## 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):
    a1 = a2 = 2**-0.5
    N = len(V)
    X = a1 * V[0,:] + a2 * V[1,:]
    for j in range(1, N//2) :
        x = a1 * V[2*j,:] + a2 * V[2*j+1,:]
        X = stack([X,x])
    return X

# Define a function that computes 
# the array of level r scaling vectors
# from the array V of level r-1 scaling vectors
def HaarW(V):
    a1 = a2 = 2**-0.5
    N = len(V)
    X = a1 * V[0,:] - a2 * V[1,:]
    for j in range(1, N//2) :
        x = a1 * V[2*j,:] - a2 * V[2*j+1,:]
        X = stack([X,x])
    return X

# 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):
    V = Id(N)
    X = [V]
    while N > 2 :
        V = HaarV(V)
        X += [V]
        N = len(V)
    V = HaarV(V)
    X += [[V]]
    return X


# 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):
    V = Id(N)
    X = [V]
    Y = []
    while N > 2 :
        Y += [HaarW(V)]
        V = HaarV(V)
        X += [V]
        N = len(V)

    Y += [[HaarW(V)]]
    V = HaarV(V)
    X += [[V]]
    return (X, Y)

V0 = Id(8)
V1 = HaarV(V0)
V2 = HaarV(V1)

f = [1,23,4,6,2,2,0,14]

a = dot(dot(f, V2[0]), V2[0]) + dot(dot(f, V2[1]), V2[1])
print(a)