import numpy as np
from numpy.core.fromnumeric import squeeze

def gauss_const(h):
    """
    Returns the normalization constant for a gaussian
    """
    return 1/(h*np.sqrt(np.pi*2))

def gauss_exp(ker_x, xi, h): 
    """
    Returns the gaussian function exponent term
    """
    num =  - 0.5*np.square((xi- ker_x))
    den = h*h
    return num/den

def gauss_exp(ker_x, xi, h): 
    """
    Returns the gaussian function exponent term
    """
    num =  - 0.5*np.square((xi- ker_x))
    den = h*h
    return num/den

def kernel_function(h, ker_x, xi): 
    """
    Returns the gaussian function value. Combines the gauss_const and
    gauss_exp to get this result
    """
    const = gauss_const(h)
    gauss_val = const*np.exp(gauss_exp(ker_x,xi,h))
    return gauss_val

def weights(bw_manual, input_x, all_input_values ): 
    w_row = []
    for x_i in all_input_values: 
        ki = kernel_function(bw_manual, x_i, input_x)
        ki_sum = np.sum(kernel_function(bw_manual, all_input_values, input_x))
        w_row.append(ki/ki_sum)
    return w_row


def single_y_pred_gauss(bw_manual, input_x, iks, igrek): 
    w = weights(bw_manual, input_x, iks)
    y_single = np.sum(np.dot(igrek,w))
    return y_single

def epanechnikov_one(h, ker_x, xi): 
    """
    Returns the epanechnikov function value.
    """
    value = 0.75*(1-np.square((xi-ker_x)/h))
    if (value < 0):
        value = 0
    return value

def epanechnikov_list(h, ker_x, xi): 
    """
    Returns the epanechnikov function value.
    """
    value = 0.75*(1-np.square((xi-ker_x)/h))
    value = [0 if i < 0 else i for i in value]
    return value


def weights_epanechnikov(bw_manual, input_x, all_input_values ): 
    w_row = []
    for x_i in all_input_values: 
        ki = epanechnikov_one(bw_manual, x_i, input_x)
        ki_sum = np.sum(epanechnikov_list(bw_manual, all_input_values, input_x))
        w_row.append(ki/ki_sum)
    return w_row

def single_y_pred_epanechnikov(bw_manual, input_x, x_values, y_values): 
    w = weights_epanechnikov(bw_manual, input_x, x_values)
    y_single = np.sum(np.dot(y_values,w))
    return y_single

def ker_reg(x_values, y_values, bw = 1,  ker_fun = 'gauss'):

    ker_x = np.arange(0,40,0.1)
    
    if (ker_fun == 'gauss'):
        Y_pred = []
        for input_x in x_values: 
            w = []
            Y_single = single_y_pred_epanechnikov(bw, input_x, x_values, y_values)
            Y_pred.append(Y_single)
    elif (ker_fun == 'epanechnikov'):
        Y_pred = []
        for input_x in x_values: 
            w = []
            Y_single = single_y_pred_gauss(bw, input_x, x_values, y_values)
            Y_pred.append(Y_single)
    else:
        return 0
    return Y_pred