numpy.polynomial.polynomial.polyint()
numpy.polynomial.polynomial.polyint
-
numpy.polynomial.polynomial.polyint(c, m=1, k=[], lbnd=0, scl=1, axis=0)
[source] -
Integrate a polynomial.
Returns the polynomial coefficients
c
integratedm
times fromlbnd
alongaxis
. At each iteration the resulting series is multiplied byscl
and an integration constant,k
, is added. The scaling factor is for use in a linear change of variable. (“Buyer beware”: note that, depending on what one is doing, one may wantscl
to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argumentc
is an array of coefficients, from low to high degree along each axis, e.g., [1,2,3] represents the polynomial1 + 2*x + 3*x**2
while [[1,2],[1,2]] represents1 + 1*x + 2*y + 2*x*y
if axis=0 isx
and axis=1 isy
.Parameters: c : array_like
1-D array of polynomial coefficients, ordered from low to high.
m : int, optional
Order of integration, must be positive. (Default: 1)
k : {[], list, scalar}, optional
Integration constant(s). The value of the first integral at zero is the first value in the list, the value of the second integral at zero is the second value, etc. If
k == []
(the default), all constants are set to zero. Ifm == 1
, a single scalar can be given instead of a list.lbnd : scalar, optional
The lower bound of the integral. (Default: 0)
scl : scalar, optional
Following each integration the result is multiplied by
scl
before the integration constant is added. (Default: 1)axis : int, optional
Axis over which the integral is taken. (Default: 0).
New in version 1.7.0.
Returns: S : ndarray
Coefficient array of the integral.
Raises: ValueError
If
m < 1
,len(k) > m
.See also
Notes
Note that the result of each integration is multiplied by
scl
. Why is this important to note? Say one is making a linear change of variablein an integral relative to
x
. Then .. math::dx = du/a
, so one will need to setscl
equal to- perhaps not what one would have first thought.
Examples
>>> from numpy.polynomial import polynomial as P >>> c = (1,2,3) >>> P.polyint(c) # should return array([0, 1, 1, 1]) array([ 0., 1., 1., 1.]) >>> P.polyint(c,3) # should return array([0, 0, 0, 1/6, 1/12, 1/20]) array([ 0. , 0. , 0. , 0.16666667, 0.08333333, 0.05 ]) >>> P.polyint(c,k=3) # should return array([3, 1, 1, 1]) array([ 3., 1., 1., 1.]) >>> P.polyint(c,lbnd=-2) # should return array([6, 1, 1, 1]) array([ 6., 1., 1., 1.]) >>> P.polyint(c,scl=-2) # should return array([0, -2, -2, -2]) array([ 0., -2., -2., -2.])
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https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.polynomial.polyint.html