Technical details of the routine

The nominal deconvolution is obtained by deconvolving the fit from the clean beam. A value of 0.0 means that the source is smaller than the clean beam in some dimension. The minimum and maximum values are obtained by deconvolving the source beam parameters with all combinations of error and listing the extreme values.

The 9 numbers printed are best fit major axis, minor axis and position angle, followed by the lower limits on these quantities and the upper limits.

The values of bmaj, bmin and pa follow the convention of JMFIT, so the major axis is defined as the angle of the ellipse East from North.

From the various 2nd moments the best least-squares quadratic fit to the values near the peak is found. The assumed form of the fit is The start parameters for the fitting routine are estimates based on moment fits of the top of the region to be fitted.

This is a Fortran implementation of Davidon's optimally conditioned variable metric (quasi-Newton) method for function minimization. It is based on the algorithm given in W. C. Davidon: Optimally conditioned optimization algorithms without line searches, Mathematical Programming, vol. 9 (1975) pp. 1-30. One should refer to that reference for the algorithmic details. Summarized we can say:

1. This algorithm can be used for under-determined problems.
2. It maintains an approximation, in factored form , to the inverse Hessian of F. At each iteration, a rank two update is added to this approximation. This approximation remains positive definite throughout the iteration. In cases where an unknown, say the Ith unknown, is ill-determined, ERR(I) will be finite on exit from this routine. So, in least-squares applications, the error estimates for ill-determined parameters are likely to be too small.
3. In the case of an under-determined problem (i.e., when the Hessian matrix is singular) is a non-singular matrix whose inverse is close to the Hessian matrix.
4. Furthermore, in cases where an excellent initial guess is supplied by the user, DVDMIN is likely to converge before it has iterated long enough to get a good approximation to the inverse Hessian. (Understand that it is trying to estimate this second-order information only from the first-order information that is supplied by FX.) So, in least-squares applications, when convergence occurs in just a couple of iterations, the derived error estimates may be inaccurate.
5. Another Fortran implementation is given in the technical report by W. C. Davidon and L. Nazareth: DRVOCR - A Fortran implementation of Davidon's optimally conditioned method, Argonne National Lab., Applied Math. Div. Technical Memo. No. 306, August 1977.
6. Comparisons of Davidon's algorithm with other quasi-Newton minimization algorithms are given in J. N. Lyness: A bench mark experiment for minimization algorithms, Math. of Computation, vol. 33 (1979) pp. 249-264. This algorithm compares quite favorably with others, including the routine QNMDER of Gill et al., and the Harwell Library routine VA13AD.
7. Argonne Lab.'s MINPACK routines (non-proprietary) or NAG Library routines (proprietary) could be used in place of DVDMIN. They would provide somewhat more flexibility. They're a bit more conservative (and therefore more robust, but perhaps less efficient).

Each component is fitted by a two-dimensional Gaussian. The output that is generated has the following measurements: 1) Peak flux, 2) Right Ascension, 3) Declination, 4) Major axis, 5) Minor axis, 6) Position angle of the Gaussian fit. Also error estimates are generated (based on the second moments. These errors are not the true errors, because the program makes the assumption that neighboring pixels in the map are not correlated, which is not true for radio maps in general. Fitting a source with a Gaussian doesn't give an estimate of the source size (especially when the source is unresolved). The source size found by the fit is in fact the true source size convolved with the beamsize of the radio telescope. This means that an unresolved source (most sources at 92 cm are unresolved) of lets say 10 arcseconds would have a fitted size of about arcseconds ( is the declination of the source).

If the mapheader contains information about the beamsize (the restoring beam during reduction) the program will also try to make a deconvolved fit of the source which will give a more accurate measure of the true source size.