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def calc_v_new(v_last, y, y_prediction, z_prediction):
    delta_k = np.transpose(f_activation_derivation_output(y_prediction)*(np.reshape(y, (y.shape[0], 1)) - y_prediction))
        
    for j in range(m):
        v_new[:,j] = v_last[:,j] + learning_rate*np.dot(delta_k,z_prediction[:,j])
            
    return v_new, delta_k


def calc_w_new(w_last, v_new, delta_k, z_prediction, x_input):

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def train_model(train_count, w_train, v_train, b_j_train, b_k_train, y_train, x_train):
    for l in range(train_count):
        z_prediction = calc_z_j(x_train, w_train, b_j_train)
        z_prediction = f_activation(z_prediction)
        
        y_prediction = calc_y_k(z_prediction, v_train, b_k_train)
        y_prediction = f_activation_output(y_prediction)
        
        v_train, delta_k = calc_v_new(v_train, y_train, y_prediction, z_prediction)
        w_train, delta_j = calc_w_new(w_train, v_train, delta_k, z_prediction, x_train)

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v, w, b_k, b_j = train_model(TRAIN_ITER, w, v, b_j, b_k, y, x)

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def test(x_test, w, v,  b_j, b_k):
    z_prediction = np.dot(x_test, np.transpose(w)) + b_j
    f_z_prediction = f_activation(z_prediction)
    
    y_prediction = np.dot(f_z_prediction, np.transpose(v)) + b_k
    f_y_prediction =  f_activation_output(y_prediction)
    
    return f_y_prediction

y_prediction_test = np.zeros(len(x), np.float32)

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t = np.linspace(1, 500, 500)

ODE_Target = np.transpose(np.array([t, Critical_Dumped], np.float32))
ODE_Output = np.transpose(np.array([t[n_sampling:], y_prediction_test[:,0]], np.float32))

ODE_Target_PD =  pd.DataFrame(data=ODE_Target[:,:],   
              index=ODE_Target[:,0],    
              columns=['t', 'x actual'])  

ODE_Output_PD = pd.DataFrame(data=ODE_Output[:,:],   

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import pandas as pd 
import numpy as np
import matplotlib.pyplot as plt


#input sampling timeseries
n_sampling = 5

#define param
n = n_sampling

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CO_TS_TRAIN = CO_TS[CO_TS.index.month < 12] #january - november time series as train data
CO_TS_TEST = CO_TS[CO_TS.index.month == 12] #december time series as test data

CO_TS_TRAIN_Arr = CO_TS_TRAIN.to_numpy()
CO_TS_TEST_Arr = CO_TS_TEST.to_numpy()

CO_TS_TRAIN_Arr = np.reshape(CO_TS_TRAIN_Arr, (CO_TS_TRAIN_Arr.shape[0]))
CO_TS_TEST_Arr = np.reshape(CO_TS_TEST_Arr, (CO_TS_TEST_Arr.shape[0]))

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def split_sequence(sequence, n_steps):
	_X, _y = list(), list()
	for i in range(len(sequence)):
		# find the end of this pattern
		end_ix = i + n_steps
		# check if we are beyond the sequence
		if end_ix > len(sequence)-1:
			break
		# gather input and output parts of the pattern
		seq_x, seq_y = sequence[i:end_ix], sequence[end_ix]

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from keras.models import Sequential
from keras.layers import Dense
from keras.optimizers import Adam 

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import os
os.environ['CUDA_VISIBLE_DEVICES'] = '-1'