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.
% Initialize
if nargin < 2
pivotstrat = 'pick';
end
if nargin < 1
n = 2 + ceil(6*rand);
A = golub(n);
end
Asave = A;
[m,n] = size(A);
shg
clf
dx = 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 off
Lcolor = [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 handle
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],'userdata',[i j], ...
'buttondownfcn','set(gcf,''userdata'',get(gco,''userdata''))');
end
end
% Menus
switch lower(pivotstrat)
case 'pick', val = 1;
case 'diagonal', val = 2;
case 'partial', val = 3;
case 'complete', val = 4;
otherwise, val = 1;
end
pivotstrat = 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'});
% Elimination
pv = 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), end
end
% Seperate L and U into two matrices
delete(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
drawnow
end
% 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]);
end
drawnow
warning(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 strings
if aij == 0
f = '%10.0f';
elseif (abs(aij) < 1.e-4) | (abs(aij) >= 1.e4)
f = '%10.1e';
else
f = '%10.4f';
end
s = sprintf(f,aij);