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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 predict_withGradients(self, X):
 """ Returns the mean, standard deviation, mean gradient and standard deviation gradient at X for all the MCMC samples. """

        if X.ndim==1: X = X[None,:]
        ps = self.model.param_array.copy()
        means = []
        stds = []
        dmdxs = []
        dsdxs = []
        for s in self.hmc_samples:
            if self.model._fixes_ is None:
                self.model[:] = s
            else:
                self.model[self.model._fixes_] = s
            self.model._trigger_params_changed()
            m, v = self.model.predict(X)
            std = np.sqrt(np.clip(v, 1e-10, np.inf))
            dmdx, dvdx = self.model.predictive_gradients(X)
            dmdx = dmdx[:,:,0]
            dsdx = dvdx / (2*std)
            means.append(m)
            stds.append(std)
            dmdxs.append(dmdx)
            dsdxs.append(dsdx)
        self.model.param_array[:] = ps
        self.model._trigger_params_changed()
        return means, stds, dmdxs, dsdxs