numpy.polyint(p, m=1, k=None)
[source]
Return an antiderivative (indefinite integral) of a polynomial.
The returned order m
antiderivative P
of polynomial p
satisfies and is defined up to m - 1
integration constants k
. The constants determine the low-order polynomial part
of P
so that .
Parameters: |
p : array_like or poly1d Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see m : int, optional Order of the antiderivative. (Default: 1) k : list of Integration constants. They are given in the order of integration: those corresponding to highest-order terms come first. If |
---|
See also
polyder
poly1d.integ
The defining property of the antiderivative:
>>> p = np.poly1d([1,1,1]) >>> P = np.polyint(p) >>> P poly1d([ 0.33333333, 0.5 , 1. , 0. ]) >>> 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. ])
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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https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polyint.html