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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 log_parameter_and_gradient_statistics(self, # pylint: disable=invalid-name model: Model, batch_grad_norm: float) -> None: """ Send the mean and std of all parameters and gradients to tensorboard, as well as logging the average gradient norm. """

        if self._should_log_parameter_statistics:
            # Log parameter values to Tensorboard
            for name, param in model.named_parameters():
                self.add_train_scalar("parameter_mean/" + name, param.data.mean())
                self.add_train_scalar("parameter_std/" + name, param.data.std())
                if param.grad is not None:
                    if param.grad.is_sparse:
                        # pylint: disable=protected-access
                        grad_data = param.grad.data._values()
                    else:
                        grad_data = param.grad.data

                    # skip empty gradients
                    if torch.prod(torch.tensor(grad_data.shape)).item() > 0: # pylint: disable=not-callable
                        self.add_train_scalar("gradient_mean/" + name, grad_data.mean())
                        self.add_train_scalar("gradient_std/" + name, grad_data.std())
                    else:
                        # no gradient for a parameter with sparse gradients
                        logger.info("No gradient for %s, skipping tensorboard logging.", name)
            # norm of gradients
            if batch_grad_norm is not None:
                self.add_train_scalar("gradient_norm", batch_grad_norm)