Matlab pivotgolf

function scoreout = pivotgolf(course,pivotstrat)% PIVOTGOLF  Pivot Pickin' Golf.%    Your goal is to use LUGUI to compute the LU decompositions of nine%    matrices with as little roundoff error as possible.  Your score for%    each hole is norm(R,inf)+norm(Leps,inf)+norm(Ueps,inf) where%    R = L*U - A(p,q) is the residual and Leps and Ueps are the nonzeros%    that should be zero in L and U.%%    The six golf courses include:%       magic -- magic squares and Golub matrices, some are rank deficient.%       testmats -- various test matrices, Pascal, Hilbert, gallery, etc.%       rand #s -- random integer matrices initialized by rand('state',s).%%    The four pivot strategies are:%       pick -- use the mouse to pick the pivots.%       diagonal -- pivot on the diagonal, it is possible to divide by zero.%       partial -- pivot is the largest element in the current column.%       complete -- pivot is the largest element in the unreduced matrix.%%    PIVOTGOLF(course,pivotstrat) bypasses the initial screen.%       course = 'magic', 'testmats', or a numeric s to set rand('state',s).%       pivotstrat = 'pick','diagonal','partial', or 'complete'.%%    Try to pick pivot elements that divide into the other elements exactly.%    If you can choose a pivot element that is a power of two, there will%    be no roundoff error at that step.  But if the pivot is small, the%    elements in the unreduced matrix might grow larger and subsequent steps%    might have larger roundoff errors.%%    You should know that "mulligan" is golf terminology for "OOPS, I want%    to take that shot over".  Good luck!%%    See also LUGUI.if nargin == 0   % Initial screen   shg   clf   axes('pos',[0 0 1 1]);   axis off   set(gcf,'double','on','name','Pivot Pickin'' Golf', ...      'menu','none','numbertitle','off','color','white')   text('units','norm','pos',[.25,.75],'color',[0 0.65 0], ...      'fontweight','bold','fontsize',16, ...      'string',sprintf('Welcome to Pivot Pickin'' Golf'))   text('units','norm','pos',[.03 .60],'fontweight','bold','string','Course:')   for k = 1:6      switch k         case 1,             str = 'magic';         case 2,             str = 'testmats';         otherwise,            str = ['rand #' int2str(k-2)];      end      b(k) = uicontrol('units','norm','pos',[.14*k .57 .12 .06], ...         'style','toggle','string',str,'back','w');   end   text('units','norm','pos',[.03 .45],'fontweight','bold','string','Strategy:')   str = {'pick','diagonal','partial','complete'};   for k = 1:4      b(k+6) = uicontrol('units','norm','pos',[.14*k .42 .12 .06], ...         'style','toggle','string',str{k},'back','w');   end   stop = uicontrol('style','toggle','string','X','fontweight','bold', ...      'back','white','units','norm','pos',[.96 .96 .04 .04]);   uicontrol('units','norm','pos',[.02 .02 .10 .05], ...      'string','help','back','white','callback','helpwin pivotgolf')   bvals = [];   while sum(bvals) < 2      if get(stop,'val'), break, end      pause(.05)      bvals = cell2mat(get(b,'val'));   end   if get(stop,'val')      close(gcf)      return   end   for k = find(bvals)'      switch k         case 1, course = 'magic';         case 2, course = 'testmats';         case {3,4,5,6}, course = k-2;         otherwise, pivotstrat = get(b(k),'string');      end   endelseif nargin == 1   pivotstrat = 'pick';endif isnumeric(course)   rand('state',course)else   course = lower(course);end% Loop over nine holes (matrices).score = 0;h = 1;A = [];while h <= 9   if isempty(A)            % Generate the matrix.      switch course         case 'magic'            n = 2+ceil(2/3*h);            switch h               case {3,6,9}                  A = golub(n);               otherwise                  A = magic(n);            end         case 'testmats'            n = h;            switch h               case 1                  n = 7;                  e = ones(n,1);                  A = full(spdiags([e (-3:3)' e],[-1 0 1],n,n));               case 2                  n = 5;                  A = vander((-2:2)');               case 3                  A = gallery(n);               case 4                  A = hadamard(n);               case 5                  A = gallery(n);               case 6                  A = pascal(n);               case 7                  n = 6;                  A = pascal(n);                  A(n,n) = A(n,n)-1;               case 8                  n = 5;                  A = 27720*hilb(n);               case 9                  n = 6;                  U = eye(n,n) - triu(ones(n,n),1);                  A = U'*U;            end         otherwise            n = ceil(2+3*rand);            A = round(10*(2*rand(n,n)-1));      end   end   % Use LUGUI to compute the LU decomposition   [L,U,p,q] = lugui(A,pivotstrat);   pause(2);   % Score   R = (L*U - A(p,q));   Leps = L.*(abs(L)<1000*norm(L,1)*eps);   Ueps = U.*(abs(U)<1000*norm(U,1)*eps);   show(abs(R)+abs(Leps)+abs(Ueps));   if all(isfinite(R(:)))      s = ceil(4*(norm(R(:),1)+norm(Leps(:),1)+norm(Ueps(:),1))/eps)/4;   else      s = Inf;   end   % Report the score and decide what to do next.   set(gcf,'name','Pivot Pickin'' Golf')   text('units','pixels','pos',[20+50*n,20+(n+2)*30], ...      'fontweight','bold','fontsize',12, ...      'color',[0 0.65 0],'string',sprintf('hole #%d',h))   text('units','pixels','pos',[50*(n-1)+25,55], ...      'fontweight','bold','fontsize',12,'color',[0 0 0.90], ...      'string',sprintf('score = %s, total = %s',sph(s),sph(score+s)))   stop = uicontrol('style','toggle','string','X','fontweight','bold', ...      'back','w','pos',[100*n+75 30*n+65 25 25]);   if isequal(pivotstrat,'pick')      next = uicontrol('units','pixels','pos',[50*(n-1) 10 90 20], ...         'style','toggle','fontweight','bold', ...         'background','white','string','next');         if h==9, set(next,'string','finish'), end      mulligan = uicontrol('units','pixels','pos',[50*(n+1) 10 90 20], ...         'style','toggle','fontweight','bold', ...         'background','white','string','mulligan');      uics = [stop next mulligan];      while all(cell2mat(get(uics,'val'))==0)         drawnow      end      if get(mulligan,'val'), continue, end   else      pause(3)   end   score = score + s;   if get(stop,'val'), break, end   h = h + 1;   A = [];end% Final screenclfset(gcf,'double','on','name','Pivot Pickin'' Golf', ...   'pos','default','menu','none','numbertitle','off','color','white')axes('pos',[0 0 1 1]);axis offtext('units','norm','pos',[.15,.60], ...   'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...   'string',sprintf('Thanks for playing Pivot Pickin'' Golf.'))if score == 0   text('units','norm','pos',[.15,.50],...      'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...      'string','Perfect score.  Congratulations!')elseif score == Inf   text('units','norm','pos',[.15,.50], ...      'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...      'color',[0 0.65 0],'string','Your score was infinite.')   text('units','norm','pos',[.15,.40], ...      'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...      'color',[0 0.65 0],'string','You have to avoid dividing by zero.')else   text('units','norm','pos',[.15,.50], ...      'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...      'string',sprintf('Your score was %s eps.',sph(score)))   if score > 100      text('units','norm','pos',[.15,.40], ...         'fontweight','bold','fontsize',16,'color',[0 0.65 0], ...         'string','Better luck next time.')   endenduicontrol('style','toggle','units','norm','pos',[.96 .96 .04 .04], ...   'string','X','fontweight','bold','callback','close(gcf)')if nargout > 0   scoreout = score;   pause(3)end%------------------------------------------------------------function show(A)% Same code as LUGUI.clfaxes('pos',[0 0 1 1]);axis off[m,n] = size(A);dx = 100;dy = 30;Acolor = [0 0 0];for j = 1:n   for i = 1:m      t(i,j) = text('units','pixels','string',spf(A(i,j)), ...         'fontname','courier','fontweight','bold','fontsize',14, ...         'horiz','right','color',Acolor, ...         'pos',[20+j*dx 20+(m+2-i)*dy]);   endend%------------------------------------------------------------function s = spf(aij)% Subfunction to format text stringsif aij == 0   f = '%10.0f';elseif (abs(aij) < 1.e-4) | (abs(aij) >= 1.e4)    f = '%10.1e';else   f = '%10.4f';ends = sprintf(f,aij);%------------------------------------------------------------function s = sph(x)% Format text strings that are integer multiples of 1/4.if x == 0   f = '%d';elseif x == round(x);   f = '%1.0f';elseif x == round(2*x)/2;   f = '%2.1f';else   f = '%3.2f';ends = sprintf(f,x);