Matlab lugui

function [L,U,pv,qv] = lugui(A,pivotstrat)%LUGUI Gaussian elimination demonstration.%%   LUGUI(A) shows the steps in LU decomposition by Gaussian elimination.%   At each step of the elimination, the pivot that would be chosen by%   MATLAB's partial pivoting algorithm is shown in magenta.  You can use%   the mouse to pick any pivot.  The pivot is shown in red, the emerging%   columns of L in green, and the emerging rows of U in blue.%%   LUGUI with no arguments uses a random integer test matrix.%   Type 'help golub' for a description of the test matrices.%%   A popup menu allows the pivot strategy to be changed dynamically.%   lugui(A,'pick'), choose pivots with the mouse.%   lugui(A,'diagonal'), use diagonal elements as pivots.%   lugui(A,'partial'), use the largest element in the current column.%   lugui(A,'complete'), use the largest element in the unreduced matrix.%%   [L,U,p,q] = lugui(A,...) returns a lower triangular L, an upper%   triangular U and permutation vectors p and q so that L*U = A(p,q).%%   See also PIVOTGOLF.% Initializeif nargin < 2   pivotstrat = 'pick';endif nargin < 1   n = 2 + ceil(6*rand);   A = golub(n);endAsave = A;[m,n] = size(A);shgclfdx = 100;dy = 30;warns = warning('off','MATLAB:divideByZero');set(gcf,'double','on','name','LU Gui', ...   'menu','none','numbertitle','off','color','white', ...   'pos',[480-(dx/2)*min(9,n) 320 (n+1)*dx (m+3)*dy], ...   'windowbuttonupfcn','set(gcf,''tag'',''pivot'')')stop = uicontrol('style','toggle','string','X','fontweight','bold', ...   'back','w','pos',[(n+1)*dx-25 (m+3)*dy-25 25 25]);axes('pos',[0 0 1 1])axis offLcolor = [0 .65 0];Ucolor = [0  0 .90];Acolor = [0 0 0];PartialPivotColor = [1 0 1];PivotColor = [1 0 0];TempColor = [1 1 1];paws = 0.1;% Each element has its own handlefor 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],'userdata',[i j], ...         'buttondownfcn','set(gcf,''userdata'',get(gco,''userdata''))');   endend% Menusswitch lower(pivotstrat)   case 'pick', val = 1;   case 'diagonal', val = 2;   case 'partial', val = 3;   case 'complete', val = 4;   otherwise, val = 1;endpivotstrat = uicontrol('pos',[60+(dx/2)*(n-2) 20 180 20],'style','pop', ...   'val',val,'fontsize',12,'back','white','string',{'Pick a pivot', ...   'Diagonal pivoting','Partial pivoting','Complete pivoting'});% Eliminationpv = 1:m;qv = 1:n;for k = 1:min(m,n)%  If possible, quit early   if all(all(A(k:m,k:n)==0)) | all(all(~isfinite(A(k:m,k:n))))      for l = k:min(m,n)         for i = l+1:m            set(t(i,l),'string',spf(A(i,l)),'color',Lcolor)            drawnow         end         for j = l:n            set(t(l,j),'string',spf(A(l,j)),'color',Ucolor)            drawnow         end      end      break   end   if (m == n) & (k == n)      p = n;      q = n;   else      pp = min(find(abs(A(k:m,k)) == max(abs(A(k:m,k)))))+k-1;      set(t(pp,k),'color',PartialPivotColor)      p = 0;      q = 0;      while p < k | q < k | p > m | q > n         switch get(pivotstrat,'val')               case 1  % Pick a pivot with mouse               pq = get(gcf,'userdata');               if isequal(get(gcf,'tag'),'pivot') & ~isempty(pq)                  p = pq(1);                  q = pq(2);                  set(gcf,'tag','','userdata',[])               else                  drawnow               end               case 2 % Diagonal pivoting               p = k;               q = k;               case 3 % Partial pivoting               p = pp;               q = k;               case 4 % Complete pivoting               [p,q] = find(abs(A(k:m,k:n)) == max(max(abs(A(k:m,k:n)))));               p = p(1)+k-1;               q = q(1)+k-1;         end         if get(stop,'value') == 1, break, end      end      if get(stop,'value') == 1, break, end      set(t(pp,k),'color',Acolor)      set(t(p,q),'color',PivotColor)   end   if get(stop,'value') == 1, break, end   pause(10*paws)%  Swap columns   A(:,[q,k]) = A(:,[k,q]);   qv([q,k]) = qv([k,q]);   for s = .05:.05:1      for i = 1:m         set(t(i,k),'pos',[20+(k+s*(q-k))*dx 20+(m+2-i)*dy])         set(t(i,q),'pos',[20+(q+s*(k-q))*dx 20+(m+2-i)*dy])      end      drawnow   end   t(:,[q,k]) = t(:,[k,q]);   for i = 1:m      set(t(i,k),'string',spf(A(i,k)),'userdata',[i k])      set(t(i,q),'string',spf(A(i,q)),'userdata',[i q])   end   pause(10*paws)%  Swap rows   A([p,k],:) = A([k,p],:);   pv([p,k]) = pv([k,p]);   for s = .05:.05:1      for j = 1:n         set(t(k,j),'pos',[20+j*dx 20+(m+2-(k+s*(p-k)))*dy])         set(t(p,j),'pos',[20+j*dx 20+(m+2-(p+s*(k-p)))*dy])      end      drawnow   end   t([p,k],:) = t([k,p],:);   pause(10*paws)   for j = k:n      set(t(k,j),'string',spf(A(k,j)),'userdata',[k j])      set(t(p,j),'string',spf(A(p,j)),'userdata',[p j])   end   pause(10*paws)%  Skip step if column is all zero   if all(A(k:m,k) == 0)      for i = k+1:m         set(t(i,k),'string',spf(A(i,k)),'color',Lcolor)         drawnow      end      for j = k:n         set(t(k,j),'string',spf(A(k,j)),'color',Ucolor)         drawnow      end   else%     Compute multipliers in L      for i = k+1:m         A(i,k) = A(i,k)/A(k,k);         set(t(i,k),'string',spf(A(i,k)),'color',Lcolor)         pause(paws)         drawnow      end%     Elimination          for j = k+1:n         for i = k+1:m            set(t(i,j),'color',TempColor)            drawnow            pause(paws)            A(i,j) = A(i,j) - A(i,k)*A(k,j);            set(t(i,j),'string',spf(A(i,j)),'color',Acolor)            drawnow            pause(paws)         end      end      for j = k:n         set(t(k,j),'string',spf(A(k,j)),'color',Ucolor)         drawnow      end      pause(paws)   end   if k < min(m,n), pause(10*paws), endend% Seperate L and U into two matricesdelete(pivotstrat)for s = .1:.1:1.5   for j = 1:n      for i = 1:m         if i <= j            set(t(i,j),'pos',[20+(j+.10*s)*dx 20+(m+2-i)*dy])         else            set(t(i,j),'pos',[20+(j-.10*s)*dx 20+(m+2-s-i)*dy])         end      end   end   drawnowend% Insert ones on diagonal of L r = min(m,n);for j = 1:r   text('units','pixels','string',spf(1.0), ...      'fontname','courier','fontweight','bold','fontsize',14, ...      'horiz','right','color',Lcolor, ...      'pos',[20+(j-0.15)*dx 20+(m+.5-j)*dy]);enddrawnowwarning(warns)if nargout > 0   L = tril(A(:,1:r),-1) + eye(m,r);   U = triu(A(1:r,:));else   set(gcf,'userdata',Asave)   set(stop,'value',0,'callback','close(gcf)')   uicontrol('pos',[(n+1)*dx-70 10 60 20],'string','repeat', ...      'back','w','fontsize',12,'callback','lugui(get(gcf,''userdata''))')end%------------------------------------------------------------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);