def compute_eig(self):
        """
        Compute the three eigenvalues of the tensor: eig1, eig2, ei3.
        """
        self.eig1 = _SHGrid.from_array(_np.zeros_like(self.vxx.data),
                                       grid='DH')
        self.eig2 = _SHGrid.from_array(_np.zeros_like(self.vxx.data),
                                       grid='DH')
        self.eig3 = _SHGrid.from_array(_np.zeros_like(self.vxx.data),
                                       grid='DH')

        for i in range(self.nlat):
            for j in range(self.nlon):
                a = _np.array([[self.vxx.data[i, j],
                                self.vxy.data[i, j],
                                self.vxz.data[i, j]],
                               [self.vyx.data[i, j],
                                self.vyy.data[i, j],
                                self.vyz.data[i, j]],
                               [self.vzx.data[i, j],
                                self.vzy.data[i, j],
                                self.vzz.data[i, j]]])

                eigs = _eigvalsh(a)

                self.eig1.data[i, j] = eigs[2]
                self.eig2.data[i, j] = eigs[1]
                self.eig3.data[i, j] = eigs[0]
Compute the three eigenvalues of the tensor: eig1, eig2, ei3.