numpy.polynomial.chebyshev.chebint(c, m=1, k=, lbnd=0, scl=1, axis=0)
Integrate a Chebyshev series.
Returns the Chebyshev series coefficients
m times from
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 series
T_0 + 2*T_1 + 3*T_2 while [[1,2],[1,2]] represents
1*T_0(x)*T_0(y) + 1*T_1(x)*T_0(y) + 2*T_0(x)*T_1(y) +
2*T_1(x)*T_1(y) if axis=0 is
x and axis=1 is
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 , so one will need to set
scl equal to - perhaps not what one would have first thought.
Also note that, in general, the result of integrating a C-series needs to be “reprojected” onto the C-series basis set. Thus, typically, the result of this function is “unintuitive,” albeit correct; see Examples section below.
>>> from numpy.polynomial import chebyshev as C >>> c = (1,2,3) >>> C.chebint(c) array([ 0.5, -0.5, 0.5, 0.5]) >>> C.chebint(c,3) array([ 0.03125 , -0.1875 , 0.04166667, -0.05208333, 0.01041667, # may vary 0.00625 ]) >>> C.chebint(c, k=3) array([ 3.5, -0.5, 0.5, 0.5]) >>> C.chebint(c,lbnd=-2) array([ 8.5, -0.5, 0.5, 0.5]) >>> C.chebint(c,scl=-2) array([-1., 1., -1., -1.])
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