how to make a matrix-function from other matrix-function?

Question

reza hamzeh 2019-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/497089-how-to-make-a-matrix-function-from-other-matrix-function

评论： reza hamzeh 2019-12-17

hi. i want to plot the function N. every thing work well except the pa-function. in fact i dont know how to make a matrix-function (pa) from the other matrix-function (ro)

in mathematica its easy to do but in matlab i dont know how to do that? is it possible? can you help me plz.

T=1;
Haf = str2func(sprintf('@(%s)%s;','var1','[var1/2 0 0 0;0 -var1/2 var1 0;0 var1 -var1/2 0;0 0 0 var1/2]'));
ro=@(var1) expm(-Haf(var1)/T)/trace(expm(-Haf(var1)/T));
range1=0:0.1:10;
pa =@(var1) [ro(1,1) ro(2,1) ro(1,3) ro(2,3);ro(1,2) ro(2,2) ro(1,4) ro(2,4);
        ro(3,1) ro(4,1) ro(3,3) ro(4,3);ro(3,2) ro(4,2) ro(3,4) ro(4,4)];
N = @(var1) 0.5*(sum(abs(eig(pa(var1))))-1);
        
for k=1:numel(range1)
    Nv(k) = N(range1(k));
end
plot(range1,Nv)

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Answer 1

Matt J 2019-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/497089-how-to-make-a-matrix-function-from-other-matrix-function#answer_406796

编辑：Matt J 2019-12-17

在 MATLAB Online 中打开

Here's yet another way, which uses only anonymous functions,

T=1;
Haf = str2func(sprintf('@(%s)%s;','var1','[var1/2 0 0 0;0 -var1/2 var1 0;0 var1 -var1/2 0;0 0 0 var1/2]'));
ro=@(var1) expm(-Haf(var1)/T)/trace(expm(-Haf(var1)/T));
ex=@(r)[r(1,1) r(2,1) r(1,3) r(2,3);r(1,2) r(2,2) r(1,4) r(2,4);
        r(3,1) r(4,1) r(3,3) r(4,3);r(3,2) r(4,2) r(3,4) r(4,4)];
    
pa=@(var1) ex(ro(var1))  ;      
    
N = @(var1) 0.5*(sum(abs(eig(pa(var1))))-1);
 
range1=0:0.1:10;
for k=1:numel(range1)
    Nv(k) = N(range1(k));
end
plot(range1,Nv)

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reza hamzeh 2019-12-17

this is very good. thank u very much

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Answer 2

Matt J 2019-12-17

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https://ww2.mathworks.cn/matlabcentral/answers/497089-how-to-make-a-matrix-function-from-other-matrix-function#answer_406791

编辑：Matt J 2019-12-17

在 MATLAB Online 中打开

One way would be to make pa() a nested function,

function mainFunc
    T=1;
    Haf = str2func(sprintf('@(%s)%s;','var1','[var1/2 0 0 0;0 -var1/2 var1 0;0 var1 -var1/2 0;0 0 0 var1/2]'));
    ro=@(var1) expm(-Haf(var1)/T)/trace(expm(-Haf(var1)/T));
    range1=0:0.1:10;
    
    N = @(var1) 0.5*(sum(abs(eig(pa(var1))))-1);
            
    for k=1:numel(range1)
        Nv(k) = N(range1(k));
    end
    plot(range1,Nv)
    
            function out=pa(var1)
            
               r=ro(var1);
               out=[r(1,1) r(2,1) r(1,3) r(2,3);r(1,2) r(2,2) r(1,4) r(2,4);
                    r(3,1) r(4,1) r(3,3) r(4,3);r(3,2) r(4,2) r(3,4) r(4,4)];
            
            end
end

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Matt J 2019-12-17

reza's answer converted to commented:

is there any other way?

Matt J 2019-12-17

编辑：Matt J 2019-12-17

在 MATLAB Online 中打开

Many others. You could also make it a local function (or put it in a separate mfile), but in that case, you would have to pass ro,

function mainFunc
    T=1;
    Haf = str2func(sprintf('@(%s)%s;','var1','[var1/2 0 0 0;0 -var1/2 var1 0;0 var1 -var1/2 0;0 0 0 var1/2]'));
    ro=@(var1) expm(-Haf(var1)/T)/trace(expm(-Haf(var1)/T));
    range1=0:0.1:10;
    
    N = @(var1) 0.5*(sum(abs(eig(pa(var1,ro))))-1);
            
    for k=1:numel(range1)
        Nv(k) = N(range1(k));
    end
    plot(range1,Nv)
end
function out=pa(var1,ro)
   r=ro(var1);
   out=[r(1,1) r(2,1) r(1,3) r(2,3);r(1,2) r(2,2) r(1,4) r(2,4);
        r(3,1) r(4,1) r(3,3) r(4,3);r(3,2) r(4,2) r(3,4) r(4,4)];
end