orthax.chebyshev.chebmul

orthax.chebyshev.chebmul(c1, c2, mode='full')Source

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 (array_like) – 1-D arrays of Chebyshev series coefficients ordered from low to high.

  • c2 (array_like) – 1-D arrays of Chebyshev series coefficients ordered from low to high.

  • mode ({"full", "same"}) – If “full”, output has shape (len(c1) + len(c2) - 1). If “same”, output has shape max(len(c1), len(c2)), possibly truncating high order modes.

Returns:

out (ndarray) – Of Chebyshev series coefficients representing their product.

See also

chebadd, chebsub, chebmulx, 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 orthax 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])