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Module « numpy.matlib »

Fonction polyint - module numpy.matlib

Signature de la fonction polyint

def polyint(p, m=1, k=None) 

Description

help(numpy.matlib.polyint)

Return an antiderivative (indefinite integral) of a polynomial.

.. note::
   This forms part of the old polynomial API. Since version 1.4, the
   new polynomial API defined in `numpy.polynomial` is preferred.
   A summary of the differences can be found in the
   :doc:`transition guide </reference/routines.polynomials>`.

The returned order `m` antiderivative `P` of polynomial `p` satisfies
:math:`\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`
integration constants `k`. The constants determine the low-order
polynomial part

.. math:: \frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1}

of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.

Parameters
----------
p : array_like or poly1d
    Polynomial to integrate.
    A sequence is interpreted as polynomial coefficients, see `poly1d`.
m : int, optional
    Order of the antiderivative. (Default: 1)
k : list of `m` scalars or scalar, optional
    Integration constants. They are given in the order of integration:
    those corresponding to highest-order terms come first.

    If ``None`` (default), all constants are assumed to be zero.
    If `m = 1`, a single scalar can be given instead of a list.

See Also
--------
polyder : derivative of a polynomial
poly1d.integ : equivalent method

Examples
--------
The defining property of the antiderivative:

>>> import numpy as np

>>> p = np.poly1d([1,1,1])
>>> P = np.polyint(p)
>>> P
 poly1d([ 0.33333333,  0.5       ,  1.        ,  0.        ]) # may vary
>>> np.polyder(P) == p
True

The integration constants default to zero, but can be specified:

>>> P = np.polyint(p, 3)
>>> P(0)
0.0
>>> np.polyder(P)(0)
0.0
>>> np.polyder(P, 2)(0)
0.0
>>> P = np.polyint(p, 3, k=[6,5,3])
>>> P
poly1d([ 0.01666667,  0.04166667,  0.16666667,  3. ,  5. ,  3. ]) # may vary

Note that 3 = 6 / 2!, and that the constants are given in the order of
integrations. Constant of the highest-order polynomial term comes first:

>>> np.polyder(P, 2)(0)
6.0
>>> np.polyder(P, 1)(0)
5.0
>>> P(0)
3.0

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