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authorS. Solomon Darnell2025-03-28 21:52:21 -0500
committerS. Solomon Darnell2025-03-28 21:52:21 -0500
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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.Polynomial` Power series
+ `~chebyshev.Chebyshev` Chebyshev series
+ `~legendre.Legendre` Legendre series
+ `~laguerre.Laguerre` Laguerre series
+ `~hermite.Hermite` Hermite series
+ `~hermite_e.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
+``np.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.Polynomial`, `~chebyshev.Chebyshev`, `~hermite.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
+
+__all__ = [
+ "set_default_printstyle",
+ "polynomial", "Polynomial",
+ "chebyshev", "Chebyshev",
+ "legendre", "Legendre",
+ "hermite", "Hermite",
+ "hermite_e", "HermiteE",
+ "laguerre", "Laguerre",
+]
+
+
+def set_default_printstyle(style):
+ """
+ Set the default format for the string representation of polynomials.
+
+ Values for ``style`` must be valid inputs to ``__format__``, i.e. 'ascii'
+ or 'unicode'.
+
+ Parameters
+ ----------
+ style : str
+ Format string for default printing style. Must be either 'ascii' or
+ 'unicode'.
+
+ Notes
+ -----
+ The default format depends on the platform: 'unicode' is used on
+ Unix-based systems and 'ascii' on Windows. This determination is based on
+ default font support for the unicode superscript and subscript ranges.
+
+ Examples
+ --------
+ >>> p = np.polynomial.Polynomial([1, 2, 3])
+ >>> c = np.polynomial.Chebyshev([1, 2, 3])
+ >>> np.polynomial.set_default_printstyle('unicode')
+ >>> print(p)
+ 1.0 + 2.0·x + 3.0·x²
+ >>> print(c)
+ 1.0 + 2.0·T₁(x) + 3.0·T₂(x)
+ >>> np.polynomial.set_default_printstyle('ascii')
+ >>> print(p)
+ 1.0 + 2.0 x + 3.0 x**2
+ >>> print(c)
+ 1.0 + 2.0 T_1(x) + 3.0 T_2(x)
+ >>> # Formatting supersedes all class/package-level defaults
+ >>> print(f"{p:unicode}")
+ 1.0 + 2.0·x + 3.0·x²
+ """
+ if style not in ('unicode', 'ascii'):
+ raise ValueError(
+ f"Unsupported format string '{style}'. Valid options are 'ascii' "
+ f"and 'unicode'"
+ )
+ _use_unicode = True
+ if style == 'ascii':
+ _use_unicode = False
+ from ._polybase import ABCPolyBase
+ ABCPolyBase._use_unicode = _use_unicode
+
+
+from numpy._pytesttester import PytestTester
+test = PytestTester(__name__)
+del PytestTester