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Added monotonicConstraint.m and corresponding documentation.
Signed-off-by: Jason Nicholson <1058191+jasonnicholson@users.noreply.github.com>
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| function [A,b] = monotonicConstraint(xGrid,dimension,dxMin) | ||
| % monotonicConstraint generates matrices for a monotonic increasing constraint of A*x<=b | ||
| % | ||
| % | ||
| % [A,b] = monotonicConstraint(xGrid) | ||
| % [A,b] = monotonicConstraint(xGrid,dimension) | ||
| % [A,b] = monotonicConstraint(xGrid,dimension,dxMin) | ||
| % | ||
| %% Inputs | ||
| % * xGrid - cell array of grid vectors | ||
| % dimension - The monotonic constraint is formed across this dimension. | ||
| % default: 1 | ||
| % * dxMin - The minimum difference between different elements of x. x(i+l) >= x(i) + dxMin | ||
| % default: 0 | ||
| % | ||
| %% Outputs | ||
| % * A - A matrix in A*x<=b | ||
| % * b - b vector in A*x<=b | ||
| % | ||
| %% Description | ||
| % This function is mainly used in conjunction with regularizeNdMatrices to create monotonic increasing constraints. | ||
| % Monotonicly decreasing constraints are just the negative of A, Aneg = -A and bneg = b. | ||
| % | ||
| % The main point of this function is to setup a monotonic increasing constraint in the Form A*x<=b that can be used | ||
| % in lsqlin or similar. To formulate this we start with | ||
| % x2 >= xl + dxMin | ||
| % x2-xl >= dxMin | ||
| % xl-x2 <= -dxMin | ||
| % | ||
| % Then generalize this to a matrix form: A*x<=b % | ||
| % A = [1 -1 0 0 ... 0; | ||
| % 0 1 -1 0 ... 0; | ||
| % 0 0 1 -1... 0; | ||
| % ... | ||
| % 0 0 0 0 1 -1]; | ||
| % | ||
| % b = [-dxMin; | ||
| % -dxMin; | ||
| % ... | ||
| % -dxMin]; | ||
| % | ||
| % Then we need to generalize this to expanding across an n-dimensional grid at the m dimension. This will produce a | ||
| % different structure in A. i.e. The 1 and -1 in a row mat not be adjacent to each other. | ||
| % | ||
| %% Example | ||
| % xGrid = {1:10}; | ||
| % [A,b] = monotonicConstraint(xGrid) | ||
| % full(A) | ||
| % | ||
| % % 2d example | ||
| % xGrid2 = {1:5, 10:15}; | ||
| % dimension = 2; | ||
| % bMax = 1e-3; | ||
| % [A,b] = monotonicConstraint(xGrid2,dimension, bMax) | ||
| % full(A) | ||
| % | ||
| % % monotonic decreasing | ||
| % Aneg = -A; | ||
| % bneg = b; | ||
| % full(Aneg) | ||
| % | ||
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| narginchk(1,3); | ||
| if nargin < 3 | ||
| dxMin =0; | ||
| if nargin <2 | ||
| dimension =1; | ||
| end | ||
| end | ||
|
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| % We want xGrid as a row vector | ||
| xGrid = reshape(xGrid,1,[]); | ||
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| % makes sure we are dealing with column vectors | ||
| xGrid = cellfun(@(x) x(:),xGrid,"UniformOutput",false); | ||
|
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| % calculate position in A matrix for lower points | ||
| subGrid = xGrid; | ||
| subGrid{dimension} = xGrid{dimension}(1:end-1); | ||
| A1 = helper(subGrid,xGrid); | ||
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| % calculate position in A matrix for upper points | ||
| subGrid{dimension} = xGrid{dimension}(2:end); | ||
| A2 = helper(subGrid,xGrid); | ||
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| % the difference between A1 and A2 is A | ||
| A = A1 - A2; | ||
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| % Calculate b | ||
| b = -dxMin*ones(size(A,1),1); | ||
| end | ||
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| function [A] = helper(subGrid,xGrid) | ||
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| % expand the grid | ||
| x = cell(size(subGrid)); | ||
| [x{:}] = ndgrid(subGrid{:}); | ||
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| % reshape all the matrices to vectors and then horizontally concatenate them. | ||
| x = cellfun(@(u) u(:), x,"UniformOutput",false); x = horzcat(x{:}); | ||
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| % run the points through regularizeNdMatrices to locate their index in the A matrix | ||
| A = regularizeNdMatrices(x, xGrid); | ||
| end |
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