In[]:=
cout0L={4.0,4.0,4.0,4.0};cout0R={4.0,4.0,4.0,4.0};​​alphaR0={{0.2,0.8,0,0},{0.9,0.1,0,0},{0,0,0.3,0.7},{0,0,0.9,0.1}};alphaL0={{0.08,0.9,0.01,0.01},{0.9,0.08,0.01,0.01},{0.01,0.01,0.08,0.9},{0.01,0.01,0.9,0.08}};​​nderaL[i1_,i2_,m_,f_]:=(Derivative@@{0,0,ConstantArray[0,m],ConstantArray[0,m],Normal[SparseArray[{{i1,i2}->1},{m,m}]],ConstantArray[0,{m,m}],0,ConstantArray[0,m],ConstantArray[0,m],ConstantArray[0,{m,m}],ConstantArray[0,{m,m}]})[f];​​ffoutsuper[flag_,LRc_,cL_,cR_,alphaL_,alphaR_,LRC_,CL_,CR_,AlphaL_,AlphaR_]:=Max[Re[Eigenvalues[alphaL.alphaR]]]​​ffoutsuper[1,0.1,cout0L,cout0R,alphaL0,alphaR0,0.1,cout0L,cout0R,alphaL0,alphaR0]​​nderaL[2,3,4,ffoutsuper][1,0.1,cout0L,cout0R,alphaL0,alphaR0,0.1,cout0L,cout0R,alphaL0,alphaR0]​​
Out[]=
1.
Out[]=
0.191315
′
Re
[1.]