v2007.09.13 - Convex Optimization
v2007.09.13 - Convex Optimization v2007.09.13 - Convex Optimization
646 APPENDIX F. MATLAB PROGRAMSif nargin < 2 | isempty(tolerance_in)tolerance_in = eps;endtolerance = max(tolerance_in, eps*N*norm(D));if nargin < 3 | isempty(verbose)verbose = ’on’;endif nargin < 5 | isempty(V)use = ’Vn’;elseuse = ’V’;end% is emptyif N < 1if strcmp(verbose,’on’), disp(’Input D is empty.’), endX = [ ];Dclosest = [ ];isisnot = ’isnot’;r = [ ];returnend% is squareif size(D,1) ~= size(D,2)if strcmp(verbose,’on’), disp(’An EDM must be square.’), endX = [ ];Dclosest = [ ];isisnot = ’isnot’;r = [ ];returnend% is realif ~isreal(D)if strcmp(verbose,’on’), disp(’Because an EDM is real,’), endisisnot = ’isnot’;D = real(D);end
F.1. ISEDM() 647% is nonnegativeif sum(sum(chop(D,tolerance) < 0))isisnot = ’isnot’;if strcmp(verbose,’on’), disp(’Because an EDM is nonnegative,’),endend% is symmetricif sum(sum(abs(chop((D - D’)/2,tolerance)) > 0))isisnot = ’isnot’;if strcmp(verbose,’on’), disp(’Because an EDM is symmetric,’), endD = (D + D’)/2; % only required conditionend% has zero diagonalif sum(abs(diag(chop(D,tolerance))) > 0)isisnot = ’isnot’;if strcmp(verbose,’on’)disp(’Because an EDM has zero main diagonal,’)endend% is EDMif strcmp(use,’Vn’)VDV = -Vn(N)’*D*Vn(N);elseVDV = -Vm(N)’*D*Vm(N);end[Evecs Evals] = signeig(VDV);if ~isempty(find(chop(diag(Evals),...max(tolerance_in,eps*N*normest(VDV))) < 0))isisnot = ’isnot’;if strcmp(verbose,’on’), disp(’Because -VDV < 0,’), endendif strcmp(verbose,’on’)if strcmp(isisnot,’isnot’)disp(’matrix input is not EDM.’)elseif tolerance_in == epsdisp(’Matrix input is EDM to machine precision.’)elsedisp(’Matrix input is EDM to specified tolerance.’)end
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- Page 688 and 689: 688 BIBLIOGRAPHY[7] Abdo Y. Alfakih
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646 APPENDIX F. MATLAB PROGRAMSif nargin < 2 | isempty(tolerance_in)tolerance_in = eps;endtolerance = max(tolerance_in, eps*N*norm(D));if nargin < 3 | isempty(verbose)verbose = ’on’;endif nargin < 5 | isempty(V)use = ’Vn’;elseuse = ’V’;end% is emptyif N < 1if strcmp(verbose,’on’), disp(’Input D is empty.’), endX = [ ];Dclosest = [ ];isisnot = ’isnot’;r = [ ];returnend% is squareif size(D,1) ~= size(D,2)if strcmp(verbose,’on’), disp(’An EDM must be square.’), endX = [ ];Dclosest = [ ];isisnot = ’isnot’;r = [ ];returnend% is realif ~isreal(D)if strcmp(verbose,’on’), disp(’Because an EDM is real,’), endisisnot = ’isnot’;D = real(D);end
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