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# Directory Listing of Routines

# general/science/spd_mtm/models/ar1

- SPD_MTM_AR1_FUN
- SPD_MTM_AR1_LGLK
- SPD_MTM_AR1_NORM

# Routine Descriptions

## SPD_MTM_AR1_FUN

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     :Description:
       First order autoregressive (AR(1)) function values
       at the given frequencies with the ar1_par parameters.

     :Params:
       INPUTS:
              f - frequency vector
         pl_par - power law parameters:
                  ar1_par[0] --> c, constant factor
                  ar1_par[1] --> rho, lag one autoregressive coefficient
            fny - Nyquist frequency

       OUTPUTS:
         ar1fun - first order autoregressive function

     :Author:
         Simone Di Matteo, Ph.D.
         8800 Greenbelt Rd
         Greenbelt, MD 20771 USA
         E-mail: simone.dimatteo@nasa.gov

(See general/science/spd_mtm/models/ar1/spd_mtm_ar1_fun.pro)

## SPD_MTM_AR1_LGLK

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     :Description:
       Evaluate the log-likelihood of
       the first order autoregressive (AR(1)) PSD model.

     :Params:
       INPUTS:
             ar1_par - first order autoregressive PSD parameters

       OUTPUTS:
                   M - log-likelihood

       COMMON VARIABLES:
         max_lklh
              psd_ml - PSD for the maximum likelihood model fit
               ff_ml - frequency vector for the maximum likelihood model fit
            alpha_ml - half degree of freedom of the PSD at each frequency

     :Uses:
         spd_mtm_ar1_norm.pro
         spd_mtm_ar1_fun.pro

     :Author:
         Simone Di Matteo, Ph.D.
         8800 Greenbelt Rd
         Greenbelt, MD 20771 USA
         E-mail: simone.dimatteo@nasa.gov

(See general/science/spd_mtm/models/ar1/spd_mtm_ar1_lglk.pro)

## SPD_MTM_AR1_NORM

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     :Description:
       Constant normalization factor for the AR(1) model estimated with
       the maximum likelihood theoretical solution.

     :Params:
       INPUTS:
           rho - lag-one autoregressive coefficient
            ff - Fourier frequencies vector
           psd - power spectral density
         alpha - half degree of freedom of Smtm for each frequency
           fny - Nyquist frequency

       OUTPUTS:
             c - constant factor

     :Author:
         Simone Di Matteo, Ph.D.
         8800 Greenbelt Rd
         Greenbelt, MD 20771 USA
         E-mail: simone.dimatteo@nasa.gov

(See general/science/spd_mtm/models/ar1/spd_mtm_ar1_norm.pro)