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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_likelihood(self, y, _const=math.log(2.0*math.pi), quiet=False):
 """ Compute the marginalized likelihood of the GP model The factorized matrix from the previous call to :func:`GP.compute` is used so ``compute`` must be called first. Args: y (array[n]):
 The observations at coordinates ``x`` from :func:`GP.compute`. quiet (bool):
 If true, return ``-numpy.inf`` for non-positive definite matrices instead of throwing an error. Returns: float: The marginalized likelihood of the GP model. Raises: ValueError: For mismatched dimensions. solver.LinAlgError: For non-positive definite matrices. """

        y = self._process_input(y)
        resid = y - self.mean.get_value(self._t)
        try:
            self._recompute()
        except solver.LinAlgError:
            if quiet:
                return -np.inf
            raise
        if len(y.shape) > 1:
            raise ValueError("dimension mismatch")
        logdet = self.solver.log_determinant()
        if not np.isfinite(logdet):
            return -np.inf
        loglike = -0.5*(self.solver.dot_solve(resid)+logdet+len(y)*_const)
        if not np.isfinite(loglike):
            return -np.inf
        return loglike