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73 lines
1.5 KiB
Org Mode
73 lines
1.5 KiB
Org Mode
* Vector to matrix indexes
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*Compute the indexes p,q of a matrix element with the vector index i*
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Vector (i) -> lower diagonal matrix (p,q), p > q
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If a matrix is antisymmetric it can be reshaped as a vector. And the
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vector can be reshaped as an antisymmetric matrix
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\begin{align*}
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\begin{pmatrix}
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0 & -1 & -2 & -4 \\
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1 & 0 & -3 & -5 \\
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2 & 3 & 0 & -6 \\
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4 & 5 & 6 & 0
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\end{pmatrix}
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\Leftrightarrow
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\begin{pmatrix}
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1 & 2 & 3 & 4 & 5 & 6
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\end{pmatrix}
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\end{align*}
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!!! Here the algorithm only work for the lower diagonal !!!
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Input:
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| i | integer | index in the vector |
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Ouput:
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| p,q | integer | corresponding indexes in the lower diagonal of a matrix |
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| | | p > q, |
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| | | p -> row, |
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| | | q -> column |
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#+BEGIN_SRC f90 :comments org :tangle vec_to_mat_index.irp.f
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subroutine vec_to_mat_index(i,p,q)
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include 'pi.h'
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BEGIN_DOC
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! Compute the indexes (p,q) of the element in the lower diagonal matrix knowing
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! its index i a vector
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END_DOC
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implicit none
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! Variables
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! in
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integer,intent(in) :: i
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! out
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integer, intent(out) :: p,q
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! internal
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integer :: a,b
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double precision :: da
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da = 0.5d0*(1+ sqrt(1d0+8d0*DBLE(i)))
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a = INT(da)
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if ((a*(a-1))/2==i) then
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p = a-1
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else
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p = a
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endif
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b = p*(p-1)/2
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! Matrix element indexes
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p = p + 1
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q = i - b
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end subroutine
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#+END_SRC
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