+            x=add_noise(x, snr)                                                                  # Adding noise
+            y=add_noise(y, snr)
+            z=add_noise(z, snr)
+            u[:,0]=x                                                                             # Defining the output matrix
+            u[:,1]=y
+            u[:,2]=z
+            np.save('/user/swarag/Rossler/signals/('+str(snr)+','+str(a)+','+str(u0)+','+str(v0)+','+str(w0)+','+str(rp_sizes[k2])+')~.npy',u)  # Save the data to a numpy file
+```
+Since we have saved the time series data to a folder, we can repeat the same steps
+
+
+```python
+input_path = '/user/swarag/Rossler/signals'                                        # directory to which the signals are saved
+RP_dir = '/user/swarag/Rossler/RP'                                                 # directory to which we want to save the RPs
+RP_computer(input_path, RP_dir)                                                    # generating RPs and saving to the specified folder
+``
+
+Since we have generated the RPs at this step, we can extract the variables from it. We have selected same window size for the sliding window approach. 
+
+
+```python
+Dict_RPs=windowed_RP(68, 'RP')                                                      # Specifying window size and folder in which RPs are saved
+First_middle_last_sliding_windows_all_vars(Dict_RPs,'Rossler_data.csv')            # Saving RQA variables to a csv file
+```
+
+Now we need to add additional columns to the data for later analysis
+
+
+```python
+data = pd.read_csv('Rossler_data.csv')
+FILE = np.array(data['group'])                                                      # In the output data, the field named 'group' will have file name which contains details
+SNR =[]
+A =[]
+U0 =[]
+V0 =[]
+W0 =[]
+SIZE =[]
+for FI in FILE:
+  info = ast.literal_eval(FI)
+  SNR.append(info[0])
+  A.append(info[1])
+  U0.append(info[2])
+  V0.append(info[3])
+  W0.append(info[4])
+  SIZE.append(info[5])
+
+data['snr'] = SNR
+data['a'] = A
+data['u0'] = U0
+data['v0'] = V0
+data['w0'] = W0
+data['length'] = SIZE
+A = np.array(A)
+
+SYNCH = 1*(A>0.2)                                                                   # Defining synchrony condition, parameter value belonging to the chaotic region
+data['synch'] = SYNCH
+```
+Now, we need to select an SNR value, scale the variables and run the classifier
+
+```python
+################################################################## Select the value of SNR ################################################################################################
+data_ = data[data['snr']==1.0].reset_index(drop = True)
+data_ = data_[data['window']== 'mode'].reset_index(drop = True)                   # mode of RQA variables from the sliding windows
+################################################################## Scale the data #########################################################################################################\
+features=['recc_rate',
+ 'percent_det',
+ 'avg_diag',
+ 'max_diag',
+ 'percent_lam',
+ 'avg_vert',
+ 'vert_ent',
+ 'diag_ent',
+ 'vert_max']
+for feature in features:
+  arr = np.array(data_[feature])
+  data_[feature] = (arr - np.mean(arr))/(np.std(arr) + 10**(-9))
+
+################################################################# Run the classification ###################################################################################################
+nested_cv(data_, features, 'synch', 'Kuramotot(SNR=1.0)', repeats=100, inner_repeats=10, outer_splits=3, inner_splits=2)
+#################################################################   DONE ! ################################################################################################################
+```