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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 partial_row_coordinates(self, X):
 """Returns the row coordinates for each group."""

        utils.validation.check_is_fitted(self, 's_')

        # Check input
        if self.check_input:
            utils.check_array(X, dtype=[str, np.number])

        # Prepare input
        X = self._prepare_input(X)

        # Define the projection matrix P
        P = len(X) ** 0.5 * self.U_ / self.s_

        # Get the projections for each group
        coords = {}
        for name, cols in sorted(self.groups.items()):
            X_partial = X.loc[:, cols]

            if not self.all_nums_[name]:
                X_partial = self.cat_one_hots_[name].transform(X_partial)

            Z_partial = X_partial / self.partial_factor_analysis_[name].s_[0]
            coords[name] = len(self.groups) * (Z_partial @ Z_partial.T) @ P

        # Convert coords to a MultiIndex DataFrame
        coords = pd.DataFrame({
            (name, i): group_coords.loc[:, i]
            for name, group_coords in coords.items()
            for i in range(group_coords.shape[1])
        })

        return coords