class GannSquare():
"""An container object for Gann Square"""
def __init__(self, size):
""" attributes and method of Gann Square
input parameters: size
output returned: an object along with its attributes
"""
self.size = size
self.even_size = size % 2 == 0
self.odd_size = size % 2 == 1
self.num_elements = size ** 2
self.matrix = self.generate()
self.horizontal_axis = self.get_horizontal_axis()
self.vertical_axis = self.get_vertical_axis()
self.diagonal_1 = self.get_diagonal_1()
self.diagonal_2 = self.get_diagonal_2()
self.diagonal_axis = self.get_diagonal_axis()
def generate(self):
"""
generate a Gann Square based on the input parameter size
"""
from numpy import array
NORTH, SOUTH, EAST, WEST = (0, 1), (0, -1), (1, 0), (-1, 0) # directional vectors
clockwise = {
WEST:NORTH,
NORTH: EAST,
EAST: SOUTH,
SOUTH: WEST
} # clockwise transformation
RIGHT, LEFT = 1, -1
# forward or backward increment
if self.size < 1:
raise ValueError
x, y = self.size // 2, self.size // 2
# the middle of the box
dx, dy = WEST # initial direction
inc = LEFT # backward increment
G = [[None] * self.size for _ in range(self.size)]
count = 0
while True:
count += 1
G[x][y] = count # visit
# follow predefined direction
_dx, _dy = clockwise[dx,dy]
_x, _y = x +inc* _dx, y +inc* _dy
if (0 <= _x < self.size and 0 <= _y < self.size and
G[_x][_y] is None):
# in the box
x, y = _x, _y
dx, dy = _dx, _dy
else: # fill in the box
x, y = x +inc* dx, y +inc* dy
if not (0 <= x < self.size and 0 <= y < self.size):
return array(G) # out of the box
def display_matrix(self):
width = len(str(max(e for row in self.matrix for e in row if e is not None)))
fmt = "{:0%dd}" % width
for row in self.matrix:
print(" ".join("_"*width if e is None else fmt.format(e) for e in row))
def get_horizontal_axis(self):
return self.matrix[:,self.size//2]
def get_vertical_axis(self):
return self.matrix[self.size//2, :]
def get_diagonal_1(self):
diagonal_1 = []
for i in range(self.size):
diagonal_1.append(self.matrix[i,self.size-i-1])
return diagonal_1
def get_diagonal_2(self):
diagonal_2 = []
for i in range(self.size):
diagonal_2.append(self.matrix[i,i])
return diagonal_2
def get_diagonal_axis(self):
from numpy import concatenate
return concatenate((self.diagonal_1, self.diagonal_2))