gridfit.m

用Matlab语言实现的三维散列数据拟合

      end

  end

end  % if params.tilesize...

% only generate xgrid and ygrid if requested.
if nargout>1
  [xgrid,ygrid]=meshgrid(xnodes,ynodes);
end

% ============================================
% End of main function - gridfit
% ============================================

% ============================================
% subfunction - parse_pv_pairs
% ============================================
function params=parse_pv_pairs(params,pv_pairs)
% parse_pv_pairs: parses sets of property value pairs, allows defaults
% usage: params=parse_pv_pairs(default_params,pv_pairs)
%
% arguments: (input)
%  default_params - structure, with one field for every potential
%             property/value pair. Each field will contain the default
%             value for that property. If no default is supplied for a
%             given property, then that field must be empty.
%
%  pv_array - cell array of property/value pairs.
%             Case is ignored when comparing properties to the list
%             of field names. Also, any unambiguous shortening of a
%             field/property name is allowed.
%
% arguments: (output)
%  params   - parameter struct that reflects any updated property/value
%             pairs in the pv_array.
%
% Example usage:
% First, set default values for the parameters. Assume we
% have four parameters that we wish to use optionally in
% the function examplefun.
%
%  - 'viscosity', which will have a default value of 1
%  - 'volume', which will default to 1
%  - 'pie' - which will have default value 3.141592653589793
%  - 'description' - a text field, left empty by default
%
% The first argument to examplefun is one which will always be
% supplied.
%
%   function examplefun(dummyarg1,varargin)
%   params.Viscosity = 1;
%   params.Volume = 1;
%   params.Pie = 3.141592653589793
%
%   params.Description = '';
%   params=parse_pv_pairs(params,varargin);
%   params
%
% Use examplefun, overriding the defaults for 'pie', 'viscosity'
% and 'description'. The 'volume' parameter is left at its default.
%
%   examplefun(rand(10),'vis',10,'pie',3,'Description','Hello world')
%
% params = 
%     Viscosity: 10
%        Volume: 1
%           Pie: 3
%   Description: 'Hello world'
%
% Note that capitalization was ignored, and the property 'viscosity'
% was truncated as supplied. Also note that the order the pairs were
% supplied was arbitrary.

npv = length(pv_pairs);
n = npv/2;

if n~=floor(n)
  error 'Property/value pairs must come in PAIRS.'
end
if n<=0
  % just return the defaults
  return
end

if ~isstruct(params)
  error 'No structure for defaults was supplied'
end

% there was at least one pv pair. process any supplied
propnames = fieldnames(params);
lpropnames = lower(propnames);
for i=1:n
  p_i = lower(pv_pairs{2*i-1});
  v_i = pv_pairs{2*i};
  
  ind = strmatch(p_i,lpropnames,'exact');
  if isempty(ind)
    ind = find(strncmp(p_i,lpropnames,length(p_i)));
    if isempty(ind)
      error(['No matching property found for: ',pv_pairs{2*i-1}])
    elseif length(ind)>1
      error(['Ambiguous property name: ',pv_pairs{2*i-1}])
    end
  end
  p_i = propnames{ind};
  
  % override the corresponding default in params
  params = setfield(params,p_i,v_i); %#ok
  
end


% ============================================
% subfunction - check_params
% ============================================
function params = check_params(params)

% check the parameters for acceptability
% smoothness == 1 by default
if isempty(params.smoothness)
  params.smoothness = 1;
else
  if (length(params.smoothness)>1) || (params.smoothness<=0)
    error 'Smoothness must be scalar, real, finite, and positive.'
  end
end

% regularizer  - must be one of 4 options - the second and
% third are actually synonyms.
valid = {'springs', 'diffusion', 'laplacian', 'gradient'};
if isempty(params.regularizer)
  params.regularizer = 'diffusion';
end
ind = find(strncmpi(params.regularizer,valid,length(params.regularizer)));
if (length(ind)==1)
  params.regularizer = valid{ind};
else
  error(['Invalid regularization method: ',params.regularizer])
end

% interp must be one of:
%    'bilinear', 'nearest', or 'triangle'
% but accept any shortening thereof.
valid = {'bilinear', 'nearest', 'triangle'};
if isempty(params.interp)
  params.interp = 'triangle';
end
ind = find(strncmpi(params.interp,valid,length(params.interp)));
if (length(ind)==1)
  params.interp = valid{ind};
else
  error(['Invalid interpolation method: ',params.interp])
end

% solver must be one of:
%    'backslash', '\', 'symmlq', 'lsqr', or 'normal'
% but accept any shortening thereof.
valid = {'backslash', '\', 'symmlq', 'lsqr', 'normal'};
if isempty(params.solver)
  params.solver = '\';
end
ind = find(strncmpi(params.solver,valid,length(params.solver)));
if (length(ind)==1)
  params.solver = valid{ind};
else
  error(['Invalid solver option: ',params.solver])
end

% extend must be one of:
%    'never', 'warning', 'always'
% but accept any shortening thereof.
valid = {'never', 'warning', 'always'};
if isempty(params.extend)
  params.extend = 'warning';
end
ind = find(strncmpi(params.extend,valid,length(params.extend)));
if (length(ind)==1)
  params.extend = valid{ind};
else
  error(['Invalid extend option: ',params.extend])
end

% tilesize == inf by default
if isempty(params.tilesize)
  params.tilesize = inf;
elseif (length(params.tilesize)>1) || (params.tilesize<3)
  error 'Tilesize must be scalar and > 0.'
end

% overlap == 0.20 by default
if isempty(params.overlap)
  params.overlap = 0.20;
elseif (length(params.overlap)>1) || (params.overlap<0) || (params.overlap>0.5)
  error 'Overlap must be scalar and 0 < overlap < 1.'
end

% ============================================
% subfunction - tiled_gridfit
% ============================================
function zgrid=tiled_gridfit(x,y,z,xnodes,ynodes,params)
% tiled_gridfit: a tiled version of gridfit, continuous across tile boundaries 
% usage: [zgrid,xgrid,ygrid]=tiled_gridfit(x,y,z,xnodes,ynodes,params)
%
% Tiled_gridfit is used when the total grid is far too large
% to model using a single call to gridfit. While gridfit may take
% only a second or so to build a 100x100 grid, a 2000x2000 grid
% will probably not run at all due to memory problems.
%
% Tiles in the grid with insufficient data (<4 points) will be
% filled with NaNs. Avoid use of too small tiles, especially
% if your data has holes in it that may encompass an entire tile.
%
% A mask may also be applied, in which case tiled_gridfit will
% subdivide the mask into tiles. Note that any boolean mask
% provided is assumed to be the size of the complete grid.
%
% Tiled_gridfit may not be fast on huge grids, but it should run
% as long as you use a reasonable tilesize. 8-)

% Note that we have already verified all parameters in check_params

% Matrix elements in a square tile
tilesize = params.tilesize;
% Size of overlap in terms of matrix elements. Overlaps
% of purely zero cause problems, so force at least two
% elements to overlap.
overlap = max(2,floor(tilesize*params.overlap));

% reset the tilesize for each particular tile to be inf, so
% we will never see a recursive call to tiled_gridfit
Tparams = params;
Tparams.tilesize = inf;

nx = length(xnodes);
ny = length(ynodes);
zgrid = zeros(ny,nx);

% linear ramp for the bilinear interpolation
rampfun = inline('(t-t(1))/(t(end)-t(1))','t');

% loop over each tile in the grid
h = waitbar(0,'Relax and have a cup of JAVA. Its my treat.');
warncount = 0;
xtind = 1:min(nx,tilesize);
while ~isempty(xtind) && (xtind(1)<=nx)
  
  xinterp = ones(1,length(xtind));
  if (xtind(1) ~= 1)
    xinterp(1:overlap) = rampfun(xnodes(xtind(1:overlap)));
  end
  if (xtind(end) ~= nx)
    xinterp((end-overlap+1):end) = 1-rampfun(xnodes(xtind((end-overlap+1):end)));
  end
  
  ytind = 1:min(ny,tilesize);
  while ~isempty(ytind) && (ytind(1)<=ny)
    % update the waitbar
    waitbar((xtind(end)-tilesize)/nx + tilesize*ytind(end)/ny/nx)
    
    yinterp = ones(length(ytind),1);
    if (ytind(1) ~= 1)
      yinterp(1:overlap) = rampfun(ynodes(ytind(1:overlap)));
    end
    if (ytind(end) ~= ny)
      yinterp((end-overlap+1):end) = 1-rampfun(ynodes(ytind((end-overlap+1):end)));
    end
    
    % was a mask supplied?
    if ~isempty(params.mask)
      submask = params.mask(ytind,xtind);
      Tparams.mask = submask;
    end
    
    % extract data that lies in this grid tile
    k = (x>=xnodes(xtind(1))) & (x<=xnodes(xtind(end))) & ...
        (y>=ynodes(ytind(1))) & (y<=ynodes(ytind(end)));
    k = find(k);
    
    if length(k)<4
      if warncount == 0
        warning 'A tile was too underpopulated to model. Filled with NaNs.'
      end
      warncount = warncount + 1;
      
      % fill this part of the grid with NaNs
      zgrid(ytind,xtind) = NaN;
      
    else
      % build this tile
      zgtile = gridfit(x(k),y(k),z(k),xnodes(xtind),ynodes(ytind),Tparams);
      
      % bilinear interpolation (using an outer product)
      interp_coef = yinterp*xinterp;
      
      % accumulate the tile into the complete grid
      zgrid(ytind,xtind) = zgrid(ytind,xtind) + zgtile.*interp_coef;
      
    end
    
    % step to the next tile in y
    if ytind(end)<ny
      ytind = ytind + tilesize - overlap;
      % are we within overlap elements of the edge of the grid?
      if (ytind(end)+max(3,overlap))>=ny
        % extend this tile to the edge
        ytind = ytind(1):ny;
      end
    else
      ytind = ny+1;
    end
    
  end % while loop over y
  
  % step to the next tile in x
  if xtind(end)<nx
    xtind = xtind + tilesize - overlap;
    % are we within overlap elements of the edge of the grid?
    if (xtind(end)+max(3,overlap))>=nx
      % extend this tile to the edge
      xtind = xtind(1):nx;
    end
  else
    xtind = nx+1;
  end

end % while loop over x

% close down the waitbar
close(h)

if warncount>0
  warning([num2str(warncount),' tiles were underpopulated & filled with NaNs'])
end