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update the templated network docs linear algebra (#1712)
we do not skip zeros, since we were doing that incorrectly previously
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Docs/source/templated_networks.rst

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@@ -384,16 +384,11 @@ Linear Algebra
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The VODE integrator needs routines to do LU factorization and back
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substitution. We build off of the linpack ``dgefa`` and ``dgesl``
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routines, but because we know at compile time which Jacobian terms are
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non-zero, we are able to use ``constexpr`` for-loops to only do the
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calculations on non-zero elements. This greatly reduces the amount of work
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in the linear algebra.
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routines, using ``constexpr`` for-loops that know the network size
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at compile time.
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Note:
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* Currently we are still storing a dense Jacobian -- we just skip computation
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on the elements that are 0.
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.. note::
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* These routines do not perform pivoting. This does not seem to be an
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issue for the types of matrices we solve with reactions (since they are
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all of the form :math:`I - \tau J`, where :math:`tau` is the timestep).
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These routines do not perform pivoting. This does not seem to be an
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issue for the types of matrices we solve with reactions (since they are
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all of the form :math:`I - \tau J`, where :math:`tau` is the timestep).

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