Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / optiminterp-0.3.3 / optiminterpn.m

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+## Copyright (C) 2008 Alexander Barth
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Loadable Function} {[@var{fi},@var{vari}] = } optiminterpn(@var{x},@var{y},@var{...},@var{f},@var{var},@var{lenx},@var{leny},@var{...},@var{m},@var{xi},@var{yi},@var{...})
+## Performs a local nD-optimal interpolation (objective analysis).
+##
+## Every elements in @var{f} corresponds to a data point (observation)
+## at location @var{x},@var{y},@var{...} with the error variance @var{var}.
+##
+## @var{lenx},@var{leny},@var{...} are correlation length in x-direction
+## y-direction,... respectively. 
+## @var{m} represents the number of influential points.
+##
+## @var{xi},@var{yi},@var{...} are the data points where the field is
+## interpolated. @var{fi} is the interpolated field and @var{vari} is 
+## its error variance.
+##
+## The background field of the optimal interpolation is zero.
+## For a different background field, the background field
+## must be subtracted from the observation, the difference 
+## is mapped by OI onto the background grid and finally the
+## background is added back to the interpolated field.
+## The error variance of the background field is assumed to 
+## have a error variance of one.
+## @end deftypefn
+
+## Copyright (C) 2008, Alexander Barth
+## Author: Alexander Barth <barth.alexander@gmail.com>
+
+# {[@var{fi},@var{vari}] = } optiminterpn(@var{x},@var{y},@var{...},@var{f},@var{var},@var{lenx},@var{leny},@var{len...},@var{m},@var{xi},@var{yi},@var{...})
+
+function [fi,vari] = optiminterpn(varargin)
+
+if nargin < 6 || mod(nargin-3,3) ~= 0
+  error('optiminterpn: wrong number of arguments');
+end
+
+n = (nargin-3)/3;
+
+x =  varargin{1};
+xi = varargin{2*n+4};
+on = numel(varargin{1});
+gsz = size(varargin{2*n+4});
+
+for i=1:n
+  tmp = varargin{i};
+
+  if on ~= numel(tmp)
+    error('optiminterpn: x, y,... must have the same number of elements');
+  end
+
+  ox(:,i) = tmp(:); 
+
+  len(i) = varargin{n+i+2};
+  tmp = varargin{2*n+3+i};
+
+  if (numel(tmp) ~= prod(gsz))
+    error('optiminterpn: xi, yi, ... must have the same number of elements');
+  end
+
+  gx(:,i) = tmp(:);
+end
+
+f = varargin{n+1};    
+var = varargin{n+2};    
+
+m = varargin{2*n+3};    
+
+if (isscalar(var))
+  var = var*ones(size(x));
+end
+
+if isvector(f) && size(f,1) == 1
+   f = f';
+end
+
+% is this correct?
+nf = size(f,n+1);
+
+if (on*nf ~= numel(f) && on ~= numel(var))
+  error('optiminterpn: x,y,...,var must have the same number of elements');
+end
+
+f=reshape(f,[on nf]);
+
+%whos ox f var len m gx
+[fi,vari] = optiminterp(ox,f,var,len,m,gx);
+
+fi = reshape(fi,[gsz nf]);
+vari = reshape(vari,gsz);