quaternion.calculus
definite_integral
definite_integral(f, t)
Source: quaternion/calculus.py
derivative
derivative(f, t)
Source: quaternion/calculus.py
Fourthorder finitedifferencing with nonuniform time steps The formula for this finite difference comes from Eq. (A 5b) of "Derivative formulas and errors for nonuniformly spaced points" by M. K. Bowen and Ronald Smith. As explained in their Eqs. (B 9b) and (B 10b), this is a fourthorder formula  though that's a squishy concept with nonuniform time steps. TODO: If there are fewer than five points, the function should revert to simpler (lowerorder) formulas.
fd_definite_integral
fd_definite_integral(f, t)
Source: quaternion/calculus.py
fd_derivative
fd_derivative(f, t)
Source: quaternion/calculus.py
Fourthorder finitedifferencing with nonuniform time steps The formula for this finite difference comes from Eq. (A 5b) of "Derivative formulas and errors for nonuniformly spaced points" by M. K. Bowen and Ronald Smith. As explained in their Eqs. (B 9b) and (B 10b), this is a fourthorder formula  though that's a squishy concept with nonuniform time steps. TODO: If there are fewer than five points, the function should revert to simpler (lowerorder) formulas.
spline_definite_integral
spline_definite_integral(f, t, t1=None, t2=None, axis=0)
Source: quaternion/calculus.py
spline_derivative
spline_derivative(f, t, derivative_order=1, axis=0)
Source: quaternion/calculus.py
spline_evaluation
spline_evaluation(
f,
t,
t_out=None,
axis=None,
spline_degree=3,
derivative_order=0,
definite_integral_bounds=None,
)
Source: quaternion/calculus.py
Approximate input data using a spline and evaluate Note that this function is somewhat more general than it needs to be, so that it can be reused for closely related functions involving derivatives, antiderivatives, and integrals.
Parameters

f
:...) array_like
,N
,(...
Real or complex function values to be interpolated.

t
:) array_like
,(N
An ND array of increasing real values. The length of f along the interpolation axis must be equal to the length of t. The number of data points must be larger than the spline degree.

t_out
:) array_like [defaults to None]
,(M
,None
The new values of
t
on which to evaluate the result. If None, it is assumed that some other feature of the data is needed, like a derivative or antiderivative, which are then output using the samet
values as the input. 
axis
:int [defaults to None]
,None
The axis of
f
with length equal to the length oft
. If None, this function searches for an axis of equal length in reverse order  that is, starting from the last axis off
. Note that this feature is helpful whenf
is onedimensional or will always satisfy that criterion, but is dangerous otherwise. Caveat emptor. 
spline_degree
:int [defaults to 3]
Degree of the interpolating spline. Must be 1 <= spline_degree <= 5.

derivative_order
:int [defaults to 0]
The order of the derivative to apply to the data. Note that this may be negative, in which case the corresponding antiderivative is returned.

definite_integral_bounds
:) array_like [defaults to None]
,(2
,None
If this is not None, the
t_out
andderivative_order
parameters are ignored, and the returned values are just the (first) definite integrals of the splines between these limits, along each remaining axis.
spline_indefinite_integral
spline_indefinite_integral(f, t, integral_order=1, axis=0)
Source: quaternion/calculus.py