sampleFunc.py

import numpy as np

def sample_xt_prim(xt, yt, params, t):
    T = len(yt)
    rand = np.random.uniform()
    x_new = gt_prime = gt_curr = 1
    if(rand <= 0.33):
        if(t > 0):
            vn = np.random.normal(0,1)
            x_new = params[0]*xt[t-1] + params[1]*vn
        else:
            x_new = np.random.normal(0, params[1]**2/(1 - params[0]**2))
        gt_prime = (1/params[1]) * np.sqrt(2/np.pi) * np.exp(
            -(x_new - params[0]*xt[t-1])**2 / (2*params[1]**2) )
        gt_curr = (1/params[1]) * np.sqrt(2/np.pi) * np.exp(
            -(xt[t-1] - params[0]*x_new)**2 / (2*params[1]**2) )
    elif(rand > 0.33 and rand <= 0.66):
        if (t < T):
            vn = np.random.normal(0,1)
            x_new = (xt[t+1] - params[1]*vn)/params[0]
            #perhaps should be minus in the second row of gt expresison
            gt_prime = (params[0]/params[1]) * np.sqrt(2/np.pi) * np.exp(
                -(xt[t+1] - x_new*params[0])**2/(2 * params[1]**2) )
            gt_curr = (params[0]/params[1]) * np.sqrt(2/np.pi) * np.exp(
                -(x_new - xt[t+1]*params[0])**2/(2 * params[1]**2) )
        else:
            x_new = xt[T]
    else:
        if(t > 0):
            wn = np.random.normal(0,1)
            x_new = 2 * np.log(np.abs(yt[t-1]) / (params[2] * np.abs(wn)))
            #perhaps should be minus in the second row of gt expresison
            gt_prime = np.abs(yt[t-1])/(np.sqrt(2*np.pi)*params[2]) * np.exp(
                -(yt[t-1]**2/(2*params[2]**2)) * np.exp(-x_new) - x_new/2   )
            gt_curr = np.abs(yt[t-1])/(np.sqrt(2*np.pi)*params[2]) * np.exp(
                -(yt[t-1]**2/(2*params[2]**2)) * np.exp(-xt[t]) - xt[t]/2   )
        else:
            x_new = xt[0]

    return x_new, gt_prime, gt_curr