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"""
A sub-package for efficiently dealing with polynomials.
Within the documentation for this sub-package, a "finite power series,"
i.e., a polynomial (also referred to simply as a "series") is represented
by a 1-D numpy array of the polynomial's coefficients, ordered from lowest
order term to highest. For example, array([1,2,3]) represents
``P_0 + 2*P_1 + 3*P_2``, where P_n is the n-th order basis polynomial
applicable to the specific module in question, e.g., `polynomial` (which
"wraps" the "standard" basis) or `chebyshev`. For optimal performance,
all operations on polynomials, including evaluation at an argument, are
implemented as operations on the coefficients. Additional (module-specific)
information can be found in the docstring for the module of interest.
This package provides *convenience classes* for each of six different kinds
of polynomials:
============ ================
**Name** **Provides**
============ ================
Polynomial Power series
Chebyshev Chebyshev series
Legendre Legendre series
Laguerre Laguerre series
Hermite Hermite series
HermiteE HermiteE series
============ ================
These *convenience classes* provide a consistent interface for creating,
manipulating, and fitting data with polynomials of different bases.
The convenience classes are the preferred interface for the `~numpy.polynomial`
package, and are available from the `numpy.polynomial` namespace.
This eliminates the need to
navigate to the corresponding submodules, e.g. ``np.polynomial.Polynomial``
or ``np.polynomial.Chebyshev`` instead of
``np.polynomial.polynomial.Polynomial`` or
``np.polynomial.chebyshev.Chebyshev``, respectively.
The classes provide a more consistent and concise interface than the
type-specific functions defined in the submodules for each type of polynomial.
For example, to fit a Chebyshev polynomial with degree ``1`` to data given
by arrays ``xdata`` and ``ydata``, the
`~chebyshev.Chebyshev.fit` class method::
>>> from numpy.polynomial import Chebyshev
>>> c = Chebyshev.fit(xdata, ydata, deg=1)
is preferred over the `chebyshev.chebfit` function from the
`numpy.polynomial.chebyshev` module::
>>> from numpy.polynomial.chebyshev import chebfit
>>> c = chebfit(xdata, ydata, deg=1)
See :doc:`routines.polynomials.classes` for more details.
Convenience Classes
===================
The following listing the various constants and methods common to the all of
the classes representing the various kinds of polynomials. In the following,
the term ``Poly`` represents any one of the convenience classes (e.g.
``Polynomial``, ``Chebyshev``, ``Hermite``, etc.) while the lowercase ``p``
represents an **instance** of a polynomial class.
Constants
---------
- ``Poly.domain`` -- Default domain
- ``Poly.window`` -- Default window
- ``Poly.basis_name`` -- String used to represent the basis
- ``Poly.maxpower`` -- Maximum value ``n`` such that ``p**n`` is allowed
- ``Poly.nickname`` -- String used in printing
Creation
--------
Methods for creating polynomial instances.
- ``Poly.basis(degree)`` -- Basis polynomial of given degree
- ``Poly.identity()`` -- ``p`` where ``p(x) = x`` for all ``x``
- ``Poly.fit(x, y, deg)`` -- ``p`` of degree ``deg`` with coefficients
determined by the least-squares fit to the data ``x``, ``y``
- ``Poly.fromroots(roots)`` -- ``p`` with specified roots
- ``p.copy()`` -- Create a copy of ``p``
Conversion
----------
Methods for converting a polynomial instance of one kind to another.
- ``p.cast(Poly)`` -- Convert ``p`` to instance of kind ``Poly``
- ``p.convert(Poly)`` -- Convert ``p`` to instance of kind ``Poly`` or map
between ``domain`` and ``window``
Calculus
--------
- ``p.deriv()`` -- Take the derivative of ``p``
- ``p.integ()`` -- Integrate ``p``
Validation
----------
- ``Poly.has_samecoef(p1, p2)`` -- Check if coefficients match
- ``Poly.has_samedomain(p1, p2)`` -- Check if domains match
- ``Poly.has_sametype(p1, p2)`` -- Check if types match
- ``Poly.has_samewindow(p1, p2)`` -- Check if windows match
Misc
----
- ``p.linspace()`` -- Return ``x, p(x)`` at equally-spaced points in ``domain``
- ``p.mapparms()`` -- Return the parameters for the linear mapping between
``domain`` and ``window``.
- ``p.roots()`` -- Return the roots of `p`.
- ``p.trim()`` -- Remove trailing coefficients.
- ``p.cutdeg(degree)`` -- Truncate p to given degree
- ``p.truncate(size)`` -- Truncate p to given size
"""
from .polynomial import Polynomial
from .chebyshev import Chebyshev
from .legendre import Legendre
from .hermite import Hermite
from .hermite_e import HermiteE
from .laguerre import Laguerre
from numpy._pytesttester import PytestTester
test = PytestTester(__name__)
del PytestTester
|
