Final tidying up
This commit is contained in:
Aidan Thompson
@ -467,235 +467,6 @@ number of columns in the global array generated by *snap* are 31, and
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931, respectively, while the number of rows is 1+3\*\ *N*\ +6, where *N*
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is the total number of atoms.
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If the *quadratic* keyword value is set to 1, then additional columns
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are generated, corresponding to the products of all distinct pairs of
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bispectrum components. If the number of bispectrum components is *K*,
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then the number of distinct pairs is *K*\ (\ *K*\ +1)/2. For compute
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*sna/atom* these columns are appended to existing *K* columns. The
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ordering of quadratic terms is upper-triangular, (1,1),(1,2)...(1,\ *K*\
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),(2,1)...(\ *K*\ -1,\ *K*\ -1),(\ *K*\ -1,\ *K*\ ),(\ *K*,\ *K*\ ).
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For computes *snad/atom* and *snav/atom* each set of *K*\ (\ *K*\ +1)/2
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additional columns is inserted directly after each of sub-block of
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linear terms i.e. linear and quadratic terms are contiguous. So the
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nesting order from inside to outside is bispectrum component, linear
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then quadratic, vector/tensor component, type.
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If the *chem* keyword is used, then the data is arranged into
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:math:`N_{elem}^3` sub-blocks, each sub-block corresponding to a
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particular chemical labeling :math:`\kappa\lambda\mu` with the last
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label changing fastest. Each sub-block contains *K* bispectrum
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components. For the purposes of handling contributions to force, virial,
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and quadratic combinations, these :math:`N_{elem}^3` sub-blocks are
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treated as a single block of :math:`K N_{elem}^3` columns.
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These values can be accessed by any command that uses per-atom values
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from a compute as input. See the :doc:`Howto output <Howto_output>` doc
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page for an overview of LAMMPS output options. To see how this command
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can be used within a Python workflow to train SNAP potentials, see the
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examples in `FitSNAP <https://github.com/FitSNAP/FitSNAP>`_.
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The value of all bispectrum components will be zero for atoms not in
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the group. Neighbor atoms not in the group do not contribute to the
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bispectrum of atoms in the group.
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The neighbor list needed to compute this quantity is constructed each
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time the calculation is performed (i.e. each time a snapshot of atoms
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is dumped). Thus it can be inefficient to compute/dump this quantity
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too frequently.
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The argument *rcutfac* is a scale factor that controls the ratio of
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atomic radius to radial cutoff distance.
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The argument *rfac0* and the optional keyword *rmin0* define the
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linear mapping from radial distance to polar angle :math:`theta_0` on the
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3-sphere, given above.
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The argument *twojmax* defines which
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bispectrum components are generated. See section below on output for a
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detailed explanation of the number of bispectrum components and the
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ordered in which they are listed.
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The keyword *switchflag* can be used to turn off the switching
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function :math:`f_c(r)`.
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The keyword *bzeroflag* determines whether or not *B0*, the bispectrum
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components of an atom with no neighbors, are subtracted from the
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calculated bispectrum components. This optional keyword normally only
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affects compute *sna/atom*\ . However, when *quadraticflag* is on, it
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also affects *snad/atom* and *snav/atom*\ .
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The keyword *quadraticflag* determines whether or not the quadratic
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combinations of bispectrum quantities are generated. These are formed
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by taking the outer product of the vector of bispectrum components with
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itself. See section below on output for a detailed explanation of the
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number of quadratic terms and the ordered in which they are listed.
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The keyword *chem* activates the explicit multi-element variant of the
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SNAP bispectrum components. The argument *nelements* specifies the
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number of SNAP elements that will be handled. This is followed by
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*elementlist*, a list of integers of length *ntypes*, with values in the
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range [0, *nelements* ), which maps each LAMMPS type to one of the SNAP
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elements. Note that multiple LAMMPS types can be mapped to the same
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element, and some elements may be mapped by no LAMMPS type. However, in
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typical use cases (training SNAP potentials) the mapping from LAMMPS
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types to elements is one-to-one.
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The explicit multi-element variant invoked by the *chem* keyword
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partitions the density of neighbors into partial densities for each
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chemical element. This is described in detail in the paper by
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:ref:`Cusentino et al. <Cusentino2020>` The bispectrum components are
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indexed on ordered triplets of elements:
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.. math::
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B_{j_1,j_2,j}^{\kappa\lambda\mu} =
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\sum_{m_1,m'_1=-j_1}^{j_1}\sum_{m_2,m'_2=-j_2}^{j_2}\sum_{m,m'=-j}^{j} (u^{\mu}_{j,m,m'})^*
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H {\scriptscriptstyle \begin{array}{l} {j} {m} {m'} \\
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{j_1} {m_1} {m'_1} \\
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{j_2} {m_2} {m'_2} \end{array}}
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u^{\kappa}_{j_1,m_1,m'_1} u^{\lambda}_{j_2,m_2,m'_2}
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where :math:`u^{\mu}_{j,m,m'}` is an expansion coefficient for the partial density of neighbors
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of element :math:`\mu`
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.. math::
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u^{\mu}_{j,m,m'} = w^{self}_{\mu_{i}\mu} U^{j,m,m'}(0,0,0) + \sum_{r_{ii'} < R_{ii'}}{\delta_{\mu\mu_{i'}}f_c(r_{ii'}) w_{\mu_{i'}} U^{j,m,m'}(\theta_0,\theta,\phi)}
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where :math:`w^{self}_{\mu_{i}\mu}` is the self-contribution, which is
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either 1 or 0 (see keyword *wselfallflag* below),
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:math:`\delta_{\mu\mu_{i'}}` indicates that the sum is only over
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neighbor atoms of element :math:`\mu`, and all other quantities are the
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same as those appearing in the original equation for :math:`u^j_{m,m'}`
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given above.
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The keyword *wselfallflag* defines the rule used for the
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self-contribution. If *wselfallflag* is on, then
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:math:`w^{self}_{\mu_{i}\mu}` = 1. If it is off then
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:math:`w^{self}_{\mu_{i}\mu}` = 0, except in the case of
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:math:`{\mu_{i}=\mu}`, when :math:`w^{self}_{\mu_{i}\mu}` = 1. When the
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*chem* keyword is not used, this keyword has no effect.
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The keyword *bnormflag* determines whether or not the bispectrum
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component :math:`B_{j_1,j_2,j}` is divided by a factor of :math:`2j+1`.
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This normalization simplifies force calculations because of the
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following symmetry relation
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.. math::
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\frac{B_{j_1,j_2,j}}{2j+1} = \frac{B_{j,j_2,j_1}}{2j_1+1} = \frac{B_{j_1,j,j_2}}{2j_2+1}
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This option is typically used in conjunction with the *chem* keyword,
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and LAMMPS will generate a warning if both *chem* and *bnormflag*
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are not both set or not both unset.
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The keyword *bikflag* determines whether or not to expand the bispectrum
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rows of the global array returned by compute snap. If *bikflag* is set
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to *1* then the bispectrum row, which is typically the per-atom bispectrum
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descriptors :math:`B_{i,k}` summed over all atoms *i* to produce
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:math:`B_k`, becomes bispectrum rows equal to the number of atoms. Thus,
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the resulting bispectrum rows are :math:`B_{i,k}` instead of just
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:math:`B_k`. In this case, the entries in the final column for these rows
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are set to zero.
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The keyword *switchinnerflag* with value 1
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activates an additional radial switching
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function similar to :math:`f_c(r)` above, but acting to switch off
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smoothly contributions from neighbor atoms at short separation distances.
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This is useful when SNAP is used in combination with a simple
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repulsive potential. For a neighbor atom at
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distance :math:`r`, its contribution is scaled by a multiplicative
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factor :math:`f_{inner}(r)` defined as follows:
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.. math::
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= & 0, r \leq S_{inner} - D_{inner} \\
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f_{inner}(r) = & \frac{1}{2}(1 - \cos(\frac{\pi}{2} (1 + \frac{r-S_{inner}}{D_{inner}})), S_{inner} - D_{inner} < r \leq S_{inner} + D_{inner} \\
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= & 1, r > S_{inner} + D_{inner}
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where the switching region is centered at :math:`S_{inner}` and it extends a distance :math:`D_{inner}`
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to the left and to the right of this.
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With this option, additional keywords *sinner* and *dinner* must be used,
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each followed by *ntypes*
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values for :math:`S_{inner}` and :math:`D_{inner}`, respectively.
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When the central atom and the neighbor atom have different types,
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the values of :math:`S_{inner}` and :math:`D_{inner}` are
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the arithmetic means of the values for both types.
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.. note::
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If you have a bonded system, then the settings of :doc:`special_bonds
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<special_bonds>` command can remove pairwise interactions between
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atoms in the same bond, angle, or dihedral. This is the default
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setting for the :doc:`special_bonds <special_bonds>` command, and
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means those pairwise interactions do not appear in the neighbor list.
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Because this fix uses the neighbor list, it also means those pairs
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will not be included in the calculation. One way to get around this,
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is to write a dump file, and use the :doc:`rerun <rerun>` command to
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compute the bispectrum components for snapshots in the dump file.
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The rerun script can use a :doc:`special_bonds <special_bonds>`
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command that includes all pairs in the neighbor list.
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----------
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Output info
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"""""""""""
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Compute *sna/atom* calculates a per-atom array, each column
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corresponding to a particular bispectrum component. The total number of
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columns and the identity of the bispectrum component contained in each
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column depend of the value of *twojmax*, as described by the following
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piece of python code:
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.. parsed-literal::
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for j1 in range(0,twojmax+1):
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for j2 in range(0,j1+1):
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for j in range(j1-j2,min(twojmax,j1+j2)+1,2):
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if (j>=j1): print j1/2.,j2/2.,j/2.
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For even twojmax = 2(*m*\ -1), :math:`K = m(m+1)(2m+1)/6`, the *m*\ -th pyramidal number. For odd twojmax = 2 *m*\ -1, :math:`K = m(m+1)(m+2)/3`, twice the *m*\ -th tetrahedral number.
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.. note::
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the *diagonal* keyword allowing other possible choices
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for the number of bispectrum components was removed in 2019,
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since all potentials use the value of 3, corresponding to the
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above set of bispectrum components.
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Compute *snad/atom* evaluates a per-atom array. The columns are arranged
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into *ntypes* blocks, listed in order of atom type *I*\ . Each block
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contains three sub-blocks corresponding to the *x*, *y*, and *z*
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components of the atom position. Each of these sub-blocks contains *K*
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columns for the *K* bispectrum components, the same as for compute
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*sna/atom*
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Compute *snav/atom* evaluates a per-atom array. The columns are arranged
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into *ntypes* blocks, listed in order of atom type *I*\ . Each block
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contains six sub-blocks corresponding to the *xx*, *yy*, *zz*,
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*yz*, *xz*, and *xy* components of the virial tensor in Voigt
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notation. Each of these sub-blocks contains *K* columns for the *K*
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bispectrum components, the same as for compute *sna/atom*
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Compute *snap* evaluates a global array. The columns are arranged into
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*ntypes* blocks, listed in order of atom type *I*\ . Each block contains
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one column for each bispectrum component, the same as for compute
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*sna/atom*\ . A final column contains the corresponding energy, force
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component on an atom, or virial stress component. The rows of the array
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appear in the following order:
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* 1 row: *sna/atom* quantities summed for all atoms of type *I*
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* 3\*\ *N* rows: *snad/atom* quantities, with derivatives w.r.t. x, y, and z coordinate of atom *i* appearing in consecutive rows. The atoms are sorted based on atom ID.
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* 6 rows: *snav/atom* quantities summed for all atoms of type *I*
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For example, if *K* =30 and ntypes=1, the number of columns in the
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per-atom arrays generated by *sna/atom*, *snad/atom*, and
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*snav/atom* are 30, 90, and 180, respectively. With *quadratic* value=1,
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the numbers of columns are 930, 2790, and 5580, respectively. The
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number of columns in the global array generated by *snap* are 31, and
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931, respectively, while the number of rows is 1+3\*\ *N*\ +6, where *N*
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is the total number of atoms.
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Compute *sna/grid* evaluates a global array.
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The array contains one row for each of the
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:math:`nx \times ny \times nz` grid points, looping over the index for *ix* fastest,
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@ -228,6 +228,7 @@ void ComputeSNAGrid::compute_array()
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const double ztmp = xgrid[2];
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// currently, all grid points are type 1
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// not clear what a better choice would be
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const int itype = 1;
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int ielem = 0;
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@ -227,6 +227,7 @@ void ComputeSNAGridLocal::compute_local()
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const double ztmp = xgrid[2];
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// currently, all grid points are type 1
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// not clear what a better choice would be
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const int itype = 1;
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int ielem = 0;
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