orthax.legendre.legmul

orthax.legendre.legmul(c1, c2, mode='full')Source

Multiply one Legendre series by another.

Returns the product 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 (array_like) – 1-D arrays of Legendre series coefficients ordered from low to high.

  • c2 (array_like) – 1-D arrays of Legendre 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 Legendre series coefficients representing their product.

See also

legadd, legsub, legmulx, legdiv, legpow

Notes

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

Examples

>>> from orthax import legendre as L
>>> c1 = (1,2,3)
>>> c2 = (3,2)
>>> L.legmul(c1,c2) # multiplication requires "reprojection"
array([  4.33333333,  10.4       ,  11.66666667,   3.6       ]) # may vary