<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def to_linear(self, index=None):
 """ Transforms the StepColormap into a LinearColormap. Parameters index : list of floats, default None The values corresponding to each color in the output colormap. It has to be sorted. If None, a regular grid between `vmin` and `vmax` is created. """

        if index is None:
            n = len(self.index)-1
            index = [self.index[i]*(1.-i/(n-1.))+self.index[i+1]*i/(n-1.) for
                     i in range(n)]

        colors = [self.rgba_floats_tuple(x) for x in index]
        return LinearColormap(colors, index=index,
                              vmin=self.vmin, vmax=self.vmax)