def knee(points: np.ndarray) -> int:
"""Returns the index of the knee point based on the DFDT method.
It uses the iterative refinement method.
Args:
points (np.ndarray): numpy array with the points (x, y)
Returns:
int: the index of the knee point
"""
x = points[:, 0]
y = points[:, 1]
gradient = grad.cfd(x, y)
knee = cutoff = 0
last_knee = -1
while last_knee < knee and (len(x) - cutoff) > 2:
last_knee = knee
knee = get_knee_gradient(gradient[cutoff:]) + cutoff
cutoff = int(math.ceil(knee / 2.0))
return knee
def knee(points: np.ndarray) -> int:
"""
Returns the index of the knee point based on the curvature equations:
$$
k = \\frac{|f''(x)|}{(1+[f'(2)]^2)^{\\frac{3}{2}}}
$$
Args:
points (np.ndarray): numpy array with the points (x, y)
Returns:
int: the index of the knee point
"""
x = points[:, 0]
y = points[:, 1]
gradient1 = grad.cfd(x, y)
gradient2 = grad.csd(x, y)
curvature = np.absolute(gradient2) / ((1.0 + gradient1**2.0)**(1.5))
# prevents the selection of the first point
#idx = np.argmax(curvature[0:-1])
idx = np.argmax(curvature[1:-1]) + 1
return idx
def get_knee(x: np.ndarray, y: np.ndarray) -> int:
"""Return the index of the knee point based on the DFDT method.
Args:
x (np.ndarray): the value of the points in the x axis coordinates
y (np.ndarray): the value of the points in the y axis coordinates
Returns:
int: the index of the knee point
"""
gradient = grad.cfd(x, y)
return get_knee_gradient(gradient)
def knee(points: np.ndarray) -> int:
"""
Returns the index of the knee point based on the curvature equations:
$$
k = \\frac{|f''(x)|}{(1+[f'(2)]^2)^{\\frac{3}{2}}}
$$
Args:
points (np.ndarray): numpy array with the points (x, y)
Returns:
int: the index of the knee point
"""
x = points[:, 0]
y = points[:, 1]
gradient1 = grad.cfd(x, y)
gradient2 = grad.csd(x, y)
curvature = gradient2 / ((1.0 + gradient1**2.0)**(1.5))
return np.argmax(curvature[0:-1])
def test_gradient_cfd_even(self):
x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
y = np.array([1, 4, 9, 16, 25, 36, 49, 64, 81])
result = gradient.cfd(x, y)
desired = np.array([2., 4., 6., 8., 10., 12., 14., 16., 18.])
npt.assert_almost_equal(result, desired, decimal=2)
def test_gradient_cfd_uneven(self):
x = np.array([1, 3, 4, 5, 6, 8, 9])
y = np.array([1, 9, 16, 25, 36, 64, 81])
result = gradient.cfd(x, y)
desired = np.array([2, 6, 8, 10, 12, 16, 18])
npt.assert_almost_equal(result, desired, decimal=2)
def test_gradient_cfd_even_2(self):
x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
y = x**3
result = gradient.cfd(x, y)
desired = np.array([1, 13, 28, 49, 76, 109, 148, 193, 241])
npt.assert_almost_equal(result, desired, decimal=2)