The line $2 \mathrm { x } + \mathrm { y } = 1$ is tangent to the hyperbola $\frac { \mathrm { x } ^ { 2 } } { \mathrm { a } ^ { 2 } } - \frac { \mathrm { y } ^ { 2 } } { \mathrm {~b} ^ { 2 } } = 1$. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is