%% Qunpack.m
% Qube_osf.m unpacks itself.
fin = fopen("Qube_osf.m",'r');
mkdir("Qube");
L = fgetl(fin);
while ~isequal(L,'%% EOF')
F = ['Qube/' L(4:end)];
disp(F)
fout = fopen(F,'w');
L = fgetl(fin);
while length(L) < 2 || ~isequal(L(1:2),'%%')
fprintf(fout,'%s\n',L);
L = fgetl(fin);
end
fclose(fout);
end
fclose(fin);
%% Qube.m
function Qube(ops)
% Linear algebra and computer science combine to power Rubik's cube.
% Most recent edit: '19-May-2022 06:00'
% info: https://blogs.mathworks.com/cleve/2022/02/13/rubiks-cube
% https://blogs.mathworks.com/cleve/2022/04/04/digital-simulation-of-rubiks-cube/
% https://blogs.mathworks.com/cleve/2022/04/12/digital-simulation-of-rubiks-cube-with-Qube/
% https://blogs.mathworks.com/cleve/2022/05/04/qube-the-movie/
% https://blogs.mathworks.com/cleve/2022/05/18/rotation-matrices/
%
% L R U D F B X Y Z: rotate clockwise, Singmaster notation,
% Left, Right, Up, Down, Front, Back, x, y, z axes.
% ' : Rotate counter-clockwise.
% <= : Apply inverse of most recent rotation.
% => : Redo most recent <=.
% <== : Unscramble, repeated <=.
% ~~> : Scramble, repeated random rotations.
% ==> : Apply stack again.
% Q0 : Initial cube.
% period: Number of repetitions required to return to Q0.
% solve: Experimental solver.
% delta: Fractional rotation, controls speed.
% type: Center=0, face=1, edge=2, corner=3.
% restart: Complete restart.
%
% Q: cube, 3x3x3 array of 8x3 vertices of cubelets.
% Q0: initial cube showing a single color on each face.
% op: one of the keys, followed by a blank, a prime or a 2.
% score: nuclear norm = sum of svd(Q{j}-Q0{j}).
% stack: string of ops displayed in a window above the cube.
% starting conditions: Q = Q0, empty stack.
%
% Copyright 2022 Cleve Moler
if nargin == 0
Qfigure
Qinit
Qshow
shg
else
shg
ops = split(string(ops))';
for k = 1:length(ops)
key([char(ops(k)) ' '])
end
end
end
%% Q0.m
function Q = Q0(~,~)
v = 0.90*qzero;
Q = cell(3,3,3);
for z = [-2 0 2]
for y = [-2 0 2]
for x = [-2 0 2]
Q{x/2+2,y/2+2,z/2+2} = v + [x y z];
end
end
end
if nargin == 2
Qshow(Q)
qstate('Q',Q)
show_stack('')
qstate('stack','')
end
end
%% Qfigure.m
function Qfigure(scale)
if nargin < 1
scale = 4;
end
% Initialize figure window for Rubik's cube
clf
set(gcf,'name','Qube, 19-May-2022', ...
'numbertitle','off', ...
'toolbar','none', ...
'menubar','none', ...
'color',0.75*[1 1 1], ...
'userdata',{})
%{
set(gcf,'windowbuttondownfcn',@wdownf, ...
'windowbuttonupfcn',@wupf)
%}
set(gca,'position',[1/3 7/24 1/2 1/2], ...
'vis','on', ...
'clipping','off')
axis(scale*[-1 1 -1 1 -1 1])
axis('square','off','vis3d')
rotate3d off
view(3)
shg
end
%% Qinit.m
function Qinit
u = 60;
alfa = 'LRUDFBXYZ'; % Singmaster alphabet
for j = 1:9
x = 4*j+2*(j>6)+8;
pushbut([alfa(j) ' '],[x 6 3 3]/u, @key)
pushbut([alfa(j) ''''],[x 2 3 3]/u, @key)
end
pushbut( "<=", [ 2 2 6 3]/u, @bs)
toggbut( "<==", [ 2 6 6 3]/u, @unscramble)
pushbut( "type", [ 2 14 6 3]/u, @typescb)
pushbut( "delta", [ 2 18 6 3]/u, @deltacb)
pushbut( "=>", [53 2 6 3]/u, @fs)
pushbut( "==>", [53 6 6 3]/u, @once)
toggbut( "~~>", [53 10 6 3]/u, @scramble)
toggbut( "gif", [53 22 6 3]/u, @gifcb)
pushbut( "Q0", [53 26 6 3]/u, @Q0)
pushbut( "restart", [53 30 6 3]/u, @restarter)
toggbut( "solve", [53 34 6 3]/u, @Qsolve)
toggbut( "period", [53 42 6 3]/u, @Qperiod)
textbut( "pcount", [53 46 6 3]/u, "pcount")
textbut( "ops", [ 2 54 6 3]/u, "ops")
textbut( "score", [53 54 6 3]/u, "score")
pushbut( " ", [12 54 38 3]/u, @stacker)
framed_mat( [ 2 29 16 11]/u)
tooltips
rng('shuffle')
end
%% Qmove.m
function Q = Qmove(op,Q)
if op(2) == '2'
op(2) = ' ';
Q = Qmove(op,Q);
Q = Qmove(op,Q);
return
end
if op(1) == 'N'
% Null
d = 1;
f = 1;
sig = 0;
return
else
[d,f,sig] = dfsig(op);
end
Qsave = Q;
% Fractional steps
delta = qstate('delta');
for n = 1:90/abs(delta)
R = Rk(d,sig*n*delta);
Q = Qrot(Qsave,d,f,R);
Qshow(Q)
if qstate('gif') == 1
gif_frame
else
drawnow
end
end
% Full quarter turn, +/- 90 degrees.
Q = Qsave;
for i = f
switch d
case 1,Q(i,:,:) = quarter(sig,d,Q(i,:,:));
case 2,Q(:,i,:) = quarter(sig,d,Q(:,i,:));
case 3,Q(:,:,i) = quarter(sig,d,Q(:,:,i));
end
end
Qshow(Q)
Qscore(Q)
end
%% Qnorm.m
function nrm = Qnorm(X,Y)
% Qnorm(X,Y) = sum of singular values of X-Y.
% Also known as nuclear norm.
nrm = 0;
for j = 1:27
nrm = nrm + sum(svd(X{j}-Y{j}));
end
end
%% Qpack.m
function Qpack
fout = fopen('../Qube_osf.m','w');
d = dir;
d = string({d.name})';
d(d=="Qunpack.m") = [];
d(d=="Qube.m") = [];
d(1) = "Qunpack.m";
d(2) = "Qube.m";
for F = d'
disp(F)
fprintf(fout,'%%%% %s\n',F);
fin = fopen(F,'r');
L = fgetl(fin);
while ~isequal(L,-1)
fprintf(fout,'%s\n',L);
L = fgetl(fin);
end
fclose(fin);
end
fprintf(fout,'%%%% %s\n','EOF');
fclose(fout);
end
%% Qperiod.m
function Qperiod(arg,~)
if nargin == 0
arg = @Qperiod;
end
v = arg.Value;
arg.BackgroundColor = 1-v*[.70 .25 .07];
counter = findobj('tag','pcount');
ops = findobj('tag','ops');
ops.String = '0';
period = 0;
Qshow(Q0)
qstate('Q',Q0)
nrm = inf;
while nrm > 0 && arg.Value > 0
once
nrm = Qnorm(qstate('Q'),Q0);
period = period+1;
counter.String = int2str(period);
drawnow
end
arg.Value = 0;
arg.BackgroundColor = 'w';
end
%% Qrot.m
function Q = Qrot(Q,d,f,R)
switch d
case 1
for j = 1:3
for k = 1:3
for i = f
Q{i,j,k} = Q{i,j,k}*R;
end
end
end
case 2
for j = 1:3
for k = 1:3
for i = f
Q{k,i,j} = Q{k,i,j}*R;
end
end
end
case 3
for j = 1:3
for k = 1:3
for i = f
Q{k,j,i} = Q{k,j,i}*R;
end
end
end
end
end
%% Qscore.m
function Qscore(Q)
counter = findobj('tag','ops');
scorer = findobj('tag','score');
nrm = Qnorm(Q,Q0);
if ~isempty(counter)
counter.Value = counter.Value + 1;
counter.String = num2str(counter.Value);
end
if ~isempty(scorer)
scorer.String = sprintf('%7.2f',round(nrm,2));
scorer.FontName = 'Lucisa Sans Typewriter';
scorer.FontWeight = 'bold';
end
end
%% Qshow.m
function Qshow(Q)
% Qshow(Q) Display Q. Default qstate('Q')
if nargin == 0
Q = qstate('Q');
end
C = [0 0 3/4 % blue
3/4 0 0 % red
1 1 1 % white
0 3/4 0 % green
1 3/5 0 % orange
1 1 0]; % yellow
F = [1 5 7 3
3 7 8 4
1 3 4 2
2 4 8 6
1 2 6 5
5 6 8 7];
gps = get(gcf,'pos');
lw = 1 + 0.5*(gps(4) > 400);
set(gca,'userdata',Q)
cla
j = 0;
for x = [-2 0 2]
for y = [-2 0 2]
for z = [-2 0 2]
j = j + 1;
nz = nnz([x y z]);
if types(nz) && j <= numel(Q)
for k = 1:6
patch( ...
Vertices = Q{j}, ...
Faces = F(k,:), ...
FaceColor = C(k,:), ...
UserData = [nz j k], ...
LineWidth = lw);
end
end
end
end
end
end
%% Qsolve.m
function Qsolve(arg,arg2,Qin,soln)
alfa = 'LRUDFB';
counter = findobj('tag','ops');
scorer = findobj('tag','score');
if nargin == 2
Qin = qstate('Q');
soln = '';
arg.BackgroundColor = colors(6);
counter.Value = 0;
counter.String = num2str(counter.Value);
poster.String = qstate('stack');
end
Q1 = Qin;
nrm1 = Qnorm(Q1,Q0);
scorer.String = sprintf('%7.2f',nrm1);
for k = 1:6
for s = [' ','''']
op = [alfa(k) s];
Q = Qmove(op,Qin);
nrm = Qnorm(Q,Q0);
scorer.String = sprintf('%7.2f',nrm);
if nrm < nrm1 || arg.Value == 0
soln = [op soln];
break
end
end
if nrm < nrm1 || arg.Value == 0
break
end
end
if nrm == 0
% solution
arg.BackgroundColor = 'w';
elseif nrm == nrm1 || arg.Value == 0
% fail
arg.BackgroundColor = [.64 .08 .18];
else
% recur
counter.Value = counter.Value + 1;
counter.String = num2str(counter.Value);
Qsolve(arg,arg2,Q,soln);
end
qstate('stack',soln)
show_stack(soln)
Qshow(Q0)
arg.Value = 0;
end
%% Rk.m
function R = Rk(k,d)
% Rk(k,d) is rotation by d degrees about k-th axis.
c = cosd(d);
s = sind(d);
switch k
case 1, R = [ 1 0 0
0 c s
0 -s c ];
case 2, R = [ c 0 s
0 1 0
-s 0 c ];
case 3, R = [ c s 0
-s c 0
0 0 1 ];
end
fmat = findobj('tag','fmat');
if ~isempty(fmat)
fmat.String = mat3(R);
end
end
%% bs.m
function bs(~,~)
% bs, backspace, inverse of first op in stack
op = pop;
if ~isempty(op)
Q = qstate('Q');
opt = transposer(op);
Q = Qmove(opt,Q);
qstate('Q',Q)
qstate('stack2',[qstate('stack2') op])
end
end
%% deltacb.m
function deltacb(arg,~)
% delta, fractional rotation.
switch arg.String
case '3', delta = '6';
case '6', delta = '15';
case '15', delta = '30';
case '30', delta = '90';
case '90', delta = 'inf';
case 'inf', delta = '3';
otherwise, delta = '30';
end
arg.String = delta;
qstate('delta',str2double(delta))
Qshow(qstate('Q'))
end
%% dfsig.m
function [d,f,sig] = dfsig(op)
% [d,f,sig] = dfsig(op), d-th dimennsion, f-th face.
[a,~] = view;
a = mod(round((a+37.5)/90),4);
switch a
case 0
W = ["L" "M" "R" "X"
"F" "S" "B" "Y"
"D" "E" "U" "Z"];
opsm = 'RFUYZSE';
case 1
W = ["B" "S" "F" "Y"
"L" "M" "R" "X"
"D" "E" "U" "Z"];
opsm = 'LFUXYZMSE';
case 2
W = ["R" "M" "L" "X"
"B" "S" "F" "Y"
"D" "E" "U" "Z"];
opsm = 'LBUXZME';
case 3
W = ["F" "S" "B" "Y"
"R" "M" "L" "X"
"D" "E" "U" "Z"];
opsm = 'RBUZE';
end
[d,f] = find(op(1)==W);
if f == 4
f = 1:3;
end
sig = 2*(op(2) == ' ')-1;
if any(op(1) == opsm)
sig = -sig;
end
end
%% framed_mat.m
function framed_mat(pos)
uicontrol( ...
'style','frame', ...
'units','normalized', ...
'position',pos, ...
'backgroundcolor',0.25*[1 1 1])
del = .003;
uicontrol( ...
'style','text', ...
'units','normalized', ...
'position',pos+[del del -2*del -2*del], ...
'fontname','Lucida Sans Typewriter', ...
'fontsize',9, ...
'fontweight','bold', ...
'horizontalalignment','left', ...
'backgroundcolor','w', ...
'string',mat3(eye(3,3)), ...
'tag','fmat')
end
%% fs.m
function fs(~,~)
% fs. "forward space"
op = pop2; % first op in stack2
if ~isempty(op)
Q = qstate('Q');
Q = Qmove(op,Q);
push(op)
qstate('Q',Q)
show_stack(qstate('stack'))
end
end
%% gifcb.m
function gifcb(arg,~)
if nargin == 0
arg = findobj('callback',@gifscb);
end
qstate('gif',arg.Value)
end
%% key.m
function key(arg,~)
if nargin == 2
op = arg.String;
else
op = arg;
end
Q = qstate('Q');
Q = Qmove(op,Q);
push(op)
qstate('Q',Q)
end
%% last.m
function lst = last(s)
% indices of last op in stack
k = find((s ~= ' ') & (s ~= ''''),2,'last');
if length(k) > 1
lst = k(2):length(s);
else
lst = 1:length(s);
end
end
%% mat3.m
function txt = mat3(M)
txt = newline;
for k = 1:3
for j = 1:3
if M(k,j) == 0
txt = [txt sprintf('%6.0f',abs(M(k,j)))];
elseif M(k,j) == round(M(k,j))
txt = [txt sprintf('%6.0f',M(k,j))];
else
txt = [txt sprintf('%6.2f',M(k,j))];
end
end
txt = [txt newline];
end
end
%% once.m
function once(~,~)
stk2 = blanks(0);
while ~isempty(peek)
stk2 = [stk2 pop];
end
Q = qstate('Q');
Qshow(Q)
while ~isempty(stk2)
tp = top(stk2);
op = stk2(tp);
stk2(tp) = [];
Q = Qmove(op,Q);
push(op)
show_stack(qstate('stack'))
end
qstate('Q',Q)
end
%% peek.m
function op = peek
% peek return top op
stk = qstate('stack');
tp = top(stk);
op = stk(tp);
end
%% pop.m
function op = pop
% pop remove op from top of stack
stk = qstate('stack');
tp = top(stk);
op = stk(tp);
stk(tp) = []; % delete top element
show_stack(stk)
qstate('stack',stk)
end
%% pop2.m
function op = pop2
% pop2 remove op from top of stack2
stk = qstate('stack2');
tp = top(stk);
op = stk(tp);
stk(tp) = []; % delete top element
qstate('stack2',stk)
end
%% push.m
function push(op,~)
% push insert op on top of stack
stk = qstate('stack');
op(op==' ') = [];
op = [op ' '];
stk = [stk op];
show_stack(stk)
qstate('stack',stk)
end
%% pushbut.m
function pushbut(string,position,callback,varargin)
uicontrol(Style = "pushbutton", ...
String = string, ...
Units = "normalized", ...
Position = position, ...
Callback = callback, ...
Fontsize = 10, ...
Fontweight = "bold", ...
BackgroundColor = 'w');
end
%% qstate.m
function vout = qstate(name,vin)
% qstate(name,set_value)
% get_value = qstate(name)
names = {'Q','stack','stack2','delta','type','gif'};
defaults = {Q0, '', '', 30, 0:3, 0};
state = get(gcf,'userdata');
if isempty(state)
state = defaults;
set(gcf,'userdata',defaults)
end
for k = 1:length(names)
if isequal(name,names{k})
if nargin == 2
state{k} = vin;
set(gcf,'userdata',state)
else
vout = state{k};
end
return
end
end
end
%% quarter.m
function Fout = quarter(sig,d,F)
F = squeeze(F);
R = Rk(d,sig*90);
for j = 1:3
for i = 1:3
if sig < 0
Fout{j,4-i} = F{i,j}*R;
else
Fout{4-j,i} = F{i,j}*R;
end
end
end
end
%% qzero.m
function q0 = qzero
% Unit cubelet.
q0 = [-1 -1 -1
-1 -1 1
-1 1 -1
-1 1 1
1 -1 -1
1 -1 1
1 1 -1
1 1 1];
end
%% randdo.m
function randdo(~,~)
op = random_op;
Q = qstate('Q');
Q = Qmove(op,Q);
push(op)
qstate('Q',Q)
end
%% random_op.m
function op = random_op
alfa = 'LMRUEDFSBXYZ';
alfa = 'LRUDFB';
op = blanks(2);
op(1) = alfa(randi(length(alfa)));
if rand > 0.5
op(2) = '''';
end
end
%% restarter.m
function restarter(~,~)
Qube
end
%% scramble.m
function scramble(arg,~)
if nargin == 0
arg = findobj('tag','scramble');
end
v = arg.Value;
arg.BackgroundColor = 1-v*[.70 .25 .07];
while arg.Value > 0
randdo(arg)
drawnow
end
arg.BackgroundColor = 'w';
end
%% show_stack.m
function show_stack(stk)
stacker = findobj('callback',@stacker);
if ~isempty(stacker)
stacker.String = stk;
end
end
%% stacker.m
function stacker(arg,~)
arg.String = '';
qstate('stack','')
end
%% textbut.m
function textbut(string,position,tag)
uicontrol(Style = "pushbutton", ...
String = string, ...
Units = "normalized", ...
Position = position, ...
Tag = tag, ...
Fontsize = 10, ...
Fontweight = "bold", ...
BackgroundColor = 'w');
end
%% toggbut.m
function toggbut(str,position,callback)
v = isequal(str,' ''');
uicontrol(Style = "toggle", ...
String = str, ...
Units = "normalized", ...
Position = position, ...
Callback = callback, ...
Value = v, ...
Fontsize = 10, ...
Fontweight = "bold", ...
BackgroundColor = 'w');
end
%% tooltips.m
function tooltips
tip = @(x,y,z) set(findobj(x,y),'tooltip',z);
tip("string", "=>", "Redo most recent <=.")
tip("string", "~~>", "Scramble with repeated random rotations.")
tip("string", "==>", "Apply stack again.")
tip("string", "<=", "Apply inverse of most recent rotation.")
tip("string", "<==", "Unscramble with repeated <=.")
tip("string", "solve", "Experimental solver.")
tip("string", "period", "Number of repetitions to return to Q0.")
tip("string", "period", "Number of repetitions to return to Q0.")
tip("string", "Q0", "Q0, clear stack.")
tip("string", "gif", "Animated diary.")
tip("string", "restart","Call Qube.")
tip("tag", "score", "Nuclear norm distance to Q0.")
tip("tag", "ops", "Total number of ops.")
tip("tag", "pcount", "period.")
tip("callback", @stacker, "Stack of ops, click to clear")
tip("callback", @deltacb, "Fractional step in rotation.")
tip("callback", @typescb, "Show center, face, edge, corner cubelets.")
end
%% top.m
function top = top(s)
% indices of first op in stack
k = find((s ~= ' ') & (s ~= '''') & (s ~= '2'),2,'last');
if length(k) > 1
top = k(2):length(s);
else
top = 1:length(s);
end
end
%% transposer.m
function op = transposer(op)
% op = op'
if isempty(op)
return
elseif isscalar(op)
op = [op char(' ' + '''' - op)];
else
op(2) = char(' ' + '''' - op(2));
end
end
%% types.m
function t = types(arg)
% cubelet type
t = ismember(arg,qstate('type'));
end
%% typescb.m
function typescb(arg,~)
if nargin == 0
arg = findobj('callback',@typescb);
end
switch arg.String
case '2:3', s = '0:3';
case '0:3', s = '0:2';
case '0:2', s = '0:1';
case '0:1', s = '0';
case '0', s = '1';
case '1', s = '2';
case '2', s = '3';
case '3', s = '2:3';
otherwise, s = '0:3';
end
arg.String = s;
qstate('type',eval(s))
Qshow
end
%% unscramble.m
function unscramble(arg,~)
% undo. bs until stack is empty.
while arg.Value > 0 && ~isempty(peek)
bs(arg)
drawnow
end
arg.BackgroundColor = 'w';
arg.Value = 0;
end
%% viewcb.m
function viewcb(arg,~)
if arg.Value == 1
arg.BackgroundColor = [.30 .75 .93];
rotate3d on
else
arg.BackgroundColor = 'w';
[a,~] = view;
a = 90*round((a+37.5)/90)-37.5;
e = 30;
view([a,e])
rotate3d off
end
end
%% wbmf.m
function wbmf(~,~)
%set(gcf,'windowbuttondownfcn',[])
%set(gcf,'windowbuttonmotionfcn',[])
%co = get(gcf,'currentobject');
cp = get(gca,'currentpoint');
%ud = co.UserData;
%k = ud(3);
k = 4;
y = cp(1,2);
x = cp(1,1);
switch k
case 4
% U
d = 3;
f = 3;
case 3
% L
d = 1;
f = 1;
case 5
% F
d = 2;
f = 1;
end
theta = atan2d(y,x);
Q = qstate('Q');
Q = Qrot(Q0,d,f,90-Rk(d,theta));
Qshow(Q)
qstate('Q',Q)
end
%% wdownf.m
function w = wdownf(src,~)
% window button down fcn
set(gcf,'windowbuttonmotionfcn',@wbmf)
%{
seltype = src.SelectionType;
if strcmp(seltype,'normal')
cp = get(gca,'currentpoint');
co = get(gcf,'currentobject');
ud = co.UserData;
set(gcf,'windowbuttonmotionfcn',@wbmf)
set(gcf,'windowbuttonupfcn',@wupf)
end
%}
end
%% wupf.m
function w = wupf(~,~)
% window button up fcn
set(gcf,'windowbuttonmotionfcn',[])
set(gcf,'windowbuttondownfcn',@wdownf)
end
%% EOF