117 lines
3.1 KiB
Mathematica
117 lines
3.1 KiB
Mathematica
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function y = max(varargin)
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%MAX (overloaded)
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%
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% t = max(X,Y,DIM)
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%
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% Creates an internal structure relating the variable t with convex
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% operator max(X).
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%
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% The variable t is primarily meant to be used in convexity preserving
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% operations such as t<=1, minimize t etc.
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%
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% If the variable is used in a non-convexity preserving operation, such as
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% t>=0, a mixed integer model will be derived.
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%
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% See built-in MAX for syntax.
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% MAX is implemented as a nonlinear operator.
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% However, for performance issues, it is not
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% implemented in the default high-level way.
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%
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% The return of the double value and the
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% construction of the epigraph/milp is done
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% in the file model.m
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%
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% To study a better example of how to create
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% your own nonlinear operator, check the
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% function sdpvar/norm instead
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% To simplify code flow, code for different #inputs
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switch nargin
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case 1
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% Three cases:
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% 1. One scalar input, return same as output
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% 2. A vector input should give scalar output
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% 3. Matrix input returns vector output
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X = varargin{1};
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if max(size(X))==1
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y = X;
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return
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elseif min(size(X))==1
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y = yalmip('addextendedvariable','max',X);
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return
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else
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% This is just short-hand for general command
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y = max(X,[],1);
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end
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case 2
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X = varargin{1};
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Y = varargin{2};
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[nx,mx] = size(X);
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[ny,my] = size(Y);
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if ~((nx*mx==1) | (ny*my==1))
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% No scalar, so they have to match
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if ~((nx==ny) & (mx==my))
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error('Array dimensions must match.');
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end
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end
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% Convert to compatible matrices
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if nx*mx==1
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X = X*ones(ny,my);
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nx = ny;
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mx = my;
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elseif ny==my
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Y = Y*ones(nx,mx);
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ny = nx;
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my = mx;
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end
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% Ok, done with error checks etc.
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y = yalmip('addextendedvariable','max',[reshape(X,1,[]);reshape(Y,1,[])]);
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y = reshape(y,nx,mx);
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case 3
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X = varargin{1};
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Y = varargin{2};
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DIM = varargin{3};
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if ~(isa(X,'sdpvar') & isempty(Y))
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error('MAX with two matrices to compare and a working dimension is not supported.');
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end
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if ~isa(DIM,'double')
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error('Dimension argument must be 1 or 2.');
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end
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if ~(length(DIM)==1)
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error('Dimension argument must be 1 or 2.');
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end
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if ~(DIM==1 | DIM==2)
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error('Dimension argument must be 1 or 2.');
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end
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if DIM==1
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% Create one extended variable per column
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y = [];
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for i = 1:size(X,2)
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inparg = extsubsref(X,1:size(X,1),i);
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if isa(inparg,'sdpvar')
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y = [y yalmip('addextendedvariable','max',inparg)];
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else
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y = [y max(inparg)];
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end
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end
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else
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% Re-use code recursively
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y = max(X',[],1)';
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end
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otherwise
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error('Too many input arguments.');
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end
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