numpy.polynomial.polynomial.polyint(c, m=1, k=[], lbnd=0, scl=1, axis=0)
[source]
Integrate a polynomial.
Returns the polynomial coefficients c
integrated m
times from lbnd
along axis
. At each iteration the resulting series is multiplied by scl
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 want scl
to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument c
is an array of coefficients, from low to high degree along each axis, e.g., [1,2,3] represents the polynomial 1 + 2*x + 3*x**2
while [[1,2],[1,2]] represents 1 + 1*x + 2*y + 2*x*y
if axis=0 is x
and axis=1 is y
.
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 lbnd : scalar, optional The lower bound of the integral. (Default: 0) scl : scalar, optional Following each integration the result is multiplied by 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 |
See also
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 variable in an integral relative to x
. Then .. math::dx = du/a
, so one will need to set scl
equal to - perhaps not what one would have first thought.
>>> 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