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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 checkgrad(self, verbose=0, step=1e-6, tolerance=1e-3, df_tolerance=1e-12):
 """ Check the gradient of this parameter with respect to the highest parent's objective function. This is a three point estimate of the gradient, wiggling at the parameters with a stepsize step. The check passes if either the ratio or the difference between numerical and analytical gradient is smaller then tolerance. :param bool verbose: whether each parameter shall be checked individually. :param float step: the stepsize for the numerical three point gradient estimate. :param float tolerance: the tolerance for the gradient ratio or difference. :param float df_tolerance: the tolerance for df_tolerance .. note:: The *dF_ratio* indicates the limit of accuracy of numerical gradients. If it is too small, e.g., smaller than 1e-12, the numerical gradients are usually not accurate enough for the tests (shown with blue). """

        # Make sure we always call the gradcheck on the highest parent
        # This ensures the assumption of the highest parent to hold the fixes
        # In the checkgrad function we take advantage of that, so it needs
        # to be set in place here.
        if self.has_parent():
            return self._highest_parent_._checkgrad(self, verbose=verbose, step=step, tolerance=tolerance, df_tolerance=df_tolerance)
        return self._checkgrad(self, verbose=verbose, step=step, tolerance=tolerance, df_tolerance=df_tolerance)