matRad_interp1

 interpolates 1-D data (table lookup) and utilizes griddedInterpolant 
 if availabe in the used MATLAB version

 call
   y = matRad_interp1(xi,yi,x)
   y = matRad_interp1(xi,yi,x,extrapolation)

 input
   xi:             sample points 
   yi:             corresponding data to sample points
   x:              query points for interpolation
   extrapolation:  (optional) strategy for extrapolation. Similar to 
                   interp1. NaN is the default extrapolation value
    
 output
   y:              interpolated data   

 Note that all input data has to be given as column vectors for a correct
 interpolation. yi can be a matrix consisting out of several 1-D datasets 
 in each column, which will all be interpolated for the given query points.

 Reference
   -

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 Copyright 2020 the matRad development team. 
 
 This file is part of the matRad project. It is subject to the license 
 terms in the LICENSE file found in the top-level directory of this 
 distribution and at https://github.com/e0404/matRad/LICENSES.txt. No part 
 of the matRad project, including this file, may be copied, modified, 
 propagated, or distributed except according to the terms contained in the 
 LICENSE file.

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

0001 function y = matRad_interp1(xi,yi,x,extrapolation)
0002 % interpolates 1-D data (table lookup) and utilizes griddedInterpolant
0003 % if availabe in the used MATLAB version
0004 %
0005 % call
0006 %   y = matRad_interp1(xi,yi,x)
0007 %   y = matRad_interp1(xi,yi,x,extrapolation)
0008 %
0009 % input
0010 %   xi:             sample points
0011 %   yi:             corresponding data to sample points
0012 %   x:              query points for interpolation
0013 %   extrapolation:  (optional) strategy for extrapolation. Similar to
0014 %                   interp1. NaN is the default extrapolation value
0015 %
0016 % output
0017 %   y:              interpolated data
0018 %
0019 % Note that all input data has to be given as column vectors for a correct
0020 % interpolation. yi can be a matrix consisting out of several 1-D datasets
0021 % in each column, which will all be interpolated for the given query points.
0022 %
0023 % Reference
0024 %   -
0025 %
0026 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %
0028 % Copyright 2020 the matRad development team.
0029 %
0030 % This file is part of the matRad project. It is subject to the license
0031 % terms in the LICENSE file found in the top-level directory of this
0032 % distribution and at https://github.com/e0404/matRad/LICENSES.txt. No part
0033 % of the matRad project, including this file, may be copied, modified,
0034 % propagated, or distributed except according to the terms contained in the
0035 % LICENSE file.
0036 %
0037 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0038 
0039 persistent isGriddedInterpolantAvailable;
0040 
0041 if isempty(isGriddedInterpolantAvailable)
0042     [env, ~] = matRad_getEnvironment();
0043     switch env
0044         case 'MATLAB'
0045             isGriddedInterpolantAvailable = exist('griddedInterpolant','class');
0046         case 'OCTAVE'
0047             isGriddedInterpolantAvailable = exist('griddedInterpolant');
0048     end
0049 end
0050 
0051 if nargin < 4
0052     extrapolation = NaN;
0053 end
0054 
0055 
0056 
0057 % manual interpolation for only one query point to save time
0058 if numel(x) == 1
0059     
0060     ix1 = find((x >= xi), 1, 'last');
0061     ix2 = find((x <= xi), 1, 'first');
0062     
0063     if ix1 == ix2
0064         y = yi(ix1,:);
0065     elseif ix2 == ix1 + 1
0066         y = yi(ix1,:) + ( yi(ix2,:)-yi(ix1,:) ) * ( x - xi(ix1) ) / ( xi(ix2) - xi(ix1) );    
0067     else
0068         if isscalar(extrapolation)
0069             y = extrapolation;
0070         elseif strcmp(extrapolation,'extrap')
0071             %In this unlikely event fall back to classic
0072             y = interp1(xi,yi,x,'linear',extrapolation);
0073         else
0074             error('Invalid extrapolation argument!');
0075         end 
0076     end
0077         
0078 elseif isGriddedInterpolantAvailable
0079     
0080     if isscalar(extrapolation)
0081         extrapmethod = 'none';
0082     elseif strcmp(extrapolation,'extrap')
0083         extrapmethod = 'linear';
0084     else 
0085         error('Invalid extrapolation argument!');
0086     end
0087     
0088     if size(yi,2) > 1
0089         % interpolation for multiple 1-D datasets
0090         samplePoints = {xi, 1:size(yi,2)};
0091         queryPoints  = {x,  1:size(yi,2)};
0092     else
0093         % interpolation for a single 1-D dataset
0094         samplePoints = {xi};
0095         queryPoints  = {x};
0096     end
0097     
0098     F = griddedInterpolant(samplePoints,yi,'linear',extrapmethod);
0099 
0100     y = F(queryPoints);
0101     
0102     if isnumeric(extrapolation) && ~isnan(extrapolation)
0103         y(isnan(y)) = extrapolation;
0104     end
0105         
0106         
0107 else
0108     
0109     % for older matlab versions use this code
0110     y = interp1(xi,yi,x,'linear',extrapolation);
0111 
0112 end