Given $f ( x ) = \sin \omega x , f \left( x _ { 1 } \right) = - 1 , f \left( x _ { 2 } \right) = 1 , \left| x _ { 1 } - x _ { 2 } \right| _ { \text {min} } = \frac { \pi } { 2 }$, then $\omega =$ \_\_\_\_