Muhammad-Yunus

# initial state: 
y0 = [1.0, 0.0]

# time coordinate to solve the ODE for
t = np.linspace(0, 10, 1000)
w0 = 2*np.pi*1.0

Muhammad-Yunus

# solve the ODE problem for three different values of the damping ratio
y1 = odeint(dy, y0, t, args=(0.0, w0)) # undamped
y2 = odeint(dy, y0, t, args=(0.1, w0)) # under damped
y3 = odeint(dy, y0, t, args=(1.1, w0)) # critial damping
y4 = odeint(dy, y0, t, args=(5.0, w0)) # over damped

Muhammad-Yunus

fig, ax = plt.subplots()
ax.plot(t[:500], y1[:500,0], 'k', label="undamped", linewidth=0.25)
ax.plot(t[:500], y2[:500,0], 'r', label="under damped")
ax.plot(t[:500], y3[:500,0], 'b', label=r"critical damping")
ax.plot(t[:500], y4[:500,0], 'g', label="over damped")
ax.legend();

Muhammad-Yunus

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

np.set_printoptions(suppress=True, precision=15)

#input sampling timeseries
n_sampling = 5

#define param

Muhammad-Yunus

#ODE Critical Dumped
Critical_Dumped = np.array(
        [1.          ,  0.9980310417,  0.9921647546,  0.982472909 ,
        0.9690414108,  0.9519697845,  0.9313706249,  0.9073689737,
        0.8801016795,  0.849716714 ,  0.8163724522,  0.7802369177,
        0.7414870035,  0.7003076647,  0.6568910904,  0.6114358603,
        0.5641460809,  0.5152305196,  0.4649017207,  0.413375126 ,
        0.3608681911,  0.3075995058,  0.2537879208,  0.1996516846,
        0.1454075937,  0.0912701602,  0.03745079  , -0.0158429971,
       -0.0684083469, -0.1200477968, -0.1705699976, -0.2197903762,

Muhammad-Yunus

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]

Muhammad-Yunus

w = np.ones([m,n], np.float32)*init_arr_item
v = np.ones([M,m], np.float32)*init_arr_item
b_j = np.zeros([m], np.float32)*init_arr_item
b_k = np.zeros([M], np.float32)*init_arr_item

z_pred = np.zeros([y.shape[0], m], np.float32)
y_pred = np.zeros([y.shape[0], M], np.float32)
E = np.zeros(M, np.float32)

v_new = np.zeros([M,m], np.float32)

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#define sigmoid activation function
def f_sigmoid(value):
    return 1.0/(1.0+np.exp(-value))

def f_sigmoid_derivation(value):
    return f_sigmoid(value)*(1-f_sigmoid(value))
  
#define linear activation function
def f_linear(value):
    return value

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def calc_z_j(x_train, w_train, b_j_train):
    for j in range(m):
        z_pred[:,j] = np.dot(x_train,w_train[j,:]) + b_j_train[j]
    
    return z_pred
    
def calc_y_k(z_train, v_train, b_k_train):
    for k in range(M):
        y_pred[:,k] = np.dot(z_train, v_train[k,:]) + b_k_train[k]
    

Muhammad-Yunus

def error_calc(target, output):
    for k in range(M):
        E[k] = 0.5*(target[k] - output[k])**2
    return np.sum(E)