sdpvar.m

国外专家做的求解LMI鲁棒控制的工具箱,可以相对高效的解决LMI问题

function sys = sdpvar(varargin)
%SDPVAR Create symbolic decision variable
%
%   You can create a sdpvar variable by:
%     X = SDPVAR(n)               Symmetric nxn matrix
%     X = SDPVAR(n,n)             Symmetric nxn matrix
%     X = SDPVAR(n,m)             Full nxm matrix
%
%   Definition of multiple scalars can be simplified
%     SDPVAR x y z w
%
%   The parametrizations supported are
%     X = SDPVAR(n,n,'symmetric') Symmetric nxn matrix
%     X = SDPVAR(n,n,'full'v)      Full nxn matrix
%     X = SDPVAR(n,n,'toeplitz')  Symmetric Toeplitz
%     X = SDPVAR(n,n,'hankel')    Symmetric Hankel
%     X = SDPVAR(n,n,'skew')      Skew-symmetric
%
%   The letters 'sy','f','ha', 't' and 'sk' are searched for in the third argument
%   hence sdpvar(n,n,'toeplitz') gives the same result as sdpvar(n,n,'t')
%
%   Only square Toeplitz and Hankel matries are supported
%
%   A scalar is defined as a 1x1 matrix
%
%   In addition to the matrix type, a fourth argument
%   can be used to obtain a complex matrix. All the
%   matrix types above apply to a complex matrix, and
%   in addition a Hermitian type is added
%
%     X = SDPVAR(n,n,'hermitian','complex') Complex Hermitian nxn matrix (X=X'=conj(X.'))
%
%   The other types are obtained as above
%     X = SDPVAR(n,n,'symmetric','complex') Complex symmetric nxn matrix (X=X.')
%     X = SDPVAR(n,n,'full','complex')      Complex full nxn matrix
%     ... and the same for Toeplitz, Hankel and skew-symmetric
%
%   See also @SDPVAR/SET, INTVAR, BINVAR, methods('sdpvar'), SEE

% Author Johan L鰂berg
% $Id: sdpvar.m,v 1.28 2005/06/23 13:31:29 joloef Exp $

% persistent optSolution
%
% % First time called, reset #free variables and solution
% %if isempty(varCount)
% if isempty(optSolution)
%    % varCount=0;
%     optSolution.info = 'Initialized by YALMIP';
%     optSolution.variables = [];
%     optSolution.optvar  =[];
% end

if nargin==0   
    return
end


if ischar(varargin{1})
    switch varargin{1}
        case 'clear'
            disp('Obsolete comand');
            return
        case 'nvars'
            sys = yalmip('nvars');%THIS IS OBSAOLETE AND SHOULD NOT BE USED
            return
        otherwise
            n = length(varargin);
            for k = 1:n
                if ~isvarname(varargin{k})
                    error('Not a valid variable name.')
                end
            end
            for k = 1:n
                varname = varargin{k};
                assignin('caller',varname,sdpvar(1,1));
            end
            return
    end
end

% Supported matrix types
% - symm
% - full
% - skew
% - hank
% - toep
switch nargin
    case 1 %Bug in MATLAB 5.3!! sdpvar called from horzcat!!!!????
        if isempty(varargin{1})
            sys = varargin{1};
            return
        end
        if isa(varargin{1},'sdpvar')
            sys = varargin{1};
            sys.typeflag = 0;
            return
        end
        n = varargin{1};
        m = varargin{1};
        if sum(n.*m)==0
            sys = zeros(n,m);
            return
        end
        if (n==m)
            matrix_type = 'symm';
            nvar = sum(n.*(n+1)/2);
        else
            matrix_type = 'full';
            nvar = sum(n.*m);
        end
    case 2
        n = varargin{1};
        m = varargin{2};
        if length(n)~=length(m)
            error('The dimensions must have the same lengths')
        end
        if sum(n.*m)==0
            sys = zeros(n,m);
            return
        end
        if (n==m)
            matrix_type = 'symm';
            nvar = sum(n.*(n+1)/2);
        else
            matrix_type = 'full';
            nvar = sum(n.*m);
        end
    case {3,4}
        n = varargin{1};
        m = varargin{2};
        if sum(n.*m)==0
            sys = zeros(n,m);
            return
        end

        % Check for complex or real
        if (nargin == 4)
            if isempty(varargin{4})
                varargin{4} = 'real';
            else
                if ~ischar(varargin{4})
                    help sdpvar
                    error('Fourth argument should be ''complex'' or ''real''')
                end
            end
            index_cmrl = strmatch(varargin{4},{'real','complex'});
            if isempty(index_cmrl)
                error('Fourth argument should be ''complex'' or ''real''. See help above')
            end
        else
            if ~ischar(varargin{3})
                help sdpvar
                error('Third argument should be ''symmetric'', ''full'', ''hermitian'',...See help above')
            end
            index_cmrl = 1;
        end;

        if isempty(varargin{3})
            if n==m
                index_type = 7; %Default symmetric
            else
                index_type = 4;
            end
        else
            if ~isempty(strmatch(varargin{3},{'complex','real'}))
                % User had third argument as complex or real
                error(['Third argument should be ''symmetric'', ''full'', ''toeplitz''... Maybe you meant sdpvar(n,n,''full'',''' varargin{3} ''')'])
            end
            index_type = strmatch(varargin{3},{'toeplitz','hankel','symmetric','full','rhankel','skew','hermitian'});
        end

        if isempty(index_type)
            error(['Matrix type "' varargin{3} '" not supported'])
        else
            switch index_type+100*(index_cmrl-1)
                case 1
                    if n~=m
                        error('Toeplitz matrix must be square')
                    else
                        matrix_type = 'toep';
                        nvar = n;
                    end

                case 2
                    if n~=m
                        error('Hankel matrix must be square')
                    else
                        matrix_type = 'hank';
                        nvar = n;
                    end

                case 3
                    if n~=m
                        error('Symmetric matrix must be square')
                    else
                        matrix_type = 'symm';
                        nvar = sum(n.*(n+1)/2);
                    end

                case 4
                    matrix_type = 'full';
                    nvar = sum(n.*m);
                    if nvar==1
                        matrix_type = 'symm';
                    end

                case 5
                    if n~=m
                        error('Hankel matrix must be square')
                    else
                        matrix_type = 'rhankel';
                        nvar = 2*n-1;
                    end

                case 6
                    if n~=m
                        error('Skew symmetric matrix must be square')
                    else
                        matrix_type = 'skew';
                        nvar = (n*(n+1)/2)-n;
                    end

                case 7
                    if n~=m
                        error('Symmetric matrix must be square')
                    else
                        matrix_type = 'symm';
                        nvar = n*(n+1)/2;
                    end

                case 101
                    if n~=m
                        error('Toeplitz matrix must be square')
                    else
                        matrix_type = 'toep complex';
                        nvar = 2*n;
                    end

                case 102
                    if n~=m
                        error('Hankel matrix must be square')
                    else
                        matrix_type = 'hank complex';
                        nvar = (2*n);
                    end

                case 103
                    if n~=m
                        error('Symmetric matrix must be square')
                    else
                        matrix_type = 'symm complex';
                        nvar = 2*n*(n+1)/2;
                    end

                case 104
                    matrix_type = 'full complex';
                    nvar = 2*n*m;
                    if nvar==1
                        matrix_type = 'symm complex';
                    end

                case 105
                    if n~=m
                        error('Hankel matrix must be square')
                    else
                        matrix_type = 'rhankel complex';
                        nvar = 2*(2*n-1);
                    end

                case 106
                    if n~=m
                        error('Skew symmetric matrix must be square')
                    else
                        matrix_type = 'skew complex';
                        nvar = 2*((n*(n+1)/2)-n);
                    end

                case 107
                    if n~=m
                        error('Hermitian matrix must be square')
                    else
                        matrix_type = 'herm complex';
                        nvar = n*(n+1)/2+(n*(n+1)/2-n);
                    end


                otherwise
                    error('Bug! Report!');
            end

        end

    case 5 % Fast version for internal use
        sys.basis = varargin{5};
        sys.lmi_variables=varargin{4};
        sys.n = varargin{1};
        sys.m = varargin{2};
        sys.typeflag = 0;
        sys.savedata = [];
        sys.extra = [];

        % Find zero-variables
        constants = find(sys.lmi_variables==0);
        if ~isempty(constants);
            sys.lmi_variables(constants)=[];
            sys.basis(:,1) = sys.basis(:,1) + sum(sys.basis(:,1+constants),2);
            sys.basis(:,1+constants)=[];
        end
        if isempty(sys.lmi_variables)
            sys = full(reshape(sys.basis(:,1),sys.n,sys.m));
        else
            sys = class(sys,'sdpvar');
        end
        return
    case 6 % Fast version for internal use
        sys.basis = varargin{5};
        sys.lmi_variables=varargin{4};
        sys.n = varargin{1};
        sys.m = varargin{2};
        sys.typeflag = varargin{6};
        sys.savedata = [];