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Diffstat (limited to 'numpy/polynomial/__init__.py')
| -rw-r--r-- | numpy/polynomial/__init__.py | 101 |
1 files changed, 101 insertions, 0 deletions
diff --git a/numpy/polynomial/__init__.py b/numpy/polynomial/__init__.py index 43b2caba3..c832094e2 100644 --- a/numpy/polynomial/__init__.py +++ b/numpy/polynomial/__init__.py @@ -12,6 +12,107 @@ 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 lists the various constants and methods common to 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 |