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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _transform_i(self, x, i):
 """return transform of x in component i"""

        x = self._shift_or_mirror_into_invertible_i(x, i)
        lb = self._lb[self._index(i)]
        ub = self._ub[self._index(i)]
        al = self._al[self._index(i)]
        au = self._au[self._index(i)]
        if x < lb + al:
            return lb + (x - (lb - al))**2 / 4 / al
        elif x < ub - au:
            return x
        elif x < ub + 3 * au:
            return ub - (x - (ub + au))**2 / 4 / au
        else:
            assert False  # shift removes this case
            return ub + au - (x - (ub + au))