integrate

var Command = &command.Command{
	Usage: `integrate [--ranges] [--stem <age>]
	[--distribution <distribution>] [-p|--particles <number>]
	[--min <float>] [--max <float>] [--mc <number>] [--parts <number>]
	[--cpu <number>] [--nomat] <project-file>`,
	Short: "integrate numerically the likelihood curve",
	Long: `
Command integrate reads a PhyGeo project, and makes a numerical integration of
the likelihood function, using a diffusion model over a sphere, by reporting
the log likelihood values of different values of lambda.

By default, it will use geographic distributions stored as points (presence-
absence maps). If no there are no point distribution, or the flags --ranges is
defined, the continuous range maps will be used.

By default, an stem branch will be added to each tree using the 10% of the root
age. To set a different stem age use the flag --stem, the value should be in
million years.

The flags --min and --max defines the bounds for the values of the lambda
(concentration) parameter of the spherical normal (equivalent to the kappa
parameter of von Mises-Fisher distribution). The units of the lambda parameter
are in 1/radians^2. The default values are 0 and 1000.

If the flag --distribution is defined, it will sample from the indicated
distribution. The sintaxis for a distribution is:

	<name>=<parameter>[,<parameter>...]

Valid distributions are:

	gamma	it requires two parameters, the shape (or alpha), and the rate
		(or lambda).

As the usual objetive of sampling from a distribution is to retrieve the
reconstructions, the flag -p, or --particles, define the number of particles
used for the stochastic mapping. The results will be stored in the file called
"<project>-<tree>-sampling-<samples>x<particles>.tab", as a TSV file. If the
flag -o or --output is defined, the value of the flag will be used as a prefix
for the output file.

By default the command performs an stepwise integration, the flag --parts
indicates the number of segments using for the integration. The default value
is 1000. If the flag --mc is defined, it will perform a Monte Carlo
integration using the indicated number of samples.

Results will be written in the standard output, as a TSV table with the
following columns:

	- tree, for the tree used in the sample
	- lambda, for the value of lambda used in the sample
		(in 1/radians^2)
	- stdDev, for the standard deviation
		(in Km/My)
	- logLike, the log likelihood for the reconstruction

By default, all available CPUs will be used in the processing. Set --cpu flag
to use a different number of CPUs.

By default, if the base pixelation is smaller than 500 pixels at the equator,
it will build a distance matrix to speed up the search. As this matrix
consumes a lot of memory, this procedure can be disabled using the flag
--nomat.
	`,
	SetFlags: setFlags,
	Run:      run,
}