  We have developed a numerical method based on the transfer matrix to
calculate the quasimodes and lasing modes in one-dimensional random systems.
Depending on the relative magnitude of the localization length versus the
system size, there are two regimes in which the quasimodes are distinct in
spatial profile and frequency distribution. In the presence of uniform gain,
the lasing modes have one-to-one correspondence to the quasimodes in both
regimes. Local excitation may enhance the weight of a mode within the gain
region due to local amplification, especially in a weakly scattering system.
