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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 normalize(x, normalize='across', internal=False, format_data=True):
 """ Z-transform the columns or rows of an array, or list of arrays This function normalizes the rows or columns of the input array(s). This can be useful because data reduction and machine learning techniques are sensitive to scaling differences between features. By default, the function is set to normalize 'across' the columns of all lists, but it can also normalize the columns 'within' each individual list, or alternatively, for each row in the array. Parameters x : Numpy array or list of arrays This can either be a single array, or list of arrays normalize : str or False or None If set to 'across', the columns of the input data will be z-scored across lists (default). That is, the z-scores will be computed with with respect to column n across all arrays passed in the list. If set to 'within', the columns will be z-scored within each list that is passed. If set to 'row', each row of the input data will be z-scored. If set to False, the input data will be returned with no z-scoring. format_data : bool Whether or not to first call the format_data function (default: True). Returns normalized_x : Numpy array or list of arrays An array or list of arrays where the columns or rows are z-scored. If the input was a list, a list is returned. Otherwise, an array is returned. """


    assert normalize in ['across','within','row', False, None], "scale_type must be across, within, row or none."

    if normalize in [False, None]:
        return x
    else:

        if format_data:
            x = formatter(x, ppca=True)

        zscore = lambda X, y: (y - np.mean(X)) / np.std(X) if len(set(y)) > 1 else np.zeros(y.shape)

        if normalize == 'across':
            x_stacked=np.vstack(x)
            normalized_x = [np.array([zscore(x_stacked[:,j], i[:,j]) for j in range(i.shape[1])]).T for i in x]

        elif normalize == 'within':
            normalized_x = [np.array([zscore(i[:,j], i[:,j]) for j in range(i.shape[1])]).T for i in x]

        elif normalize == 'row':
            normalized_x = [np.array([zscore(i[j,:], i[j,:]) for j in range(i.shape[0])]) for i in x]

        if internal or len(normalized_x)>1:
            return normalized_x
        else:
            return normalized_x[0]