[37] | 1 | function varargout=abs(varargin) |
---|
| 2 | %ABS (overloaded) |
---|
| 3 | % |
---|
| 4 | % t = abs(x) |
---|
| 5 | % |
---|
| 6 | % The variable t can only be used in convexity preserving |
---|
| 7 | % operations such as t<0, min t etc. |
---|
| 8 | |
---|
| 9 | % Author Johan Löfberg |
---|
| 10 | % $Id: abs.m,v 1.17 2005/11/24 10:05:33 joloef Exp $ |
---|
| 11 | |
---|
| 12 | %% *************************************************** |
---|
| 13 | % This file defines a nonlinear operator for YALMIP |
---|
| 14 | % |
---|
| 15 | % It can take three different inputs |
---|
| 16 | % For double inputs, it returns standard double values |
---|
| 17 | % For sdpvar inputs, it genreates a an internal variable |
---|
| 18 | % When first input is 'model' it generates the epigraph |
---|
| 19 | |
---|
| 20 | %% *************************************************** |
---|
| 21 | switch class(varargin{1}) |
---|
| 22 | |
---|
| 23 | case 'double' |
---|
| 24 | error('Overloaded SDPVAR/ABS CALLED WITH DOUBLE. Report error') |
---|
| 25 | |
---|
| 26 | case 'sdpvar' % Overloaded operator for SDPVAR objects. Pass on args and save them. |
---|
| 27 | if isreal(varargin{1}) |
---|
| 28 | varargout{1} = yalmip('addextendedvariable',mfilename,varargin{1}); |
---|
| 29 | else |
---|
| 30 | % For complex args, abs(X) is defined [norm(X(i,j),2)] in MATLAB |
---|
| 31 | y = []; |
---|
| 32 | x = varargin{1}; |
---|
| 33 | for i = 1:size(x,1) |
---|
| 34 | temp = []; |
---|
| 35 | for j = 1:size(x,2) |
---|
| 36 | temp = [temp norm(extsubsref(x,i,j))]; |
---|
| 37 | end |
---|
| 38 | y = [y;temp]; |
---|
| 39 | end |
---|
| 40 | varargout{1} = y; |
---|
| 41 | end |
---|
| 42 | |
---|
| 43 | case 'char' % YALMIP send 'graph' when it wants the epigraph or hypograph |
---|
| 44 | switch varargin{1} |
---|
| 45 | case 'graph' |
---|
| 46 | % Description using epigraphs |
---|
| 47 | t = varargin{2}; |
---|
| 48 | X = varargin{3}; |
---|
| 49 | varargout{1} = set(-t <= X <= t); |
---|
| 50 | varargout{2} = struct('convexity','convex','monotonicity','none','definiteness','positive'); |
---|
| 51 | varargout{3} = X; |
---|
| 52 | |
---|
| 53 | case 'milp' |
---|
| 54 | % Exact description using binary variables |
---|
| 55 | t = varargin{2}; |
---|
| 56 | X = varargin{3}; |
---|
| 57 | F = set([]); |
---|
| 58 | [M,m]=derivebounds(X); |
---|
| 59 | if m>=0 |
---|
| 60 | F = F + set(t == X); |
---|
| 61 | elseif M<0 |
---|
| 62 | F = F + set(t == -X); |
---|
| 63 | else |
---|
| 64 | d = binvar(1,1); |
---|
| 65 | F = F + set(X <= M*d) + set(-2*(M-m)*d <= t+X <= 2*(M-m)*d); |
---|
| 66 | F = F + set(X >= m*(1-d)) + set(-2*(M-m)*(1-d) <= t-X <= 2*(M-m)*(1-d)); |
---|
| 67 | end |
---|
| 68 | varargout{1} = F; |
---|
| 69 | varargout{2} = struct('convexity','milp','monotonicity','milp','definiteness','positive'); |
---|
| 70 | varargout{3} = X; |
---|
| 71 | otherwise |
---|
| 72 | error('SDPVAR/ABS called with CHAR argument?'); |
---|
| 73 | end |
---|
| 74 | otherwise |
---|
| 75 | error('Strange type on first argument in SDPVAR/ABS'); |
---|
| 76 | end |
---|