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43 lines
1.2 KiB
ReStructuredText
43 lines
1.2 KiB
ReStructuredText
.. _det_manip:
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Manipulations of determinants
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=============================
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.. warning::
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This library is stable, but documentation is currently being written
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and needs a serious rereading and cleaning
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The purpose of this little class is to regroup standard block manipulations on determinant, used in several algorithms.
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Given a function :math:`F(x,y)`, and two sets of values :math:`x_i,y_i \ 0\leq i < N`,
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we can define the :math:`N\times N` square matrix
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.. math::
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M_{i,j} = F(x_i,y_j)
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When adding/removing a line and column (i.e. a value of x, y),
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:math:`M^{-1}` and :math:`det M` can be fast updated using standard block matrix computations.
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This class implements these general operations. It contains :
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* Datas :
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* :math:`M^{-1}` and :math:`det M`
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* a vector containing :math:`x_i,y_i \ 0\leq i \leq N`
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* Methods to quickly update :math:`M^{-1}` and :math:`\det M` when one :
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* adds/removes a line and a column (i.e. adding or removing one x and one y)
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* adds/removes two lines and two columns (i.e. adding or removing two x and two y)
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* changes a line/colum, etc...
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.. toctree::
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:maxdepth: 2
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det_manip
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behind
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cookbook/contents
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