`numpy.polynomial.polyutils:mapdomain`

Signature

def mapdomain(x, old, new)

Apply linear map to input points.

The linear map offset + scale*x that maps the domain old to the domain new is applied to the points x.

x : array_like: Points to be mapped. If x is a subtype of ndarray the subtype will be preserved.
old, new : array_like: The two domains that determine the map. Each must (successfully) convert to 1-d arrays containing precisely two values.

x_out : ndarray: Array of points of the same shape as x, after application of the linear map between the two domains.

Effectively, this implements:

x_o u t = n e w [0] + m (x - o l d [0])

where

m = \frac{n e w [ 1 ] - n e w [ 0 ]}{o l d [ 1 ] - o l d [ 0 ]}

import numpy as np
from numpy.polynomial import polyutils as pu
old_domain = (-1,1)
new_domain = (0,2*np.pi)
x = np.linspace(-1,1,6); x

✓

array([-1. , -0.6, -0.2,  0.2,  0.6,  1. ])

x_out = pu.mapdomain(x, old_domain, new_domain); x_out

✗

array([0.    , 1.2566, 2.5133, 3.7699, 5.0265, 6.2832])

x - pu.mapdomain(x_out, new_domain, old_domain)

✓

array([0., 0., 0., 0., 0., 0.])

Also works for complex numbers (and thus can be used to map any line in the complex plane to any other line therein).

i = complex(0,1)
old = (-1 - i, 1 + i)
new = (-1 + i, 1 - i)
z = np.linspace(old[0], old[1], 6); z

✓

array([-1. -1.j , -0.6-0.6j, -0.2-0.2j,  0.2+0.2j,  0.6+0.6j,  1. +1.j ])

new_z = pu.mapdomain(z, old, new); new_z

✗

array([-1. +1.j , -0.6+0.6j, -0.2+0.2j,  0.2-0.2j,  0.6-0.6j,  1. -1.j ])