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-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/CVS/Entries6
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/CVS/Repository1
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/CVS/Root1
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/amnio.m135
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/asia_dt1.m100
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/id1.m50
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/oil1.m91
-rw-r--r--sourcecodes/bnt-master/BNT/examples/limids/pigs1.m153
8 files changed, 537 insertions, 0 deletions
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/CVS/Entries b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Entries
new file mode 100644
index 00000000..f7f12046
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Entries
@@ -0,0 +1,6 @@
+/amnio.m/1.1.1.1/Mon Sep 13 03:21:04 2004//
+/asia_dt1.m/1.1.1.1/Mon Jun  7 15:53:54 2004//
+/id1.m/1.1.1.1/Wed May 29 15:59:54 2002//
+/oil1.m/1.1.1.1/Mon Sep 13 02:27:08 2004//
+/pigs1.m/1.1.1.1/Wed May 29 15:59:54 2002//
+D
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/CVS/Repository b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Repository
new file mode 100644
index 00000000..bd5dd5af
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Repository
@@ -0,0 +1 @@
+FullBNT/BNT/examples/limids
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/CVS/Root b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Root
new file mode 100644
index 00000000..f3bd14a6
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/CVS/Root
@@ -0,0 +1 @@
+:ext:nsaunier@bnt.cvs.sourceforge.net:/cvsroot/bnt
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/amnio.m b/sourcecodes/bnt-master/BNT/examples/limids/amnio.m
new file mode 100644
index 00000000..fd621b6c
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/amnio.m
@@ -0,0 +1,135 @@
+
+clear all
+B0 = 1; Rtriple = 2; Damnio = 3;
+B1 = 4; Ramnio = 5; Dabort = 6; 
+B2 = 7; U = 8;
+
+N = 8;
+dag = zeros(N,N);
+dag(B0, [Rtriple B1 Ramnio]) = 1;
+dag(Rtriple, [Damnio Dabort]) = 1;
+dag(Damnio, [B1 Ramnio]) = 1;
+dag(B1, B2) = 1;
+dag(Ramnio, [Dabort U]) = 1;
+dag(Dabort, B2) = 1;
+dag(B2, U) = 1;
+
+
+
+ns = zeros(1,N);
+ns(B0) = 2;
+ns(B1) = 3;
+ns(B2) = 4;
+ns(Rtriple) = 2;
+ns(Ramnio) = 3;
+ns(Damnio) = 2;
+ns(Dabort) = 2;
+ns(U) = 1;
+
+limid = mk_limid(dag, ns, 'chance', [B0 B1 B2], ...
+		 'decision', [Damnio Dabort], 'utility', [U]);
+
+% states of nature
+healthy = 1; downs = 2; miscarry = 3; aborted = 4;
+% test results
+pos = 1; neg = 2; unk = 3;
+% actions
+yes = 1; no = 2;
+
+% Prior probability baby has downs syndrome
+tbl = zeros(2,1);
+p = 1/1000; % from www.downs-syndrome.org.uk figure
+p = 24/10000; % www-personal.umich.edu/~bobwolfe/560/review/Downs.pdf (for women agen 35-40)
+tbl(healthy) = 1-p;
+tbl(downs) = p;
+limid.CPD{B0} = tabular_CPD(limid, B0, tbl);
+
+% Reliability of triple screen test
+% Unreliable sensor
+% B0 -> Rtriple
+tbl = zeros(2,2); % Rtriple = pos, neg
+p = 0.5;  % high false positive rate (guess)
+tbl(healthy, :) = [p 1-p];
+p = 0.6; % low detection rate (march of dimes figure)
+tbl(downs, :) = [p 1-p]; 
+limid.CPD{Rtriple} = tabular_CPD(limid, Rtriple, tbl);
+
+limid.CPD{Damnio} = tabular_decision_node(limid, Damnio);
+
+% Effect of amnio on baby  B0,Damnio -> B1
+ % 1/200 risk of miscarry 
+p = 1/200; % (march of dimes figure)
+tbl = zeros(2, 2, 3); % B1 = healthy, downs, miscarry
+tbl(healthy, no, :) =  [1     0     0];
+tbl(downs, no, :) =    [0     1     0];
+tbl(healthy, yes, :) = [1-p     0   p];
+tbl(downs, yes, :) =   [0     1-p   p];
+limid.CPD{B1} = tabular_CPD(limid, B1, tbl);
+
+% Reliability of amnio  B0, Damnio -> Ramnio
+% Perfect sensor
+tbl = zeros(2,2,3); % Ramnio = pos, neg, unk
+tbl(:, no, :) =        repmat([0 0 1], 2 ,1);
+tbl(healthy, yes, :) = [0 1 0]; 
+tbl(downs, yes, :) =   [1 0 0]; 
+limid.CPD{Ramnio} = tabular_CPD(limid, Ramnio, tbl);
+
+limid.CPD{Dabort} = tabular_decision_node(limid, Dabort);
+
+% Effect of abortion on baby  B1, Dabort -> B2
+tbl = zeros(3, 2, 4); % B2 = healthy, downs, miscarry, aborted
+tbl(:, yes, :) =       repmat([0 0 0 1], 3, 1);
+tbl(healthy, no, :) =  [1 0 0 0];
+tbl(downs, no, :) =    [0 1 0 0];
+tbl(miscarry, no, :) = [0 0 1 0];
+limid.CPD{B2} = tabular_CPD(limid, B2, tbl);
+
+% Utility U(Ramnio, B2)
+tbl = zeros(3, 4);
+tbl(:, healthy) = 5000;
+tbl(:, downs) = -50000;
+tbl(:, miscarry) = -1000;
+tbl(:, aborted) = -1000;
+
+if 0
+%tbl(unk, miscarry) = 0; % this case is impossible
+tbl(pos, miscarry) = -1;
+tbl(neg, miscarry) = -1000;
+if 1
+  tbl(unk, aborted) = -100;
+  tbl(pos, aborted) = -1;
+  tbl(neg, aborted) = -500;
+else % pro-life utility fn
+  tbl(unk, aborted) = -500000;
+  tbl(pos, aborted) = -500000;
+  tbl(neg, aborted) = -500000;
+end 
+end
+
+limid.CPD{U} = tabular_utility_node(limid, U,  tbl);
+
+
+
+engine = jtree_limid_inf_engine(limid);
+[strategy, MEU] = solve_limid(engine);
+
+% Rtriple U(Damnio=1=yes)  U(Damnio=2=no)
+% 1=pos    0               1
+% 2=neg    0               1
+dispcpt(strategy{Damnio})
+if isequal(strategy{Damnio}(1,:), strategy{Damnio}(2,:))
+  % Rtriple result irrelevant
+  doAmnio = argmax(strategy{Damnio}(1,:))
+else
+  doAmnio = 1;
+end
+
+% Rtriple Ramnio U(Dabort=yes=1) U(Dabort=no=2)
+% 1=pos   1=pos  1               0
+% 2=neg   1=pos  1               0
+% 1=pos   2=neg  0               1
+% 2=neg   2=neg  0               1
+% 1=pos   3=unk  0               1
+% 2=neg   3=unk  0               1
+dispcpt(strategy{Dabort})
+
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/asia_dt1.m b/sourcecodes/bnt-master/BNT/examples/limids/asia_dt1.m
new file mode 100644
index 00000000..de305818
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/asia_dt1.m
@@ -0,0 +1,100 @@
+% decision theoretic version of asia network
+% Cowell et al, p177
+% We explicitely add the no-forgetting arcs.
+
+Smoking = 1;
+VisitToAsia = 2;
+Bronchitis = 3;
+LungCancer = 4;
+TB = 5;
+Do_Xray = 6;
+TBorCancer = 7;
+Util_Xray = 8;
+Dys = 9;
+posXray = 10;
+Do_Hosp = 11;
+Util_Hosp = 12;
+
+n = 12;
+dag = zeros(n);
+dag(Smoking, [Bronchitis LungCancer]) = 1;
+dag(VisitToAsia, [TB Do_Xray Do_Hosp]) = 1;
+dag(Bronchitis, Dys) = 1;
+dag(LungCancer, [Util_Hosp TBorCancer]) = 1;
+dag(TB, [Util_Hosp TBorCancer Util_Xray]) = 1;
+dag(Do_Xray, [posXray Util_Xray Do_Hosp]) = 1;
+dag(TBorCancer, [Dys posXray]) = 1;
+dag(Dys, Do_Hosp) = 1;
+dag(posXray, Do_Hosp) = 1;
+dag(Do_Hosp, Util_Hosp) = 1;
+
+dnodes = [Do_Xray Do_Hosp];
+unodes = [Util_Xray Util_Hosp];
+cnodes = mysetdiff(1:n, [dnodes unodes]); % chance nodes
+ns = 2*ones(1,n);
+ns(unodes) = 1;
+limid = mk_limid(dag, ns, 'chance', cnodes, 'decision', dnodes, 'utility', unodes);
+
+% 1 = yes, 2 = no
+limid.CPD{VisitToAsia} = tabular_CPD(limid, VisitToAsia, [0.01 0.99]);
+limid.CPD{Bronchitis} = tabular_CPD(limid, Bronchitis, [0.6 0.3  0.4 0.7]);
+limid.CPD{Dys} = tabular_CPD(limid, Dys, [0.9 0.7 0.8 0.1  0.1 0.3 0.2 0.9]);
+limid.CPD{TBorCancer} = tabular_CPD(limid, TBorCancer, [1 1 1 0  0 0 0 1]);
+
+limid.CPD{LungCancer} = tabular_CPD(limid, LungCancer, [0.1 0.01  0.9 0.99]);
+limid.CPD{Smoking} = tabular_CPD(limid, Smoking, [0.5 0.5]);
+limid.CPD{TB} = tabular_CPD(limid, TB, [0.05 0.01  0.95 0.99]);
+limid.CPD{posXray} = tabular_CPD(limid, posXray, [0.98 0.5 0.05 0.5  0.02 0.5 0.95 0.5]);
+
+limid.CPD{Util_Hosp} = tabular_utility_node(limid, Util_Hosp, [180 120 160 15  2 4 0 40]);
+limid.CPD{Util_Xray} = tabular_utility_node(limid, Util_Xray, [0 1 10 10]);
+
+for i=dnodes(:)'
+  limid.CPD{i} = tabular_decision_node(limid, i);
+end
+
+engines = {};
+engines{end+1} = global_joint_inf_engine(limid);
+engines{end+1} = jtree_limid_inf_engine(limid);
+%engines{end+1} = belprop_inf_engine(limid);
+
+exact = [1 2];
+%approx = 3;
+approx = [];
+
+
+NE = length(engines);
+MEU = zeros(1, NE);
+niter = zeros(1, NE);
+strategy = cell(1, NE);
+
+tol = 1e-2;
+for e=1:length(engines)
+  [strategy{e}, MEU(e), niter(e)] = solve_limid(engines{e});
+end
+
+for e=exact(:)'
+  assert(approxeq(MEU(e), 47.49, tol))
+  assert(isequal(strategy{e}{Do_Xray}(:)', [1 0 0 1]))
+  
+  % Check the hosptialize strategy is correct (p180)
+  % We assume the patient has not been to Asia and therefore did not have an Xray.
+  % In this case it is optimal not to hospitalize regardless of whether the patient has
+  % dyspnoea or not (and of course regardless of the value of pos_xray).
+  asia = 2;
+  do_xray = 2;
+  for dys = 1:2
+    for pos_xray = 1:2
+      assert(argmax(squeeze(strategy{e}{Do_Hosp}(asia, do_xray, dys, pos_xray, :))) == 2)
+    end
+  end
+end
+
+
+for e=approx(:)'
+  approxeq(strategy{exact(1)}{Do_Xray}, strategy{e}{Do_Xray})
+  approxeq(strategy{exact(1)}{Do_Hosp}, strategy{e}{Do_Hosp})
+end
+
+ 
+
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/id1.m b/sourcecodes/bnt-master/BNT/examples/limids/id1.m
new file mode 100644
index 00000000..ddacd67a
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/id1.m
@@ -0,0 +1,50 @@
+% influence diagram with no loops
+%
+% rv  dec
+%  \  /
+%  utility
+
+N = 3;
+dag = zeros(N);
+X = 1; D = 2; U = 3;
+dag([X D], U)=1;
+
+ns = zeros(1,N);
+ns(X) = 2; ns(D) = 2; ns(U) = 1;
+
+limid = mk_limid(dag, ns, 'chance', X, 'decision', D, 'utility', U);
+
+% use random params
+limid.CPD{X} = tabular_CPD(limid, X);
+limid.CPD{D} = tabular_decision_node(limid, D);
+limid.CPD{U} = tabular_utility_node(limid, U);
+
+%fname = '/home/cs/murphyk/matlab/Misc/loopybel.txt';
+global BNT_HOME
+fname = sprintf('%s/loopybel.txt', BNT_HOME);
+
+engines = {};
+engines{end+1} = global_joint_inf_engine(limid);
+engines{end+1} = jtree_limid_inf_engine(limid);
+%engines{end+1} = belprop_inf_engine(limid, 'max_iter', 2*N, 'filename', fname);
+engines{end+1} = belprop_inf_engine(limid, 'max_iter', 2*N);
+
+exact = [1 2];
+approx = 3;
+
+E = length(engines);
+strategy = cell(1, E);
+MEU = zeros(1, E);
+for e=1:E
+  [strategy{e}, MEU(e)] = solve_limid(engines{e});
+  MEU
+end
+MEU
+
+for e=exact(:)'
+  assert(approxeq(strategy{exact(1)}{D}, strategy{e}{D}))
+end
+
+for e=approx(:)'
+  approxeq(strategy{exact(1)}{D}, strategy{e}{D})
+end
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/oil1.m b/sourcecodes/bnt-master/BNT/examples/limids/oil1.m
new file mode 100644
index 00000000..192acc9d
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/oil1.m
@@ -0,0 +1,91 @@
+% oil wildcatter influence diagram in Cowell et al p172
+
+% T = test for oil?
+% UT = utility (negative cost) of testing
+% O = amount of oil = Dry, Wet or Soaking
+% R = results of test = NoStrucure, OpenStructure, ClosedStructure or NoResult
+% D = drill?
+% UD = utility of drilling
+
+% Decision sequence = T R D O
+
+T = 1; UT = 2; O = 3; R = 4; D = 5; UD = 6;
+N = 6;
+dag = zeros(N);
+dag(T, [UT R D]) = 1;
+dag(O, [R UD]) = 1;
+dag(R, D) = 1;
+dag(D, UD) = 1;
+
+ns = zeros(1,N);
+ns(O) = 3; ns(R) = 4; ns(T) = 2; ns(D) = 2; ns(UT) = 1; ns(UD) = 1;
+
+limid = mk_limid(dag, ns, 'chance', [O R], 'decision', [T D], 'utility', [UT UD]);
+
+limid.CPD{O} = tabular_CPD(limid, O, [0.5 0.3 0.2]);
+tbl = [0.6 0 0.3 0 0.1 0  0.3 0 0.4 0 0.4 0  0.1 0 0.3 0 0.5 0  0 1 0 1 0 1];
+limid.CPD{R} = tabular_CPD(limid, R, tbl);
+
+limid.CPD{UT} = tabular_utility_node(limid, UT,  [-10 0]);
+limid.CPD{UD} = tabular_utility_node(limid, UD, [-70 50 200  0 0 0]);
+
+if 1
+  % start with uniform policies
+  limid.CPD{T} = tabular_decision_node(limid, T);
+  limid.CPD{D} = tabular_decision_node(limid, D);
+else
+  % hard code optimal policies
+  limid.CPD{T} = tabular_decision_node(limid, T, [1.0 0.0]);        
+  a = 0.5; b = 1-a; % arbitrary value
+  tbl = myreshape([0 a 1 a 1 a a a  1 b 0 b 0 b b b], ns([T R D]));
+  limid.CPD{D} = tabular_decision_node(limid, D,  tbl);
+end
+
+%fname = '/home/cs/murphyk/matlab/Misc/loopybel.txt';
+
+engines = {};
+engines{end+1} = global_joint_inf_engine(limid);
+engines{end+1} = jtree_limid_inf_engine(limid);
+%engines{end+1} = belprop_inf_engine(limid, 'max_iter', 3*N, 'filename', fname);
+
+exact = [1 2];
+%approx = 3;
+approx = [];
+
+E = length(engines);
+strategy = cell(1, E);
+MEU = zeros(1, E);
+for e=1:E
+  [strategy{e}, MEU(e)] = solve_limid(engines{e});
+  MEU
+end
+MEU
+
+for e=exact(:)'
+  assert(approxeq(MEU(e), 22.5))
+  % U(T=yes)  U(T=no)
+  % 1         0
+  assert(argmax(strategy{e}{T}) == 1); % test = yes
+  t = 1; % test = yes
+  % strategy{D} T       R      U(D=yes=1)  U(D=no=2)
+  %             1=yes   1=noS  0           1         Don't drill
+  %             2=no    1=noS  1           0
+  %             1=yes   2=opS  1           0
+  %             2=no    2=opS  1           0
+  %             1=yes   3=clS  1           0
+  %             2=no    3=clS  1           0
+  %             1=yes   4=unk  1           0
+  %             2=no    4=unk  1           0
+  
+  for r=[2 3] % OpS, ClS
+    assert(argmax(squeeze(strategy{e}{D}(t,r,:))) == 1); % drill = yes
+  end
+  r = 1; % noS
+  assert(argmax(squeeze(strategy{e}{D}(t,r,:))) == 2); % drill = no
+end
+
+
+for e=approx(:)'
+  approxeq(strategy{exact(1)}{T}, strategy{e}{T})
+  approxeq(strategy{exact(1)}{D}, strategy{e}{D})
+end
diff --git a/sourcecodes/bnt-master/BNT/examples/limids/pigs1.m b/sourcecodes/bnt-master/BNT/examples/limids/pigs1.m
new file mode 100644
index 00000000..6a56ad04
--- /dev/null
+++ b/sourcecodes/bnt-master/BNT/examples/limids/pigs1.m
@@ -0,0 +1,153 @@
+% pigs model from Lauritzen and Nilsson, 2001
+
+seed = 0;
+rand('state', seed);
+randn('state', seed);
+
+% we number nodes down and to the right
+h = [1 5 9 13];
+t = [2 6 10];
+d = [3 7 11];
+u = [4 8 12 14];
+
+N = 14;
+dag = zeros(N);
+
+% causal arcs
+for i=1:3
+  dag(h(i), [t(i) h(i+1)]) = 1;
+  dag(d(i), [u(i) h(i+1)]) = 1;
+end
+dag(h(4), u(4)) = 1;
+
+% information arcs
+fig = 2;
+switch fig
+ case 0,
+  % no info arcs
+ case 1,
+   % no-forgetting policy (figure 1)
+   for i=1:3
+     dag(t(i), d(i:3)) = 1;
+   end
+ case 2,
+  % reactive policy (figure 2)
+  for i=1:3
+    dag(t(i), d(i)) = 1;
+  end
+ case 7,
+  % omniscient policy (figure 7: di has access to hidden state h(i-1))
+  dag(t(1), d(1)) = 1;
+  for i=2:3
+    %dag([h(i-1) t(i-1) d(i-1)], d(i)) = 1;
+    dag([h(i-1) d(i-1)], d(i)) = 1; % t(i-1) is redundant given h(i-1)
+  end
+end
+
+
+ns = 2*ones(1,N);
+ns(u) = 1;
+
+% parameter tying
+params = ones(1,N);
+uparam = 1;
+final_uparam = 2;
+tparam = 3;
+h1_param = 4;
+hparam = 5;
+dparams = 6:8;
+
+params(u(1:3)) = uparam;
+params(u(4)) = final_uparam;
+params(t) = tparam;
+params(h(1)) = h1_param;
+params(h(2:end)) = hparam;
+params(d) = dparams;
+
+limid = mk_limid(dag, ns, 'chance', [h t], 'decision', d, 'utility', u, 'equiv_class', params);
+
+% h = 1 means healthy, h = 2 means diseased
+% d = 1 means don't treat, d = 2 means treat
+% t = 1 means test shows healthy, t = 2 means test shows diseased
+
+if 0
+  % use random params
+  limid.CPD{final_uparam} = tabular_utility_node(limid, u(4));
+  limid.CPD{uparam} = tabular_utility_node(limid, u(1));
+  limid.CPD{tparam} = tabular_CPD(limid, t(1));
+  limid.CPD{h1_param} = tabular_CPD(limid, h(1));
+  limid.CPD{hparam} = tabular_CPD(limid, h(2));
+else
+  limid.CPD{final_uparam} = tabular_utility_node(limid, u(4), [1000 300]);
+  limid.CPD{uparam} = tabular_utility_node(limid, u(1), [0 -100]); % costs have negative utility!
+  
+  % h  P(t=1) P(t=2)
+  % 1  0.9   0.1
+  % 2  0.2   0.8
+  limid.CPD{tparam} = tabular_CPD(limid, t(1), [0.9 0.2 0.1 0.8]);
+  
+  % P(h1)
+  limid.CPD{h1_param} = tabular_CPD(limid, h(1), [0.9 0.1]);
+  
+  % hi di P(hj=1) P(hj=2),  j = i+1, i=1:3
+  % 1  1  0.8     0.2
+  % 2  1  0.1     0.9
+  % 1  2  0.9     0.1
+  % 2  2  0.5     0.5
+  limid.CPD{hparam} = tabular_CPD(limid, h(2), [0.8 0.1 0.9 0.5 0.2 0.9 0.1 0.5]);
+end
+
+% Decision nodes get assigned uniform policies by default
+for i=1:3
+  limid.CPD{dparams(i)} = tabular_decision_node(limid, d(i));
+end
+
+
+fname = '/home/cs/murphyk/matlab/Misc/loopybel.txt';
+
+engines = {};
+engines{end+1} = global_joint_inf_engine(limid);
+engines{end+1} = jtree_limid_inf_engine(limid);
+%engines{end+1} = belprop_inf_engine(limid, 'max_iter', 1*N, 'filename', fname, 'tol', 1e-3);
+
+exact = [1 2];
+%approx = 3;
+approx = [];
+
+max_iter = 1;
+order = d(end:-1:1);
+%order = d(1:end);
+
+NE = length(engines);
+MEU = zeros(1, NE);
+niter = zeros(1, NE);
+strategy = cell(1, NE);
+for e=1:NE
+  [strategy{e}, MEU(e), niter(e)] = solve_limid(engines{e}, 'max_iter', max_iter, 'order',  order);
+end
+MEU
+
+% check results match those in the paper (p. 22)
+direct_policy = eye(2); % treat iff test is positive
+never_policy = [1 0; 1 0]; % never treat
+tol = 1e-0; % results in paper are reported to 0dp
+for e=exact(:)'
+  switch fig
+   case 2, % reactive policy
+    assert(approxeq(MEU(e), 727, tol));
+    assert(approxeq(strategy{e}{d(1)}(:), never_policy(:)))
+    assert(approxeq(strategy{e}{d(2)}(:), direct_policy(:)))
+    assert(approxeq(strategy{e}{d(3)}(:), direct_policy(:)))
+   case 1, assert(approxeq(MEU(e), 729, tol));
+   case 7, assert(approxeq(MEU(e), 732, tol));
+  end
+end
+
+
+for e=approx(:)'
+  for i=1:3
+    approxeq(strategy{exact(1)}{d(i)}, strategy{e}{d(i)})
+    dispcpt(strategy{e}{d(i)})
+  end
+end
+