numpy.polynomial
#
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 |
---|---|
Power series |
|
Chebyshev series |
|
Legendre series |
|
Laguerre series |
|
Hermite series |
|
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 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
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 Using the convenience 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 domainPoly.window
– Default windowPoly.basis_name
– String used to represent the basisPoly.maxpower
– Maximum valuen
such thatp**n
is allowedPoly.nickname
– String used in printing
Creation#
Methods for creating polynomial instances.
Poly.basis(degree)
– Basis polynomial of given degreePoly.identity()
–p
wherep(x) = x
for allx
Poly.fit(x, y, deg)
–p
of degreedeg
with coefficients determined by the least-squares fit to the datax
,y
Poly.fromroots(roots)
–p
with specified rootsp.copy()
– Create a copy ofp
Conversion#
Methods for converting a polynomial instance of one kind to another.
p.cast(Poly)
– Convertp
to instance of kindPoly
p.convert(Poly)
– Convertp
to instance of kindPoly
or map betweendomain
andwindow
Calculus#
p.deriv()
– Take the derivative ofp
p.integ()
– Integratep
Validation#
Poly.has_samecoef(p1, p2)
– Check if coefficients matchPoly.has_samedomain(p1, p2)
– Check if domains matchPoly.has_sametype(p1, p2)
– Check if types matchPoly.has_samewindow(p1, p2)
– Check if windows match
Misc#
p.linspace()
– Returnx, p(x)
at equally-spaced points indomain
p.mapparms()
– Return the parameters for the linear mapping betweendomain
andwindow
.p.roots()
– Return the roots ofp
.p.trim()
– Remove trailing coefficients.p.cutdeg(degree)
– Truncatep
to given degreep.truncate(size)
– Truncatep
to given size
Configuration#
Set the default format for the string representation of polynomials. |