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WeightedMotorSimplicialComplex.m
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WeightedMotorSimplicialComplex.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Core Model, 2022
% Written by Maya Davis
% Concept by Maya Davis and Melissa A. Redford
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% METHODS
%
% WeightedMotorSimplicialComplex
%
% CONTAINMENT
% Contains
%
% DISTANCES
% DistancesToCoordinates
%
% ACTIVATION
% ActivationOfMotorMatrix
% DistanceToActivationFunction
%
% EXPAND REGION
% Expand
% AddPointToSimplicialComplex
%
% PLOTTINGINFO
% PlottingInfo
classdef WeightedMotorSimplicialComplex
properties
MotorVertexList;
SimplexMatrix;
Weights;
NumSimplices;
SpaceDimension;
SimplexDimension;
Full;
BoundaryFaceList;
DigitsToRoundTo;
end
methods
% Creating an object
function obj = WeightedMotorSimplicialComplex(MotorVertexList, SimplexMatrix, Weights)
assert(size(Weights, 1) == 1);
obj.DigitsToRoundTo = 4;
obj.MotorVertexList = round(MotorVertexList, obj.DigitsToRoundTo);
obj.SimplexMatrix = SimplexMatrix;
obj.Weights = Weights;
obj.NumSimplices = length(Weights);
obj.SimplexDimension = rank(MotorVertexList - MotorVertexList(1,:));
obj.SpaceDimension = size(MotorVertexList, 2);
% Is the object of max dimension
obj.Full = (obj.SimplexDimension == obj.SpaceDimension);
% if obj.Full
% obj.BoundaryFaceSize = obj.SimplexDimension - 1;
% else
% obj.BoundaryFaceSize = obj.SimplexDimension;
% end
% obj.MaxOverlapNonBoundary = 1;
% If the object is of max dimension
if obj.Full
AllIndexListWithRepeats = [];
for s = 1:size(SimplexMatrix, 1)
AllMotorVertexIndices = SimplexMatrix(s, :);
for ov = 1:length(AllMotorVertexIndices)
if ov == 1
IndexSubset = (ov + 1):length(AllMotorVertexIndices);
elseif ov == length(AllMotorVertexIndices)
IndexSubset = 1:(ov - 1);
else
IndexSubset = [1:(ov - 1), (ov + 1):length(AllMotorVertexIndices)];
end
AllIndexListWithRepeats = [AllIndexListWithRepeats; AllMotorVertexIndices(IndexSubset)];
SortedListWithRepeats = sortrows(sort(AllIndexListWithRepeats, 2));
% The indices that get used when making a list of
% the unique row vectors
[~, UniqueIndexIndices, ~] = unique(SortedListWithRepeats, "rows");
% The indices that DON'T get used when making a
% list of the unique row vectors -- i.e. repeats
AllIndexIndices = 1:size(SortedListWithRepeats, 1);
RepeatIndexIndices = setdiff(AllIndexIndices, UniqueIndexIndices);
Faces = setdiff(SortedListWithRepeats, ...
SortedListWithRepeats(RepeatIndexIndices, :), ...
"rows");
end
end
obj.BoundaryFaceList = Faces;
% Otherwise, if it's not of max dimension, then it's just equal
% to the SimplexMatrix -- i.e. every simplex is a boundary
% simplex.
else
obj.BoundaryFaceList = SimplexMatrix;
end
end
%% CONTAINTMENT
% FUNCTIONS
% Contains
% Finding whether a motor point is contained in one or more of the
% simplices. If so, the indices of the simplices is returned. If
% not, [] is returned.
function SimplexIndices = Contains(obj, MotorCoordinates)
% This will really only have been tested for like 2 dimensions,
% maybe 3, but I'm trying to make it so it works in general
MinDistances = round(obj.DistancesToCoordinates(MotorCoordinates), obj.DigitsToRoundTo);
SimplexIndices = find(~MinDistances);
end
%% DISTANCES
% FUNCTIONS
% DistancesToCoordinates
% NEEDS TO BE FURTHER TESTED
% TO MAKE SURE IT ACTUALLY WORKS!!!!!!!!!!
function MinDistances = DistancesToCoordinates(obj, ...
MotorCoordinates)
MinDistances = nan(size(MotorCoordinates, 2), ...
obj.NumSimplices);
for p = 1:size(MinDistances, 1)
Point = transpose(MotorCoordinates(:, p));
for s = 1:size(MinDistances, 2)
SimplexVertices = obj.MotorVertexList( ...
obj.SimplexMatrix(s, :), :);
MinDistance = DistancePointToSimplex(Point, ...
SimplexVertices);
MinDistances(p, s) = MinDistance;
end
end
end
%% ACTIVATION
% FUNCTIONS
% ActivationOfMotorMatrix
% DistanceToActivationFunction
% EXAMPLE
% EX| obj.MotorVertexList = [0 0; 0 3; 4 3; 4 0]
% EX| obj.SimplexMatrix = [1 2 3; 1 3 4]
% EX| obj.Weights = [2 6]
function Activation = ActivationOfMotorMatrix(obj, MotorMatrix, ...
HighestActivation, DropoffSlope)
% EX| HighestActivation = 1
% EX| DropoffSlope = 0.1
% EX| MotorMatrix = [5 0 4; 3 0 3]
MinDistances = obj.DistancesToCoordinates(MotorMatrix);
% EX| MinDistances = [1 1; 0 0; 0 0]
CurrentActivations = obj.DistanceToActivationFunction( ...
MinDistances, HighestActivation, DropoffSlope);
% EX| CurrentActivations = [0.9 0.9; 1 1; 1 1]
ActivationVector = transpose(CurrentActivations);
% EX| ActivationVector = [0.9 1 1; 0.9 1 1]
Activations = (obj.Weights * ActivationVector)/sum(obj.Weights);
% EX| Activations = [7.2 8 8]/8 = [0.9 1 1]
Activation = mean(Activations);
% EX| Activation = 0.9666667
end
function ActivationFromDistance = DistanceToActivationFunction( ...
~, Distance, HighestActivation, DropoffSlope)
ActivationFromDistance = max(0, HighestActivation - ( ...
DropoffSlope * Distance));
end
%% EXPAND REGION
% FUNCTIONS
% Expand
% AddPointToSimplicialComplex
function NewSimplicialComplex = Expand(obj, NewCoordinates)
% If the point is already contained we just return the current
% object with weights changed
NewCoordinates = round(NewCoordinates, obj.DigitsToRoundTo);
RegionsContaining = obj.Contains(NewCoordinates);
if RegionsContaining
NewSimplicialComplex = obj;
NewSimplicialComplex.Weights(RegionsContaining) = NewSimplicialComplex.Weights(RegionsContaining) + 1;
return;
else
NewVertex = transpose(NewCoordinates);
[NewMotorVertexList, NewSimplexMatrix, NewWeights] = ...
obj.AddPointToSimplicialComplex(NewVertex);
NewSimplicialComplex = WeightedMotorSimplicialComplex( ...
NewMotorVertexList, NewSimplexMatrix, NewWeights);
end
end
% RIGHT NOW THE SIMPLICES ARE GOING TO OVERLAP AND I NEED TO FIX THAT
function [NewSimplexVertices, NewSimplexMatrix, NewWeights] = ...
AddPointToSimplicialComplex(obj, Point)
% ROUND THINGS FIRST TO NOT HAVE PROBLEMS
Point = round(Point, obj.DigitsToRoundTo);
SimplexVertices = round(obj.MotorVertexList, obj.DigitsToRoundTo);
assert(size(obj.SimplexMatrix, 1) == length(obj.Weights));
for v = 1:size(SimplexVertices, 1)
assert(any(SimplexVertices(v, :) ~= Point));
end
NewSimplexVertices = [SimplexVertices; Point];
NewSimplexMatrix = [];
NewWeights = [];
NewIndex = size(SimplexVertices, 1) + 1;
% Are the simplices already of max dimension?
if obj.Full
% This is the case where we're going to be adding more simplices
% rather than expanding INTO simplices -- it doesn't increase the
% dimension
% Initialize
NewSimplexMatrix = obj.SimplexMatrix;
NewWeights = obj.Weights;
% Go through all the boundary faces
for n = 1:size(obj.BoundaryFaceList, 1)
% Only use boundary faces to expand w/ new point -- not
% interior faces
CurrentVertexIndices = obj.BoundaryFaceList(n, :);
% Combine the new point with the current boundary face
PotentialShiftedVertexSet = SimplexVertices(CurrentVertexIndices, :) - Point;
% See if it creates a new simplex (i.e. the new point
% isn't .... collinear I think? .... with the points
% already on the face
CreatesNewSimplex = isempty(null(transpose(PotentialShiftedVertexSet)));
% See if it overlaps with a simplex we already have --
% if so, we don't want to add it...
% If it only overlaps at a point or a face or something
% I think it's fine, but it's more overlap than that
% that we're concerned about.
if CreatesNewSimplex
OverlapsWithExistingSimplex = false;
% For each simplex in the list
for s = 1:size(obj.SimplexMatrix, 1)
% If the current vertex indices we're using are a
% face of this simplex
if all(ismember(CurrentVertexIndices, obj.SimplexMatrix(s, :)))
% See if this simplex and the new simplex
% intersect
AdditionalPointInExistingSimplex = ...
SimplexVertices(setdiff( ...
obj.SimplexMatrix(s, :), ...
CurrentVertexIndices), :);
OverlapsWithExistingSimplex = ...
DoSimplicesIntersect(SimplexVertices( ...
CurrentVertexIndices, :), Point, ...
AdditionalPointInExistingSimplex);
if OverlapsWithExistingSimplex
break;
end
end
end
if ~OverlapsWithExistingSimplex
NewSimplexMatrix = [NewSimplexMatrix; [CurrentVertexIndices NewIndex]];
NewWeights = [NewWeights 1];
end
end
end
else
% If it's not already max dimension, then does it increase the
% dimension of the simplices?
FirstSet = SimplexVertices(obj.SimplexMatrix(1, :), :);
ShiftedFirstSet = FirstSet - Point;
if isempty(null(transpose(ShiftedFirstSet)))
% This is if it does increase the dimension
for n = 1:size(obj.SimplexMatrix, 1)
PotentialVertexIndexSet = obj.SimplexMatrix(n, :);
CorrespondingWeight = obj.Weights(n);
PotentialShiftedVertexSet = SimplexVertices(PotentialVertexIndexSet, :) - Point;
CreatesNewSimplex = isempty(null(transpose(PotentialShiftedVertexSet)));
if CreatesNewSimplex
NewSimplexMatrix = [NewSimplexMatrix; [PotentialVertexIndexSet NewIndex]];
NewWeights = [NewWeights CorrespondingWeight + 1];
end
end
else
% Otherwise, if it doesn't increase the dimension, then
% find all the sets of vertices of size one fewer than
% the max dimension; e.g. if our vertex lists are
% currently 3 long, find all possible pairs of
% vertices.
% Then we'll go through and see if each of these pairs
% is actually already in a threesome. If not, it's
% because they're not meant to be in any group
% together, so we won't try to use them. If they do,
% then they're allowed to be in a group together, but
% then we have to test if adding this new vertex we
% have would create a simplex that overlaps with an
% already existing one -- if so, then this is also a
% problem and this new threesome won't be added
PossibleVertexCombinations = nchoosek(1:size(SimplexVertices, 1), obj.SimplexDimension - 1);
for vc = 1:size(PossibleVertexCombinations, 1)
PotentialVertexIndexSet = PossibleVertexCombinations(vc);
AdditionalVertices = [];
for s = 1:size(obj.SimplexMatrix, 1)
if all(ismember(PotentialVertexIndexSet, obj.SimplexMatrix(s, :)))
AdditionalVertex = setdiff( ...
obj.SimplexMatrix(s, :), ...
PotentialVertexIndexSet);
AdditionalVertices = [AdditionalVertices; AdditionalVertex];
end
end
if AdditionalVertices
for v = 1:length(AdditionalVertices)
AdditionalPointInExistingSimplex = ...
SimplexVertices(AdditionalVertices(v), :);
OverlapsWithExistingSimplex = ...
DoSimplicesIntersect(SimplexVertices( ...
PotentialVertexIndexSet, :), Point, ...
AdditionalPointInExistingSimplex);
if OverlapsWithExistingSimplex
break;
end
end
if ~OverlapsWithExistingSimplex
NewSimplexMatrix = [NewSimplexMatrix; [PotentialVertexIndexSet NewIndex]];
NewWeights = [NewWeights 1];
end
end
end
end
end
end
%% PLOTTING INFO
% FUNCTIONS
% PlottingInfo
% Plotting info -- gives a matrix where each row is the vertices of
% the polygon that will represent this motor region -- it will be a
% regular polygon with the NumberOfVertices given as input
function [FaceData, VertexData, AlphaData] = PlottingInfo(obj, AlphaRangeOptions)
arguments
obj
AlphaRangeOptions.AlphaMin {mustBeNumeric} = 0.1;
AlphaRangeOptions.AlphaMax {mustBeNumeric} = 0.3;
end
VertexData = obj.MotorVertexList;
FaceData = obj.SimplexMatrix;
AlphaDataRaw = transpose(obj.Weights/sum(obj.Weights));
RawMin = min(AlphaDataRaw);
RawMax = max(AlphaDataRaw);
if (RawMax - RawMin == 0)
AlphaData = AlphaRangeOptions.AlphaMax * ones(size(AlphaDataRaw));
else
StretchFactor = (AlphaRangeOptions.AlphaMax - AlphaRangeOptions.AlphaMin)/(RawMax - RawMin);
StretchedAlphaData = StretchFactor * AlphaDataRaw;
ShiftFactor = AlphaRangeOptions.AlphaMax - max(StretchedAlphaData);
AlphaData = StretchedAlphaData + ShiftFactor;
end
end
end
end