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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 pointColors(self, scalars, cmap="jet", alpha=1, bands=None, vmin=None, vmax=None):
 """ Set individual point colors by providing a list of scalar values and a color map. `scalars` can be a string name of the ``vtkArray``. :param cmap: color map scheme to transform a real number into a color. :type cmap: str, list, vtkLookupTable, matplotlib.colors.LinearSegmentedColormap :param alpha: mesh transparency. Can be a ``list`` of values one for each vertex. :type alpha: float, list :param int bands: group scalars in this number of bins, typically to form bands or stripes. :param float vmin: clip scalars to this minimum value :param float vmax: clip scalars to this maximum value .. hint:: |mesh_coloring| |mesh_coloring.py|_ |mesh_alphas| |mesh_alphas.py|_ |mesh_bands| |mesh_bands.py|_ |mesh_custom| |mesh_custom.py|_ """

        poly = self.polydata(False)

        if isinstance(scalars, str):  # if a name is passed
            scalars = vtk_to_numpy(poly.GetPointData().GetArray(scalars))

        n = len(scalars)
        useAlpha = False
        if n != poly.GetNumberOfPoints():
            colors.printc('~times pointColors Error: nr. of scalars != nr. of points',
                          n, poly.GetNumberOfPoints(), c=1)
        if utils.isSequence(alpha):
            useAlpha = True
            if len(alpha) > n:
                colors.printc('~times pointColors Error: nr. of scalars < nr. of alpha values',
                              n, len(alpha), c=1)
                exit()
        if bands:
            scalars = utils.makeBands(scalars, bands)

        if vmin is None:
            vmin = np.min(scalars)
        if vmax is None:
            vmax = np.max(scalars)

        lut = vtk.vtkLookupTable()  # build the look-up table

        if utils.isSequence(cmap):
            sname = "pointColors_custom"
            lut.SetNumberOfTableValues(len(cmap))
            lut.Build()
            for i, c in enumerate(cmap):
                col = colors.getColor(c)
                r, g, b = col
                if useAlpha:
                    lut.SetTableValue(i, r, g, b, alpha[i])
                else:
                    lut.SetTableValue(i, r, g, b, alpha)

        elif isinstance(cmap, vtk.vtkLookupTable):
            sname = "pointColors_lut"
            lut = cmap

        else:
            if isinstance(cmap, str):
                sname = "pointColors_" + cmap
            else:
                sname = "pointColors"
            lut.SetNumberOfTableValues(512)
            lut.Build()
            for i in range(512):
                r, g, b = colors.colorMap(i, cmap, 0, 512)
                if useAlpha:
                    idx = int(i / 512 * len(alpha))
                    lut.SetTableValue(i, r, g, b, alpha[idx])
                else:
                    lut.SetTableValue(i, r, g, b, alpha)

        arr = numpy_to_vtk(np.ascontiguousarray(scalars), deep=True)
        arr.SetName(sname)
        self.mapper.SetScalarRange(vmin, vmax)
        self.mapper.SetLookupTable(lut)
        self.mapper.ScalarVisibilityOn()
        poly.GetPointData().SetScalars(arr)
        poly.GetPointData().SetActiveScalars(sname)
        return self