atm_Gaussian_single_peak.m

function f = atm_gaussian_single_peak(pars,t)
% ------------------------------------------------------------------------------------------------------------------------------------------------------------------
% SUMMARY:          The atm_gaussian_single_peak function can be used as a function or a function handle for input into a nonlinear regression.
%                   
% SYNTAX:           use as a function handle: @atm_gaussian_single_peak
%                   use as a function:        atm_gaussian_single_peak(pars,t)
%
% ------------------------------------------------------------------------------------------------------------------------------------------------------------------
% INPUT PARAMETERS
% 
%  pars             Array with 4 input parameters for a Gaussian function with a single peak as follows: 
%                   e_g1 = pars(1); % signal baseline 1
%                   a_g1 = pars(2); % amplitude 1
%                   t_g1 = pars(3); % peak location 1
%                   s_g1 = pars(4); % 1-sigma peak width = standard deviation
%                   
%  t                Array of ATM waveform time tags with laser trigger time in nano seconds (e.g., atm_wvfm.shots(shot_nr).wf(rcv_gate).t)  
%
% ------------------------------------------------------------------------------------------------------------------------------------------------------------------
% OUTPUT PARAMETERS 
%                   function f when used as function handle or
%                   result of nonlinear regression when used as a function
% 
% ------------------------------------------------------------------------------------------------------------------------------------------------------------------
% Author:           Michael Studinger, NASA Goddard Space Flight Center, Greenbelt MD, USA.
% Version:          1.02 - August 19, 2015
% See also:         
% ------------------------------------------------------------------------------------------------------------------------------------------------------------------

%% check input parameters

% check number of input arguments
if (nargin ~= 2)    
        error('atm_gaussian_single_peak:nargin', ['\n\tERROR: Number of input arguments must be 2:\n', ...
        '\tSYNTAX: atm_gaussian_single_peak(pars,t);\n'])
end

% check pars array
if (any(~isfinite(pars)) || ~isvector(pars) || numel(pars) ~= 4)
    error('atm_gaussian_single_peak:pars', '\n\tERROR: pars input values must be finite and a 4 element vector.\n');
end

if (isvector(t) == 1)     % means is a not column vector (dimension 1 x n)
    t = double(t);
elseif (isvector(t) == 0) % is a column vector (dimension n x 1) that needs to be transformed into a vector 
    t = double(t)';
end

e_g = pars(1); % signal baseline
A_g = pars(2); % Amplitude
t_g = pars(3); % peak location
s_g = pars(4); % 1-sigma peak with = standard deviation

%% set Gaussian function with a single peaks and baseline

f = e_g + A_g.* exp(-0.5.*(t - t_g).^2./(s_g^2));

end