Subclassing PPoly / BPoly to have custom out-of-bounds behavior. Eg: periodic boundary conditions, custom asymptotics.

asympt.py

from __future__ import division, print_function, absolute_import
import numpy as np

from scipy.interpolate import BPoly, PPoly

class MixinAsympt(object):
    def _evaluate(self, x, nu, extrapolate, out):
        super(MixinAsympt, self)._evaluate(x, nu, False, out)

        below, above = x < self.x[0], x > self.x[-1]
        np.place(out, below, self.f_below(x[below]))
        np.place(out, above, self.f_above(x[above]))
        return out

    def f_above(self, x):
        return f_lim(x)

    def f_below(self, x):
        return f_lim(x)


class BPolyAsympt(MixinAsympt, BPoly):
    pass


class PPolyAsympt(MixinAsympt, PPoly):
    pass


def f(x):
    return np.log(1. + np.exp(x**4))


def f_lim(x):
    return x**4


if __name__ == "__main__":
    xi = np.linspace(-5, 5, 30)
    yi = [[f(x)] for x in xi]

    bp = BPolyAsympt.from_derivatives(xi, yi)
    pp = PPolyAsympt.from_bernstein_basis(bp)

    import matplotlib.pyplot as plt
    fig, ax = plt.subplots()

    xx = np.linspace(-3, 7, 50)

    ax.plot(xi, yi, 'ro', mec='r', ms=12, label='tabulated')
    ax.plot(xx, bp(xx), 'm-', lw=6, alpha=0.4, label='bernstein')
    ax.plot(xx, pp(xx), 'b-', lw=2, label='power, conv')

    ax.legend(loc='lower left')
    ax.set_yscale('log')
    plt.savefig('asympt.png')

periodic.py

from __future__ import division, print_function, absolute_import
import numpy as np

from scipy.interpolate import BPoly, PPoly

"""
Piecewise polynomials w/ periodic boundary conditions.
"""

class MixinPBC(object):
    def _evaluate(self, x, nu, extrapolate, out):
        x = np.mod(x - self.x[0], self.x[-1] - self.x[0]) + self.x[0]
        return super(MixinPBC, self)._evaluate(x, nu, False, out)


class BPolyPBC(MixinPBC, BPoly):
    pass


class PPolyPBC(MixinPBC, PPoly):
    pass


def plot_cos():
    xi = np.linspace(0, np.pi, 20)
    yi = np.asarray([[np.cos(x), -np.sin(x)] for x in xi])

    bp = BPolyPBC.from_derivatives(xi, yi)
    pp = PPolyPBC.from_bernstein_basis(bp)

    import matplotlib.pyplot as plt
    fig, (ax, ax1) = plt.subplots(2,1)

    xx = np.linspace(-5, 5, 100)

    ax.plot(xi, yi[:, 0], 'ro', mec='r', ms=12, label='tabulated')
    ax.plot(xx, bp(xx), 'm-', lw=6, alpha=0.4, label='bernstein')
    ax.plot(xx, pp(xx), 'b-', lw=2, label='converted')
    ax.legend(loc='lower left')

    # derivative
    bpd = bp.derivative()
    ppd = pp.derivative()

    ax1.plot(xi, yi[:, 1], 'ro', mec='r', ms=12, label='f\', tabulated')
    ax1.plot(xx, bpd(xx), 'm-', lw=6, alpha=0.4, label='f\', bernstein')
    ax1.plot(xx, ppd(xx), 'b-', lw=2, label='f\', converted')
    ax1.legend(loc='lower left')

    plt.savefig('periodic.png')


if __name__ == "__main__":
    plot_cos()