## L421_x
'''
Computing the Haar scaling and wavelet arrays
'''

# Utilities
from cdi import *
import numpy as np
import matplotlib.pyplot as plt

# Synonyms
Id = np.eye
#sqrt = np.sqrt
pi = np.pi
cos = np.cos
sin = np.sin
array = np.array
stack = np.vstack
splice= np.hstack
dot = np.dot
ls  = np.linspace
zeros=np.zeros
mat=np.matrix
transpose=np.transpose
view = plt.imshow
canvas = plt.figure

# Define a function that computes 
# the array of level r scaling vectors
# from the array V of level r-1 scaling vectors
def HaarV(V):
    return 
    
# Define a function that computes 
# the array of level r scaling vectors
# from the array V of level r-1 scaling vectors
def HaarV(V):
    return 
    
# Define a function that computes 
# the array of all scaling vectors, that is,
# its r-th component is the matrix of level r
# scaling vectors
def HaarVA(N):
    return 

# Define a function that computes a pair 
# formed with the array of all scaling vectors
# and the array of all wavelet vectors
def HaarVWA(N):
    return