def arccurv(x, y):
""" Just calculates the curvature and the arclengths corresponding to those curvatures.
"""
curv = curvature(x, y)
steps = np.sqrt(np.diff(x, axis=0)**2 + np.diff(y, axis=0)**2)[:-1]
arc = np.cumsum(steps)
return arc, curv
def lombs(x, y):
""" lombs calculates LombScargle for inputs x, y.
"""
# Calculate curvature.
curv = curvature(x, y)
steps = np.sqrt(np.diff(x, axis=0)**2 + np.diff(y, axis=0)**2)[:-1]
arc = np.cumsum(steps)
# Calculate LS.
ls_f, ls_p = LombScargle(arc, curv).autopower()
return ls_f, ls_p
def calc_dtds(x,y):
""" dtds calculates the derivative dT/ds, with respect to the tangent.
"""
# Deal with arrays again.
x = np.asarray(x)
y = np.asarray(y)
x = x.reshape(len(x),)
y = y.reshape(len(y),)
# Calculate curvature.
kappa = curvature(x,y)
normvec = -np.diff(y) + np.diff(x)*1j
return kappa*(normvec[0:-1] + normvec[1:])/2
def calc_dnds(x,y):
""" dnds calculates the derivative dN/ds, with respect to the normal vector.
"""
# Deal with arrays again.
x = np.asarray(x)
y = np.asarray(y)
x = x.reshape(len(x),)
y = y.reshape(len(y),)
# Calculate curvature.
kappa = curvature(x,y)
tanvec = np.diff(x) + np.diff(y)*1j
return -kappa*(tanvec[0:-1] + tanvec[1:])/2
def arccurv_i(x, y, l=0):
""" Calculates the curvature and associated arclength for an interpolated channel.
"""
if l == 0:
l = len(x)
interp_coords = ia.interparc(l, x, y)
x_i = interp_coords[:, 0]
y_i = interp_coords[:, 1]
# Calculate curvature.
curv = curvature(x_i, y_i)
steps = np.sqrt(np.diff(x_i, axis=0)**2 + np.diff(y_i, axis=0)**2)[:-1]
arc = np.cumsum(steps)
return arc, curv
def periodogram_i(x, y, l=0):
""" periodogram_i calculates per. for inputs x, y, after interpolating over l=len(x) (default).
"""
if l == 0:
l = len(x)
interp_coords = ia.interparc(l, x, y)
x_i = interp_coords[:, 0]
y_i = interp_coords[:, 1]
# Calculate curvature.
curv = curvature(x_i, y_i)
steps = np.sqrt(np.diff(x_i, axis=0)**2 + np.diff(y_i, axis=0)**2)[:-1]
arc = np.cumsum(steps)
fs = 1. / steps[0]
# Calculate periodogram.
per_f, per_p = psdfull(curv, fs)
return per_f, per_p, fs