The 'FMM' package contains several internal functions called by other functions that are not designed to be called by the user.

To fit a 'FMM' model: The fitting function `fitFMM()`

calls different internal functions for fits in different situations. `fitFMM_unit()`

function fits a monocomponent 'FMM' model and `fitFMM_back()`

fits a multicomponent 'FMM' model via a backfitting algorithm. `refineFMM()`

fits a 'FMM' model from a previous object of class 'FMM'. For restricted version, `fitFMM_unit_restr()`

is used to fit a monocomponent FMM model with fixed omega; `fitFMM_restr_beta()`

, `fitFMM_restr_omegaBeta()`

and `fitFMM_restr()`

are used to fit multicomponent 'FMM' models with equality constraints for the beta and omega parameters.

To fit a single 'FMM' component: The functions `step1FMM()`

, `bestStep1()`

are used to find the initial parameter estimations and their optimal values in the first step of the fitting process. `step2FMM()`

computes the residual sum of squares in the second step of 'FMM' fitting process. In the restricted version, this function is called `step2FMM_restr()`

. In addition, `stepomega()`

function is used in an extra optimization step of omega.

To check the convergence criterion for the backfitting algorithm: `alwaysFalse()`

is used to force a number of iterations while `R2()`

is used to check if the stop condition, based on the difference between the variability explained in two consecutive iterations, is reached.

Additional functions: The functions `PV()`

, `PVj()`

and `angularmean()`

are used in the fitting process to compute the total percentage of variability explained, the percentage of variability explained by each component of 'FMM' model and the angular mean,respectively. `seqTimes()`

is used to build a sequence of equally time points spaced in range [0,2*pi].

These are not to be called directly by the user.

Depending on the returned value:

`fitFMM_unit()`

,`fitFMM_back()`

,`refineFMM()`

,`fitFMM_unit_restr()`

,`fitFMM_restr_beta()`

,`fitFMM_restr_omegaBeta()`

and`fitFMM_restr()`

return an S4 object of class`'FMM'`

.`step1FMM()`

and`bestStep1()`

return a numerical vector with the initial parameter estimations and residual sum of squares, respectively.`PVj()`

returns a vector with the percentage of variability explained by each component of 'FMM' model.`seqTime()`

returns a numerical vector with a sequence of equally time points spaced in range [0,2*pi].`step2FMM()`

,`step2FMM_restr()`

and`stepomega()`

return a numerical value with residual sum of squares of a possible solution.`PV()`

returns the total percentage of variability explained by the model.`angularmean()`

returns the angular mean of the input angles.`R2()`

and`alwaysFalse()`

return a logical value.`alwaysFalse()`

always returns`FALSE`

while`R2()`

returns`TRUE`

when the convergence criterion is reached.

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