octave:2> A=rand(4);
octave:3> phi1m(A)
ans =

   1.86357   0.93891   0.67553   0.56164
   0.55032   1.61815   0.32314   0.56672
   0.18352   0.21269   1.20536   0.40196
   0.53641   0.43434   0.68935   1.27325

octave:4> A\(expm(A)-eye(4))
ans =

   1.86357   0.93891   0.67553   0.56164
   0.55032   1.61815   0.32314   0.56672
   0.18352   0.21269   1.20536   0.40196
   0.53641   0.43434   0.68935   1.27325

octave:5> phi1m(zeros(4))
ans =

   1   0   0   0
   0   1   0   0
   0   0   1   0
   0   0   0   1

octave:6> ese11ODE
octave:7> ese1PDE
octave:8> ese1PDE
octave:9> ese1PDE
octave:10> ese1PDE
octave:11> ese1PDE
octave:12> ese1PDE
octave:13> ese1PDE
octave:14> ese1PDEbis
octave:15> ese1PDEbis
octave:16> ese1PDEbis
octave:17> ese1PDEbis
octave:18> ese1PDEbis
octave:19> ese1PDEbis
octave:20> u=rand(4,1)
u =

   0.760569
   0.019524
   0.341855
   0.040409

octave:21> A=rand(4)
A =

   0.47599   0.71650   0.40218   0.12202
   0.71937   0.18186   0.73508   0.54550
   0.33045   0.98468   0.14534   0.49127
   0.71588   0.29663   0.16033   0.57321

octave:22> v=rand(4,1)
v =

   0.804758
   0.851900
   0.237349
   0.031688

octave:23> v.*(A*u)
ans =

   0.417212
   0.701978
   0.080720
   0.019908

octave:24> (diag(v)*A)*u
ans =

   0.417212
   0.701978
   0.080720
   0.019908

octave:25> diag(v)
ans =

Diagonal Matrix

   0.804758          0          0          0
          0   0.851900          0          0
          0          0   0.237349          0
          0          0          0   0.031688

octave:26> diag(v)*(A*u)
ans =

   0.417212
   0.701978
   0.080720
   0.019908

octave:27> A*diag(v)*u
ans =

   0.33605
   0.50367
   0.23106
   0.45685

octave:28> ese1PDE
octave:29> diary off