def test_fwt1Db(self):
"""test that fwt1D works on example vectors"""
D = 4
N = 8
X = Numeric.zeros(N, Numeric.Float)
for i in range(len(X)):
X[i] = i + 1
Y = fwt(X, D)
Y = Y - Numeric.array(
[
12.72792206135786,
-4.38134139536131,
0.36602540378444,
-3.83012701892219,
0.0,
0.0,
0.0,
-2.82842712474619,
]
)
assert Numeric.allclose(Y, 0)
def test_columnwise_fwt_b(self):
"""test thath columnwise fwt works"""
X = Numeric.ones(8 * 4, Numeric.Float)
X = Numeric.reshape(X, (8, 4))
for i in range(8):
X[i, 0] = i + 1
X[i, 1] = 1
X[i, 2] = i + 1
X[i, 3] = 2
# Numeric.transpose(X))
Y = fwt(X)
Y_ref = Numeric.array(
[
[12.72792206135786, sqrt(8), 12.72792206135786, sqrt(32)],
[-4.38134139536131, 0.0, -4.38134139536131, 0.0],
[0.36602540378444, 0.0, 0.36602540378444, 0.0],
[-3.83012701892219, 0.0, -3.83012701892219, 0.0],
[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0],
[-2.82842712474619, 0.0, -2.82842712474619, 0.0],
]
)
Y -= Y_ref
assert Numeric.allclose(Y, 0)
def test_ifwt1D_basic(self):
"""test that ifwt1D works basically"""
X = Numeric.ones(8, Numeric.Float)
Y = fwt(X)
X1 = ifwt(Y)
assert Numeric.allclose(X - X1, 0)
def test_fwt1Dc8(self):
"""test that fwt1D works on a 'random' vector, D=8"""
# Matlab random vector
X = Numeric.array(
[
0.81797434083925,
0.66022755644160,
0.34197061827022,
0.28972589585624,
0.34119356941488,
0.53407901762660,
0.72711321692968,
0.30929015979096,
]
)
# Result from fwt(X, 8) in Matlab
Y_ref = Numeric.array(
[
1.42184125586417,
-0.27774330567583,
0.26539391030148,
0.02521137886213,
0.13638973750197,
0.31441497909028,
-0.20260945655043,
0.05934606703242,
]
)
Y = fwt(X, 8)
assert Numeric.allclose(Y - Y_ref, 0)
def test_fwt1Dc6(self):
"""test that fwt1D works on a 'random' vector, D=6"""
# Matlab random vector
X = Numeric.array(
[
0.81797434083925,
0.66022755644160,
0.34197061827022,
0.28972589585624,
0.34119356941488,
0.53407901762660,
0.72711321692968,
0.30929015979096,
]
)
# Result from fwt(X, 6) in Matlab
Y_ref = Numeric.array(
[
1.42184125586417,
-0.27979815817808,
0.21836186329686,
0.17939935114879,
0.00345049516774,
0.22893484261518,
0.25762577687352,
-0.18246978758220,
]
)
Y = fwt(X, 6)
assert Numeric.allclose(Y - Y_ref, 0)
def test_fwt1Dc4(self):
"""test that fwt1D works on a 'random' vector, D=4"""
# Matlab random vector
X = Numeric.array(
[
0.81797434083925,
0.66022755644160,
0.34197061827022,
0.28972589585624,
0.34119356941488,
0.53407901762660,
0.72711321692968,
0.30929015979096,
]
)
# Result from fwt(X, 4) in Matlab
Y_ref = Numeric.array(
[
1.42184125586417,
-0.15394808354817,
0.05192707167183,
0.37115044369886,
-0.10770249228974,
-0.08172091206233,
0.29500215027890,
0.20196258114742,
]
)
Y = fwt(X, 4)
assert Numeric.allclose(Y - Y_ref, 0)
def test_fwt1Dc(self):
"""test that fwt1D works as a 2D vector"""
X = Numeric.ones(8, Numeric.Float)
X = Numeric.reshape(X, (8, 1))
Y = fwt(X)
Y[0][0] -= sqrt(len(Y))
assert Numeric.allclose(Y, 0)
def test_ifwt1D_inverse_b(self):
"""test that fwt1D works as an inverse to ifwt"""
for j in range(1, 9):
N = 2 ** j
for P in range(number_of_filters):
D = 2 * (P + 1)
X = Numeric.ones(N, Numeric.Float)
Y = ifwt(X, D)
X1 = fwt(Y, D)
assert Numeric.allclose(X - X1, 0)
def test_fwt1Da(self):
"""test that fwt1D works on constant vector: ones"""
for j in range(1, 9):
N = 2 ** j
for P in range(number_of_filters):
D = 2 * (P + 1)
X = Numeric.ones(N, Numeric.Float)
Y = fwt(X, D)
Y[0] -= sqrt(len(Y))
assert Numeric.allclose(Y, 0)
def test_columnwise_fwt_a(self):
"""test thath columnwise fwt works"""
X = Numeric.ones(8 * 4, Numeric.Float)
X = Numeric.reshape(X, (8, 4))
Y = fwt(X)
rows, cols = Y.shape
for i in range(cols):
Y[0, i] -= sqrt(rows)
assert Numeric.allclose(Y, 0)
def test_scale_energy(self):
D = 4
N = 8
d = 3
X = Numeric.zeros(N, Numeric.Float)
for i in range(len(X)):
X[i] = i + 1
Wx = fwt(X, D, d)
Evec = scale_energy(Wx, d + 1) # All details + avg
Evec_ref = Numeric.array([0.03921568627451, 0.07256788028085, 0.09409878638582, 0.79411764705882])
assert Numeric.allclose(Evec - Evec_ref, 0)
def test_callfwt(self):
"""test that fwt can be called"""
X = Numeric.array([[1, 2, 1], [3, 4, 3], [5, 6, 5], [7, 8, 7], [9.0, 10, 9]])
Y = fwt(X)