import numpy as np
def trapz_inte_edge(y, x):
""" Trapezoidal integration including edge grids
Parameters:
y: Array of y-axis value
x: Array of x-axis value
Returns:
Area corresponded to each y (or x) value
For Example,
Area corresponded to at y_n is
..math:
0.5*y_n ((x_{n} - x_{n-1}) + (x_{n+1} - x_{n}))
Area corresponded to at y_0 (start point(edge)) is
..math:
0.5*y_0(x_{1} - x_{0})
"""
weight_x_0 = 0.5 * (x[1] - x[0])
weight_x_f = 0.5 * (x[-1] - x[-2])
weight_x_n = 0.5 * (x[1:-1] - x[:-2]) + 0.5 * (x[2:] - x[1:-1])
weight_x = np.r_[weight_x_0, weight_x_n, weight_x_f]
return weight_x*y
