numpy.polynomial.legendre.legder — NumPy v1.13 Manual (original) (raw)
numpy.polynomial.legendre. legder(c, m=1, scl=1, axis=0)[source]¶
Differentiate a Legendre series.
Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl (the scaling factor is for use in a linear change of variable). The argument_c_ is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series 1*L_0 + 2*L_1 + 3*L_2while [[1,2],[1,2]] represents 1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y) if axis=0 is x and axis=1 isy.
| Parameters: | c : array_like Array of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Number of derivatives taken, must be non-negative. (Default: 1) scl : scalar, optional Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1) axis : int, optional Axis over which the derivative is taken. (Default: 0). New in version 1.7.0. |
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| Returns: | der : ndarray Legendre series of the derivative. |
Notes
In general, the result of differentiating a Legendre series does not resemble the same operation on a power series. Thus the result of this function may be “unintuitive,” albeit correct; see Examples section below.
Examples
from numpy.polynomial import legendre as L c = (1,2,3,4) L.legder(c) array([ 6., 9., 20.]) L.legder(c, 3) array([ 60.]) L.legder(c, scl=-1) array([ -6., -9., -20.]) L.legder(c, 2,-1) array([ 9., 60.])