Difference between revisions of "Lmn2lin.m"

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Converts L,M,N Wigner function specification to linear indexing speci-
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{{DISPLAYTITLE:lin2lmn.m}} __NOTOC__
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fication. In the linear indexing convention, the Wigner functions are
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Converts L,M,N indices of Wigner D functions into linear indices. In the linear indexing convention, Wigner D functions are listed in the order of increasing L rank. Within each L, the functions are listed in the order of decreasing left index M, and, for each M, in the order of decreasing N index. One base counting is used:
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listed in the order of increasing L rank. Within each L rank, the func-
 
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tions are listed in the order of decreasing left index, and, for each
 
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left index, in the order of decreasing right index. Syntax:
 
  
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                          I=lmn2lin(L,M,N)
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                    (L=0,M=0,N=0) -> I=1
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                    (L=1,M=1,N=1) -> I=2
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                    (L=1,M=1,N=0) -> I=3, et cetera...
  
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Wigner functions are enumerated using base one indexing, that is:
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==Syntax==
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                      (L=0,M=0,N=0) -> I=1
 
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                      (L=1,M=1,N=1) -> I=2
 
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                      (L=1,M=1,N=0) -> I=3, et cetera...
 
  
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Arrays of any dimension are accepted as arguments.
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    I=lmn2lin(L,M,N)
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==Arguments==
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    L  - ranks of Wigner D functions
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    M  - row indices of Wigner D functions
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    N  - column indices of Wigner D functions
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==Outputs==
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    I  - linear indices of Wigner D functions, with
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          I=1 corresponding to L=0, M=0, N=0.
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==See also==
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[[lin2lm.m]], [[lm2lin.m]], [[lin2lmn.m]], [[wigner.m]], [[dcm2wigner.m]], [[irr_sph_ten.m]]
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''Version 2.3, authors: [[Ilya Kuprov]]''

Revision as of 16:59, 28 December 2018

Converts L,M,N indices of Wigner D functions into linear indices. In the linear indexing convention, Wigner D functions are listed in the order of increasing L rank. Within each L, the functions are listed in the order of decreasing left index M, and, for each M, in the order of decreasing N index. One base counting is used:

                    (L=0,M=0,N=0) -> I=1
                    (L=1,M=1,N=1) -> I=2
                    (L=1,M=1,N=0) -> I=3, et cetera...

Syntax

    I=lmn2lin(L,M,N)

Arguments

    L   - ranks of Wigner D functions

    M   - row indices of Wigner D functions

    N   - column indices of Wigner D functions

Outputs

    I   - linear indices of Wigner D functions, with
          I=1 corresponding to L=0, M=0, N=0.

See also

lin2lm.m, lm2lin.m, lin2lmn.m, wigner.m, dcm2wigner.m, irr_sph_ten.m


Version 2.3, authors: Ilya Kuprov