def test_bound_extrapolation_simple(self):
emd = EMD()
emd.extrema_detection = "simple"
emd.nbsym = 1
emd.DTYPE = np.int64
S = [0, -3, 1, 4, 3, 2, -2, 0, 1, 2, 1, 0, 1, 2, 5, 4, 0, -2, -1]
S = np.array(S)
T = np.arange(len(S))
pp = emd.prepare_points
# There are 4 cases for both (L)eft and (R)ight ends. In case of left (L) bound:
# L1) ,/ -- ext[0] is min, s[0] < ext[1] (1st max)
# L2) / -- ext[0] is min, s[0] > ext[1] (1st max)
# L3) ^. -- ext[0] is max, s[0] > ext[1] (1st min)
# L4) \ -- ext[0] is max, s[0] < ext[1] (1st min)
## CASE 1
# L1, R1 -- no edge MIN & no edge MIN
s = S.copy()
t = T.copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
self.assertEqual([-1, 3, 9, 14, 20], maxExtrema[0].tolist())
self.assertEqual([4, 4, 2, 5, 5], maxExtrema[1].tolist())
self.assertEqual([-4, 1, 6, 11, 17, 23], minExtrema[0].tolist())
self.assertEqual([-2, -3, -2, 0, -2, 0], minExtrema[1].tolist())
## CASE 2
# L2, R2 -- edge MIN, edge MIN
s = S[1:-1].copy()
t = T[1:-1].copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
self.assertEqual([-1, 3, 9, 14, 20], maxExtrema[0].tolist())
self.assertEqual([4, 4, 2, 5, 5], maxExtrema[1].tolist())
self.assertEqual([1, 6, 11, 17], minExtrema[0].tolist())
self.assertEqual([-3, -2, 0, -2], minExtrema[1].tolist())
## CASE 3
# L3, R3 -- no edge MAX & no edge MAX
s, t = S[2:-3], T[2:-3]
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
self.assertEqual([-3, 3, 9, 14, 19], maxExtrema[0].tolist())
self.assertEqual([2, 4, 2, 5, 2], maxExtrema[1].tolist())
self.assertEqual([0, 6, 11, 17], minExtrema[0].tolist())
self.assertEqual([-2, -2, 0, 0], minExtrema[1].tolist())
## CASE 4
# L4, R4 -- edge MAX & edge MAX
s, t = S[3:-4], T[3:-4]
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
self.assertEqual([3, 9, 14], maxExtrema[0].tolist())
self.assertEqual([4, 2, 5], maxExtrema[1].tolist())
self.assertEqual([0, 6, 11, 17], minExtrema[0].tolist())
self.assertEqual([-2, -2, 0, 0], minExtrema[1].tolist())
def test_bound_extrapolation_parabol(self):
emd = EMD()
emd.extrema_detection = "parabol"
emd.nbsym = 1
emd.DTYPE = np.float64
S = [0, -3, 1, 4, 3, 2, -2, 0, 1, 2, 1, 0, 1, 2, 5, 4, 0, -2, -1]
S = np.array(S)
T = np.arange(len(S))
pp = emd.prepare_points
# There are 4 cases for both (L)eft and (R)ight ends. In case of left (L) bound:
# L1) ,/ -- ext[0] is min, s[0] < ext[1] (1st max)
# L2) / -- ext[0] is min, s[0] > ext[1] (1st max)
# L3) ^. -- ext[0] is max, s[0] > ext[1] (1st min)
# L4) \ -- ext[0] is max, s[0] < ext[1] (1st min)
## CASE 1
# L1, R1 -- no edge MIN & no edge MIN
s = S.copy()
t = T.copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
maxExtrema = np.round(maxExtrema, decimals=3)
minExtrema = np.round(minExtrema, decimals=3)
self.assertEqual([-1.393, 3.25, 9, 14.25, 20.083],
maxExtrema[0].tolist())
self.assertEqual([4.125, 4.125, 2, 5.125, 5.125],
maxExtrema[1].tolist())
self.assertEqual([-4.31, 0.929, 6.167, 11, 17.167, 23.333],
minExtrema[0].tolist())
self.assertEqual([-2.083, -3.018, -2.083, 0, -2.042, 0],
minExtrema[1].tolist())
## CASE 2
# L2, R2 -- edge MIN, edge MIN
s = S[1:-1].copy()
t = T[1:-1].copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
maxExtrema = np.round(maxExtrema, decimals=3)
minExtrema = np.round(minExtrema, decimals=3)
self.assertEqual([-1.25, 3.25, 9, 14.25, 19.75],
maxExtrema[0].tolist())
self.assertEqual([4.125, 4.125, 2, 5.125, 5.125],
maxExtrema[1].tolist())
self.assertEqual([1, 6.167, 11, 17], minExtrema[0].tolist())
self.assertEqual([-3, -2.083, 0, -2], minExtrema[1].tolist())
## CASE 3
# L3, R3 -- no edge MAX & no edge MAX
s = S[2:-3].copy()
t = T[2:-3].copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
maxExtrema = np.round(maxExtrema, decimals=3)
minExtrema = np.round(minExtrema, decimals=3)
self.assertEqual([-2.5, 3.25, 9, 14.25, 19.5], maxExtrema[0].tolist())
self.assertEqual([2, 4.125, 2, 5.125, 2], maxExtrema[1].tolist())
self.assertEqual([0.333, 6.167, 11, 17.5], minExtrema[0].tolist())
self.assertEqual([-2.083, -2.083, 0, 0], minExtrema[1].tolist())
## CASE 4
# L4, R4 -- edge MAX & edge MAX
s = S[3:-4].copy()
t = T[3:-4].copy()
maxPos, maxVal, minPos, minVal, nz = emd.find_extrema(t, s)
# Should extrapolate left and right bounds
maxExtrema, minExtrema = pp(t, s, \
maxPos, maxVal, minPos, minVal)
maxExtrema = np.round(maxExtrema, decimals=3)
minExtrema = np.round(minExtrema, decimals=3)
self.assertEqual([3, 9, 14], maxExtrema[0].tolist())
self.assertEqual([4, 2, 5], maxExtrema[1].tolist())
self.assertEqual([-0.167, 6.167, 11, 17], minExtrema[0].tolist())
self.assertEqual([-2.083, -2.083, 0, 0], minExtrema[1].tolist())