46 lines
1.3 KiB
Matlab
46 lines
1.3 KiB
Matlab
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function [ RS, J ] = eliminate(Ab, js)
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%ELIMINATE This is a simple scalar-level function for eliminating the
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%matrix Ab into a conditional part RS and a marginal part J. The scalars
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%in js are the ones eliminated (corresponding to columns of Ab). Note that
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%the returned matrices RS and J will both be the same width as Ab and will
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%contain columns of all zeros - that is, the column indices will stay the
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%same in all matrices, unlike in GTSAM where matrix data is only stored for
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%involved variables.
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if size(Ab,1) < size(Ab,2)-1
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Ab = [ Ab; zeros(size(Ab,2)-1-size(Ab,1), size(Ab,2)) ];
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end
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% Permute columns
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origCols = 1:size(Ab,2);
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jsFront = js;
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jsBack = setdiff(origCols, js);
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jsPermuted = [ jsFront jsBack ];
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Abpermuted = Ab(:,jsPermuted);
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% Eliminate (this sparse stuff prevents qr from introducing a permutation
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R = full(qr(sparse(Abpermuted)));
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% Find row split
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firstRowOfMarginal = numel(jsFront) + 1;
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for i = size(R,1) : -1 : 1
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firstNnz = find(R(i,:), 1, 'first');
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if ~isempty(firstNnz)
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if firstNnz > numel(jsFront)
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firstRowOfMarginal = i;
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else
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break;
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end
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end
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end
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% Undo permutation
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Runpermuted(:,jsPermuted) = R;
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% Split up
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RS = Runpermuted(1:firstRowOfMarginal-1, :);
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J = Runpermuted(firstRowOfMarginal:size(Ab,2)-1, :);
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end
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