flopscope.

flopscope.numpy.polyint

fnp.polyint(p, m=1, k=None)[flopscope source][numpy source]

Return an antiderivative (indefinite integral) of a polynomial.

Adapted from NumPy docs np.polyint

Areacore
Typecustom
NumPy Refnp.polyint
Cost
nn
Flopscope Context

Integrate polynomial. Cost: n FLOPs.

Note.

This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in flops.polynomial is preferred. A summary of the differences can be found in the transition guide.

The returned order m antiderivative P of polynomial p satisfies dmdxmP(x)=p(x)\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

km−10!x0+…+k0(m−1)!xm−1\frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1}

of P so that P(j)(0)=km−j−1P^{(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

Examples

The defining property of the antiderivative:

>>> import flopscope.numpy as fnp
>>> p = flops.poly1d([1,1,1])
>>> P = flops.polyint(p)
>>> P
 poly1d([ 0.33333333,  0.5       ,  1.        ,  0.        ]) # may vary
>>> flops.polyder(P) == p
True

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

>>> P = flops.polyint(p, 3)
>>> P(0)
0.0
>>> flops.polyder(P)(0)
0.0
>>> flops.polyder(P, 2)(0)
0.0
>>> P = flops.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:

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