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user64494
user64494
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efficient Efficient ways to generate a matrix from multiplying two elements of some matrix

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AsukaMinato
AsukaMinato
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I am working on the single particle entanglement entropy and in the process I have something like

Table[Sum[states[[eindexTable[
    Sum[
        states[[eindex, spaceindex]]*states[[eindexspaceindex]] * states[[eindex, spaceindex2]], 
        {eindex,1, Na/2}(*trace over lower-half filling*)
    ], 
    {spaceindex, 1, Nb}, 
    {spaceindex2, 1, Nb}(*some subsystem*) 
]

where states is a Na by Na square matrix, from diagonalizing some other matrix. 1<Nb<Na is some sub-system. The matrix I am trying to construct is essentially $C_{i,j}=Tr[states[k,i]*states[k,j]]$ traced over the first index.

The above code gets the job done but I wonder if there are more efficient ways.

Also, I keep getting myself into this situation where I need to generate a matrix efficiently via similar constructions, for example, projection matrices. I would also like to know some general ways to directly translate the equations into efficient code.

I am working on the single particle entanglement entropy and in the process I have something like

Table[Sum[states[[eindex, spaceindex]]*states[[eindex, spaceindex2]], {eindex,1, Na/2}(*trace over lower-half filling*)], {spaceindex, 1, Nb}, {spaceindex2, 1, Nb}(*some subsystem*)]

where states is a Na by Na square matrix, from diagonalizing some other matrix. 1<Nb<Na is some sub-system. The matrix I am trying to construct is essentially $C_{i,j}=Tr[states[k,i]*states[k,j]]$ traced over the first index.

The above code gets the job done but I wonder if there are more efficient ways.

Also, I keep getting myself into this situation where I need to generate a matrix efficiently via similar constructions, for example, projection matrices. I would also like to know some general ways to directly translate the equations into efficient code.

I am working on the single particle entanglement entropy and in the process I have something like

Table[
    Sum[
        states[[eindex, spaceindex]] * states[[eindex, spaceindex2]], 
        {eindex,1, Na/2}(*trace over lower-half filling*)
    ], 
    {spaceindex, 1, Nb}, 
    {spaceindex2, 1, Nb}(*some subsystem*) 
]

where states is a Na by Na square matrix, from diagonalizing some other matrix. 1<Nb<Na is some sub-system. The matrix I am trying to construct is essentially $C_{i,j}=Tr[states[k,i]*states[k,j]]$ traced over the first index.

The above code gets the job done but I wonder if there are more efficient ways.

Also, I keep getting myself into this situation where I need to generate a matrix efficiently via similar constructions, for example, projection matrices. I would also like to know some general ways to directly translate the equations into efficient code.

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wooohooo
wooohooo
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efficient ways to generate a matrix from multiplying two elements of some matrix

I am working on the single particle entanglement entropy and in the process I have something like

Table[Sum[states[[eindex, spaceindex]]*states[[eindex, spaceindex2]], {eindex,1, Na/2}(*trace over lower-half filling*)], {spaceindex, 1, Nb}, {spaceindex2, 1, Nb}(*some subsystem*)]

where states is a Na by Na square matrix, from diagonalizing some other matrix. 1<Nb<Na is some sub-system. The matrix I am trying to construct is essentially $C_{i,j}=Tr[states[k,i]*states[k,j]]$ traced over the first index.

The above code gets the job done but I wonder if there are more efficient ways.

Also, I keep getting myself into this situation where I need to generate a matrix efficiently via similar constructions, for example, projection matrices. I would also like to know some general ways to directly translate the equations into efficient code.