  The high latitude translucent molecular cloud L1642 has been mapped in the
J=1-0 and J=2-1 transitions of 12CO, 13CO and C18O using the SEST radio
telescope. We have analysed the morphology and velocity structure of the cloud
using the Positive Matrix Factorization (PMF) method. The results show that
L1642 is composed of a main structure at radial velocity 0.2 km/s while the
higher velocity components at ~0.5 and 1.0 km/s form an incomplete ring around
it, suggesting an expanding shell structure. Fainter emission extends to the
north with a still higher velocity of up to 1.6 km/s. Such a velocity structure
suggests an elongated morphology in the line of sight direction. The physical
properties of the cloud have been investigated assuming LTE conditions, but
non-LTE radiative transfer models are also constructed for the 13CO
observations. We confirm that L1642 follows an r^-1 density distribution in its
outer parts while the distribution is considerably flatter in the core. The
cloud is close to virial equilibrium. In an Appendix the PMF results are
compared with the view obtained through the analysis of channel maps and by the
use of Principal Component Analysis (PCA). Both PMF and PCA present the
observations as a linear combination of basic spectral shapes that are
extracted from the data. Comparison of the methods shows that the PMF method in
particular is able to produce a presentation of the complex velocity that is
both compact and easily interpreted.
