import numpy as np
import math


def gauss(stdev, rank):
    """Creates Gauss average mask given stdev and rank"""

    def gaussian_f(r):
        """Gaussian function"""
        num = math.e ** (- (r ** 2) / (2 * (stdev ** 2)))
        den = stdev * math.sqrt(2 * math.pi)

        return num / den

    mask = np.fromfunction(
        lambda x, y: gaussian_f(abs(x - rank // 2) + abs(y - rank // 2)),
        (rank, rank),
        dtype=float)

    # Normalize mask to have unitary sum of elements
    return mask / np.sum(mask)


def avg(rank):
    """Creates Average mask given rank"""
    return np.ones((rank, rank)) / (rank ** 2)

# Commonly used masks for convenience
sharpen = [
    np.array([[0,  -1,  0],
              [-1,  5, -1],
              [0,  -1,  0]]),

    np.array([[-1, -1, -1],
              [-1,  9, -1],
              [-1, -1, -1]]),

    np.array([[1, -2,  1],
              [-2, 5, -2],
              [1, -2,  1]])
]

prewitt = [
    np.array([[-1, -1, -1],
              [0,   0,  0],
              [1,   1,  1]]),

    np.array([[-1, 0, 1],
              [-1, 0, 1],
              [-1, 0, 1]])
]

sobel = [
    np.array([[-1, -2, -1],
              [0,   0,  0],
              [1,   2,  1]]),

    np.array([[-1, 0, 1],
              [-2, 0, 2],
              [-1, 0, 1]])
]

import numpy as np
import math


def gauss(stdev, rank):
    """Creates Gauss average mask given stdev and rank"""

    def gaussian_f(r):
        """Gaussian function"""
        num = math.e ** (- (r ** 2) / (2 * (stdev ** 2)))
        den = stdev * math.sqrt(2 * math.pi)

        return num / den

    mask = np.fromfunction(
        lambda x, y: gaussian_f(abs(x - rank // 2) + abs(y - rank // 2)),
        (rank, rank),
        dtype=float)

    # Normalize mask to have unitary sum of elements
    return mask / np.sum(mask)


def avg(rank):
    """Creates Average mask given rank"""
    return np.ones((rank, rank)) / (rank ** 2)

# Commonly used masks for convenience
sharpen = [
    np.array([[0,  -1,  0],
              [-1,  5, -1],
              [0,  -1,  0]]),

    np.array([[-1, -1, -1],
              [-1,  9, -1],
              [-1, -1, -1]]),

    np.array([[1, -2,  1],
              [-2, 5, -2],
              [1, -2,  1]])
]

prewitt = [
    np.array([[-1, -1, -1],
              [0,   0,  0],
              [1,   1,  1]]),

    np.array([[-1, 0, 1],
              [-1, 0, 1],
              [-1, 0, 1]])
]

sobel = [
    np.array([[-1, -2, -1],
              [0,   0,  0],
              [1,   2,  1]]),

    np.array([[-1, 0, 1],
              [-2, 0, 2],
              [-1, 0, 1]])
]

Creates Gauss average mask given stdev and rank Gaussian function # Normalize mask to have unitary sum of elements Creates Average mask given rank # Commonly used masks for convenience