numpy.polynomial.legendre.legdiv(c1, c2)
[source]
Divide one Legendre series by another.
Returns the quotient-with-remainder of two Legendre series c1
/ c2
. The arguments are sequences of coefficients from lowest order “term” to highest, e.g., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2
.
Parameters: |
c1, c2 : array_like 1-D arrays of Legendre series coefficients ordered from low to high. |
---|---|
Returns: |
quo, rem : ndarrays Of Legendre series coefficients representing the quotient and remainder. |
In general, the (polynomial) division of one Legendre series by another results in quotient and remainder terms that are not in the Legendre polynomial basis set. Thus, to express these results as a Legendre series, it is necessary to “reproject” the results onto the Legendre basis set, which may produce “unintuitive” (but correct) results; see Examples section below.
>>> from numpy.polynomial import legendre as L >>> c1 = (1,2,3) >>> c2 = (3,2,1) >>> L.legdiv(c1,c2) # quotient "intuitive," remainder not (array([ 3.]), array([-8., -4.])) >>> c2 = (0,1,2,3) >>> L.legdiv(c2,c1) # neither "intuitive" (array([-0.07407407, 1.66666667]), array([-1.03703704, -2.51851852]))
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https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.polynomial.legendre.legdiv.html