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185 lines
6.6 KiB
185 lines
6.6 KiB
"""
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A sub-package for efficiently dealing with polynomials.
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Within the documentation for this sub-package, a "finite power series,"
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i.e., a polynomial (also referred to simply as a "series") is represented
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by a 1-D numpy array of the polynomial's coefficients, ordered from lowest
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order term to highest. For example, array([1,2,3]) represents
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``P_0 + 2*P_1 + 3*P_2``, where P_n is the n-th order basis polynomial
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applicable to the specific module in question, e.g., `polynomial` (which
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"wraps" the "standard" basis) or `chebyshev`. For optimal performance,
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all operations on polynomials, including evaluation at an argument, are
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implemented as operations on the coefficients. Additional (module-specific)
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information can be found in the docstring for the module of interest.
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This package provides *convenience classes* for each of six different kinds
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of polynomials:
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======================== ================
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**Name** **Provides**
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======================== ================
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`~polynomial.Polynomial` Power series
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`~chebyshev.Chebyshev` Chebyshev series
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`~legendre.Legendre` Legendre series
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`~laguerre.Laguerre` Laguerre series
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`~hermite.Hermite` Hermite series
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`~hermite_e.HermiteE` HermiteE series
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======================== ================
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These *convenience classes* provide a consistent interface for creating,
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manipulating, and fitting data with polynomials of different bases.
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The convenience classes are the preferred interface for the `~numpy.polynomial`
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package, and are available from the ``numpy.polynomial`` namespace.
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This eliminates the need to navigate to the corresponding submodules, e.g.
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``np.polynomial.Polynomial`` or ``np.polynomial.Chebyshev`` instead of
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``np.polynomial.polynomial.Polynomial`` or
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``np.polynomial.chebyshev.Chebyshev``, respectively.
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The classes provide a more consistent and concise interface than the
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type-specific functions defined in the submodules for each type of polynomial.
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For example, to fit a Chebyshev polynomial with degree ``1`` to data given
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by arrays ``xdata`` and ``ydata``, the
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`~chebyshev.Chebyshev.fit` class method::
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>>> from numpy.polynomial import Chebyshev
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>>> c = Chebyshev.fit(xdata, ydata, deg=1)
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is preferred over the `chebyshev.chebfit` function from the
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``np.polynomial.chebyshev`` module::
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>>> from numpy.polynomial.chebyshev import chebfit
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>>> c = chebfit(xdata, ydata, deg=1)
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See :doc:`routines.polynomials.classes` for more details.
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Convenience Classes
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===================
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The following lists the various constants and methods common to all of
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the classes representing the various kinds of polynomials. In the following,
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the term ``Poly`` represents any one of the convenience classes (e.g.
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`~polynomial.Polynomial`, `~chebyshev.Chebyshev`, `~hermite.Hermite`, etc.)
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while the lowercase ``p`` represents an **instance** of a polynomial class.
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Constants
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---------
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- ``Poly.domain`` -- Default domain
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- ``Poly.window`` -- Default window
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- ``Poly.basis_name`` -- String used to represent the basis
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- ``Poly.maxpower`` -- Maximum value ``n`` such that ``p**n`` is allowed
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- ``Poly.nickname`` -- String used in printing
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Creation
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--------
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Methods for creating polynomial instances.
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- ``Poly.basis(degree)`` -- Basis polynomial of given degree
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- ``Poly.identity()`` -- ``p`` where ``p(x) = x`` for all ``x``
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- ``Poly.fit(x, y, deg)`` -- ``p`` of degree ``deg`` with coefficients
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determined by the least-squares fit to the data ``x``, ``y``
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- ``Poly.fromroots(roots)`` -- ``p`` with specified roots
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- ``p.copy()`` -- Create a copy of ``p``
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Conversion
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----------
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Methods for converting a polynomial instance of one kind to another.
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- ``p.cast(Poly)`` -- Convert ``p`` to instance of kind ``Poly``
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- ``p.convert(Poly)`` -- Convert ``p`` to instance of kind ``Poly`` or map
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between ``domain`` and ``window``
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Calculus
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--------
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- ``p.deriv()`` -- Take the derivative of ``p``
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- ``p.integ()`` -- Integrate ``p``
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Validation
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----------
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- ``Poly.has_samecoef(p1, p2)`` -- Check if coefficients match
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- ``Poly.has_samedomain(p1, p2)`` -- Check if domains match
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- ``Poly.has_sametype(p1, p2)`` -- Check if types match
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- ``Poly.has_samewindow(p1, p2)`` -- Check if windows match
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Misc
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----
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- ``p.linspace()`` -- Return ``x, p(x)`` at equally-spaced points in ``domain``
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- ``p.mapparms()`` -- Return the parameters for the linear mapping between
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``domain`` and ``window``.
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- ``p.roots()`` -- Return the roots of `p`.
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- ``p.trim()`` -- Remove trailing coefficients.
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- ``p.cutdeg(degree)`` -- Truncate p to given degree
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- ``p.truncate(size)`` -- Truncate p to given size
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"""
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from .polynomial import Polynomial
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from .chebyshev import Chebyshev
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from .legendre import Legendre
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from .hermite import Hermite
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from .hermite_e import HermiteE
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from .laguerre import Laguerre
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__all__ = [
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"set_default_printstyle",
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"polynomial", "Polynomial",
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"chebyshev", "Chebyshev",
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"legendre", "Legendre",
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"hermite", "Hermite",
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"hermite_e", "HermiteE",
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"laguerre", "Laguerre",
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]
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def set_default_printstyle(style):
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"""
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Set the default format for the string representation of polynomials.
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Values for ``style`` must be valid inputs to ``__format__``, i.e. 'ascii'
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or 'unicode'.
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Parameters
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----------
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style : str
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Format string for default printing style. Must be either 'ascii' or
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'unicode'.
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Notes
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-----
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The default format depends on the platform: 'unicode' is used on
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Unix-based systems and 'ascii' on Windows. This determination is based on
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default font support for the unicode superscript and subscript ranges.
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Examples
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--------
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>>> p = np.polynomial.Polynomial([1, 2, 3])
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>>> c = np.polynomial.Chebyshev([1, 2, 3])
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>>> np.polynomial.set_default_printstyle('unicode')
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>>> print(p)
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1.0 + 2.0·x¹ + 3.0·x²
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>>> print(c)
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1.0 + 2.0·T₁(x) + 3.0·T₂(x)
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>>> np.polynomial.set_default_printstyle('ascii')
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>>> print(p)
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1.0 + 2.0 x**1 + 3.0 x**2
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>>> print(c)
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1.0 + 2.0 T_1(x) + 3.0 T_2(x)
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>>> # Formatting supersedes all class/package-level defaults
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>>> print(f"{p:unicode}")
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1.0 + 2.0·x¹ + 3.0·x²
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"""
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if style not in ('unicode', 'ascii'):
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raise ValueError(
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f"Unsupported format string '{style}'. Valid options are 'ascii' "
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f"and 'unicode'"
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)
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_use_unicode = True
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if style == 'ascii':
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_use_unicode = False
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from ._polybase import ABCPolyBase
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ABCPolyBase._use_unicode = _use_unicode
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from numpy._pytesttester import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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