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64 lines
1.2 KiB
Org Mode
64 lines
1.2 KiB
Org Mode
* Matrix to vector index
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*Compute the index i of a vector element from the indexes p,q of a
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matrix element*
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Lower diagonal matrix (p,q), p > q -> vector (i)
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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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| p,q | integer | indexes of a matrix element in the lower diagonal |
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| | | p > q, q -> column |
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| | | p -> row, |
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| | | q -> column |
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Input:
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| i | integer | corresponding index in the vector |
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#+BEGIN_SRC f90 :comments org :tangle mat_to_vec_index.irp.f
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subroutine mat_to_vec_index(p,q,i)
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include 'pi.h'
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implicit none
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! Variables
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! in
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integer, intent(in) :: p,q
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! out
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integer, intent(out) :: i
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! internal
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integer :: a,b
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double precision :: da
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! Calculation
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a = p-1
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b = a*(a-1)/2
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i = q+b
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end subroutine
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#+END_SRC
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