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numpy.polynomial.chebyshev.chebmul

numpy.polynomial.chebyshev.chebmul(c1, c2)

Multiply one Chebyshev series by another.

Returns the product of two Chebyshev series c1 * c2. The arguments are sequences of coefficients, from lowest order “term” to highest, e.g., [1,2,3] represents the series T_0 + 2*T_1 + 3*T_2.

Parameters:

c1, c2 : array_like

1-D arrays of Chebyshev series coefficients ordered from low to high.

Returns:

out : ndarray

Of Chebyshev series coefficients representing their product.

See also

chebadd, chebsub, chebdiv, chebpow

Notes

In general, the (polynomial) product of two C-series results in terms that are not in the Chebyshev polynomial basis set. Thus, to express the product as a C-series, it is typically necessary to “reproject” the product onto said basis set, which typically produces “unintuitive live” (but correct) results; see Examples section below.

Examples

>>>

>>> from numpy.polynomial import chebyshev as C
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> C.chebmul(c1,c2) # multiplication requires "reprojection"
array([  6.5,  12. ,  12. ,   4. ,   1.5])