polyder(c, m=1, scl=1, axis=0)¶
Differentiate a polynomial.
Returns the polynomial 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 polynomial
1 + 2*x + 3*x**2while [[1,2],[1,2]] represents
1 + 1*x + 2*y + 2*x*yif axis=0 is
xand axis=1 is
c : array_like
Array of polynomial 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.
der : ndarray
Polynomial coefficients of the derivative.
>>> from numpy.polynomial import polynomial as P >>> c = (1,2,3,4) # 1 + 2x + 3x**2 + 4x**3 >>> P.polyder(c) # (d/dx)(c) = 2 + 6x + 12x**2 array([ 2., 6., 12.]) >>> P.polyder(c,3) # (d**3/dx**3)(c) = 24 array([ 24.]) >>> P.polyder(c,scl=-1) # (d/d(-x))(c) = -2 - 6x - 12x**2 array([ -2., -6., -12.]) >>> P.polyder(c,2,-1) # (d**2/d(-x)**2)(c) = 6 + 24x array([ 6., 24.])