Improve logging of homotopy-based initialization (-ils)

[Francesco Casella]

The current implementation of the homotopy-based initialization produces the following log, when turning on LOG_NLS:

LOG_INIT          | info    | homotopy process
...
LOG_INIT          | info    | | lambda = 0 done
...
LOG_INIT          | info    | | lambda = 0.1 done
...
...
LOG_INIT          | info    | | lambda = 1 done

IMHO this is a bit confusing, and also a bit awkward to search for in huge log files. I would propose to change the logging to get the following output

LOG_INIT          | info    | homotopy process
LOG_INIT          | info    | ---------------------------
LOG_INIT          | info    | | homotopy parameter lambda = 0
...
LOG_INIT          | info    | | homotopy parameter lambda = 0 done
LOG_INIT          | info    | ---------------------------
LOG_INIT          | info    | | homotopy parameter lambda = 0.1
...
LOG_INIT          | info    | | homotopy parameter lambda = 0.1 done
LOG_INIT          | info    | ---------------------------
...
...
LOG_INIT          | info    | | homotopy parameter lambda = 1 done

This would make the debug log much easier to search and interpret.

[Lennart Ochel]

​OMCompiler#1385 changes the dump to the following output:

...
LOG_INIT          | info    | homotopy parameter lambda = 0.894737 done
|                 | |       | ---------------------------
LOG_INIT          | info    | homotopy parameter lambda = 0.947368
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              x  =        3.1132868          nom =        3.1132868          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              x  =        3.0545544          nom =        3.1132868          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              y  =       -3.1132868          nom =        3.1132868          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              y  =       -3.0545544          nom =        3.1132868          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_INIT          | info    | homotopy parameter lambda = 0.947368 done
|                 | |       | ---------------------------
LOG_INIT          | info    | homotopy parameter lambda = 1
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              x  =        3.0545544          nom =        3.0545544          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              x  =                3          nom =        3.0545544          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              y  =       -3.0545544          nom =        3.0545544          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_NLS           | info    | nls status
|                 | |       | | variables
|                 | |       | | [ 1]                              y  =               -3          nom =        3.0545544          min =  -1.7976931e+308          max =   1.7976931e+308
LOG_INIT          | info    | homotopy parameter lambda = 1 done
|                 | |       | ---------------------------
...