Class PiecewisePolynomial

Construct a piecewise polynomial

Parameters
----------
xi : array-like of length N
    a sorted list of x-coordinates
yi : list of lists of length N
    yi[i] is the list of derivatives known at xi[i]
orders : list of integers, or integer
    a list of polynomial orders, or a single universal order
direction : {None, 1, -1}
    indicates whether the xi are increasing or decreasing
    +1 indicates increasing
    -1 indicates decreasing
    None indicates that it should be deduced from the first two xi

Notes
-----
If orders is None, or orders[i] is None, then the degree of the
polynomial segment is exactly the degree required to match all i
available derivatives at both endpoints. If orders[i] is not None,
then some derivatives will be ignored. The code will try to use an
equal number of derivatives from each end; if the total number of
derivatives needed is odd, it will prefer the rightmost endpoint. If
not enough derivatives are available, an exception is raised.

Overrides: object.__init__

Append a single point with derivatives to the PiecewisePolynomial

Parameters
----------
xi : float
yi : array-like
    yi is the list of derivatives known at xi
order : integer or None
    a polynomial order, or instructions to use the highest
    possible order

Extend the PiecewisePolynomial by a list of points

Parameters
----------
xi : array-like of length N1
    a sorted list of x-coordinates
yi : list of lists of length N1
    yi[i] is the list of derivatives known at xi[i]
orders : list of integers, or integer
    a list of polynomial orders, or a single universal order
direction : {None, 1, -1}
    indicates whether the xi are increasing or decreasing
    +1 indicates increasing
    -1 indicates decreasing
    None indicates that it should be deduced from the first two xi

Evaluate the piecewise polynomial

Parameters
----------
x : scalar or array-like of length N

Returns
-------
y : scalar or array-like of length R or length N or N by R

Evaluate a derivative of the piecewise polynomial

Parameters
----------
x : scalar or array-like of length N
der : integer
    which single derivative to extract

Returns
-------
y : scalar or array-like of length R or length N or N by R

Notes
-----
This currently computes all derivatives of the curve segment
containing each x but returns only one. This is because the
number of nonzero derivatives that a segment can have depends
on the degree of the segment, which may vary.

Evaluate a derivative of the piecewise polynomial

Parameters
----------
x : scalar or array-like of length N
der : integer
    how many derivatives (including the function value as
    0th derivative) to extract

Returns
-------
y : array-like of shape der by R or der by N or der by N by R