numpy.polynomial.polyutils.mapdomain¶
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numpy.polynomial.polyutils.
mapdomain
(x, old, new)[source]¶ 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.Parameters: 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.
Returns: x_out : ndarray
Array of points of the same shape as x, after application of the linear map between the two domains.
Notes
Effectively, this implements:
where
Examples
>>> 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. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, 6.28318531]) >>> 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([-1.0-1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1.0+1.j ]) >>> new_z = P.mapdomain(z, old, new); new_z array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ])