# numpy.polynomial.polyutils.mapdomain

polynomial.polyutils.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.

  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.

  See also

  `getdomain`, `mapparms`

  Notes

  Effectively, this implements:

  \[x\_out = new[0] + m(x - old[0])\]

  where

  \[m = \frac{new[1]-new[0]}{old[1]-old[0]}\]

  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, # may vary
              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. -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([-1.0+1.j , -0.6+0.6j, -0.2+0.2j,  0.2-0.2j,  0.6-0.6j,  1.0-1.j ]) # may vary

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