append embedding (unified) partition data
this function is supposed to be used whenever an appendUnifiedPartition
was called as it adds information to the last unified partition(!)
The following fields are added:
.this: data that is true for vectors in the interior of the domain
.projection: several projection matrices that apply
.embeddingDomain: representation of partition in proper embedding
.boundary: information on the boundaries of the partition and the
neighbours of that partition
THIS IS NO USER FUNCTION0001 function dec = appendPartitionDataForEmbedding(dec, partitionData, zerotol) 0002 % append embedding (unified) partition data 0003 % 0004 % this function is supposed to be used whenever an appendUnifiedPartition 0005 % was called as it adds information to the last unified partition(!) 0006 % 0007 % The following fields are added: 0008 % .this: data that is true for vectors in the interior of the domain 0009 % .projection: several projection matrices that apply 0010 % .embeddingDomain: representation of partition in proper embedding 0011 % .boundary: information on the boundaries of the partition and the 0012 % neighbours of that partition 0013 % 0014 % THIS IS NO USER FUNCTION 0015 0016 % The elk-library: convex geometry applied to crystallization modeling. 0017 % Copyright (C) 2013 Alexander Reinhold 0018 % 0019 % This program is free software: you can redistribute it and/or modify it 0020 % under the terms of the GNU General Public License as published by the 0021 % Free Software Foundation, either version 3 of the License, or (at your 0022 % option) any later version. 0023 % 0024 % This program is distributed in the hope that it will be useful, but 0025 % WITHOUT ANY WARRANTY; without even the implied warranty of 0026 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0027 % General Public License for more details. 0028 % 0029 % You should have received a copy of the GNU General Public License along 0030 % with this program. If not, see <http://www.gnu.org/licenses/>. 0031 0032 %% unified partition index 0033 this.embeddingUnifiedIndex = partitionData.unifiedIndex; 0034 0035 %% validity projection (by partition) 0036 % projection information for all facets that HAVE disappeared for 0037 % hC-vectors in the interior of that partition. 0038 projection.invalidConstraintIndexVector = ... 0039 partitionData.debug.projectionData.violatedConstraintIndexVector; 0040 projection.invalidGroupIndexVector = ... 0041 partitionData.debug.projectionData.invalidFacetGroupVector; 0042 projection.projectionIndexVector = ... 0043 partitionData.debug.projectionData.projectionIndexVector; 0044 0045 % the required validity projection (this does not yet map to the 0046 % corresponding subspace in the proper embedding) 0047 projection.validity = partitionData.validityProjectionMatrix; 0048 0049 % direct maping FROM embedding proper representation (assuming 0050 % the hE-vector is on the proper domain in hE-space, if not we take 0051 % the closest hE vector with that property) 0052 projection.fromProper = pinv(projection.validity*... 0053 dec.properData.mappingNewToProper); 0054 0055 % the projection that uses validity projection (if possible) to 0056 % reach the corresponding subspace in the proper embedding 0057 projection.validityOntoSubspace = ... 0058 projection.validity*dec.properData.mappingNewToProper*... 0059 projection.fromProper; 0060 0061 % orthogonal projection onto the corresponding subspace (in 0062 % embedding space) 0063 thisOrth = orth(projection.validity*... 0064 dec.properData.projectionMatrix); 0065 projection.orthogonalOntoSubspace = thisOrth*thisOrth'; 0066 thisNull = null(projection.orthogonalOntoSubspace); 0067 0068 %% representation in proper embedding 0069 % the concise representation of the domain in embedding space covered 0070 % by the unified partition was already constructed and saved in the 0071 % partition generation 0072 embeddingDomain.hrep.A = partitionData.debug.embeddingConstraintMatrix; 0073 %! DEV: therefore, the old code is deprecated: 0074 % thisEmbedding.hrep.A = dec.unifiedPartition{end}.A * pinv(... 0075 % thisEmbedding.validityProjection*... 0076 % dec.properData.mappingNewToProper); 0077 %/ 0078 embeddingDomain.hrep.h = zeros(size(embeddingDomain.hrep.A, 1), 1); 0079 % also save a reduced form 0080 embeddingDomain.hrepReduced = reduceHrep(embeddingDomain.hrep); 0081 % the strict representation of the domain above: 0082 embeddingDomain.hrepStrict.A = [embeddingDomain.hrep.A; ... 0083 thisNull'; -1*thisNull']; 0084 embeddingDomain.hrepStrict.h = [embeddingDomain.hrep.h; ... 0085 zeros(2*size(thisNull, 2), 1)]; 0086 0087 %% validity projection filter (for confinement mapping) 0088 % For the confinement mapping of growth vectors, the current partition of 0089 % the hC-vector is pivotal. If a given boundary from 0090 % properData.confinementMapping must be considered and, hence, the 0091 % corresponding facet validity applies depends on the confinement 0092 % condition. To ensure the right decision, the representation of the 0093 % boundaries in the improper space must be considered. 0094 constraintMatrix = dec.properData.confinementMappingData.A * ... 0095 dec.properData.mappingNewToProper; 0096 responsibleGroupVector = ... 0097 dec.properData.confinementMappingData.responsibleVector; 0098 projection.applyConstraintFilter = false(1, size(constraintMatrix, 1)); 0099 directionMatrix = dec.properData.confinementMappingData.directionMatrix; 0100 for iCon = 1:size(constraintMatrix, 1) 0101 % Ignore the constraint when it indicates a zero-mapping (dissolution, 0102 % disappearing shape) 0103 if responsibleGroupVector(iCon) == dec.properData.nC+1 0104 continue; 0105 end 0106 0107 % Ignore constraints for which the facet groups have already 0108 % disappeared by the current partition. The projection might switch 0109 % in this case, but if it was confined beforehand, it will be 0110 % confined thereafter. 0111 if any(projection.invalidGroupIndexVector == ... 0112 responsibleGroupVector(iCon)); 0113 continue; 0114 end 0115 0116 % We also ignore a constraint that has now a zero-vector as normal 0117 % vector. These constraints will always be fulfilled. 0118 if all(constraintMatrix(iCon, :) < zerotol) 0119 continue; 0120 end 0121 0122 % Now we have to check confinement. A unique list of facet groups that 0123 % already have disappeared are: 0124 thisDisappearedGroupVector = projection.invalidGroupIndexVector; 0125 % These indices cannot contain (nC+1) since all partitions are inside 0126 % the empty-polytope-cone. They also cannot contain the current 0127 % direction (see above). 0128 % Usually only one group disappears but when two constraints are 0129 % equivalent in hC-space, then the corresponding facet groups also 0130 % disappear at the same time. Both of these constraints must then be 0131 % considered even though none would indicate unconfinement 0132 % separately. 0133 thisConstraintFilter = all(abs(bsxfun(@minus, ... 0134 constraintMatrix, constraintMatrix(iCon, :))) < zerotol, 2); 0135 thisGroupVector = unique([thisDisappearedGroupVector ... 0136 responsibleGroupVector(thisConstraintFilter)]); 0137 if rank([directionMatrix(:, thisGroupVector) ... 0138 dec.properData.mappingNewToProper]) == ... 0139 length(thisGroupVector) + dec.nC 0140 continue; 0141 else 0142 projection.applyConstraintFilter(iCon) = true; 0143 end 0144 end 0145 0146 0147 % save results 0148 dec.unifiedPartition{end}.projection = projection; 0149 dec.unifiedPartition{end}.embeddingDomain = embeddingDomain; 0150 % dec.unifiedPartition{end}.boundary = boundary; 0151 dec.unifiedPartition{end}.this = this; 0152