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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 approxQuantile(self, col, probabilities, relativeError):
 """ Calculates the approximate quantiles of numerical columns of a DataFrame. The result of this algorithm has the following deterministic bound: If the DataFrame has N elements and if we request the quantile at probability `p` up to error `err`, then the algorithm will return a sample `x` from the DataFrame so that the *exact* rank of `x` is close to (p * N). More precisely, floor((p - err) * N) <= rank(x) <= ceil((p + err) * N). This method implements a variation of the Greenwald-Khanna algorithm (with some speed optimizations). The algorithm was first present in [[https://doi.org/10.1145/375663.375670 Space-efficient Online Computation of Quantile Summaries]] by Greenwald and Khanna. Note that null values will be ignored in numerical columns before calculation. For columns only containing null values, an empty list is returned. :param col: str, list. Can be a single column name, or a list of names for multiple columns. :param probabilities: a list of quantile probabilities Each number must belong to [0, 1]. For example 0 is the minimum, 0.5 is the median, 1 is the maximum. :param relativeError: The relative target precision to achieve (>= 0). If set to zero, the exact quantiles are computed, which could be very expensive. Note that values greater than 1 are accepted but give the same result as 1. :return: the approximate quantiles at the given probabilities. If the input `col` is a string, the output is a list of floats. If the input `col` is a list or tuple of strings, the output is also a list, but each element in it is a list of floats, i.e., the output is a list of list of floats. .. versionchanged:: 2.2 Added support for multiple columns. """


        if not isinstance(col, (basestring, list, tuple)):
            raise ValueError("col should be a string, list or tuple, but got %r" % type(col))

        isStr = isinstance(col, basestring)

        if isinstance(col, tuple):
            col = list(col)
        elif isStr:
            col = [col]

        for c in col:
            if not isinstance(c, basestring):
                raise ValueError("columns should be strings, but got %r" % type(c))
        col = _to_list(self._sc, col)

        if not isinstance(probabilities, (list, tuple)):
            raise ValueError("probabilities should be a list or tuple")
        if isinstance(probabilities, tuple):
            probabilities = list(probabilities)
        for p in probabilities:
            if not isinstance(p, (float, int, long)) or p < 0 or p > 1:
                raise ValueError("probabilities should be numerical (float, int, long) in [0,1].")
        probabilities = _to_list(self._sc, probabilities)

        if not isinstance(relativeError, (float, int, long)) or relativeError < 0:
            raise ValueError("relativeError should be numerical (float, int, long) >= 0.")
        relativeError = float(relativeError)

        jaq = self._jdf.stat().approxQuantile(col, probabilities, relativeError)
        jaq_list = [list(j) for j in jaq]
        return jaq_list[0] if isStr else jaq_list