Inverse Distance Weighted (IDW) or Simple Moving Average (SMA) INTERPOLATION

This function computes at (Xi,Yi) unknown locations the IDW (w<0) or the SMA (w=0) predictions.

This function computes at (Xi,Yi) unknown locations the IDW (w<0) or the SMA (w=0) predictions using r1 neighbourhood type ('n':number of points; 'r':radius) and r2 neighbourhood size from Vc measured values at (Xc,Yc) locations.

%% OUTPUTS
% Vi: (mandatory) [PxQ] gIDW interpolated values
% --> P=1, Q=1 yields interpolation at one
% point
% --> P>1, Q=1 yields interpolation at a
% vector of points
% --> P>1, Q>1 yields interpolation at a
% (ir)regular grid of points
%========================================

%% INPUTS
% Xc: (mandatory) [Nx1] x coordinates of known points
% Yc: (mandatory) [Nx1] y coordinates of known points
% Vc: (mandatory) [Nx1] known values at [Xc, Yc] locations
% Xi: (mandatory) [PxQ] x coordinates of points to be interpolated
% Yi: (mandatory) [PxQ] y coordinates of points to be interpolated
% w: (mandatory) [scalar] distance weight
% --> w<0, for Inverse Distance Weighted
% interpolation [IDW]
% --> w=0, for Simple Moving Average (only
% if neighorhood size is local and not
% global) [SMA]
% r1: (optional) [string] neighbourhood type
% --> 'n' (default) number of neighbours
% --> 'r' fixed radius length
% r2: (optional) [scalar] neighbourhood size
% --> number of neighbours, if r1=='n'
% default is length(Xc)
% --> radius length, if r1=='r'
% default is largest distance between known points
%========================================

%% SYNTAX
% --- IDW ---
% all inputs:
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,-2,'n',30);
% 6 inputs:
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,-2);
% --> r1='n'; r2=length(Xc);
% 7 inputs:
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,-2,'n');
% --> r2=length(Xc);
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,-2,'r');
% --> r2=largest distance between know points [Xi,Yi] (see D1 calculation)
% --- SMA ---
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,0,'n',10);
% --- Spatial Map ---
% Vi = gIDW(Xc,Yc,Vc,Xi,Yi,-2,'n',10);
% -with Xi and Yi 2D arrays of coordinates relative to an (ir)regular
% grid.
%========================================

%% EXAMPLES
% Interpolation at one point location:
% Vi = gIDW([1:1:10]',[2:2:20]',rand(10,1)*100,5.5,11,-2,'n');
% ---
% Interpolation at a regular grid of unknown points:
% XYc = [1:1:10]';
% Vc = rand(10,1)*100;
% Xi = rand(50,50)*10;
% Yi = rand(50,50)*10;
% [Xi,Yi] = meshgrid(XYc);
% Vi = gIDW(XYc,XYc,Vc,Xi,Yi,-2,'r',3);
% hold on
% mapshow(Xi,Yi,Vi,'DisplayType','surface')
% colormap gray
% scatter(XYc,XYc,Vc,'filled','MarkerFaceColor','g','MarkerEdgeColor','y')
% axis([0,11,0,11])
% hold off