# Math
import math
import numpy as np

# Tools
def tabulate(x, y, f):
    """Return a table of f(x, y). Useful for the Gram-like operations."""
    return np.vectorize(f)(*np.meshgrid(x, y, sparse=True))

def cos_sum(a, b):
    """To work with tabulate."""
    return(math.cos(a+b))

def gramian_angular_field(serie):
    """
    Compute the Gramian Angular Field of a given time serie.
    Parameters:
    - serie: (np.array of shape (n, 1)) input time-serie

    Output:
    - gaf: (np.array of shape (n, n)) Gramian Angular Field generated
    """
    # Min-Max scaling
    min_ = np.min(serie)
    max_ = np.max(serie)
    scaled_serie = (2*serie - max_ - min_)/(max_ - min_)

    # Floating point inaccuracy!
    scaled_serie = np.where(scaled_serie >= 1., 1., scaled_serie)
    scaled_serie = np.where(scaled_serie <= -1., -1., scaled_serie)

    # Polar encoding
    phi = np.arccos(scaled_serie)
    r = np.linspace(0, 1, len(scaled_serie))

    # GAF Computation (every term of the matrix)
    gaf = tabulate(phi, phi, cos_sum)
    return(gaf)