remove trailing whitespace

doc/src/compute_orientorder_atom.rst

@@ -61,8 +61,8 @@ The summation is over the *nnn* nearest
 neighbors of the central atom.
 The angles :math:`theta` and :math:`phi` are the standard spherical polar angles
 defining the direction of the bond vector :math:`r_{ij}`.
-The phase and sign of :math:`Y_{lm}` follow the standard conventions, 
-so that :math:`{\rm sign}(Y_{ll}(0,0)) = (-1)^l`.   
+The phase and sign of :math:`Y_{lm}` follow the standard conventions,
+so that :math:`{\rm sign}(Y_{ll}(0,0)) = (-1)^l`.
 The second equation defines :math:`Q_l`, which is a
 rotationally invariant non-negative amplitude obtained by summing
 over all the components of degree *l*\ .
@@ -181,13 +181,13 @@ values for each atom will be added to the output array, which are real numbers.
 
 If the keyword *components* is set, then the real and imaginary parts
 of each component of *normalized* :math:`\hat{Y}_{lm}` will be added to the
-output array in the following order: :math:`{\rm Re}(\hat{Y}_{-m}), {\rm Im}(\hat{Y}_{-m}), 
-{\rm Re}(\hat{Y}_{-m+1}), {\rm Im}(\hat{Y}_{-m+1}), \dots , {\rm Re}(\hat{Y}_m), {\rm Im}(\hat{Y}_m)`.  
+output array in the following order: :math:`{\rm Re}(\hat{Y}_{-m}), {\rm Im}(\hat{Y}_{-m}),
+{\rm Re}(\hat{Y}_{-m+1}), {\rm Im}(\hat{Y}_{-m+1}), \dots , {\rm Re}(\hat{Y}_m), {\rm Im}(\hat{Y}_m)`.
 
 In summary, the per-atom array will contain *nlvalues* columns, followed by
 an additional *nlvalues* columns if *wl* is set to yes, followed by
 an additional *nlvalues* columns if *wl/hat* is set to yes, followed
-by an additional 2\*(2\* *ldegree*\ +1) columns if the *components* 
+by an additional 2\*(2\* *ldegree*\ +1) columns if the *components*
 keyword is set.
 
 These values can be accessed by any command that uses per-atom values

doc/src/pair_mliap.rst

@@ -16,19 +16,19 @@ Examples
 .. code-block:: LAMMPS
 
    pair_style mliap model linear InP.mliap.model descriptor sna InP.mliap.descriptor
-   pair_style mliap model quadratic W.mliap.model descriptor sna W.mliap.descriptor 
+   pair_style mliap model quadratic W.mliap.model descriptor sna W.mliap.descriptor
    pair_coeff * * In P
 
 Description
 """""""""""
 
-Pair style *mliap* provides a general interface to families of 
-machine-learning interatomic potentials. It provides separate 
+Pair style *mliap* provides a general interface to families of
+machine-learning interatomic potentials. It provides separate
 definitions of the interatomic potential functional form (*model*)
 and the geometric quantities that characterize the atomic positions
-(*descriptor*). By defining *model* and *descriptor* separately, 
+(*descriptor*). By defining *model* and *descriptor* separately,
 it is possible to use many different models with a given descriptor,
-or many different descriptors with a given model. Currently, the pair_style 
+or many different descriptors with a given model. Currently, the pair_style
 supports just two models, *linear* and *quadratic*,
 and one descriptor, *sna*, the SNAP descriptor used by :doc:`pair_style snap <pair_snap>`, including the linear, quadratic,
 and chem variants. Work is currently underway to extend
@@ -37,23 +37,23 @@ and it is also straightforward to add new descriptor styles.
 
 The pair_style *mliap* command must be followed by two keywords
 *model* and *descriptor* in either order. A single
-*pair_coeff* command is also required. The first 2 arguments 
+*pair_coeff* command is also required. The first 2 arguments
 must be \* \* so as to span all LAMMPS atom types.
 This is followed by a list of N arguments
 that specify the mapping of MLIAP
-element names to LAMMPS atom types, 
+element names to LAMMPS atom types,
 where N is the number of LAMMPS atom types.
 
 The *model* keyword is followed by a model style, currently limited to
 either *linear* or *quadratic*. In both cases,
-this is followed by a single argument specifying the model filename containing the 
-linear or quadratic coefficients for a set of elements. 
+this is followed by a single argument specifying the model filename containing the
+linear or quadratic coefficients for a set of elements.
 The model filename usually ends in the *.mliap.model* extension.
 It may contain coefficients for many elements. The only requirement is that it
 contain at least those element names appearing in the
 *pair_coeff* command.
 
-The top of the model file can contain any number of blank and comment lines (start with #), 
+The top of the model file can contain any number of blank and comment lines (start with #),
 but follows a strict format after that. The first non-blank non-comment
 line must contain two integers:
 
@@ -64,20 +64,20 @@ This is followed by one block for each of the *nelem* elements.
 Each block consists of *ncoeff* coefficients, one per line.
 Note that this format is similar, but not identical to that used
 for the :doc:`pair_style snap <pair_snap>` coefficient file.
-Specifically, the line containing the element weight and radius is omitted, 
+Specifically, the line containing the element weight and radius is omitted,
 since these are handled by the *descriptor*.
 
 The *descriptor* keyword is followed by a descriptor style, and additional arguments.
-Currently the only descriptor style is *sna*, indicating the bispectrum component 
-descriptors used by the Spectral Neighbor Analysis Potential (SNAP) potentials of 
+Currently the only descriptor style is *sna*, indicating the bispectrum component
+descriptors used by the Spectral Neighbor Analysis Potential (SNAP) potentials of
 :doc:`pair_style snap <pair_snap>`.
-The \'p\' in SNAP is dropped, because keywords that match pair_styles are silently stripped 
-out by the LAMMPS command parser. A single additional argument specifies the descriptor filename 
-containing the parameters and setting used by the SNAP descriptor. 
+The \'p\' in SNAP is dropped, because keywords that match pair_styles are silently stripped
+out by the LAMMPS command parser. A single additional argument specifies the descriptor filename
+containing the parameters and setting used by the SNAP descriptor.
 The descriptor filename usually ends in the *.mliap.descriptor* extension.
 
-The SNAP descriptor file closely follows the format of the 
-:doc:`pair_style snap <pair_snap>` parameter file. 
+The SNAP descriptor file closely follows the format of the
+:doc:`pair_style snap <pair_snap>` parameter file.
 The file can contain blank and comment lines (start
 with #) anywhere. Each non-blank non-comment line must contain one
 keyword/value pair. The required keywords are *rcutfac* and
@@ -87,7 +87,7 @@ In addition, the SNAP descriptor file must contain
 the *nelems*, *elems*, *radelems*, and *welems* keywords.
 The *nelems* keyword specifies the number of elements
 provided in the other three keywords.
-The *elems* keyword is followed by a list of *nelems* 
+The *elems* keyword is followed by a list of *nelems*
 element names that must include the element
 names appearing in the *pair_coeff* command,
 but can contain other names too.

doc/src/pair_snap.rst

@@ -25,9 +25,9 @@ Description
 """""""""""
 
 Pair style *snap* defines the spectral
-neighbor analysis potential (SNAP), a machine-learning 
+neighbor analysis potential (SNAP), a machine-learning
 interatomic potential :ref:`(Thompson) <Thompson20142>`.
-Like the GAP framework of Bartok et al. :ref:`(Bartok2010) <Bartok20102>`, 
+Like the GAP framework of Bartok et al. :ref:`(Bartok2010) <Bartok20102>`,
 SNAP uses bispectrum components
 to characterize the local neighborhood of each atom
 in a very general way. The mathematical definition of the
@@ -139,7 +139,7 @@ The SNAP parameter file can contain blank and comment lines (start
 with #) anywhere. Each non-blank non-comment line must contain one
 keyword/value pair. The required keywords are *rcutfac* and
 *twojmax*\ . Optional keywords are *rfac0*\ , *rmin0*\ ,
-*switchflag*\ , *bzeroflag*\ , *quadraticflag*\ , *chemflag*\ , 
+*switchflag*\ , *bzeroflag*\ , *quadraticflag*\ , *chemflag*\ ,
 *bnormflag*\ , *wselfallflag*\ , and *chunksize*\ .
 
 The default values for these keywords are
@@ -154,34 +154,34 @@ The default values for these keywords are
 * *wselfallflag* = 0
 * *chunksize* = 2000
 
-If *quadraticflag* is set to 1, then the SNAP energy expression includes additional quadratic terms 
+If *quadraticflag* is set to 1, then the SNAP energy expression includes additional quadratic terms
 that have been shown to increase the overall accuracy of the potential without much increase
-in computational cost :ref:`(Wood) <Wood20182>`. 
+in computational cost :ref:`(Wood) <Wood20182>`.
 
 .. math::
 
    E^i_{SNAP}(\mathbf{B}^i) = \beta^{\mu_i}_0 + \boldsymbol{\beta}^{\mu_i} \cdot \mathbf{B}_i + \frac{1}{2}\mathbf{B}^t_i \cdot \boldsymbol{\alpha}^{\mu_i} \cdot \mathbf{B}_i
 
-where :math:`\mathbf{B}_i` is the *K*-vector of bispectrum components, 
-:math:`\boldsymbol{\beta}^{\mu_i}` is the *K*-vector of linear coefficients 
-for element :math:`\mu_i`, and :math:`\boldsymbol{\alpha}^{\mu_i}` 
+where :math:`\mathbf{B}_i` is the *K*-vector of bispectrum components,
+:math:`\boldsymbol{\beta}^{\mu_i}` is the *K*-vector of linear coefficients
+for element :math:`\mu_i`, and :math:`\boldsymbol{\alpha}^{\mu_i}`
 is the symmetric *K* by *K* matrix of quadratic coefficients.
 The SNAP element file should contain *K*\ (\ *K*\ +1)/2 additional coefficients
 for each element, the upper-triangular elements of :math:`\boldsymbol{\alpha}^{\mu_i}`.
 
 If *chemflag* is set to 1, then the energy expression is written in terms of explicit multi-element bispectrum
 components indexed on ordered triplets of elements, which has been shown to increase the ability of the SNAP
-potential to capture energy differences in chemically complex systems, 
+potential to capture energy differences in chemically complex systems,
 at the expense of a significant increase in computational cost :ref:`(Cusentino) <Cusentino20202>`.
 
 .. math::
 
-   E^i_{SNAP}(\mathbf{B}^i) = \beta^{\mu_i}_0 + \sum_{\kappa,\lambda,\mu} \boldsymbol{\beta}^{\kappa\lambda\mu}_{\mu_i} \cdot \mathbf{B}^{\kappa\lambda\mu}_i 
+   E^i_{SNAP}(\mathbf{B}^i) = \beta^{\mu_i}_0 + \sum_{\kappa,\lambda,\mu} \boldsymbol{\beta}^{\kappa\lambda\mu}_{\mu_i} \cdot \mathbf{B}^{\kappa\lambda\mu}_i
 
-where :math:`\mathbf{B}^{\kappa\lambda\mu}_i` is the *K*-vector of bispectrum components 
-for neighbors of elements :math:`\kappa`, :math:`\lambda`, and :math:`\mu` and 
-:math:`\boldsymbol{\beta}^{\kappa\lambda\mu}_{\mu_i}` is the corresponding *K*-vector 
-of linear coefficients for element :math:`\mu_i`. The SNAP element file should contain 
+where :math:`\mathbf{B}^{\kappa\lambda\mu}_i` is the *K*-vector of bispectrum components
+for neighbors of elements :math:`\kappa`, :math:`\lambda`, and :math:`\mu` and
+:math:`\boldsymbol{\beta}^{\kappa\lambda\mu}_{\mu_i}` is the corresponding *K*-vector
+of linear coefficients for element :math:`\mu_i`. The SNAP element file should contain
 a total of :math:`K N_{elem}^3` coefficients for each of the :math:`N_{elem}` elements.
 
 The keyword *chunksize* is only applicable when using the