Commit 60fa49e4 authored by jml1g18's avatar jml1g18
Browse files

cleanup of moved/deleted files

parent dcdf9be0
function B=inpaint_nans(A,method) % INPAINT_NANS: in-paints over nans in an array % usage: B=INPAINT_NANS(A) % default method % usage: B=INPAINT_NANS(A,method) % specify method used % % Solves approximation to one of several pdes to % interpolate and extrapolate holes in an array % % arguments (input): % A - nxm array with some NaNs to be filled in % % method - (OPTIONAL) scalar numeric flag - specifies % which approach (or physical metaphor to use % for the interpolation.) All methods are capable % of extrapolation, some are better than others. % There are also speed differences, as well as % accuracy differences for smooth surfaces. % % methods {0,1,2} use a simple plate metaphor. % method 3 uses a better plate equation, % but may be much slower and uses % more memory. % method 4 uses a spring metaphor. % method 5 is an 8 neighbor average, with no % rationale behind it compared to the % other methods. I do not recommend % its use. % % method == 0 --> (DEFAULT) see method 1, but % this method does not build as large of a % linear system in the case of only a few % NaNs in a large array. % Extrapolation behavior is linear. % % method == 1 --> simple approach, applies del^2 % over the entire array, then drops those parts % of the array which do not have any contact with % NaNs. Uses a least squares approach, but it % does not modify known values. % In the case of small arrays, this method is % quite fast as it does very little extra work. % Extrapolation behavior is linear. % % method == 2 --> uses del^2, but solving a direct % linear system of equations for nan elements. % This method will be the fastest possible for % large systems since it uses the sparsest % possible system of equations. Not a least % squares approach, so it may be least robust % to noise on the boundaries of any holes. % This method will also be least able to % interpolate accurately for smooth surfaces. % Extrapolation behavior is linear. % % Note: method 2 has problems in 1-d, so this % method is disabled for vector inputs. % % method == 3 --+ See method 0, but uses del^4 for % the interpolating operator. This may result % in more accurate interpolations, at some cost % in speed. % % method == 4 --+ Uses a spring metaphor. Assumes % springs (with a nominal length of zero) % connect each node with every neighbor % (horizontally, vertically and diagonally) % Since each node tries to be like its neighbors, % extrapolation is as a constant function where % this is consistent with the neighboring nodes. % % method == 5 --+ See method 2, but use an average % of the 8 nearest neighbors to any element. % This method is NOT recommended for use. % % % arguments (output): % B - nxm array with NaNs replaced % % % Example: % [x,y] = meshgrid(0:.01:1); % z0 = exp(x+y); % znan = z0; % znan(20:50,40:70) = NaN; % znan(30:90,5:10) = NaN; % znan(70:75,40:90) = NaN; % % z = inpaint_nans(znan); % % % See also: griddata, interp1 % % Author: John D'Errico % e-mail address: woodchips@rochester.rr.com % Release: 2 % Release date: 4/15/06 % I always need to know which elements are NaN, % and what size the array is for any method [n,m]=size(A); A=A(:); nm=n*m; k=isnan(A(:)); % list the nodes which are known, and which will % be interpolated nan_list=find(k); known_list=find(~k); % how many nans overall nan_count=length(nan_list); % convert NaN indices to (r,c) form % nan_list==find(k) are the unrolled (linear) indices % (row,column) form [nr,nc]=ind2sub([n,m],nan_list); % both forms of index in one array: % column 1 == unrolled index % column 2 == row index % column 3 == column index nan_list=[nan_list,nr,nc]; % supply default method if (nargin<2) || isempty(method) method = 0;elseif ~ismember(method,0:5) error 'If supplied, method must be one of: {0,1,2,3,4,5}.'end % for different methodsswitch method case 0 % The same as method == 1, except only work on those % elements which are NaN, or at least touch a NaN. % is it 1-d or 2-d? if (m == 1) || (n == 1) % really a 1-d case work_list = nan_list(:,1); work_list = unique([work_list;work_list - 1;work_list + 1]); work_list(work_list <= 1) = []; work_list(work_list >= nm) = []; nw = numel(work_list); u = (1:nw)'; fda = sparse(repmat(u,1,3),bsxfun(@plus,work_list,-1:1), ... repmat([1 -2 1],nw,1),nw,nm); else % a 2-d case % horizontal and vertical neighbors only talks_to = [-1 0;0 -1;1 0;0 1]; neighbors_list=identify_neighbors(n,m,nan_list,talks_to); % list of all nodes we have identified all_list=[nan_list;neighbors_list]; % generate sparse array with second partials on row % variable for each element in either list, but only % for those nodes which have a row index > 1 or < n L = find((all_list(:,2) > 1) & (all_list(:,2) < n)); nl=length(L); if nl>0 fda=sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-1 0 1],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); else fda=spalloc(n*m,n*m,size(all_list,1)*5); end % 2nd partials on column index L = find((all_list(:,3) > 1) & (all_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-n 0 n],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); end end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list(:,1)),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 1 % least squares approach with del^2. Build system % for every array element as an unknown, and then % eliminate those which are knowns. % Build sparse matrix approximating del^2 for % every element in A. % is it 1-d or 2-d? if (m == 1) || (n == 1) % a 1-d case u = (1:(nm-2))'; fda = sparse(repmat(u,1,3),bsxfun(@plus,u,0:2), ... repmat([1 -2 1],nm-2,1),nm-2,nm); else % a 2-d case % Compute finite difference for second partials % on row variable first [i,j]=ndgrid(2:(n-1),1:m); ind=i(:)+(j(:)-1)*n; np=(n-2)*m; fda=sparse(repmat(ind,1,3),[ind-1,ind,ind+1], ... repmat([1 -2 1],np,1),n*m,n*m); % now second partials on column variable [i,j]=ndgrid(1:n,2:(m-1)); ind=i(:)+(j(:)-1)*n; np=n*(m-2); fda=fda+sparse(repmat(ind,1,3),[ind-n,ind,ind+n], ... repmat([1 -2 1],np,1),nm,nm); end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 2 % Direct solve for del^2 BVP across holes % generate sparse array with second partials on row % variable for each nan element, only for those nodes % which have a row index > 1 or < n % is it 1-d or 2-d? if (m == 1) || (n == 1) % really just a 1-d case error('Method 2 has problems for vector input. Please use another method.') else % a 2-d case L = find((nan_list(:,2) > 1) & (nan_list(:,2) < n)); nl=length(L); if nl>0 fda=sparse(repmat(nan_list(L,1),1,3), ... repmat(nan_list(L,1),1,3)+repmat([-1 0 1],nl,1), ... repmat([1 -2 1],nl,1),n*m,n*m); else fda=spalloc(n*m,n*m,size(nan_list,1)*5); end % 2nd partials on column index L = find((nan_list(:,3) > 1) & (nan_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,3), ... repmat(nan_list(L,1),1,3)+repmat([-n 0 n],nl,1), ... repmat([1 -2 1],nl,1),n*m,n*m); end % fix boundary conditions at extreme corners % of the array in case there were nans there if ismember(1,nan_list(:,1)) fda(1,[1 2 n+1])=[-2 1 1]; end if ismember(n,nan_list(:,1)) fda(n,[n, n-1,n+n])=[-2 1 1]; end if ismember(nm-n+1,nan_list(:,1)) fda(nm-n+1,[nm-n+1,nm-n+2,nm-n])=[-2 1 1]; end if ismember(nm,nan_list(:,1)) fda(nm,[nm,nm-1,nm-n])=[-2 1 1]; end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); % and solve... B=A; k=nan_list(:,1); B(k)=fda(k,k)\rhs(k); end case 3 % The same as method == 0, except uses del^4 as the % interpolating operator. % del^4 template of neighbors talks_to = [-2 0;-1 -1;-1 0;-1 1;0 -2;0 -1; ... 0 1;0 2;1 -1;1 0;1 1;2 0]; neighbors_list=identify_neighbors(n,m,nan_list,talks_to); % list of all nodes we have identified all_list=[nan_list;neighbors_list]; % generate sparse array with del^4, but only % for those nodes which have a row & column index % >= 3 or <= n-2 L = find( (all_list(:,2) >= 3) & ... (all_list(:,2) <= (n-2)) & ... (all_list(:,3) >= 3) & ... (all_list(:,3) <= (m-2))); nl=length(L); if nl>0 % do the entire template at once fda=sparse(repmat(all_list(L,1),1,13), ... repmat(all_list(L,1),1,13) + ... repmat([-2*n,-n-1,-n,-n+1,-2,-1,0,1,2,n-1,n,n+1,2*n],nl,1), ... repmat([1 2 -8 2 1 -8 20 -8 1 2 -8 2 1],nl,1),nm,nm); else fda=spalloc(n*m,n*m,size(all_list,1)*5); end % on the boundaries, reduce the order around the edges L = find((((all_list(:,2) == 2) | ... (all_list(:,2) == (n-1))) & ... (all_list(:,3) >= 2) & ... (all_list(:,3) <= (m-1))) | ... (((all_list(:,3) == 2) | ... (all_list(:,3) == (m-1))) & ... (all_list(:,2) >= 2) & ... (all_list(:,2) <= (n-1)))); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,5), ... repmat(all_list(L,1),1,5) + ... repmat([-n,-1,0,+1,n],nl,1), ... repmat([1 1 -4 1 1],nl,1),nm,nm); end L = find( ((all_list(:,2) == 1) | ... (all_list(:,2) == n)) & ... (all_list(:,3) >= 2) & ... (all_list(:,3) <= (m-1))); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3) + ... repmat([-n,0,n],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); end L = find( ((all_list(:,3) == 1) | ... (all_list(:,3) == m)) & ... (all_list(:,2) >= 2) & ... (all_list(:,2) <= (n-1))); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3) + ... repmat([-1,0,1],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list(:,1)),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 4 % Spring analogy % interpolating operator. % list of all springs between a node and a horizontal % or vertical neighbor hv_list=[-1 -1 0;1 1 0;-n 0 -1;n 0 1]; hv_springs=[]; for i=1:4 hvs=nan_list+repmat(hv_list(i,:),nan_count,1); k=(hvs(:,2)>=1) & (hvs(:,2)<=n) & (hvs(:,3)>=1) & (hvs(:,3)<=m); hv_springs=[hv_springs;[nan_list(k,1),hvs(k,1)]]; end % delete replicate springs hv_springs=unique(sort(hv_springs,2),'rows'); % build sparse matrix of connections, springs % connecting diagonal neighbors are weaker than % the horizontal and vertical springs nhv=size(hv_springs,1); springs=sparse(repmat((1:nhv)',1,2),hv_springs, ... repmat([1 -1],nhv,1),nhv,nm); % eliminate knowns rhs=-springs(:,known_list)*A(known_list); % and solve... B=A; B(nan_list(:,1))=springs(:,nan_list(:,1))\rhs; case 5 % Average of 8 nearest neighbors % generate sparse array to average 8 nearest neighbors % for each nan element, be careful around edges fda=spalloc(n*m,n*m,size(nan_list,1)*9); % -1,-1 L = find((nan_list(:,2) > 1) & (nan_list(:,3) > 1)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([-n-1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % 0,-1 L = find(nan_list(:,3) > 1); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([-n, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % +1,-1 L = find((nan_list(:,2) < n) & (nan_list(:,3) > 1)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([-n+1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % -1,0 L = find(nan_list(:,2) > 1); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([-1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % +1,0 L = find(nan_list(:,2) < n); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % -1,+1 L = find((nan_list(:,2) > 1) & (nan_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([n-1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % 0,+1 L = find(nan_list(:,3) < m); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([n, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % +1,+1 L = find((nan_list(:,2) < n) & (nan_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,2), ... repmat(nan_list(L,1),1,2)+repmat([n+1, 0],nl,1), ... repmat([1 -1],nl,1),n*m,n*m); end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); % and solve... B=A; k=nan_list(:,1); B(k)=fda(k,k)\rhs(k); end % all done, make sure that B is the same shape as % A was when we came in. B=reshape(B,n,m); % ==================================================== % end of main function % ==================================================== % ==================================================== % begin subfunctions % ==================================================== function neighbors_list=identify_neighbors(n,m,nan_list,talks_to) % identify_neighbors: identifies all the neighbors of % those nodes in nan_list, not including the nans % themselves % % arguments (input): % n,m - scalar - [n,m]=size(A), where A is the % array to be interpolated % nan_list - array - list of every nan element in A % nan_list(i,1) == linear index of i'th nan element % nan_list(i,2) == row index of i'th nan element % nan_list(i,3) == column index of i'th nan element % talks_to - px2 array - defines which nodes communicate % with each other, i.e., which nodes are neighbors. % % talks_to(i,1) - defines the offset in the row % dimension of a neighbor % talks_to(i,2) - defines the offset in the column % dimension of a neighbor % % For example, talks_to = [-1 0;0 -1;1 0;0 1] % means that each node talks only to its immediate % neighbors horizontally and vertically. % % arguments(output): % neighbors_list - array - list of all neighbors of % all the nodes in nan_list if ~isempty(nan_list) % use the definition of a neighbor in talks_to nan_count=size(nan_list,1); talk_count=size(talks_to,1); nn=zeros(nan_count*talk_count,2); j=[1,nan_count]; for i=1:talk_count nn(j(1):j(2),:)=nan_list(:,2:3) + ... repmat(talks_to(i,:),nan_count,1); j=j+nan_count; end % drop those nodes which fall outside the bounds of the % original array L = (nn(:,1)<1)|(nn(:,1)>n)|(nn(:,2)<1)|(nn(:,2)>m); nn(L,:)=[]; % form the same format 3 column array as nan_list neighbors_list=[sub2ind([n,m],nn(:,1),nn(:,2)),nn]; % delete replicates in the neighbors list neighbors_list=unique(neighbors_list,'rows'); % and delete those which are also in the list of NaNs. neighbors_list=setdiff(neighbors_list,nan_list,'rows'); else neighbors_list=[]; end
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function B=inpaint_nans_bc(A,method,bcclass) % INPAINT_NANS_BC: in-paints over nans in an array, with spherical or toroidal boundary conditions % usage: B=inpaint_nsns_bc(A) % default method % usage: B=inpaint_nsns_bc(A,method) % specify method used % usage: B=inpaint_nsns_bc(A,method,bcclass) % specify class of boundary conditions applied % % Solves approximation to one of several pdes to % interpolate and extrapolate holes in an array. % Depending upon the boundary conditions specified, % the array will effectively be treated as if it lies % on either the surface of a sphere or a toroid. % % arguments (input): % A - nxm array with some NaNs to be filled in % % method - (OPTIONAL) scalar numeric flag - specifies % which approach (or physical metaphor to use % for the interpolation.) All methods are capable % of extrapolation, some are better than others. % There are also speed differences, as well as % accuracy differences for smooth surfaces. % % The methods employed here are a subset of the % methods of the original inpaint_nans. % % methods {0,1} use a simple plate metaphor. % method 4 uses a spring metaphor. % % method == 0 --> (DEFAULT) see method 1, but % this method does not build as large of a % linear system in the case of only a few % NaNs in a large array. % Extrapolation behavior is linear. % % method == 1 --> simple approach, applies del^2 % over the entire array, then drops those parts % of the array which do not have any contact with % NaNs. Uses a least squares approach, but it % does not modify known values. % In the case of small arrays, this method is % quite fast as it does very little extra work. % Extrapolation behavior is linear. % % method == 4 --> Uses a spring metaphor. Assumes % springs (with a nominal length of zero) % connect each node with every neighbor % (horizontally, vertically and diagonally) % Since each node tries to be like its neighbors, % extrapolation is as a constant function where % this is consistent with the neighboring nodes. % % DEFAULT: 0 % % bcclass - (OPTIONAL) character flag, indicating how % the array boundaries will be treated in the % inpainting operation. bcclass may be either % 'sphere' or 'toroid', or any simple contraction % of these words. % % bcclass = 'sphere' --> The first and last rows % of the array will be treated as if they are % at the North and South poles of a sphere. % Adjacent to those rows will be singular % phantom nodes at each pole. % % bcclass = 'toroid' --> The first and last rows % of the array will be treated as if they are % adjacent to ech other. As well, the first and % last columns will be adjacent to each other. % % DEFAULT: 'sphere' % % arguments (output): % B - nxm array with NaNs replaced % % % Example: % [x,y] = meshgrid(0:.01:1); % z0 = exp(x+y); % znan = z0; % znan(20:50,40:70) = NaN; % znan(30:90,5:10) = NaN; % znan(70:75,40:90) = NaN; % % z = inpaint_nans(znan); % % % See also: griddata, interp1 % % Author: John D'Errico % e-mail address: woodchips@rochester.rr.com % Release: 2 % Release date: 4/15/06 % I always need to know which elements are NaN, % and what size the array is for any method [n,m]=size(A); A=A(:); nm=n*m; k=isnan(A(:)); % list those nodes which are known, and which will % be interpolated nan_list=find(k); known_list=find(~k); % how many nans overall nan_count=length(nan_list); % convert NaN indices to (r,c) form % nan_list==find(k) are the unrolled (linear) indices % (row,column) form [nr,nc]=ind2sub([n,m],nan_list); % both forms of index in one array: % column 1 == unrolled index % column 2 == row index % column 3 == column index nan_list=[nan_list,nr,nc]; % supply default method if (nargin<2) || isempty(method) method = 0;elseif ~ismember(method,[0 1 4]) error('INPAINT_NANS_BC:improperargument', ... 'If supplied, method must be one of: {0,1,4}.')end % supply default value for bcclassif (nargin < 3) || isempty(bcclass) bcclass = 'sphere';elseif ~ischar(bcclass) error('INPAINT_NANS_BC:improperargument', ... 'If supplied, bcclass must be ''sphere'' or ''toroid''')else % it was a character string valid = {'sphere' 'toroid'}; % check to see if it is valid [bcclass,errorclass] = validstring(arg,valid); if ~isempty(errorclass) error('INPAINT_NANS_BC:improperargument', ... 'If supplied, bcclass must be ''sphere'' or ''toroid''') endend % choice of methodsswitch method case 0 % The same as method == 1, except only work on those % elements which are NaN, or at least touch a NaN. % horizontal and vertical neighbors only talks_to = [-1 0;0 -1;1 0;0 1]; neighbors_list=identify_neighbors(n,m,nan_list,talks_to); % list of all nodes we have identified all_list=[nan_list;neighbors_list]; % generate sparse array with second partials on row % variable for each element in either list, but only % for those nodes which have a row index > 1 or < n L = find((all_list(:,2) > 1) & (all_list(:,2) < n)); nl=length(L); if nl>0 fda=sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-1 0 1],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); else fda=spalloc(n*m,n*m,size(all_list,1)*5); end % 2nd partials on column index L = find((all_list(:,3) > 1) & (all_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-n 0 n],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list(:,1)),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 1 % least squares approach with del^2. Build system % for every array element as an unknown, and then % eliminate those which are knowns. % Build sparse matrix approximating del^2 for % every element in A. % Compute finite difference for second partials % on row variable first [i,j]=ndgrid(1:n,1:m); ind=i(:)+(j(:)-1)*n; np=n*m; switch bcclass case 'sphere' % we need to have two phantom nodes at the poles np = np + 2; end fda=sparse(repmat(ind,1,3),[ind-1,ind,ind+1], ... repmat([1 -2 1],np,1),n*m,n*m); % now second partials on column variable [i,j]=ndgrid(1:n,2:(m-1)); ind=i(:)+(j(:)-1)*n; np=n*(m-2); fda=fda+sparse(repmat(ind,1,3),[ind-n,ind,ind+n], ... repmat([1 -2 1],np,1),nm,nm); % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 4 % Spring analogy % interpolating operator. % list of all springs between a node and a horizontal % or vertical neighbor hv_list=[-1 -1 0;1 1 0;-n 0 -1;n 0 1]; hv_springs=[]; for i=1:4 hvs=nan_list+repmat(hv_list(i,:),nan_count,1); k=(hvs(:,2)>=1) & (hvs(:,2)<=n) & (hvs(:,3)>=1) & (hvs(:,3)<=m); hv_springs=[hv_springs;[nan_list(k,1),hvs(k,1)]]; end % delete replicate springs hv_springs=unique(sort(hv_springs,2),'rows'); % build sparse matrix of connections, springs % connecting diagonal neighbors are weaker than % the horizontal and vertical springs nhv=size(hv_springs,1); springs=sparse(repmat((1:nhv)',1,2),hv_springs, ... repmat([1 -1],nhv,1),nhv,nm); % eliminate knowns rhs=-springs(:,known_list)*A(known_list); % and solve... B=A; B(nan_list(:,1))=springs(:,nan_list(:,1))\rhs; end % all done, make sure that B is the same shape as% A was when we came in.B=reshape(B,n,m); end % mainline % ====================================================% end of main function% ====================================================% ====================================================% begin subfunctions% ====================================================function neighbors_list=identify_neighbors(n,m,nan_list,talks_to)% identify_neighbors: identifies all the neighbors of% those nodes in nan_list, not including the nans% themselves%% arguments (input):% n,m - scalar - [n,m]=size(A), where A is the% array to be interpolated% nan_list - array - list of every nan element in A% nan_list(i,1) == linear index of i'th nan element% nan_list(i,2) == row index of i'th nan element% nan_list(i,3) == column index of i'th nan element% talks_to - px2 array - defines which nodes communicate% with each other, i.e., which nodes are neighbors.%% talks_to(i,1) - defines the offset in the row% dimension of a neighbor% talks_to(i,2) - defines the offset in the column% dimension of a neighbor% % For example, talks_to = [-1 0;0 -1;1 0;0 1]% means that each node talks only to its immediate% neighbors horizontally and vertically.% % arguments(output):% neighbors_list - array - list of all neighbors of% all the nodes in nan_list if ~isempty(nan_list) % use the definition of a neighbor in talks_to nan_count=size(nan_list,1); talk_count=size(talks_to,1); nn=zeros(nan_count*talk_count,2); j=[1,nan_count]; for i=1:talk_count nn(j(1):j(2),:)=nan_list(:,2:3) + ... repmat(talks_to(i,:),nan_count,1); j=j+nan_count; end % form the same format 3 column array as nan_list neighbors_list=[sub2ind([n,m],nn(:,1),nn(:,2)),nn]; % delete replicates in the neighbors list neighbors_list=unique(neighbors_list,'rows'); % and delete those which are also in the list of NaNs. neighbors_list=setdiff(neighbors_list,nan_list,'rows'); else neighbors_list=[];end end % function identify_neighbors function [str,errorclass] = validstring(arg,valid)% validstring: compares a string against a set of valid options% usage: [str,errorclass] = validstring(arg,valid)%% If a direct hit, or any unambiguous shortening is found, that% string is returned. Capitalization is ignored.%% arguments: (input)% arg - character string, to be tested against a list% of valid choices. Capitalization is ignored.%% valid - cellstring array of alternative choices%% Arguments: (output)% str - string - resulting choice resolved from the% list of valid arguments. If no unambiguous% choice can be resolved, then str will be empty.%% errorclass - string - A string argument that explains% the error. It will be one of the following% possibilities:%% '' --> No error. An unambiguous match for arg % was found among the choices. % % 'No match found' --> No match was found among % the choices provided in valid. % % 'Ambiguous argument' --> At least two ambiguous % matches were found among those provided % in valid. % % % Example: % valid = {'off' 'on' 'The sky is falling'} % % % See also: parse_pv_pairs, strmatch, strcmpi % % Author: John D'Errico % e-mail: woodchips@rochester.rr.com % Release: 1.0 % Release date: 3/25/2010 ind = strmatch(lower(arg),lower(valid)); if isempty(ind) % No hit found errorclass = 'No match found'; str = ''; elseif (length(ind) > 1) % Ambiguous arg, hitting more than one of the valid options errorclass = 'Ambiguous argument'; str = ''; return else errorclass = ''; str = valid{ind}; end end % function validstring
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%% Surface Fit Artifact Removal
%% Construct the Surface
[x,y] = meshgrid(0:.01:1);
z0 = exp(x+y);
close all
figure
surf(z0)
title 'Original surface'
znan = z0;
znan(20:50,40:70) = NaN;
znan(30:90,5:10) = NaN;
znan(70:75,40:90) = NaN;
figure
surf(znan)
title 'Artifacts (large holes) in surface'
%% In-paint Over NaNs
z = inpaint_nans(znan,3);
figure
surf(z)
title 'Inpainted surface'
figure
surf(z-z0)
title 'Inpainting error surface (Note z-axis scale)'
%% Comapre to GRIDDATA
k = isnan(znan);
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
zg = znan;
zg(k) = zk;
figure
surf(zg)
title(['Griddata inpainting (',num2str(sum(isnan(zg(:)))),' NaNs remain)'])
figure
surf(zg-z0)
title 'Griddata error surface'
%% create a random u
u = randn(32, 64, 24, 'single')-10;
S = 17;
failed = false;
for dim = 1:3
ushift = shiftdim(u, dim-1);
[minu_true, maxu_true] = minmaxfilt1d_m(ushift, S);
minu_true = shiftdim(minu_true, 4 - dim);
maxu_true = shiftdim(maxu_true, 4 - dim);
[minu_mex, maxu_mex] = minmaxfilt1d(u, S, dim);
if any(minu_mex(:) ~= minu_true(:)) || any(maxu_mex(:) ~= maxu_true(:))
fprintf('sliding minimum/maximum filter failed on dimension %d\n', dim);
failed = true;
end
minu_mex = minfilt1d(u, S, dim);
maxu_mex = maxfilt1d(u, S, dim);
if any(minu_mex(:) ~= minu_true(:))
fprintf('sliding minimum filter failed on dimension %d\n', dim);
failed = true;
end
if any(maxu_mex(:) ~= maxu_true(:))
fprintf('sliding maximum filter failed on dimension %d\n', dim);
failed = true;
end
end
if ~failed
fprintf('test of minfilt1d, maxfilminmaxfilt1d was successful\n');
end
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function [frameInfo]=MakeFrameInfo(Frame)
Names = Frame.ComponentNames;
frameInfo.choices = zeros(12,1);
for i=1:size(Names,1),
if strcmp(Names{i},'U0')==1, frameInfo.choices( 1) = i; end;
if strcmp(Names{i},'V0')==1, frameInfo.choices( 2) = i; end;
if strcmp(Names{i},'W0')==1, frameInfo.choices( 3) = i; end;
if strcmp(Names{i},'U1')==1, frameInfo.choices( 4) = i; end;
if strcmp(Names{i},'V1')==1, frameInfo.choices( 5) = i; end;
if strcmp(Names{i},'W1')==1, frameInfo.choices( 6) = i; end;
if strcmp(Names{i},'U2')==1, frameInfo.choices( 7) = i; end;
if strcmp(Names{i},'V2')==1, frameInfo.choices( 8) = i; end;
if strcmp(Names{i},'W2')==1, frameInfo.choices( 9) = i; end;
if strcmp(Names{i},'U3')==1, frameInfo.choices(10) = i; end;
if strcmp(Names{i},'V3')==1, frameInfo.choices(11) = i; end;
if strcmp(Names{i},'W3')==1, frameInfo.choices(12) = i; end;
if strcmp(Names{i},'ACTIVE_CHOICE')== 1, frameInfo.best = i; end;
if strcmp(Names{i},'ENABLED') == 1, frameInfo.enable = i; end;
if strcmp(Names{i},'MASK') == 1, frameInfo.mask = i; end;
end
frameInfo.Grids = Frame.Grids;
frameInfo.Scales.X = Frame.Scales.X;
frameInfo.Scales.Y = Frame.Scales.Y;
frameInfo.Scales.Z = Frame.Scales.Z;
frameInfo.Scales.I = Frame.Scales.I;
frameInfo.is3D = (frameInfo.choices(3) > 0);
frameInfo.hasChoices = (frameInfo.choices(4) > 0);
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