def test_vanishing_moments(self):
"""Test that coefficients in lp satisfy the
vanishing moments condition
"""
from daubfilt import daubfilt, number_of_filters
for i in range(number_of_filters):
D = 2*(i+1)
P = D/2 # Number of vanishing moments
N = P-1 # Dimension of nullspace of the matrix A
R = P+1 # Rank of A, R = D-N = P+1 equations
lp, hp = daubfilt(D)
# Condition number of A grows with P, so we test only
# the first 6 (and eps is slightly larger than machine precision)
A = zeros((R,D), Float) # D unknowns, D-N equations
b = zeros((R,1), Float) # Right hand side
b[0] = sqrt(2)
A[0,:] = ones(D, Float) # Coefficients must sum to sqrt(2)
for p in range(min(P,6)): # the p'th vanishing moment (Cond Ap)
for k in range(D):
m=D-k;
A[p+1,k] = (-1)**m * k**p;
assert allclose(b, mvmul(A,lp))
def test_filterlength(self):
from daubfilt import daubfilt
for p in range(1,26):
D=2*p
lp, hp = daubfilt(D)
if len(lp) != D: # Test number of coefficients
S = 'Bad filter length (%d), D = %d' %(length(lp), D)
raise S
def test_conservation_of_area(self):
"""Test that coefficients in lp satisfy the dilation equation
"""
from daubfilt import daubfilt, number_of_filters
for p in range(number_of_filters):
D = 2*(p+1)
lp, hp = daubfilt(D)
err = abs(sum(lp)-sqrt(2))
#assert abs(err) <= epsilon, 'Error == %e' %err
assert allclose(err, 0), 'Error == %e' %err
def test_orthogonality(self):
"""Test that coefficients in lp satisfy orthogonality condition
"""
from daubfilt import daubfilt, number_of_filters
for p in range(number_of_filters):
D = 2*(p+1)
P = D/2 # Number of vanishing moments
N = P-1 # Dimension of nullspace of the matrix A
lp, hp = daubfilt(D)
for k in range(1, N+1): #FIXME: use P
o = ortho(k,lp);
if k==0:
o = 1-o
err = abs(o)
#assert abs(err) <= epsilon, 'Error == %e' %err
assert allclose(err, 0), 'Error == %e' %err