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documentation:language_reference:functions:blockbanddiagonalize [2024/12/31 14:09] – Maurits W. Haverkortdocumentation:language_reference:functions:blockbanddiagonalize [2025/08/08 16:08] (current) – Micheangelo Tagliavini
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 ====== BlockBandDiagonalize ====== ====== BlockBandDiagonalize ======
- 
 ### ###
 The function //BlockBandDiagonalize()// can be used to reduce the number of basis (spin-)orbitals by making linear combinations of (spin-)orbitals, according to the tight-binding structure (hopping matrix elements) within the (spin-)orbitals. As a simple example to make the idea clear, consider the following 3-by-3 matrix: The function //BlockBandDiagonalize()// can be used to reduce the number of basis (spin-)orbitals by making linear combinations of (spin-)orbitals, according to the tight-binding structure (hopping matrix elements) within the (spin-)orbitals. As a simple example to make the idea clear, consider the following 3-by-3 matrix:
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 ### ###
  
 +====== Input ======
 +Case 1:
 +  * //matrix//: hermitian matrix
 +  * //blockSize//: size of the block (as number) or list of vectors representing the starting states
 +
 +Case 2:
 +  * //operator//: hermitian operator
 +  * //wave function //: single wave function of list of wave functions
 +
 +Case 3:
 +  * //tightbindingObject//: tight binding object
 +  * //startingBlock //: list of atoms with positions, shells and orbitals used as starting block
 +
 +
 +//(Optional) Third argument (in all cases)//
 +
 +   *NTri : (//integer//) maximum number of blocks included (//default: $\infty$//)
 +
 +   *NOrtho : (//integer//) maximum number of reorthogonalizations (//default: $\infty$//)
 +
 +  *ReOrthogonalize: (//boolean//) use additional Gran-Schmidt orthogonalization after the Löwdin orthogonalization (//default: true//)
 +
 +====== Output ======
 +case1:
 +   *//ResponseFunction//:Response Function in tri representation.
 +   *//matrix//: Transformation Matrix to transform the input matrix into the Block band diagonalized one. 
  
 ===== Table of contents ===== ===== Table of contents =====
 {{indexmenu>.#1}} {{indexmenu>.#1}}
  

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