Add APIP package.

2025-04-08 15:26:45 +02:00
parent 16db8e1515
commit 535d08895a
75 changed files with 99196 additions and 8 deletions
--- a/cmake/CMakeLists.txt
+++ b/cmake/CMakeLists.txt
@ -276,6 +276,7 @@ option(CMAKE_VERBOSE_MAKEFILE "Generate verbose Makefiles" OFF)
 set(STANDARD_PACKAGES
  ADIOS
  AMOEBA
  APIP
  ASPHERE
  ATC
  AWPMD
@ -605,7 +606,7 @@ else()
 endif()
 foreach(PKG_WITH_INCL KSPACE PYTHON ML-IAP VORONOI COLVARS ML-HDNNP MDI MOLFILE NETCDF
-        PLUMED QMMM ML-QUIP SCAFACOS MACHDYN VTK KIM COMPRESS ML-PACE LEPTON EXTRA-COMMAND)
+        PLUMED QMMM ML-QUIP SCAFACOS MACHDYN VTK KIM COMPRESS APIP ML-PACE LEPTON EXTRA-COMMAND)
  if(PKG_${PKG_WITH_INCL})
    include(Packages/${PKG_WITH_INCL})
  endif()
--- a/cmake/Modules/Packages/APIP.cmake
+++ b/cmake/Modules/Packages/APIP.cmake
@ -0,0 +1,3 @@
 if(NOT PKG_ML-PACE)
  message(FATAL_ERROR "Must enable ML-PACE package for enabling APIP package")
 endif()
--- a/cmake/presets/all_off.cmake
+++ b/cmake/presets/all_off.cmake
@ -4,6 +4,7 @@
 set(ALL_PACKAGES
  ADIOS
  AMOEBA
  APIP
  ASPHERE
  ATC
  AWPMD
--- a/cmake/presets/all_on.cmake
+++ b/cmake/presets/all_on.cmake
@ -6,6 +6,7 @@
 set(ALL_PACKAGES
  ADIOS
  AMOEBA
  APIP
  ASPHERE
  ATC
  AWPMD
--- a/cmake/presets/nolib.cmake
+++ b/cmake/presets/nolib.cmake
@ -3,6 +3,7 @@
 set(PACKAGES_WITH_LIB
  ADIOS
  APIP
  ATC
  AWPMD
  COMPRESS
--- a/doc/src/Commands_fix.rst
+++ b/doc/src/Commands_fix.rst
@ -22,6 +22,7 @@ OPT.
   * :doc:`append/atoms <fix_append_atoms>`
   * :doc:`atc <fix_atc>`
   * :doc:`atom/swap <fix_atom_swap>`
   * :doc:`apip_atom_weight <fix_apip_atom_weight>`
   * :doc:`ave/atom <fix_ave_atom>`
   * :doc:`ave/chunk <fix_ave_chunk>`
   * :doc:`ave/correlate <fix_ave_correlate>`
@ -89,6 +90,7 @@ OPT.
   * :doc:`imd <fix_imd>`
   * :doc:`indent <fix_indent>`
   * :doc:`ipi <fix_ipi>`
   * :doc:`lambda <fix_lambda>`
   * :doc:`langevin (k) <fix_langevin>`
   * :doc:`langevin/drude <fix_langevin_drude>`
   * :doc:`langevin/eff <fix_langevin_eff>`
@ -97,6 +99,7 @@ OPT.
   * :doc:`lb/momentum <fix_lb_momentum>`
   * :doc:`lb/viscous <fix_lb_viscous>`
   * :doc:`lineforce <fix_lineforce>`
   * :doc:`lambda_thermostat <fix_lambda_thermostat>`
   * :doc:`manifoldforce <fix_manifoldforce>`
   * :doc:`mdi/qm <fix_mdi_qm>`
   * :doc:`mdi/qmmm <fix_mdi_qmmm>`
--- a/doc/src/Commands_pair.rst
+++ b/doc/src/Commands_pair.rst
@ -96,7 +96,9 @@ OPT.
   * :doc:`eam/cd <pair_eam>`
   * :doc:`eam/cd/old <pair_eam>`
   * :doc:`eam/fs (gikot) <pair_eam>`
   * :doc:`eam/fs/apip <pair_eam_apip>`
   * :doc:`eam/he <pair_eam>`
   * :doc:`eam/apip <pair_eam_apip>`
   * :doc:`edip (o) <pair_edip>`
   * :doc:`edip/multi <pair_edip>`
   * :doc:`edpd (g) <pair_mesodpd>`
@ -124,6 +126,9 @@ OPT.
   * :doc:`ilp/tmd (t) <pair_ilp_tmd>`
   * :doc:`kolmogorov/crespi/full <pair_kolmogorov_crespi_full>`
   * :doc:`kolmogorov/crespi/z <pair_kolmogorov_crespi_z>`
   * :doc:`lambda/zone <pair_lambda_zone>`
   * :doc:`lambda_input <pair_lambda_input>`
   * :doc:`lambda_input/csp <pair_lambda_input>`
   * :doc:`lcbop <pair_lcbop>`
   * :doc:`lebedeva/z <pair_lebedeva_z>`
   * :doc:`lennard/mdf <pair_mdf>`
@ -236,6 +241,9 @@ OPT.
   * :doc:`oxrna2/coaxstk <pair_oxrna2>`
   * :doc:`pace (k) <pair_pace>`
   * :doc:`pace/extrapolation (k) <pair_pace>`
   * :doc:`pace/apip <pair_pace_apip>`
   * :doc:`pace/apip/fast <pair_pace_apip>`
   * :doc:`pace/apip/precise <pair_pace_apip>`
   * :doc:`pedone (o) <pair_pedone>`
   * :doc:`pod (k) <pair_pod>`
   * :doc:`peri/eps <pair_peri>`
--- a/doc/src/Howto.rst
+++ b/doc/src/Howto.rst
@ -91,6 +91,7 @@ Packages howto
   Howto_manifold
   Howto_rheo
   Howto_spins
   Howto_apip
 Tutorials howto
 ===============
--- a/doc/src/Howto_apip.rst
+++ b/doc/src/Howto_apip.rst
@ -0,0 +1,130 @@
 Adaptive-precision interatomic potentials (APIP)
 ================================================
 The :ref:`APIP package <PKG-APIP>` allows to use adaptive-precision potentials
 according to :ref:`(Immel) <Immel2025_1>`.
 The potential energy :math:`E_i` of an atom :math:`i` of an adaptive-precision
 interatomic potential is given by :ref:`(Immel) <Immel2025_1>`
 .. math::
   E_i = \lambda_i E_i^\text{(fast)} + (1-\lambda_i) E_i^\text{(precise)},
 whereas :math:`E_i^\text{(fast)}` is the potential energy of atom :math:`i`
 according to a fast interatomic potential,
 :math:`E_i^\text{(precise)}` is the potential energy according to a precise
 interatomic potential and :math:`\lambda_i\in[0,1]` is the
 switching parameter that decides which potential energy is used.
 The currently implemented potentials are:
 .. list-table::
   :header-rows: 1
   * - Fast potential
     - Precise potential
   * - :doc:`ACE <pair_pace_apip>`
     - :doc:`ACE <pair_pace_apip>`
   * - :doc:`EAM <pair_eam_apip>`
     -
 In theory, any short-range potential can be used for an adaptive-precision
 interatomic potential. How to implement a new (fast or precise)
 adaptive-precision
 potential is explained in :ref:`here <implementing_new_apip_styles>`.
 To run a simulation with an adaptive-precision potential, one needs the
 following components:
  #. :doc:`atom_style apip <atom_style>` so that the switching parameter :math:`\lambda_i` can be stored.
  #. A fast potential: :doc:`eam/apip <pair_eam_apip>` or :doc:`pace/apip/fast <pair_pace_apip>`.
  #. A precise potential: :doc:`pace/apip/precise <pair_pace_apip>`.
  #. :doc:`pair_style lambda_input  <pair_lambda_input>` to calculate :math:`\lambda_i^\text{input}`, from which :math:`\lambda_i` is calculated.
  #. :doc:`fix lambda <fix_lambda>` to calculate the switching parameter.
  #. :doc:`pair_style lambda/zone <pair_lambda_zone>` to calculate the spatial transition zone of the switching parameter.
  #. :doc:`pair_style hybrid/overlay <pair_hybrid>` to combine the previously mentioned pair_styles.
  #. :doc:`fix lambda_thermostat <fix_lambda_thermostat>` to conserve the energy when switching parameters change.
  #. :doc:`fix apip_atom_weight <fix_apip_atom_weight>` to approximate the load caused by every atom, as the computations of the pair_styles are only required for a subset of atoms.
  #. :doc:`fix balance <fix_balance>` to perform dynamic load balancing with the calculated load.
 Example
 """""""
 .. note::
   How to select the values of the parameters of an adaptive-precision
   interatomic potential is discussed in detail in :ref:`(Immel) <Immel2025_1>`.
 The affected parts of a LAMMPS script can look as follows:
 .. code-block:: LAMMPS
   atom_style apip
   comm_style tiled
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda/zone 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda/zone
   fix 2 all lambda 2.5 3.0 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01
   fix 3 all lambda_thermostat N_rescaling 200
   fix 4 all apip_atom_weight 100 eam ace lambda_input lambda all
   variable myweight atom f_4
   fix 5 all balance 100 1.1 rcb weight var myweight
 First, the :doc:`atom_style <atom_style>` and the communication style are set.
 .. note::
   Note, that :doc:`comm_style <comm_style>` *tiled* is required for the style *rcb* of
   :doc:`fix balance <fix_balance>`, but not for APIP.
   However, the flexibility offered by the balancing style *rcb*, compared to the
   balancing style *shift*, is advantageous for APIP.
 An adaptive-precision EAM-ACE potential, for which the switching parameter
 :math:`\lambda` is calculated from the CSP is defined via
 :doc:`pair_style hybrid/overlay <pair_hybrid>`.
 The fixes ensure that the switching parameter is calculated, the energy conserved,
 the weight for the load balancing calculated and the load-balancing itself is done.
 ----------
 .. _implementing_new_apip_styles:
 Implementing new APIP pair styles
 """""""""""""""""""""""""""""""""
 One can introduce adaptive-precision to an existing pair style by modifying
 the original pair style.
 One should calculate the force
 :math:`F_i = - \nabla_i \sum_j E_j^\text{original}` for a fast potential or
 :math:`F_i = - (1-\nabla_i) \sum_j E_j^\text{original}` for a precise
 potential from the original potential
 energy :math:`E_j^\text{original}` to see where the switching parameter
 :math:`\lambda_i` needs to be introduced in the force calculation.
 The switching parameter :math:`\lambda_i` is known for all atoms :math:`i`
 in force calculation routine.
 One needs to introduce an abortion criterion based on :math:`\lambda_i` to
 ensure that all not required calculations are skipped and compute time can
 be saved.
 Furthermore, one needs to provide the number of calculations and measure the
 computation time.
 Communication within the force calculation needs to be prevented to allow
 effective load-balancing.
 With communication, the load balancer cannot balance few calculations of the
 precise potential on one processor with many computations of the fast
 potential on another processor.
 All changes in the pair_style pace/apip compared to the pair_style pace
 are annotated and commented.
 Thus, the pair_style pace/apip can serve as an example for the implementation
 of new adaptive-precision potentials.
 ----------
 .. _Immel2025_1:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/Packages_details.rst
+++ b/doc/src/Packages_details.rst
@ -28,6 +28,7 @@ gives those details.
   * :ref:`ADIOS <PKG-ADIOS>`
   * :ref:`AMOEBA <PKG-AMOEBA>`
   * :ref:`APIP <PKG-APIP>`
   * :ref:`ASPHERE <PKG-ASPHERE>`
   * :ref:`ATC <PKG-ATC>`
   * :ref:`AWPMD <PKG-AWPMD>`
@ -186,6 +187,58 @@ provided by the Ponder group in their
 ----------
 .. _PKG-APIP:
 APIP package
 ------------
 **Contents:**
 This package provides adaptive-precision interatomic potentials (APIP) as
 described in:
 D. Immel, R. Drautz and G. Sutmann, "Adaptive-precision potentials for
 large-scale atomistic simulations", J. Chem. Phys. 162, 114119 (2025)
 `link <immel2025_doi_>`_
 Adaptive-precision means, that a fast interatomic potential, such as EAM,
 is coupled to a
 precise interatomic potential, such as ACE.
 This package provides the required pair_styles and fixes to run an efficient,
 energy-conserving adaptive-precision simulation.
 .. _immel2025_doi: https://doi.org/10.1063/5.0245877
 **Authors:**
 This package was written by David Immel^1,
 Ralf Drautz^2 and Godehard Sutmann^1^2.
 ^1: Forschungszentrum Juelich, Juelich, Germany
 ^2: Ruhr-University Bochum, Bochum, Germany
 **Install:**
 The APIP package requires also the installation of ML-PACE, which has
 :ref:`specific installation instructions <ml-pace>` on the
 :doc:`Build extras <Build_extras>` page.
 **Supporting info:**
 * ``src/APIP``: filenames -> commands
 * :doc:`Howto APIP <Howto_apip>`
 * ``examples/PACKAGES/apip``
 * :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 * :doc:`fix lambda <fix_lambda>`
 * :doc:`fix lambda_thermostat <fix_lambda_thermostat>`
 * :doc:`pair_style eam/apip <pair_eam_apip>`
 * :doc:`pair_style lambda/zone <pair_lambda_zone>`
 * :doc:`pair_style lambda_input <pair_lambda_input>`
 * :doc:`pair_style pace/apip <pair_pace_apip>`
 ----------
 .. _PKG-ASPHERE:
 ASPHERE package
--- a/doc/src/Packages_list.rst
+++ b/doc/src/Packages_list.rst
@ -38,6 +38,11 @@ whether an extra library is needed to build and use the package:
     - :doc:`AMOEBA and HIPPO howto <Howto_amoeba>`
     - amoeba
     - no
   * - :ref:`APIP <PKG-APIP>`
     - adaptive-precision interatomic potentials
     - :doc:`Howto APIP <Howto_apip>`
     - ``PACKAGES/APIP``
     - ext
   * - :ref:`ASPHERE <PKG-ASPHERE>`
     - aspherical particle models
     - :doc:`Howto spherical <Howto_spherical>`
--- a/doc/src/atom_style.rst
+++ b/doc/src/atom_style.rst
@ -10,7 +10,7 @@ Syntax
   atom_style style args
-* style = *amoeba* or *angle* or *atomic* or *body* or *bond* or *charge* or *dielectric* or *dipole* or  *dpd* or *edpd* or *electron* or *ellipsoid* or *full* or *line* or *mdpd* or *molecular* or *oxdna* or *peri* or *smd* or *sph* or *sphere* or *bpm/sphere* or *spin* or *tdpd* or *tri* or *template* or *wavepacket* or *hybrid*
+* style = *amoeba* or *angle* or *apip* or *atomic* or *body* or *bond* or *charge* or *dielectric* or *dipole* or  *dpd* or *edpd* or *electron* or *ellipsoid* or *full* or *line* or *mdpd* or *molecular* or *oxdna* or *peri* or *smd* or *sph* or *sphere* or *bpm/sphere* or *spin* or *tdpd* or *tri* or *template* or *wavepacket* or *hybrid*
  .. parsed-literal::
@ -117,6 +117,10 @@ the Additional Information section below.
     - *bond* + "angle data"
     - :ref:`MOLECULE <PKG-MOLECULE>`
     - bead-spring polymers with stiffness
   * - *apip*
     - *atomic* + lambda, lambda_required, lambda_input, lambda_const, lambda_input_ta, e_simple, e_complex, f_const_lambda, f_dyn_lambda
     - :ref:`APIP <PKG-APIP>`
     - adaptive-precision interatomic potentials(APIP), see :doc:`APIP howto <Howto_apip>`
   * - *atomic*
     - tag, type, x, v, f, image, mask
     -
--- a/doc/src/fix.rst
+++ b/doc/src/fix.rst
@ -201,6 +201,7 @@ accelerated styles exist.
 * :doc:`append/atoms <fix_append_atoms>` - append atoms to a running simulation
 * :doc:`atc <fix_atc>` - initiates a coupled MD/FE simulation
 * :doc:`atom/swap <fix_atom_swap>` - Monte Carlo atom type swapping
 * :doc:`apip_atom_weight <fix_apip_atom_weight>` - compute atomic load of an :doc:`APIP potential <Howto_apip>` for load balancing
 * :doc:`ave/atom <fix_ave_atom>` - compute per-atom time-averaged quantities
 * :doc:`ave/chunk <fix_ave_chunk>` - compute per-chunk time-averaged quantities
 * :doc:`ave/correlate <fix_ave_correlate>` - compute/output time correlations
@ -268,6 +269,7 @@ accelerated styles exist.
 * :doc:`imd <fix_imd>` - implements the "Interactive MD" (IMD) protocol
 * :doc:`indent <fix_indent>` - impose force due to an indenter
 * :doc:`ipi <fix_ipi>` - enable LAMMPS to run as a client for i-PI path-integral simulations
 * :doc:`lambda <fix_lambda>` - compute switching parameter, that controls the precision of an :doc:`APIP potential <Howto_apip>`
 * :doc:`langevin <fix_langevin>` - Langevin temperature control
 * :doc:`langevin/drude <fix_langevin_drude>` - Langevin temperature control of Drude oscillators
 * :doc:`langevin/eff <fix_langevin_eff>` - Langevin temperature control for the electron force field model
@ -276,6 +278,7 @@ accelerated styles exist.
 * :doc:`lb/momentum <fix_lb_momentum>` - :doc:`fix momentum <fix_momentum>` replacement for use with a lattice-Boltzmann fluid
 * :doc:`lb/viscous <fix_lb_viscous>` - :doc:`fix viscous <fix_viscous>` replacement for use with a lattice-Boltzmann fluid
 * :doc:`lineforce <fix_lineforce>` - constrain atoms to move in a line
 * :doc:`lambda_thermostat <fix_lambda_thermostat>` - apply energy conserving correction for an :doc:`APIP potential <Howto_apip>`
 * :doc:`manifoldforce <fix_manifoldforce>` - restrain atoms to a manifold during minimization
 * :doc:`mdi/qm <fix_mdi_qm>` - LAMMPS operates as a client for a quantum code via the MolSSI Driver Interface (MDI)
 * :doc:`mdi/qmmm <fix_mdi_qmmm>` - LAMMPS operates as client for QM/MM simulation with a quantum code via the MolSSI Driver Interface (MDI)
--- a/doc/src/fix_apip_atom_weight.rst
+++ b/doc/src/fix_apip_atom_weight.rst
@ -0,0 +1,143 @@
 .. index:: fix apip_atom_weight
 fix apip_atom_weight command
 ============================
 Syntax
 """"""
 .. code-block:: LAMMPS
   fix ID group-ID apip_atom_weight nevery fast_potential precise_potential lambda_input lambda group_lambda_input [no_rescale]
 * ID, group-ID are documented in :doc:`fix <fix>` command
 * apip_atom_weight = style name of this fix command
 * nevery = perform load calculation every this many steps
 * fast_potential = *eam* or *ace* for time measurements of the corresponding pair_style or float for constant time
 * precise_potential = *ace* for a time measurement of the pair_style pace/apip or float for constant time
 * lambda_input = *lambda_input* for a time measurement of pair_style lambda_input or float for constant time
 * lambda = *lambda/zone* for a time measurement of pair_style lambda/zone or float for constant time
 * group_lambda_input = group-ID of the group for which lambda_input is computed
 * no_rescale = do not rescale the work per processor to the measured total force-computation time
 Examples
 """"""""
 .. code-block:: LAMMPS
   fix 2 all apip_atom_weight 50 eam ace lambda_input lambda/zone all
   fix 2 all apip_atom_weight 50 1e-05 0.0004 4e-06 4e-06 all
   fix 2 all apip_atom_weight 50 ace ace 4e-06 4e-06 all no_rescale
 Description
 """""""""""
 This command approximates the load every atom causes when an
 adaptive-precision interatomic potential (APIP) according to
 :ref:`(Immel) <Immel2025_2>` is used.
 This approximated load can be saved as atomic variable and
 used as input for the dynamic load balancing via the
 :doc:`fix balance <fix_balance>` command.
 An adaptive-precision potential like :doc:`eam/apip <pair_eam_apip>`
 and :doc:`pace/apip <pair_pace_apip>` is calculated only
 for a subset of atoms.
 The switching parameter that determines per atom, which potential energy is
 used, can be also calculated by
 :doc:`pair_style lambda_input <pair_lambda_input>`.
 A spatial switching zone, that ensures a smooth transition between two
 different interatomic potentials, can be calculated by
 :doc:`pair_style lambda/zone <pair_lambda_zone>`.
 Thus, there are up to four force-subroutines, that are computed only for a
 subset of atoms and combined via the pair_style :doc:`hybrid/overlay <pair_hybrid>`.
 For all four force-subroutines, the average work per atom is be measured
 per processor by the corresponding pair_style.
 This fix extracts these measurements of the pair styles every *nevery*
 steps. The average compute times are used to calculates a per-atom vector with
 the approximated atomic weight, whereas the average compute time of the four
 subroutines contributes only to the load of atoms, for which the corresponding
 subroutine was calculated.
 If not disabled via *no_rescale*, the so calculated load is
 rescaled per processor so that the total atomic compute time matches the
 also measured total compute time of the whole pair_style.
 This atomic weight is intended to be used
 as input for :doc:`fix balance <fix_balance>`:
 .. code-block:: LAMMPS
   variable nevery equal 10
   fix weight_atom all apip_atom_weight ${nevery} eam ace lambda_input lambda/zone all
   variable myweight atom f_weight_atom
   fix balance all balance ${nevery} 1.1 rcb weight var myweight
 Furthermore, this fix provides the over the processors averaged compute time of the
 four pair_styles, which are used to approximate the atomic weight, as vector.
 ----------
 Restart, fix_modify, output, run start/stop, minimize info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 No information about this fix is written to
 :doc:`binary restart files <restart>`.  None of the
 :doc:`fix_modify <fix_modify>` options are relevant to this fix.
 This fix produces a per-atom vector that contains the atomic
 weight of each atom.
 The per-atom vector can only be accessed on timesteps that are multiples
 of *nevery*.
 Furthermore, this fix computes a global vector of length 4 with
 statistical information about the four different (possibly)
 measured compute times per force subroutine. The four
 values in the vector are as follows:
  #. average compute time for one atom using the fast pair_style
  #. average compute time for one atom using the precise pair_style
  #. average compute time of lambda_input for one atom
  #. average compute time of lambda/zone for one atom
 The compute times are computed as average of all processors that
 measured at least one computation of the corresponding style.
 The vector values calculated by this fix are "intensive" and
 updated whenever the per-atom vector is computed, i.e., in
 timesteps that are multiples of *nevery*.
 The vector and the per-atom vector can be accessed by various
 :doc:`output commands <Howto_output>`.
 No parameter of this fix can be used with the *start/stop* keywords of
 the :doc:`run <run>` command.  This fix is not invoked during
 :doc:`energy minimization <minimize>`.
 ----------
 Restrictions
 """"""""""""
 This fix is part of the APIP package. It is only enabled if
 LAMMPS was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`fix balance <fix_balance>`,
 :doc:`fix lambda <fix_lambda>`,
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`pair_style pace/apip  <pair_pace_apip>`,
 Default
 """""""
 *no_rescale* is not used by default.
 ----------
 .. _Immel2025_2:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/fix_lambda.rst
+++ b/doc/src/fix_lambda.rst
@ -0,0 +1,262 @@
 .. index:: fix lambda
 fix lambda command
 ==============================
 Syntax
 """"""
 .. code-block:: LAMMPS
   fix ID group-ID lambda thr_lo thr_hi keyword args ...
 * ID, group-ID are documented in :doc:`fix <fix>` command
 * lambda = style name of this fix command
 * thr_lo = value below which :math:`\lambda_i^\text{input}` results in a switching parameter of 1
 * thr_hi = value above which :math:`\lambda_i^\text{input}` results in a switching parameter of 0
 * zero or one keyword/args pairs may be appended
 * keyword = *time_averaged_zone* or *min_delta_lambda* or *lambda_non_group* or *store_atomic_stats* or *dump_atomic_history* or *group_fast* or *group_precise* or *group_ignore_lambda_input*
  .. parsed-literal::
       *time_averaged_zone* args = cut_lo cut_hi history_len_lambda_input history_len_lambda
         cut_lo = distance at which the radial function decreases from 1
         cut_hi = distance from which on the radial function is 0
         history_len_lambda_input = number of time steps for which lambda_input is averaged
         history_len_lambda = number of time steps for which the switching parameter is averaged
       *min_delta_lambda* args = delta
         delta = value below which changes of the switching parameter are neglegted (>= 0)
       *lambda_non_group* args = lambda_ng
         lambda_ng = *precise* or *fast* or float
           *precise* = assign a constant switching parameter of 0 to atoms, that are not in the group specified by group-ID
           *fast* = assign a constant switching parameter of 1 to atoms, that are not in the group specified by group-ID
           float = assign this constant switching parameter to atoms, that are not in the group specified by group-ID (0 <= float <= 1)
       *group_fast* args = group-ID-fast
         group-ID-fast = the switching parameter of 1 is used instead of the one computed by lambda_input for atoms in the group specified by group-ID-fast
       *group_precise* args = group-ID-precise
         group-ID-precise = the switching parameter of 0 is used instead of the one computed by lambda_input for atoms in the group specified by group-ID-precise
       *group_ignore_lambda_input* args = group-ID-ignore-lambda-input
         group-ID-ignore-lambda-input = the switching parameter of lambda_ng is used instead of the one computed by lambda_input for atoms in the group specified by group-ID-ignore-lambda-input
       *store_atomic_stats* args = none
       *dump_atomic_history* args = none
 Examples
 """"""""
 .. code-block:: LAMMPS
   fix 2 all lambda 3.0 3.5 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01
   fix 2 mobile lambda 3.0 3.5 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01 group_ignore_lambda_input immobile lambda_non_group fast
 Description
 """""""""""
 The potential energy :math:`E_i` of an atom :math:`i` of an adaptive-precision
 potential according to :ref:`(Immel) <Immel2025_3>` is given by
 .. math::
   E_i = \lambda_i E_i^\text{(fast)} + (1-\lambda_i) E_i^\text{(precise)},
 whereas :math:`E_i^\text{(fast)}` is the potential energy of atom :math:`i`
 according to a fast interatomic potential like EAM,
 :math:`E_i^\text{(precise)}` is the potential energy according to a precise
 interatomic potential such as ACE and :math:`\lambda_i\in[0,1]` is the
 switching parameter that decides which potential energy is used.
 This fix calculates the switching parameter :math:`\lambda_i` based on the
 input provided from :doc:`pair_style lambda_input <pair_lambda_input>`.
 The calculation of the switching parameter is described in detail in
 :ref:`(Immel) <Immel2025_3>`.
 This fix calculates the switching parameter for all atoms in the
 :doc:`group <group>`
 described by group-ID, while the value of *lambda_non_group* is used
 as switching parameter for all other atoms.
 First, this fix calculates per atom :math:`i` the time averaged input
 :math:`\lambda^\text{input}_{\text{avg},i}` from
 :math:`\lambda^\text{input}_{i}`, whereas the number of averaged timesteps
 can be set via *time_averaged_zone*.
 .. note::
   :math:`\lambda^\text{input}_{i}` is calculated by
   :doc:`pair_style lambda_input <pair_lambda_input>`, which needs to be included
   in the input script as well.
 The time averaged input :math:`\lambda^\text{input}_{\text{avg},i}` is then
 used to calculate the switching parameter
 .. math::
   \lambda_{0,i}(t) = f^\text{(cut)} \left(\frac{\lambda_{\text{avg},i}^\text{input}(t) - \lambda_\text{lo}^\text{input}}{\lambda_\text{hi}^\text{input} - \lambda_\text{lo}^\text{input}} \right)\,,
 whereas the thresholds :math:`\lambda_\text{hi}^\text{input}`
 and  :math:`\lambda_\text{lo}^\text{input}` are set by the
 values provided as *thr_lo* and *thr_hi* and :math:`f^\text{(cut)}(x)` is a cutoff function
 that is 1 for :math:`x\leq 0`, decays from 1 to 0 for :math:`x\in[0,1]`, and
 is 0 for :math:`x\geq 1`.
 If the *group_precise* argument is used, :math:`\lambda_{0,i}=0` is used for all
 atoms :math:`i` assigned to the corresponding :doc:`group <group>`.
 If the *group_fast* argument is used, :math:`\lambda_{0,i}=1` is used for all
 atoms :math:`i` assigned to the corresponding :doc:`group <group>`.
 If an atom is in the groups *group_fast* and *group_precise*,
 :math:`\lambda_{0,i}=0` is used.
 If the *group_ignore_lambda_input* argument is used,
 :math:`\lambda_i^\text{input}` is not computed for all atoms :math:`i` assigned
 to the corresponding :doc:`group <group>`; instead, if the value is not already
 set by *group_fast* or *group_precise*, the value of *lambda_non_group* is
 used.
 .. note::
   The computation of :math:`\lambda_i^\text{input}` is not required for
   atoms that are in the groups *group_fast* and *group_precise*.
   Thus, one should use *group_ignore_lambda_input* and prevent the
   computation of :math:`\lambda_i^\text{input}` for all atoms, for
   which a constant input is used.
 A spatial transition zone between the fast and the precise potential is
 introduced via
 .. math::
   \lambda_{\text{min},i}(t) = \text{min}\left(\left\{1 - (1 -\lambda_{0,j}(t)) f^\text{(cut)}\left(\frac{r_{ij}(t)-r_{\lambda,\text{lo}}}{r_{\lambda,\text{hi}} - r_{\lambda,\text{lo}}}\right) : j \in \Omega_{\lambda,i} \right\}\right)\,,
 whereas the thresholds :math:`r_{\lambda,\text{lo}}` and
 :math:`r_{\lambda,\text{hi}}`
 of the cutoff function are set via *time_averaged_zone* and
 :math:`\Omega_{\lambda,i}` is the set of
 neighboring atoms of atom :math:`i`.
 .. note::
   :math:`\lambda_{\text{min},i}` is calculated by
   :doc:`pair_style lambda/zone <pair_lambda_zone>`, which needs to be included
   in the input script as well.
 The switching parameter is smoothed by the calculation of the time average
 .. math::
   \lambda_{\text{avg},i}(t) = \frac{1}{N_{\lambda,\text{avg}}} \sum_{n=1}^{N_{\lambda,\text{avg}}} \lambda_{\text{min},i}(t - n \Delta t)\,,
 whereas :math:`\Delta t` is the :doc:`timestep <timestep>` and
 :math:`N_{\lambda,\text{avg}}` is the number of averaged timesteps, that
 can be set via *time_averaged_zone*.
 Finally, numerical fluctuations of the switching parameter are suppressed by the usage of
 .. math::
   \lambda_{i}(t) = \left\{
   \begin{array}{ll}
   \lambda_{\text{avg},i}(t) & \text{ for } \left|\lambda_{\text{avg},i}(t) - \lambda_{i}(t-\Delta t)\right|\geq \Delta\lambda_\text{min} \text{ or } \lambda_{\text{avg},i}(t)\in\{0,1\}, \\
   \lambda_{i}(t-\Delta t) & \text{ otherwise}\,,
   \end{array}
   \right.
 whereas the minimum change :math:`\Delta\lambda_\text{min}` is set by the
 *min_delta_lambda* argument.
 .. note::
   *group_fast* affects only :math:`\lambda_{0,i}(t)`. The switching parameter
   of atoms in this :doc:`group <group>` may change due to the calculation of the
   spatial switching zone.
   A switching parameter of 1 can be enforced by excluding the corresponding
   atoms from the :doc:`group <group>` described by group-ID and using *lambda_non_group* 1
   as argument.
 ----------
 A code example for the calculation of the switching parameter for an
 adaptive-precision potential is given in the following:
 The adaptive-precision potential is created
 by combining :doc:`pair_style eam/fs/apip <pair_eam_apip>`
 and :doc:`pair_style pace/apip/precise <pair_pace_apip>`.
 The input, from which the switching parameter is calculated, is provided
 by :doc:`pair lambda_input/csp <pair_lambda_input>`.
 The switching parameter is calculated by this fix, whereas the spatial
 transition zone of the switching parameter is calculated by
 :doc:`pair_style lambda/zone <pair_lambda_zone>`.
 .. code-block:: LAMMPS
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda
   fix 2 all lambda 3.0 3.5 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01
 ----------
 Restart, fix_modify, output, run start/stop, minimize info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 The saved history of the switching parameter :math:`\lambda_i`
 and the saved history of
 :math:`\lambda_i^\text{input}` are written to
 :doc:`binary restart files <restart>` allow a smooth restart of a simulation.
 None of the :doc:`fix_modify <fix_modify>` options are relevant to this fix.
 If the *store_atomic_stats* argument is used, basic statistics is provided as
 per-atom array:
  #. :math:`\lambda_i^\text{input}(t)`
  #. :math:`\lambda_{\text{avg},i}^\text{input}(t)`
  #. :math:`\lambda_{0,i}(t)`
  #. :math:`\lambda_{\text{min},i}(t)`
  #. :math:`\lambda_{i}(t)`
 If the *dump_atomic_history* argument is used, the whole saved history
 of :math:`\lambda_i^\text{input}(t)` is appended to the previously
 mentioned array per atom.
 The per-atom vector can be accessed by various
 :doc:`output commands <Howto_output>`.
 No parameter of this fix can be used with the *start/stop* keywords of
 the :doc:`run <run>` command.  This fix is not invoked during
 :doc:`energy minimization <minimize>`.
 ----------
 Restrictions
 """"""""""""
 This fix is part of the APIP package. It is only enabled if
 LAMMPS was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`pair_style pace/apip  <pair_pace_apip>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 Default
 """""""
 *min_delta_lambda* = 0,
 *lambda_non_group* = 1,
 *cut_lo* = 4.0,
 *cut_hi* = 12.0,
 *history_len_lambda_input* = 100,
 *history_len_lambda* = 100,
 *store_atomic_stats* is not used,
 *dump_atomic_history* is not used,
 *group_fast* is not used,
 *group_precise* is not used,
 *group_ignore_lambda_input* is not used
 ----------
 .. _Immel2025_3:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/fix_lambda_thermostat.rst
+++ b/doc/src/fix_lambda_thermostat.rst
@ -0,0 +1,176 @@
 .. index:: fix lambda_thermostat
 fix lambda_thermostat command
 =============================
 Syntax
 """"""
 .. code-block:: LAMMPS
   fix ID group-ID lambda_thermostat keyword values ...
 * ID, group-ID are documented in :doc:`fix <fix>` command
 * lambda_thermostat = style name of this fix command
 * zero or more keyword/value pairs may be appended
 * keyword = *seed* or *store_atomic_forces* or *N_rescaling*
  .. parsed-literal::
       *seed* value = integer
         integer = integer that is used as seed for the random number generator (> 0)
       *store_atomic_forces* value = nevery
         nevery = provide per-atom output every this many steps
       *N_rescaling* value = groupsize
         groupsize = rescale this many neighboring atoms (> 1)
 Examples
 """"""""
 .. code-block:: LAMMPS
   fix 2 all lambda_thermostat
   fix 2 all lambda_thermostat N_rescaling 100
   fix 2 all lambda_thermostat seed 42
   fix 2 all lambda_thermostat seed 42 store_atomic_forces 1000
 Description
 """""""""""
 This command applies the local thermostat described in
 :ref:`(Immel) <Immel2025_4>`
 to conserve the energy when the switching parameters of an
 :doc:`adaptive-precision interatomic potential <Howto_apip>` (APIP)
 are updated while the gradient
 of the switching parameter is neglected in the force calculation.
 .. warning::
   The temperature change caused by this fix is only the means to the end of
   conserving the energy. Thus, this fix is not a classical thermostat, that
   ensures a given temperature in the system.
   All available thermostats are listed :doc:`here <Howto_thermostat>`.
 The potential energy :math:`E_i` of an atom :math:`i` is given by the formula from
 :ref:`(Immel) <Immel2025_4>`
 .. math::
   E_i = \lambda_i E_i^\text{(fast)} + (1-\lambda_i) E_i^\text{(precise)},
 whereas :math:`E_i^\text{(fast)}` is the potential energy of atom :math:`i`
 according to a fast interatomic potential like EAM,
 :math:`E_i^\text{(precise)}` is the potential energy according to a precise
 interatomic potential such as ACE and :math:`\lambda_i\in[0,1]` is the
 switching parameter that decides which potential energy is used.
 This potential energy and the corresponding forces are conservative when
 the switching parameter :math:`\lambda_i` is constant in time for all atoms
 :math:`i`.
 For a conservative force calculation and dynamic switching parameters,
 the atomic force on an atom is given by
 :math:`F_i = -\nabla_i \sum_j E_j` and includes the derivative of the switching
 parameter :math:`\lambda_i`.
 The force contribution of this gradient of the switching function can cause
 large forces which are not similar to the forces of the fast or the precise
 interatomic potential as discussed in :ref:`(Immel) <Immel2025_4>`.
 Thus, one can neglect the gradient of the switching parameter in the force
 calculation and compensate for the violation of energy conservation by
 the application of the local thermostat implemented in this fix.
 One can compute the violation of the energy conservation :math:`\Delta H_i`
 for all atoms :math:`i` as discussed in :ref:`(Immel) <Immel2025_4>`.
 To locally correct this energy violation :math:`\Delta H_i`, one
 can rescale the velocity of atom :math:`i`  and of neighboring atoms.
 The rescaling is done relative to the center-of-mass velocity of the
 group and, thus, conserves the momentum.
 .. note::
   This local thermostat provides the NVE ensemble rather than the NVT
   ensemble as
   the energy :math:`\Delta H_i` determines the rescaling factor rather than
   a temperature.
 Velocities :math:`v` are updated by the integrator according to
 :math:`\Delta v_i = (F_i/m_i)\Delta t`, whereas `m` denotes the mass of atom
 :math:`i` and :math:`\Delta t` is the time step.
 One can interpret the velocity difference :math:`\Delta v` caused by the
 rescaling as the application of an additional force which is given by
 :math:`F^\text{lt}_i = (v^\text{unscaled}_i - v^\text{rescaled}_i) m_i
 / \Delta t` :ref:`(Immel) <Immel2025_4>`.
 This additional force is computed when the *store_atomic_forces* option
 is used.
 The local thermostat is not appropriate for simulations at a temperature of 0K.
 .. note::
   The maximum decrease of the kinetic energy is achieved with a rescaling
   factor of 0, i.e., the relative velocity of the group of rescaled atoms
   is set to zero. One cannot decrease the energy further. Thus, the
   local thermostat can fail, which is, however, reported by the returned
   vector.
 ----------
 Restart, fix_modify, output, run start/stop, minimize info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 No information about this fix is written to
 :doc:`binary restart files <restart>`.  None of the
 :doc:`fix_modify <fix_modify>` options are relevant to this fix.
 If the *store_atomic_forces* option is used, this fix produces every
 *nevery* time steps a per-atom array that contains the theoretical force
 applied by the local thermostat in all three spatial dimensions in the first
 three components. :math:`\Delta H_i` is the fourth component of the per-atom
 array.
 The per-atom array can only be accessed on timesteps that are multiples
 of *nevery*.
 Furthermore, this fix computes a global vector of length 6 with
 information about the rescaling:
  #. number of atoms whose energy changed due to the last :math:`\lambda` update
  #. contribution of the potential energy to the last computed :math:`\Delta H`
  #. contribution of the kinetic energy to the last computed :math:`\Delta H`
  #. sum over all atoms of the absolute energy change caused by the last rescaling step
  #. energy change that could not be compensated accumulated over all timesteps
  #. number of atoms whose energy change could not be compensated accumulated over all timesteps
 The vector and the per-atom vector can be accessed by various
 :doc:`output commands <Howto_output>`.
 No parameter of this fix can be used with the *start/stop* keywords of
 the :doc:`run <run>` command.  This fix is not invoked during
 :doc:`energy minimization <minimize>`.
 ----------
 Restrictions
 """"""""""""
 This fix is part of the APIP package. It is only enabled if
 LAMMPS was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`fix lambda <fix_lambda>`,
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`pair_style pace/apip  <pair_pace_apip>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 Default
 """""""
 seed = 42, N_rescaling = 200, *store_atomic_forces* is not used
 ----------
 .. _Immel2025_4:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/pair_eam_apip.rst
+++ b/doc/src/pair_eam_apip.rst
@ -0,0 +1,126 @@
 .. index:: pair_style eam/apip
 .. index:: pair_style eam/fs/apip
 pair_style eam/apip command
 =============================
 Constant precision variant: *eam*
 pair_style eam/fs/apip command
 ================================
 Constant precision variant: *eam/fs*
 Syntax
 """"""
 .. code-block:: LAMMPS
   pair_style eam/apip
   pair_style eam/fs/apip
 Examples
 """"""""
 .. code-block:: LAMMPS
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda
 Description
 """""""""""
 Style *eam* computes pairwise interactions for metals and metal alloys
 using embedded-atom method (EAM) potentials :ref:`(Daw) <Daw2>`.  The total
 energy :math:`E_i` of an atom :math:`i` is given by
 .. math::
   E_i^\text{EAM} = F_\alpha \left(\sum_{j \neq i}\ \rho_\beta (r_{ij})\right) +
         \frac{1}{2} \sum_{j \neq i} \phi_{\alpha\beta} (r_{ij})
 where :math:`F` is the embedding energy which is a function of the atomic
 electron density :math:`\rho`, :math:`\phi` is a pair potential interaction,
 and :math:`\alpha` and :math:`\beta` are the element types of atoms
 :math:`i` and :math:`j`.  The multi-body nature of the EAM potential is a
 result of the embedding energy term. Both summations in the formula are over
 all neighbors :math:`j` of atom :math:`i` within the cutoff distance.
 EAM is documented in detail in :doc:`pair_style eam <pair_eam>`.
 The potential energy :math:`E_i` of an atom :math:`i` of an adaptive-precision
 interatomic potential (APIP) according to :ref:`(Immel) <Immel2025_5>` is given by
 .. math::
   E_i^\text{APIP} = \lambda_i E_i^\text{(fast)} + (1-\lambda_i) E_i^\text{(precise)}\,,
 whereas the switching parameter :math:`\lambda_i` is computed by
 :doc:`fix lambda <fix_lambda>`.
 The pair style *eam/fs/apip* computes the potential energy
 :math:`\lambda_i E_i^\text{EAM}` and the
 corresponding force and should be combined
 with a precise potential like
 :doc:`pair_style pace/apip/precise <pair_pace_apip>` that computes the
 potential energy :math:`(1-\lambda_i) E_i^\text{(precise)}` and the
 corresponding force via :doc:`pair_style hybrid/overlay <pair_hybrid>`.
 Mixing, shift, table, tail correction, restart, rRESPA info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 For atom type pairs I,J and I != J, where types I and J correspond to
 two different element types, mixing is performed by LAMMPS as
 described above with the individual styles.  You never need to specify
 a pair_coeff command with I != J arguments for the eam/apip styles.
 This pair style does not support the :doc:`pair_modify <pair_modify>`
 shift, table, and tail options.
 The eam/apip pair styles do not write their information to :doc:`binary
 restart files <restart>`, since it is stored in tabulated potential
 files.  Thus, you need to re-specify the pair_style and pair_coeff
 commands in an input script that reads a restart file.
 The eam/apip pair styles can only be used via the *pair* keyword of the
 :doc:`run_style respa <run_style>` command.  They do not support the
 *inner*, *middle*, *outer* keywords.
 ----------
 Restrictions
 """"""""""""
 This pair styles are part of the APIP package.  It is only enabled if
 LAMMPS was built with that package.  See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`pair_style eam  <pair_eam>`,
 :doc:`pair_style hybrid/overlay <pair_hybrid>`,
 :doc:`fix lambda <fix_lambda>`,
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style pace/apip <pair_pace_apip>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 Default
 """""""
 none
 ----------
 .. _Immel2025_5:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
 .. _Daw2:
 **(Daw)** Daw, Baskes, Phys Rev Lett, 50, 1285 (1983).
 Daw, Baskes, Phys Rev B, 29, 6443 (1984).
--- a/doc/src/pair_lambda_input.rst
+++ b/doc/src/pair_lambda_input.rst
@ -0,0 +1,151 @@
 .. index:: pair_style lambda_input
 .. index:: pair_style lambda_input/csp
 pair_style lambda_input command
 ===============================
 Syntax
 """"""
 .. code-block:: LAMMPS
   pair_style lambda_input cutoff
 * lambda_input = style name of this pair style
 * cutoff = global cutoff (distance units)
 pair_style lambda_input/csp command
 ===================================
 Syntax
 """"""
 .. code-block:: LAMMPS
   pair_style lambda_input/csp lattice keyword args
 * lambda_input/csp = style name of this pair style
 * lattice = *fcc* or *bcc* or integer
  .. parsed-literal::
       *fcc* = use 12 nearest neighbors to calculate the CSP like in a perfect fcc lattice
       *bcc* = use 8 nearest neighbors to calculate the CSP like in a perfect bcc lattice
       integer = use N nearest neighbors to calculate the CSP
 * zero or more keyword/args pairs may be appended
 * keyword = *cutoff* or *N_buffer*
  .. parsed-literal::
       *cutoff* args = cutoff
         cutoff = distance in which neighbouring atoms are considered (> 0)
       *N_buffer* args = N_buffer
         N_buffer = numer of additional neighbours, which are included in the j-j+N/2 calculation
 Examples
 """"""""
 .. code-block:: LAMMPS
   pair_style lambda_input/csp fcc
   pair_style lambda_input/csp fcc cutoff 5.0
   pair_style lambda_input/csp bcc cutoff 5.0 N_buffer 2
   pair_style lambda_input/csp 14
 Description
 """""""""""
 This pair_styles calculates :math:`\lambda_i^\text{input}(t)`, which
 is required for :doc:`fix lambda <fix_lambda>`.
 The pair_style lambda_input sets :math:`\lambda_i^\text{input}(t) = 0`.
 The pair_style lambda_input/csp calculates
 :math:`\lambda_i^\text{input}(t) = \text{CSP}_i(t)`.
 The centro-symmetry parameter (CSP) :ref:`(Kelchner) <Kelchner_2>` is described
 in :doc:`compute centro/atom <compute_centro_atom>`.
 The lattice argument is described in
 :doc:`compute centro/atom <compute_centro_atom>` and determines
 the number of neighboring atoms that are used to compute the CSP.
 The *N_buffer* argument allows to include more neighboring atoms in
 the calculation of the contributions from the pair j,j+N/2 to the CSP as
 discussed in :ref:`(Immel) <Immel2025_6>`.
 The computation of :math:`\lambda_i^\text{input}(t)` is done by this
 pair_style instead of by :doc:`fix lambda <fix_lambda>`, as this computation
 takes time and this pair_style can be included in the load-balancing via
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`.
 A code example for the calculation of the switching parameter for an adaptive-
 precision potential is given in the following:
 The adaptive-precision potential is created
 by combining :doc:`pair_style eam/fs/apip <pair_eam_apip>`
 and :doc:`pair_style pace/apip/precise <pair_pace_apip>`.
 The input, from which the switching parameter is calculated, is provided
 by this pair_style.
 The switching parameter is calculated by :doc:`fix lambda <fix_lambda>`,
 whereas the spatial
 transition zone of the switching parameter is calculated by
 :doc:`pair_style lambda/zone <pair_lambda_zone>`.
 .. code-block:: LAMMPS
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda
   fix 2 all lambda 3.0 3.5 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01
 ----------
 Mixing, shift, table, tail correction, restart, rRESPA info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 The cutoff distance for this pair style can be mixed.  The default mix
 value is *geometric*\ .  See the "pair_modify" command for details.
 This pair style does not support the :doc:`pair_modify <pair_modify>`
 shift, table, and tail options.
 This pair style writes no information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands need
 to be specified in an input script that reads a restart file.
 This pair style does not support the use of the *inner*, *middle*,
 and *outer* keywords of the :doc:`run_style respa <run_style>` command.
 ----------
 Restrictions
 """"""""""""
 This fix is part of the APIP package. It is only enabled if
 LAMMPS was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`compute centro/atom <compute_centro_atom>`,
 :doc:`fix lambda <fix_lambda>`,
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`pair_style pace/apip  <pair_pace_apip>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 Default
 """""""
 N_buffer=0, cutoff=5.0
 ----------
 .. _Kelchner_2:
 **(Kelchner)** Kelchner, Plimpton, Hamilton, Phys Rev B, 58, 11085 (1998).
 .. _Immel2025_6:
 **(Immel)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/pair_lambda_zone.rst
+++ b/doc/src/pair_lambda_zone.rst
@ -0,0 +1,106 @@
 .. index:: pair_style lambda/zone
 pair_style lambda/zone command
 ==============================
 Syntax
 """"""
 .. code-block:: LAMMPS
   pair_style lambda/zone cutoff
 * lambda/zone = style name of this pair style
 * cutoff = global cutoff (distance units)
 Examples
 """"""""
 .. code-block:: LAMMPS
   pair_style lambda/zone 12.0
 Description
 """""""""""
 This pair_style calculates :math:`\lambda_{\text{min},i}`, which
 is required for :doc:`fix lambda <fix_lambda>`.
 The meaning of :math:`\lambda_{\text{min},i}` is documented in
 :doc:`fix lambda <fix_lambda>`, as this pair_style is for use with
 :doc:`fix lambda <fix_lambda>` only.
 This pair_style requires only the global cutoff as argument.
 The remaining quantities, that are required to calculate
 :math:`\lambda_{\text{min},i}` are extracted from
 :doc:`fix lambda <fix_lambda>` and, thus,
 do not need to be passed to this pair_style as arguments.
 .. warning::
   The cutoff given as argument to this pair style is only relevant for the
   neighbor list creation. The radii, which define :math:`r_{\lambda,\text{hi}}` and :math:`r_{\lambda,\text{lo}}` are defined by :doc:`fix lambda <fix_lambda>`.
 The computation of :math:`\lambda_{\text{min},i}` is done by this
 pair_style instead of by :doc:`fix lambda <fix_lambda>`, as this computation
 takes time and this pair_style can be included in the load-balancing via
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`.
 A code example for the calculation of the switching parameter for an
 adaptive-precision interatomic potential (APIP) is given in the following:
 The adaptive-precision potential is created
 by combining :doc:`pair_style eam/fs/apip <pair_eam_apip>`
 and :doc:`pair_style pace/apip/precise <pair_pace_apip>`.
 The input, from which the switching parameter is calculated, is provided
 by :doc:`pair lambda_input/csp <pair_lambda_input>`.
 The switching parameter is calculated by :doc:`fix lambda <fix_lambda>`,
 whereas the spatial transition zone of the switching parameter is calculated
 by this pair style.
 .. code-block:: LAMMPS
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda/zone 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda/zone
   fix 2 all lambda 3.0 3.5 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda 0.01
 ----------
 Mixing, shift, table, tail correction, restart, rRESPA info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 The cutoff distance for this pair style can be mixed.  The default mix
 value is *geometric*\ .  See the "pair_modify" command for details.
 This pair style does not support the :doc:`pair_modify <pair_modify>`
 shift, table, and tail options.
 This pair style writes no information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands need
 to be specified in an input script that reads a restart file.
 This pair style does not support the use of the *inner*, *middle*,
 and *outer* keywords of the :doc:`run_style respa <run_style>` command.
 ----------
 Restrictions
 """"""""""""
 This fix is part of the APIP package. It is only enabled if
 LAMMPS was built with that package. See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`fix lambda <fix_lambda>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`pair_style pace/apip  <pair_pace_apip>`,
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 Default
 """""""
 none
--- a/doc/src/pair_pace_apip.rst
+++ b/doc/src/pair_pace_apip.rst
@ -0,0 +1,146 @@
 .. index:: pair_style pace/apip
 .. index:: pair_style pace/apip/fast
 .. index:: pair_style pace/apip/precise
 pair_style pace/apip command
 ==============================
 pair_style pace/apip/fast command
 ===================================
 pair_style pace/apip/precise command
 ======================================
 Constant precision variant: *pace*
 Syntax
 """"""
 .. code-block:: LAMMPS
   pair_style pace/apip ... keyword values ...
   pair_style pace/apip/fast ... keyword values ...
   pair_style pace/apip/precise ... keyword values ...
 * one or more keyword/value pairs may be appended
  .. parsed-literal::
     keyword = keywords of :doc:`pair pace <pair_pace>`
 Examples
 """"""""
 .. code-block:: LAMMPS
   pair_style hybrid/overlay pace/apip/fast pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda 12.0
   pair_coeff * * pace/apip/fast Cu_fast.yace Cu
   pair_coeff * * pace/apip/precise Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda
   pair_style hybrid/overlay eam/fs/apip pace/apip/precise lambda_input/csp fcc cutoff 5.0 lambda 12.0
   pair_coeff * * eam/fs/apip Cu.eam.fs Cu
   pair_coeff * * pace/apip Cu_precise.yace Cu
   pair_coeff * * lambda_input/csp
   pair_coeff * * lambda
 Description
 """""""""""
 Pair style :doc:`pace <pair_pace>` computes interactions using the Atomic
 Cluster Expansion (ACE), which is a general expansion of the atomic energy in
 multi-body basis functions :ref:`(Drautz19) <Drautz2019_2>`.  The *pace*
 pair style provides an efficient implementation that is described in
 this paper :ref:`(Lysogorskiy21) <Lysogorskiy20211_2>`.
 The potential energy :math:`E_i` of an atom :math:`i` of an adaptive-precision
 interatomic potential (APIP) according to
 :ref:`(Immel25) <Immel2025_7>` is given by
 .. math::
   E_i^\text{APIP} = \lambda_i E_i^\text{(fast)} + (1-\lambda_i) E_i^\text{(precise)}\,,
 whereas the switching parameter :math:`\lambda_i` is computed by
 :doc:`fix lambda <fix_lambda>`.
 The pair style *pace/apip/precise* computes the potential energy
 :math:`(1-\lambda_i) E_i^\text{(pace)}` and the
 corresponding force and should be combined
 with a fast potential that computes the potential energy
 :math:`\lambda_i E_i^\text{(fast)}` and the corresponding force
 via :doc:`pair_style hybrid/overlay <pair_hybrid>`.
 The pair style *pace/apip/fast* computes the potential energy
 :math:`\lambda_i E_i^\text{(pace)}` and the
 corresponding force and should be combined
 with a precise potential that computes the potential energy
 :math:`(1-\lambda_i) E_i^\text{(precise)}` and the corresponding force
 via :doc:`pair_style hybrid/overlay <pair_hybrid>`.
 The pair_styles *pace/apip/fast* and *pace/apip/precise*
 commands may be followed by the optional keywords of
 :doc:`pair_style pace <pair_pace>`, which are described
 :doc:`here <pair_pace>`.
 Mixing, shift, table, tail correction, restart, rRESPA info
 """""""""""""""""""""""""""""""""""""""""""""""""""""""""""
 For atom type pairs I,J and I != J, where types I and J correspond to
 two different element types, mixing is performed by LAMMPS with
 user-specifiable parameters as described above.  You never need to
 specify a pair_coeff command with I != J arguments for this style.
 This pair styles does not support the :doc:`pair_modify <pair_modify>`
 shift, table, and tail options.
 This pair styles does not write its information to :doc:`binary restart
 files <restart>`, since it is stored in potential files.  Thus, you need
 to re-specify the pair_style and pair_coeff commands in an input script
 that reads a restart file.
 This pair styles can only be used via the *pair* keyword of the
 :doc:`run_style respa <run_style>` command.  It does not support the
 *inner*, *middle*, *outer* keywords.
 ----------
 Restrictions
 """"""""""""
 This pair styles are part of the APIP package.  It is only enabled if
 LAMMPS was built with that package.  See the :doc:`Build package
 <Build_package>` page for more info.
 Related commands
 """"""""""""""""
 :doc:`pair_style pace  <pair_pace>`,
 :doc:`pair_style hybrid/overlay <pair_hybrid>`,
 :doc:`fix lambda <fix_lambda>`,
 :doc:`fix lambda_thermostat <fix_lambda_thermostat>`,
 :doc:`pair_style lambda/zone <pair_lambda_zone>`,
 :doc:`pair_style lambda_input  <pair_lambda_input>`,
 :doc:`pair_style eam/apip <pair_eam_apip>`,
 :doc:`fix apip_atom_weight <fix_apip_atom_weight>`
 Default
 """""""
 See :doc:`pair_style pace <pair_pace>`.
 ----------
 .. _Drautz2019_2:
 **(Drautz19)** Drautz, Phys Rev B, 99, 014104 (2019).
 .. _Lysogorskiy20211_2:
 **(Lysogorskiy21)** Lysogorskiy, van der Oord, Bochkarev, Menon, Rinaldi, Hammerschmidt, Mrovec, Thompson, Csanyi, Ortner, Drautz, npj Comp Mat, 7, 97 (2021).
 .. _Immel2025_7:
 **(Immel25)** Immel, Drautz and Sutmann, J Chem Phys, 162, 114119 (2025)
--- a/doc/src/pair_style.rst
+++ b/doc/src/pair_style.rst
@ -188,7 +188,9 @@ accelerated styles exist.
 * :doc:`eam/cd <pair_eam>` - concentration-dependent EAM
 * :doc:`eam/cd/old <pair_eam>` - older two-site model for concentration-dependent EAM
 * :doc:`eam/fs <pair_eam>` - Finnis-Sinclair EAM
 * :doc:`eam/fs/apip <pair_eam_apip>` - :doc:`adaptive precision <Howto_apip>` version of FS EAM, used as fast potential
 * :doc:`eam/he <pair_eam>` - Finnis-Sinclair EAM modified for Helium in metals
 * :doc:`eam/apip <pair_eam_apip>` - :doc:`adaptive-precision <Howto_apip>` version of EAM, used as fast potential
 * :doc:`edip <pair_edip>` - three-body EDIP potential
 * :doc:`edip/multi <pair_edip>` - multi-element EDIP potential
 * :doc:`edpd <pair_mesodpd>` - eDPD particle interactions
@ -217,6 +219,9 @@ accelerated styles exist.
 * :doc:`kim <pair_kim>` - interface to potentials provided by KIM project
 * :doc:`kolmogorov/crespi/full <pair_kolmogorov_crespi_full>` - Kolmogorov-Crespi (KC) potential with no simplifications
 * :doc:`kolmogorov/crespi/z <pair_kolmogorov_crespi_z>` - Kolmogorov-Crespi (KC) potential with normals along z-axis
 * :doc:`lambda/zone <pair_lambda_zone>` - transition zone of an :doc:`adaptive-precision interatomic potential <Howto_apip>`
 * :doc:`lambda_input <pair_lambda_input>` - constant as input for the precision calculation of an :doc:`adaptive-precision interatomic potential (APIP) <Howto_apip>`
 * :doc:`lambda_input/csp <pair_lambda_input>` - CSP as input for the precision calculation of an :doc:`adaptive-precision interatomic potential (APIP) <Howto_apip>`
 * :doc:`lcbop <pair_lcbop>` - long-range bond-order potential (LCBOP)
 * :doc:`lebedeva/z <pair_lebedeva_z>` - Lebedeva interlayer potential for graphene with normals along z-axis
 * :doc:`lennard/mdf <pair_mdf>` - LJ potential in A/B form with a taper function
@ -329,6 +334,9 @@ accelerated styles exist.
 * :doc:`oxrna2/xstk <pair_oxrna2>` -
 * :doc:`pace <pair_pace>` - Atomic Cluster Expansion (ACE) machine-learning potential
 * :doc:`pace/extrapolation <pair_pace>` - Atomic Cluster Expansion (ACE) machine-learning potential with extrapolation grades
 * :doc:`pace/apip <pair_pace_apip>` - :doc:`adaptive-precision <Howto_apip>` version of ACE, used as precise potential
 * :doc:`pace/apip/fast <pair_pace_apip>` - :doc:`adaptive-precision <Howto_apip>` version of ACE, used as fast potential
 * :doc:`pace/apip/precise <pair_pace_apip>` - :doc:`adaptive-precision <Howto_apip>` version of ACE, used as precise potential
 * :doc:`pedone <pair_pedone>` - Pedone (PMMCS) potential (non-Coulomb part)
 * :doc:`pod <pair_pod>` - Proper orthogonal decomposition (POD) machine-learning potential
 * :doc:`peri/eps <pair_peri>` - Peridynamic EPS potential
--- a/doc/utils/sphinx-config/false_positives.txt
+++ b/doc/utils/sphinx-config/false_positives.txt
@ -131,6 +131,8 @@ anton
 Antonelli
 anysize
 api
 apip
 APIP
 apolar
 Apoorva
 Appl
@ -640,6 +642,7 @@ CSiC
 csld
 cslib
 CSlib
 csp
 cstdio
 cstdlib
 cstring
@ -1354,6 +1357,7 @@ gmres
 gname
 gneb
 GNEB
 Godehard
 Goerigk
 Goga
 Goldfarb
@ -1588,6 +1592,7 @@ Imageint
 Imagemagick
 imagename
 imd
 Immel
 Impey
 impl
 impropers
@ -3780,6 +3785,7 @@ Thiaville
 Thibaudeau
 Thijsse
 Thirumalai
 thr
 threebody
 thrid
 ThunderX
--- a/examples/PACKAGES/apip/Cu-1.yace
+++ b/examples/PACKAGES/apip/Cu-1.yace
@ -0,0 +1,34 @@
 NOTE: This is a simple potential for the example. Production usage without testing is not recommended. Provided by Yury Lysogorskiy (ICAMS, RUB, Germany).
 elements: [Cu]
 E0: [0]
 deltaSplineBins: 0.001
 embeddings:
  0: {ndensity: 2, FS_parameters: [1, 1, 1, 0.5], npoti: FinnisSinclairShiftedScaled, rho_core_cutoff: 100000, drho_core_cutoff: 250}
 bonds:
  [0, 0]: {nradmax: 2, lmax: 2, nradbasemax: 15, radbasename: ChebPow, radparameters: [2], radcoefficients: [[[0.99440439385969503, -0.085048653403583918, -0.23248632054717755, -0.22732701549371864, 0.026354948476648921, 0.21853318667456997, 0.05745747498169812, -0.19717925712228765, -0.11474256770370879, 0.12738668745839368, 0.053777769435472259, -0.11094768379576209, 0.072620812391582482, -0.058715761632824881, 0.030359986427775303], [0.96259704765772924, -0.10129488003029259, -0.10345557604916655, -0.020393848425879282, 0.076671442494272601, 0.10318554794001746, 0.0555341702761026, 0.00083194423680727696, -0.018184436957498409, -0.021866885826555403, -0.020179969116479776, 0.021880011516616484, 0.053112509345249602, -0.083707026393616657, 0.020611714544479017], [1.001530579978529, -0.030080648426358471, -0.13318582671063051, -0.24371635685809706, -0.22760541127468878, -0.041144767051648642, 0.18080289144697201, 0.24543156067198274, 0.11014559411659355, -0.069512010077804498, -0.1172049950938457, -0.027509386703874331, 0.056985864219913585, 0.037536629112081353, -0.044222474537374087]], [[0.25716120576634355, 1.7485527550537943, 0.91889737965719875, 0.50902244208852199, -0.15895537149482841, -0.48109723575282892, -0.17843605933015286, 0.39450608859531944, 0.59293909285591195, 0.18268386912819001, -0.34706543720907351, -0.3210061634328315, 0.21678650779400246, 0.39500148786376449, -0.31820913370341625], [0.0079213202761679105, 1.0212489038630681, 0.011530454475879359, -0.049445152058907642, -0.15268524878755677, -0.2319378608755131, -0.20612580998548105, -0.067027395211212315, 0.08241096034972574, 0.11288597065081186, 0.01355948960244063, -0.074722461388416803, -0.022724332047049267, 0.088871664887057056, 0.031667459613258314], [-0.0069872405356639312, 0.9939655327342134, 0.035044055182587928, 0.099765277857093104, 0.11687607289674087, 0.030241996404391416, -0.12367698594314165, -0.22480900218170197, -0.17727517861619441, -0.015144941558075584, 0.11375495728241894, 0.090680932947050971, -0.041190210394591399, -0.10085768296286811, 0.055789864104988186]]], prehc: 0, lambdahc: 0, rcut: 3.8999999999999999, dcut: 0.01, rcut_in: 0, dcut_in: 0, inner_cutoff_type: density}
 functions:
  0:
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [1], ls: [0], ms_combs: [0], ctildes: [0.26072556900842869, -0.03073189825062177]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [2], ls: [0], ms_combs: [0], ctildes: [0.64429175483702295, -0.1630534353246999]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [3], ls: [0], ms_combs: [0], ctildes: [0.51856313423563594, -0.4259316875879266]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [4], ls: [0], ms_combs: [0], ctildes: [-0.078113533662468398, -0.70352070540668643]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [5], ls: [0], ms_combs: [0], ctildes: [-0.45633111544093646, -0.7859368117550467]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [6], ls: [0], ms_combs: [0], ctildes: [-0.19608401600520556, -0.59151667874441172]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [7], ls: [0], ms_combs: [0], ctildes: [0.30580228338697285, -0.29248216980800118]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [8], ls: [0], ms_combs: [0], ctildes: [0.40167461008815436, -0.15647925731818518]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [9], ls: [0], ms_combs: [0], ctildes: [0.053519057558225343, -0.25900906688118652]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [10], ls: [0], ms_combs: [0], ctildes: [-0.20446546815457517, -0.40019216010057629]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [11], ls: [0], ms_combs: [0], ctildes: [-0.070020661105060208, -0.33441939205411986]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [12], ls: [0], ms_combs: [0], ctildes: [0.15734064575001952, -0.055233119903794807]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [13], ls: [0], ms_combs: [0], ctildes: [0.10021406559793103, 0.18641744536767416]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [14], ls: [0], ms_combs: [0], ctildes: [-0.14066730990975543, 0.14711096149210373]}
    - {mu0: 0, rank: 1, ndensity: 2, num_ms_combs: 1, mus: [0], ns: [15], ls: [0], ms_combs: [0], ctildes: [0.031100766650549283, -0.13720067925313634]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 1, mus: [0, 0], ns: [1, 1], ls: [0, 0], ms_combs: [0, 0], ctildes: [1.0984212008195524, 0.49756623164565855]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 2, mus: [0, 0], ns: [1, 1], ls: [1, 1], ms_combs: [0, 0, 1, -1], ctildes: [0.2591109116320176, 0.21348077494861176, -0.5182218232640351, -0.4269615498972234]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 3, mus: [0, 0], ns: [1, 1], ls: [2, 2], ms_combs: [0, 0, 1, -1, 2, -2], ctildes: [0.015905361441871636, 0.023783303055646809, -0.031810722883743273, -0.047566606111293624, 0.031810722883743286, 0.047566606111293638]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 1, mus: [0, 0], ns: [2, 1], ls: [0, 0], ms_combs: [0, 0], ctildes: [0.63958612617724186, 1.6623415103929948]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 2, mus: [0, 0], ns: [2, 1], ls: [1, 1], ms_combs: [0, 0, 1, -1], ctildes: [0.14199022782503917, 0.0069900458821809735, -0.28398045565007829, -0.013980091764361944]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 3, mus: [0, 0], ns: [2, 1], ls: [2, 2], ms_combs: [0, 0, 1, -1, 2, -2], ctildes: [0.028732470496968317, -0.037173039560267927, -0.05746494099393664, 0.074346079120535868, 0.057464940993936654, -0.074346079120535882]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 1, mus: [0, 0], ns: [2, 2], ls: [0, 0], ms_combs: [0, 0], ctildes: [0.056442895466964321, 0.0054387873274233034]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 2, mus: [0, 0], ns: [2, 2], ls: [1, 1], ms_combs: [0, 0, 1, -1], ctildes: [0.025326283180140272, -0.19511149476156769, -0.050652566360280531, 0.39022298952313533]}
    - {mu0: 0, rank: 2, ndensity: 2, num_ms_combs: 3, mus: [0, 0], ns: [2, 2], ls: [2, 2], ms_combs: [0, 0, 1, -1, 2, -2], ctildes: [0.012754475331985416, -0.058934602152610385, -0.025508950663970836, 0.11786920430522078, 0.025508950663970843, -0.11786920430522081]}
--- a/examples/PACKAGES/apip/Cu_300K_Immel_2023.eam.fs
+++ b/examples/PACKAGES/apip/Cu_300K_Immel_2023.eam.fs
--- a/examples/PACKAGES/apip/README
+++ b/examples/PACKAGES/apip/README
@ -0,0 +1,11 @@
 The APIP package is based on the paper:
 David Immel, Ralf Drautz, Godehard Sutmann; Adaptive-precision potentials for large-scale atomistic simulations. J. Chem. Phys. 14 March 2025; 162 (11): 114119. https://doi.org/10.1063/5.0245877
 The pair_style pace/apip requires the installation of lib/pace of the ML-PACE package.
 The installation of lib/pace is described in src/ML-PACE/README .
 Examples of how to use an adaptive-precision potential are provided in examples/PACKAGES/apip .
 in.vacancy contains a small example that can be used to visualize the transition region and get a visual impression of the selected parameters.
 in.surface.balance in a more realistic example, in which a surface is simulated and the benefit of fix apip_atom_weight and fix balance for adaptive-precision interatomic potentials is demonstrated.
--- a/examples/PACKAGES/apip/data.surface.balance
+++ b/examples/PACKAGES/apip/data.surface.balance
--- a/examples/PACKAGES/apip/data.vacancy
+++ b/examples/PACKAGES/apip/data.vacancy
--- a/examples/PACKAGES/apip/in.surface.balance
+++ b/examples/PACKAGES/apip/in.surface.balance
@ -0,0 +1,73 @@
 ##################################################
 # parameters of the adaptive-precision potential #
 ##################################################
 # We couple an EAM potential with an ACE potential.
 variable	eamfs_file string "Cu_300K_Immel_2023.eam.fs"
 variable	ace_file1 string "Cu-1.yace"
 variable	ace_file2 string "../../../potentials/Cu-PBE-core-rep.ace"
 # The csp is used as detection mechanism for atoms of interest.
 variable	csp_lattice string "fcc"
 variable	csp_cutoff equal 6.0
 # The range [r_sw_lo, r_sw_hi] determines where the switching parameter changes from 0 to 1.
 variable	r_sw_lo equal 4.0
 variable	r_sw_hi equal 12.0
 # Thresholds between which the switching parameter changes from 1 to 0 based on the csp.
 variable	lambda_input_thr_lo equal 7.5
 variable	lambda_input_thr_hi equal 8.0
 # Number of averaged steps.
 variable	lambda_input_histlen equal 110
 variable	lambda_histlen equal 110
 # Minimum required change of the switching parameter
 variable	min_delta_lambda equal 1/${lambda_histlen}
 # number of atoms rescaled by the lambda_thermostat
 variable	N_rescaling equal 600
 # basic stuff
 units		metal
 dimension	3
 boundary	p p s
 atom_style	apip # own atom style required for APIP
 timestep	0.001
 read_data	data.surface.balance
 fix		nve all nve
 comm_style	tiled
 # Only the upper surface should be treated precisely.
 # Thus, we create group, for whose atoms the csp is ignored, as the corresponding
 # argument of fix lambda is used.
 region		bottom block INF INF INF INF INF 0 units box
 group		group_ignore_csp region bottom
 # use adaptive-precision eam-ace potential with lambda_thermostat
 pair_style	hybrid/overlay eam/fs/apip pace/apip lambda_input/csp ${csp_lattice} cutoff ${csp_cutoff} lambda/zone ${r_sw_hi}
 pair_coeff	* * eam/fs/apip ${eamfs_file} Cu
 pair_coeff	* * pace/apip ${ace_file2} Cu
 pair_coeff	* * lambda_input/csp
 pair_coeff	* * lambda/zone
 fix		lambda all lambda ${lambda_input_thr_lo} ${lambda_input_thr_hi} time_averaged_zone ${r_sw_lo} ${r_sw_hi} ${lambda_input_histlen} ${lambda_histlen} min_delta_lambda ${min_delta_lambda} group_ignore_lambda_input group_ignore_csp
 fix		lambda_thermostat all lambda_thermostat N_rescaling ${N_rescaling}
 fix		weight_atom all apip_atom_weight 10 eam ace lambda_input lambda/zone all
 # store weight in variable
 fix		property_atom all property/atom d_usedweight
 variable	myweight atom f_weight_atom
 #dump		1 all custom 10 dump/surface_ap_balance.dump.* id type x y z lambda lambda_input f_weight_atom proc d_usedweight
 ## apply load balancing
 ## no load-balancing
 #fix		balance all balance 10 0.9 report weight time 1.0 weight store usedweight
 ## load balancing with times per atom per processor
 #fix		balance all balance 10 0.9 rcb weight time 1.0 weight store usedweight
 ## load balancing with an approximated load per atom by fix apip_atom_weight
 fix		balance all balance 10 0.9 rcb weight var myweight weight store usedweight
 thermo_style	custom step f_balance spcpu f_weight_atom[*]
 thermo		10
 run		100
--- a/examples/PACKAGES/apip/in.vacancy
+++ b/examples/PACKAGES/apip/in.vacancy
@ -0,0 +1,92 @@
 ##################################################
 # parameters of the adaptive-precision potential #
 ##################################################
 # We couple an EAM potential with an ACE potential.
 variable	eamfs_file string "Cu_300K_Immel_2023.eam.fs"
 variable	ace_file1 string "Cu-1.yace"
 variable	ace_file2 string "../../../potentials/Cu-PBE-core-rep.ace"
 # The csp is used as detection mechanism for atoms of interest.
 variable	csp_lattice string "fcc"
 variable	csp_cutoff equal 6.0
 # The range [r_sw_lo, r_sw_hi] determines where the switching parameter changes from 0 to 1.
 variable	r_sw_lo equal 4.0
 variable	r_sw_hi equal 12.0
 # Thresholds between which the switching parameter changes from 1 to 0 based on the csp.
 variable	lambda_input_thr_lo equal 2.5
 variable	lambda_input_thr_hi equal 3.0
 # Number of averaged steps.
 variable	lambda_input_histlen equal 110
 variable	lambda_histlen equal 110
 # Minimum required change of the switching parameter
 variable	min_delta_lambda equal 1/${lambda_histlen}
 # number of atoms rescaled by the lambda_thermostat
 variable	N_rescaling equal 600
 ## basic stuff
 units		metal
 atom_style	apip # own atom style required for APIP
 timestep	0.001
 # copper at room temperature with a vacancy
 read_data	data.vacancy
 fix		nve all nve
 ## Use adaptive-precision ace-ace potential without lambda_thermostat.
 ## Calculate atomic weight that could be used for load balancing.
 #pair_style	hybrid/overlay pace/apip/fast pace/apip/precise lambda_input/csp ${csp_lattice} cutoff ${csp_cutoff} lambda/zone ${r_sw_hi}
 #pair_coeff	* * pace/apip/fast ${ace_file1} Cu
 #pair_coeff	* * pace/apip/precise ${ace_file2} Cu
 #pair_coeff	* * lambda_input/csp
 #pair_coeff	* * lambda/zone
 #fix		lambda all lambda ${lambda_input_thr_lo} ${lambda_input_thr_hi} time_averaged_zone ${r_sw_lo} ${r_sw_hi} ${lambda_input_histlen} ${lambda_histlen} min_delta_lambda ${min_delta_lambda}
 #fix		weight_atom all apip_atom_weight 100 ace ace lambda_input lambda/zone all
 # Use adaptive-precision eam-ace potential without lambda_thermostat.
 # Calculate atomic weight that could be used for load balancing.
 pair_style	hybrid/overlay eam/fs/apip pace/apip lambda_input/csp ${csp_lattice} cutoff ${csp_cutoff} lambda/zone ${r_sw_hi}
 pair_coeff	* * eam/fs/apip ${eamfs_file} Cu
 pair_coeff	* * pace/apip ${ace_file2} Cu
 pair_coeff	* * lambda_input/csp
 pair_coeff	* * lambda/zone
 fix		lambda all lambda ${lambda_input_thr_lo} ${lambda_input_thr_hi} time_averaged_zone ${r_sw_lo} ${r_sw_hi} ${lambda_input_histlen} ${lambda_histlen} min_delta_lambda ${min_delta_lambda}
 fix		weight_atom all apip_atom_weight 100 eam ace lambda_input lambda/zone all
 ## One can comment out fix lambda_thermostat to see the energy change caused by the neglection of the
 ## gradient of the switching function. This neglection can be compensated by the local thermostat and the
 ## energy can be conserved within numerical precision.
 fix		lambda_thermostat all lambda_thermostat N_rescaling ${N_rescaling} store_atomic_forces 100
 thermo_style	custom step etotal
 thermo		1
 run		100
 # dump atoms
 #write_dump	all custom dump/vacancy.dump.* id type x y z fx fy fz lambda lambda_input f_weight_atom f_lambda_thermostat[*]
 ## A smooth restart of the simulation is possible as the history of lambda and lambda_input is stored.
 #write_restart	vacancy_ap.restart
 #clear
 #read_restart	vacancy_ap.restart
 #pair_style	hybrid/overlay eam/fs/apip pace/apip lambda_input/csp fcc cutoff 6.0 lambda/zone 12.0
 #pair_coeff	* * eam/fs/apip "Cu_300K_Immel_2023.eam.fs" Cu
 #pair_coeff	* * pace/apip "../../../potentials/Cu-PBE-core-rep.ace" Cu
 #pair_coeff	* * lambda_input/csp
 #pair_coeff	* * lambda/zone
 #fix		lambda all lambda 2.5 3.0 time_averaged_zone 4.0 12.0 110 110 min_delta_lambda $(1/110)
 #fix		lambda_thermostat all lambda_thermostat N_rescaling ${N_rescaling} store_atomic_forces 100
 #fix		nve all nve
 #thermo_style	custom step etotal
 #thermo		1
 #run		10
 #shell		rm vacancy_ap.restart
--- a/examples/PACKAGES/apip/log.04Feb25.surface.balance.nolb.g++.4
+++ b/examples/PACKAGES/apip/log.04Feb25.surface.balance.nolb.g++.4
@ -0,0 +1,108 @@
 LAMMPS (4 Feb 2025 - Development - )
 Reading data file ...
  orthogonal box = (0 0 -1.1656272) to (36.15 36.15 362.81506)
  1 by 1 by 4 MPI processor grid
  reading atoms ...
  40200 atoms
  reading velocities ...
  40200 velocities
  read_data CPU = 1.143 seconds
 200 atoms in group group_ignore_csp
 ACE version: 2023.11.25
 Recursive evaluator is used by ACE
 Loading ../../../potentials/Cu-PBE-core-rep.ace
 Total number of basis functions
 	Cu: 16 (r=1) 726 (r>1)
 Mapping LAMMPS atom type #1(Cu) -> ACE species type #0
 atomic load lambda:
 	fast potential: extract eam/apip:time_per_atom
 	precise potential: extract pace/apip:time_per_atom
 	lambda_input: extract lambda_input:time_per_atom
 	lambda: extract lambda_zone:time_per_atom
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Your simulation uses code contributions which should be cited:
 - fix lambda command: doi.org/10.1063/5.0245877
 The log file lists these citations in BibTeX format.
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Neighbor list info ...
  update: every = 1 steps, delay = 0 steps, check = yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 14
  ghost atom cutoff = 14
  binsize = 7, bins = 6 6 52
  5 neighbor lists, perpetual/occasional/extra = 5 0 0
  (1) pair eam/fs/apip, perpetual
      attributes: full, newton on
      pair build: full/bin/atomonly
      stencil: full/bin/3d
      bin: standard
  (2) pair pace/apip, perpetual, trim from (4)
      attributes: full, newton on, cut 9.4
      pair build: trim
      stencil: none
      bin: none
  (3) pair lambda_input/csp, perpetual, trim from (2)
      attributes: full, newton on, cut 8
      pair build: trim
      stencil: none
      bin: none
  (4) pair lambda/zone, perpetual
      attributes: full, newton on, ghost, cut 14
      pair build: full/bin/ghost
      stencil: full/ghost/bin/3d
      bin: standard
  (5) fix lambda_thermostat, perpetual, copy from (1)
      attributes: full, newton on
      pair build: copy
      stencil: none
      bin: none
 Setting up Verlet run ...
  Unit style    : metal
  Current step  : 0
  Time step     : 0.001
 Per MPI rank memory allocation (min/avg/max) = 297.9 | 306.9 | 315.9 Mbytes
   Step       f_balance        S/CPU      f_weight_atom[1] f_weight_atom[2] f_weight_atom[3] f_weight_atom[4]
         0   1.0139303      0              0              0              0              0            
        10   2.4606058      1.8697255      5.5957166e-06  0.0002553649   2.7500342e-06  4.6802407e-06
        20   2.0765883      1.7644069      5.9864867e-06  0.0002751227   2.9574758e-06  5.078614e-06 
        30   2.0955022      1.729507       5.9541701e-06  0.00028593742  3.1165205e-06  5.2349106e-06
        40   2.1015667      1.7241359      6.0115135e-06  0.00028640643  3.1154236e-06  5.2528746e-06
        50   2.0981491      1.6201337      6.0470102e-06  0.00028778687  3.1443635e-06  5.2497711e-06
        60   2.1327959      1.3101362      7.7658865e-06  0.00037855901  4.1641447e-06  6.9162514e-06
        70   2.098134       1.3357863      7.5378657e-06  0.00037046011  4.0510159e-06  6.9345367e-06
        80   2.1000138      1.3475583      7.5679751e-06  0.00036818876  4.0188623e-06  6.7257237e-06
        90   2.0966073      1.1728052      7.6393621e-06  0.00036755436  4.0052073e-06  6.6818754e-06
       100   1.8896711      1.3506386      7.5946481e-06  0.00036649967  3.984174e-06   6.6518701e-06
 Loop time of 67.2407 on 4 procs for 100 steps with 40200 atoms
 Performance: 0.128 ns/day, 186.780 hours/ns, 1.487 timesteps/s, 59.785 katom-step/s
 99.8% CPU use with 4 MPI tasks x no OpenMP threads
 MPI task timing breakdown:
 Section |  min time  |  avg time  |  max time  |%varavg| %total
 ---------------------------------------------------------------
 Pair    | 10.34      | 21.891     | 56.059     | 421.6 | 32.56
 Neigh   | 8.1064     | 9.1925     | 10.667     |  33.9 | 13.67
 Comm    | 1.3105     | 23.525     | 45.141     | 437.6 | 34.99
 Output  | 0.00053598 | 0.73462    | 2.8834     | 144.7 |  1.09
 Modify  | 1.4504     | 2.6152     | 5.8041     | 114.0 |  3.89
 Other   |            | 9.282      |            |       | 13.80
 Nlocal:          10050 ave       10180 max       10000 min
 Histogram: 2 1 0 0 0 0 0 0 0 1
 Nghost:        27854.5 ave       30385 max       25525 min
 Histogram: 2 0 0 0 0 0 0 0 0 2
 Neighs:              0 ave           0 max           0 min
 Histogram: 4 0 0 0 0 0 0 0 0 0
 FullNghs:  9.49222e+06 ave 9.76687e+06 max 9.29466e+06 min
 Histogram: 2 0 0 0 0 0 1 0 0 1
 Total # of neighbors = 37968882
 Ave neighs/atom = 944.49955
 Neighbor list builds = 10
 Dangerous builds = 0
 Total wall time: 0:01:11
--- a/examples/PACKAGES/apip/log.04Feb25.surface.balance.rcb.myweight.g++.4
+++ b/examples/PACKAGES/apip/log.04Feb25.surface.balance.rcb.myweight.g++.4
@ -0,0 +1,108 @@
 LAMMPS (4 Feb 2025 - Development - )
 Reading data file ...
  orthogonal box = (0 0 -1.1656272) to (36.15 36.15 362.81506)
  1 by 1 by 4 MPI processor grid
  reading atoms ...
  40200 atoms
  reading velocities ...
  40200 velocities
  read_data CPU = 1.141 seconds
 200 atoms in group group_ignore_csp
 ACE version: 2023.11.25
 Recursive evaluator is used by ACE
 Loading ../../../potentials/Cu-PBE-core-rep.ace
 Total number of basis functions
 	Cu: 16 (r=1) 726 (r>1)
 Mapping LAMMPS atom type #1(Cu) -> ACE species type #0
 atomic load lambda:
 	fast potential: extract eam/apip:time_per_atom
 	precise potential: extract pace/apip:time_per_atom
 	lambda_input: extract lambda_input:time_per_atom
 	lambda: extract lambda_zone:time_per_atom
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Your simulation uses code contributions which should be cited:
 - fix lambda command: doi.org/10.1063/5.0245877
 The log file lists these citations in BibTeX format.
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Neighbor list info ...
  update: every = 1 steps, delay = 0 steps, check = yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 14
  ghost atom cutoff = 14
  binsize = 7, bins = 6 6 52
  5 neighbor lists, perpetual/occasional/extra = 5 0 0
  (1) pair eam/fs/apip, perpetual
      attributes: full, newton on
      pair build: full/bin/atomonly
      stencil: full/bin/3d
      bin: standard
  (2) pair pace/apip, perpetual, trim from (4)
      attributes: full, newton on, cut 9.4
      pair build: trim
      stencil: none
      bin: none
  (3) pair lambda_input/csp, perpetual, trim from (2)
      attributes: full, newton on, cut 8
      pair build: trim
      stencil: none
      bin: none
  (4) pair lambda/zone, perpetual
      attributes: full, newton on, ghost, cut 14
      pair build: full/bin/ghost
      stencil: full/ghost/bin/3d
      bin: standard
  (5) fix lambda_thermostat, perpetual, copy from (1)
      attributes: full, newton on
      pair build: copy
      stencil: none
      bin: none
 Setting up Verlet run ...
  Unit style    : metal
  Current step  : 0
  Time step     : 0.001
 Per MPI rank memory allocation (min/avg/max) = 298.1 | 306.3 | 314.5 Mbytes
   Step       f_balance        S/CPU      f_weight_atom[1] f_weight_atom[2] f_weight_atom[3] f_weight_atom[4]
         0   1              0              0              0              0              0            
        10   1.0010585      1.8144651      5.3526071e-06  0.00025703793  2.7730117e-06  4.7190461e-06
        20   1.0016587      3.0895281      6.0547706e-06  0.00030627156  2.9311147e-06  2.8627034e-06
        30   1.0006595      2.1815977      7.7086095e-06  0.00034346642  3.4831025e-06  3.6494203e-06
        40   1.0003702      2.7847348      6.9889341e-06  0.00031605872  3.2092228e-06  2.9177266e-06
        50   1.0013639      2.8085372      7.1723284e-06  0.00032050748  3.2148509e-06  2.9280764e-06
        60   1.001567       2.7692583      7.3191318e-06  0.00032348311  3.2792367e-06  3.0731907e-06
        70   1.0008473      2.7848811      7.4547446e-06  0.00032207119  3.2487866e-06  3.0045227e-06
        80   1.0008791      2.1902426      8.8463371e-06  0.00037692301  3.878561e-06   3.5166374e-06
        90   1.0005633      2.0207998      1.0049193e-05  0.00043004983  4.4508803e-06  4.0369005e-06
       100   1.0011185      2.11148        9.5552543e-06  0.00040548477  4.282726e-06   4.0021617e-06
 Loop time of 41.9356 on 4 procs for 100 steps with 40200 atoms
 Performance: 0.206 ns/day, 116.488 hours/ns, 2.385 timesteps/s, 95.861 katom-step/s
 99.2% CPU use with 4 MPI tasks x no OpenMP threads
 MPI task timing breakdown:
 Section |  min time  |  avg time  |  max time  |%varavg| %total
 ---------------------------------------------------------------
 Pair    | 21.856     | 23.33      | 25.627     |  29.8 | 55.63
 Neigh   | 12.078     | 12.235     | 12.335     |   2.8 | 29.18
 Comm    | 1.8098     | 3.4438     | 5.8848     |  91.3 |  8.21
 Output  | 0.0013883  | 0.0067437  | 0.010676   |   4.1 |  0.02
 Modify  | 1.7044     | 1.8301     | 1.9304     |   7.0 |  4.36
 Other   |            | 1.09       |            |       |  2.60
 Nlocal:          10050 ave       10381 max        9892 min
 Histogram: 1 2 0 0 0 0 0 0 0 1
 Nghost:          52763 ave       52921 max       52432 min
 Histogram: 1 0 0 0 0 0 0 0 2 1
 Neighs:              0 ave           0 max           0 min
 Histogram: 4 0 0 0 0 0 0 0 0 0
 FullNghs:  9.49222e+06 ave 9.80751e+06 max 9.34231e+06 min
 Histogram: 1 2 0 0 0 0 0 0 0 1
 Total # of neighbors = 37968882
 Ave neighs/atom = 944.49955
 Neighbor list builds = 10
 Dangerous builds = 0
 Total wall time: 0:00:46
--- a/examples/PACKAGES/apip/log.04Feb25.surface.balance.rcb.time.g++.4
+++ b/examples/PACKAGES/apip/log.04Feb25.surface.balance.rcb.time.g++.4
@ -0,0 +1,108 @@
 LAMMPS (4 Feb 2025 - Development - )
 Reading data file ...
  orthogonal box = (0 0 -1.1656272) to (36.15 36.15 362.81506)
  1 by 1 by 4 MPI processor grid
  reading atoms ...
  40200 atoms
  reading velocities ...
  40200 velocities
  read_data CPU = 1.549 seconds
 200 atoms in group group_ignore_csp
 ACE version: 2023.11.25
 Recursive evaluator is used by ACE
 Loading ../../../potentials/Cu-PBE-core-rep.ace
 Total number of basis functions
 	Cu: 16 (r=1) 726 (r>1)
 Mapping LAMMPS atom type #1(Cu) -> ACE species type #0
 atomic load lambda:
 	fast potential: extract eam/apip:time_per_atom
 	precise potential: extract pace/apip:time_per_atom
 	lambda_input: extract lambda_input:time_per_atom
 	lambda: extract lambda_zone:time_per_atom
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Your simulation uses code contributions which should be cited:
 - fix lambda command: doi.org/10.1063/5.0245877
 The log file lists these citations in BibTeX format.
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Neighbor list info ...
  update: every = 1 steps, delay = 0 steps, check = yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 14
  ghost atom cutoff = 14
  binsize = 7, bins = 6 6 52
  5 neighbor lists, perpetual/occasional/extra = 5 0 0
  (1) pair eam/fs/apip, perpetual
      attributes: full, newton on
      pair build: full/bin/atomonly
      stencil: full/bin/3d
      bin: standard
  (2) pair pace/apip, perpetual, trim from (4)
      attributes: full, newton on, cut 9.4
      pair build: trim
      stencil: none
      bin: none
  (3) pair lambda_input/csp, perpetual, trim from (2)
      attributes: full, newton on, cut 8
      pair build: trim
      stencil: none
      bin: none
  (4) pair lambda/zone, perpetual
      attributes: full, newton on, ghost, cut 14
      pair build: full/bin/ghost
      stencil: full/ghost/bin/3d
      bin: standard
  (5) fix lambda_thermostat, perpetual, copy from (1)
      attributes: full, newton on
      pair build: copy
      stencil: none
      bin: none
 Setting up Verlet run ...
  Unit style    : metal
  Current step  : 0
  Time step     : 0.001
 Per MPI rank memory allocation (min/avg/max) = 298.1 | 306.3 | 314.5 Mbytes
   Step       f_balance        S/CPU      f_weight_atom[1] f_weight_atom[2] f_weight_atom[3] f_weight_atom[4]
         0   1              0              0              0              0              0            
        10   1.0001725      1.7198837      5.5314343e-06  0.00025930431  2.7883957e-06  4.707143e-06 
        20   1.0001862      1.8265719      5.6099429e-06  0.00027931903  2.9758981e-06  5.002563e-06 
        30   1.00056        1.8317507      5.9076763e-06  0.0002894911   3.1109902e-06  5.1394341e-06
        40   1.0004862      2.5730799      6.243133e-06   0.00030439841  3.1674858e-06  3.784468e-06 
        50   1.0001422      1.7867846      6.1734458e-06  0.00029065411  3.1286655e-06  5.1705237e-06
        60   1.0008942      1.4365047      7.2226216e-06  0.00035501193  3.8052887e-06  6.42234e-06  
        70   1.0001463      1.9946081      8.1287731e-06  0.00038928999  4.1631973e-06  4.9840279e-06
        80   1.0004234      1.4099223      7.8487793e-06  0.00037185703  4.022587e-06   6.8562431e-06
        90   1.000166       1.6477504      1.1740135e-05  0.00039310073  4.5190508e-06  5.9037201e-06
       100   1.0004352      1.3977939      7.9664586e-06  0.00037057101  4.0412051e-06  6.8616558e-06
 Loop time of 58.5219 on 4 procs for 100 steps with 40200 atoms
 Performance: 0.148 ns/day, 162.561 hours/ns, 1.709 timesteps/s, 68.692 katom-step/s
 99.7% CPU use with 4 MPI tasks x no OpenMP threads
 MPI task timing breakdown:
 Section |  min time  |  avg time  |  max time  |%varavg| %total
 ---------------------------------------------------------------
 Pair    | 13.129     | 22.408     | 43.047     | 253.7 | 38.29
 Neigh   | 2.9649     | 8.8754     | 14.209     | 175.4 | 15.17
 Comm    | 4.4729     | 19.561     | 38.596     | 306.3 | 33.43
 Output  | 0.0076245  | 0.28239    | 0.93926    |  72.3 |  0.48
 Modify  | 1.0567     | 2.2026     | 4.445      |  92.5 |  3.76
 Other   |            | 5.192      |            |       |  8.87
 Nlocal:          10050 ave       16633 max        2176 min
 Histogram: 1 0 1 0 0 0 0 0 0 2
 Nghost:          27619 ave       42218 max        8849 min
 Histogram: 1 0 0 1 0 0 0 0 0 2
 Neighs:              0 ave           0 max           0 min
 Histogram: 4 0 0 0 0 0 0 0 0 0
 FullNghs:  9.49222e+06 ave 1.56603e+07 max 1.80672e+06 min
 Histogram: 1 0 1 0 0 0 0 0 0 2
 Total # of neighbors = 37968882
 Ave neighs/atom = 944.49955
 Neighbor list builds = 10
 Dangerous builds = 0
 Total wall time: 0:01:02
--- a/examples/PACKAGES/apip/log.04Feb25.vacancy.lambda.no.thermostat.g++.4
+++ b/examples/PACKAGES/apip/log.04Feb25.vacancy.lambda.no.thermostat.g++.4
@ -0,0 +1,193 @@
 LAMMPS (4 Feb 2025 - Development - )
 Reading data file ...
  orthogonal box = (0 0 0) to (28.92 28.92 28.92)
  1 by 2 by 2 MPI processor grid
  reading atoms ...
  2047 atoms
  reading velocities ...
  2047 velocities
  read_data CPU = 0.037 seconds
 ACE version: 2023.11.25
 Recursive evaluator is used by ACE
 Loading ../../../potentials/Cu-PBE-core-rep.ace
 Total number of basis functions
 	Cu: 16 (r=1) 726 (r>1)
 Mapping LAMMPS atom type #1(Cu) -> ACE species type #0
 atomic load lambda:
 	fast potential: extract eam/apip:time_per_atom
 	precise potential: extract pace/apip:time_per_atom
 	lambda_input: extract lambda_input:time_per_atom
 	lambda: extract lambda_zone:time_per_atom
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Your simulation uses code contributions which should be cited:
 - fix lambda command: doi.org/10.1063/5.0245877
 The log file lists these citations in BibTeX format.
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 WARNING: The energy is not conserved when lambda changes as fix lambda_thermostat is not used. (../fix_lambda.cpp:247)
 Neighbor list info ...
  update: every = 1 steps, delay = 0 steps, check = yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 14
  ghost atom cutoff = 14
  binsize = 7, bins = 5 5 5
  4 neighbor lists, perpetual/occasional/extra = 4 0 0
  (1) pair eam/fs/apip, perpetual
      attributes: full, newton on
      pair build: full/bin/atomonly
      stencil: full/bin/3d
      bin: standard
  (2) pair pace/apip, perpetual, trim from (4)
      attributes: full, newton on, cut 9.4
      pair build: trim
      stencil: none
      bin: none
  (3) pair lambda_input/csp, perpetual, trim from (2)
      attributes: full, newton on, cut 8
      pair build: trim
      stencil: none
      bin: none
  (4) pair lambda/zone, perpetual
      attributes: full, newton on, ghost, cut 14
      pair build: full/bin/ghost
      stencil: full/ghost/bin/3d
      bin: standard
 Setting up Verlet run ...
  Unit style    : metal
  Current step  : 0
  Time step     : 0.001
 Per MPI rank memory allocation (min/avg/max) = 58.65 | 58.75 | 59.03 Mbytes
   Step         TotEng    
         0  -7409.9869    
         1  -7409.9869    
         2  -7409.987     
         3  -7409.987     
         4  -7409.987     
         5  -7409.987     
         6  -7409.987     
         7  -7409.987     
         8  -7409.987     
         9  -7409.987     
        10  -7409.9871    
        11  -7409.9876    
        12  -7409.9876    
        13  -7409.9876    
        14  -7409.988     
        15  -7409.9876    
        16  -7409.9864    
        17  -7409.9864    
        18  -7409.9853    
        19  -7409.9847    
        20  -7409.9865    
        21  -7409.9852    
        22  -7409.9867    
        23  -7409.9864    
        24  -7409.9869    
        25  -7409.9844    
        26  -7409.9849    
        27  -7409.9856    
        28  -7409.9851    
        29  -7409.9835    
        30  -7409.9843    
        31  -7409.9861    
        32  -7409.9862    
        33  -7409.9869    
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        35  -7409.9885    
        36  -7409.9924    
        37  -7409.9945    
        38  -7409.9942    
        39  -7409.9903    
        40  -7409.9909    
        41  -7409.9962    
        42  -7409.996     
        43  -7409.9959    
        44  -7410.0004    
        45  -7410.0044    
        46  -7409.9993    
        47  -7409.9948    
        48  -7409.9923    
        49  -7409.9844    
        50  -7409.9861    
        51  -7409.9849    
        52  -7409.986     
        53  -7409.9828    
        54  -7409.9799    
        55  -7409.9804    
        56  -7409.9782    
        57  -7409.9777    
        58  -7409.9777    
        59  -7409.9781    
        60  -7409.982     
        61  -7409.982     
        62  -7409.9824    
        63  -7409.9844    
        64  -7409.9826    
        65  -7409.9816    
        66  -7409.9788    
        67  -7409.9769    
        68  -7409.9727    
        69  -7409.9716    
        70  -7409.9693    
        71  -7409.9674    
        72  -7409.9691    
        73  -7409.9693    
        74  -7409.9682    
        75  -7409.9664    
        76  -7409.9678    
        77  -7409.966     
        78  -7409.9674    
        79  -7409.9654    
        80  -7409.9649    
        81  -7409.9636    
        82  -7409.967     
        83  -7409.9693    
        84  -7409.9655    
        85  -7409.9654    
        86  -7409.9644    
        87  -7409.961     
        88  -7409.9609    
        89  -7409.9594    
        90  -7409.96      
        91  -7409.9643    
        92  -7409.9603    
        93  -7409.9622    
        94  -7409.9603    
        95  -7409.9584    
        96  -7409.9555    
        97  -7409.9596    
        98  -7409.9587    
        99  -7409.9585    
       100  -7409.9602    
 Loop time of 10.6279 on 4 procs for 100 steps with 2047 atoms
 Performance: 0.813 ns/day, 29.522 hours/ns, 9.409 timesteps/s, 19.261 katom-step/s
 99.2% CPU use with 4 MPI tasks x no OpenMP threads
 MPI task timing breakdown:
 Section |  min time  |  avg time  |  max time  |%varavg| %total
 ---------------------------------------------------------------
 Pair    | 7.4326     | 8.9455     | 10.524     |  49.4 | 84.17
 Neigh   | 0          | 0          | 0          |   0.0 |  0.00
 Comm    | 0.089305   | 1.6676     | 3.18       | 114.5 | 15.69
 Output  | 0.0028034  | 0.0041679  | 0.0061404  |   1.9 |  0.04
 Modify  | 0.0040779  | 0.0053928  | 0.0062702  |   1.1 |  0.05
 Other   |            | 0.005266   |            |       |  0.05
 Nlocal:         511.75 ave         529 max         502 min
 Histogram: 1 1 0 1 0 0 0 0 0 1
 Nghost:        7684.25 ave        7693 max        7668 min
 Histogram: 1 0 0 0 0 0 0 1 1 1
 Neighs:              0 ave           0 max           0 min
 Histogram: 4 0 0 0 0 0 0 0 0 0
 FullNghs:       490648 ave      507159 max      481313 min
 Histogram: 1 1 0 1 0 0 0 0 0 1
 Total # of neighbors = 1962590
 Ave neighs/atom = 958.76404
 Neighbor list builds = 0
 Dangerous builds = 0
 Total wall time: 0:00:12
--- a/examples/PACKAGES/apip/log.04Feb25.vacancy.lambda.thermostat.g++.4
+++ b/examples/PACKAGES/apip/log.04Feb25.vacancy.lambda.thermostat.g++.4
@ -0,0 +1,197 @@
 LAMMPS (4 Feb 2025 - Development - )
 Reading data file ...
  orthogonal box = (0 0 0) to (28.92 28.92 28.92)
  1 by 2 by 2 MPI processor grid
  reading atoms ...
  2047 atoms
  reading velocities ...
  2047 velocities
  read_data CPU = 0.041 seconds
 ACE version: 2023.11.25
 Recursive evaluator is used by ACE
 Loading ../../../potentials/Cu-PBE-core-rep.ace
 Total number of basis functions
 	Cu: 16 (r=1) 726 (r>1)
 Mapping LAMMPS atom type #1(Cu) -> ACE species type #0
 atomic load lambda:
 	fast potential: extract eam/apip:time_per_atom
 	precise potential: extract pace/apip:time_per_atom
 	lambda_input: extract lambda_input:time_per_atom
 	lambda: extract lambda_zone:time_per_atom
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Your simulation uses code contributions which should be cited:
 - fix lambda command: doi.org/10.1063/5.0245877
 The log file lists these citations in BibTeX format.
 CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE-CITE
 Neighbor list info ...
  update: every = 1 steps, delay = 0 steps, check = yes
  max neighbors/atom: 2000, page size: 100000
  master list distance cutoff = 14
  ghost atom cutoff = 14
  binsize = 7, bins = 5 5 5
  5 neighbor lists, perpetual/occasional/extra = 5 0 0
  (1) pair eam/fs/apip, perpetual
      attributes: full, newton on
      pair build: full/bin/atomonly
      stencil: full/bin/3d
      bin: standard
  (2) pair pace/apip, perpetual, trim from (4)
      attributes: full, newton on, cut 9.4
      pair build: trim
      stencil: none
      bin: none
  (3) pair lambda_input/csp, perpetual, trim from (2)
      attributes: full, newton on, cut 8
      pair build: trim
      stencil: none
      bin: none
  (4) pair lambda/zone, perpetual
      attributes: full, newton on, ghost, cut 14
      pair build: full/bin/ghost
      stencil: full/ghost/bin/3d
      bin: standard
  (5) fix lambda_thermostat, perpetual, copy from (1)
      attributes: full, newton on
      pair build: copy
      stencil: none
      bin: none
 Setting up Verlet run ...
  Unit style    : metal
  Current step  : 0
  Time step     : 0.001
 Per MPI rank memory allocation (min/avg/max) = 61.44 | 61.63 | 62.2 Mbytes
   Step         TotEng    
         0  -7409.9869    
         1  -7409.9869    
         2  -7409.987     
         3  -7409.987     
         4  -7409.987     
         5  -7409.987     
         6  -7409.987     
         7  -7409.987     
         8  -7409.987     
         9  -7409.987     
        10  -7409.987     
        11  -7409.9871    
        12  -7409.9871    
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        33  -7409.9872    
        34  -7409.9872    
        35  -7409.9872    
        36  -7409.9872    
        37  -7409.9873    
        38  -7409.9873    
        39  -7409.9873    
        40  -7409.9873    
        41  -7409.9873    
        42  -7409.9874    
        43  -7409.9874    
        44  -7409.9874    
        45  -7409.9874    
        46  -7409.9875    
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        48  -7409.9875    
        49  -7409.9875    
        50  -7409.9875    
        51  -7409.9876    
        52  -7409.9876    
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        55  -7409.9876    
        56  -7409.9876    
        57  -7409.9876    
        58  -7409.9876    
        59  -7409.9876    
        60  -7409.9876    
        61  -7409.9876    
        62  -7409.9875    
        63  -7409.9875    
        64  -7409.9875    
        65  -7409.9875    
        66  -7409.9874    
        67  -7409.9874    
        68  -7409.9874    
        69  -7409.9873    
        70  -7409.9873    
        71  -7409.9873    
        72  -7409.9873    
        73  -7409.9872    
        74  -7409.9872    
        75  -7409.9872    
        76  -7409.9872    
        77  -7409.9872    
        78  -7409.9871    
        79  -7409.9871    
        80  -7409.9871    
        81  -7409.9871    
        82  -7409.9871    
        83  -7409.9871    
        84  -7409.9871    
        85  -7409.9871    
        86  -7409.9871    
        87  -7409.9871    
        88  -7409.9871    
        89  -7409.9871    
        90  -7409.9871    
        91  -7409.9871    
        92  -7409.9871    
        93  -7409.9872    
        94  -7409.9872    
        95  -7409.9872    
        96  -7409.9872    
        97  -7409.9872    
        98  -7409.9872    
        99  -7409.9872    
       100  -7409.9872    
 Loop time of 11.8395 on 4 procs for 100 steps with 2047 atoms
 Performance: 0.730 ns/day, 32.887 hours/ns, 8.446 timesteps/s, 17.290 katom-step/s
 99.2% CPU use with 4 MPI tasks x no OpenMP threads
 MPI task timing breakdown:
 Section |  min time  |  avg time  |  max time  |%varavg| %total
 ---------------------------------------------------------------
 Pair    | 8.1066     | 9.7912     | 11.642     |  53.8 | 82.70
 Neigh   | 0          | 0          | 0          |   0.0 |  0.00
 Comm    | 0.057574   | 1.9086     | 3.5932     | 121.8 | 16.12
 Output  | 0.022525   | 0.027196   | 0.031414   |   2.2 |  0.23
 Modify  | 0.10334    | 0.10795    | 0.11223    |   1.2 |  0.91
 Other   |            | 0.004525   |            |       |  0.04
 Nlocal:         511.75 ave         529 max         502 min
 Histogram: 1 1 0 1 0 0 0 0 0 1
 Nghost:        7684.25 ave        7693 max        7668 min
 Histogram: 1 0 0 0 0 0 0 1 1 1
 Neighs:              0 ave           0 max           0 min
 Histogram: 4 0 0 0 0 0 0 0 0 0
 FullNghs:       490648 ave      507159 max      481313 min
 Histogram: 1 1 0 1 0 0 0 0 0 1
 Total # of neighbors = 1962590
 Ave neighs/atom = 958.76404
 Neighbor list builds = 0
 Dangerous builds = 0
 Total wall time: 0:00:13
--- a/src/.gitignore
+++ b/src/.gitignore
@ -109,6 +109,30 @@
 /pair_pace_extrapolation.cpp
 /pair_pace_extrapolation.h
 /fix_lambda.cpp
 /fix_lambda.h
 /fix_lambda_thermostat.cpp
 /fix_lambda_thermostat.h
 /pair_lambda_input.cpp
 /pair_lambda_input.h
 /pair_lambda_input_csp.cpp
 /pair_lambda_input_csp.h
 /pair_eam_fs_apip.cpp
 /pair_eam_fs_apip.h
 /pair_eam_apip.cpp
 /pair_eam_apip.h
 /pair_lambda_zone.cpp
 /pair_lambda_zone.h
 /pair_pace_apip.cpp
 /pair_pace_apip.h
 /pair_pace_apip_precise.cpp
 /pair_pace_apip_precise.h
 /pair_pace_apip_fast.cpp
 /pair_pace_apip_fast.h
 /fix_apip_atom_weight.cpp
 /fix_apip_atom_weight.h
 /pair_pod.cpp
 /pair_pod.h
 /eapod.cpp
--- a/src/APIP/Install.sh
+++ b/src/APIP/Install.sh
@ -0,0 +1,73 @@
 # Install/unInstall package files in LAMMPS
 # mode = 0/1/2 for uninstall/install/update
 mode=$1
 # enforce using portable C locale
 LC_ALL=C
 export LC_ALL
 # arg1 = file, arg2 = file it depends on
 action () {
  if (test $mode = 0) then
    rm -f ../$1
  elif (! cmp -s $1 ../$1) then
    if (test -z "$2" || test -e ../$2) then
      cp $1 ..
      if (test $mode = 2) then
        echo "  updating src/$1"
      fi
    fi
  elif (test -n "$2") then
    if (test ! -e ../$2) then
      rm -f ../$1
    fi
  fi
 }
 # all package files with no dependencies
 for file in *.cpp *.h; do
  test -f ${file} && action $file
 done
 # edit 2 Makefile.package files to include/exclude package info
 if (test $1 = 1) then
  if (test -e ../Makefile.package) then
    sed -i -e 's/[^ \t]*pace[^ \t]* //' ../Makefile.package
    sed -i -e 's|^PKG_SYSINC =[ \t]*|&$(pace_SYSINC) |' ../Makefile.package
    sed -i -e 's|^PKG_SYSLIB =[ \t]*|&$(pace_SYSLIB) |' ../Makefile.package
    sed -i -e 's|^PKG_SYSPATH =[ \t]*|&$(pace_SYSPATH) |' ../Makefile.package
  fi
  if (test -e ../Makefile.package.settings) then
    sed -i -e '/^[ \t]*include.*pace.*$/d' ../Makefile.package.settings
    # multiline form needed for BSD sed on Macs
    sed -i -e '4 i \
 include ..\/..\/lib\/pace\/Makefile.lammps
 ' ../Makefile.package.settings
  fi
 elif (test $1 = 0) then
  # The ML-PACE package depends also on the pace library.
  # Remove in Makefiles only if there are no remaining includes from ML-PACE.
  # grep searches also in kspace.cpp and thus returns no error.
  if (test $(grep '#include "ace' ../*pace*.cpp | wc -l) = 0) then
    # update Makefiles
    if (test -e ../Makefile.package) then
      sed -i -e 's/[^ \t]*pace[^ \t]* //' ../Makefile.package
    fi
    if (test -e ../Makefile.package.settings) then
      sed -i -e '/^[ \t]*include.*pace.*$/d' ../Makefile.package.settings
    fi
  fi
 fi
--- a/src/APIP/README
+++ b/src/APIP/README
@ -0,0 +1,8 @@
 The APIP package is based on the paper:
 David Immel, Ralf Drautz, Godehard Sutmann; Adaptive-precision potentials for large-scale atomistic simulations. J. Chem. Phys. 14 March 2025; 162 (11): 114119. https://doi.org/10.1063/5.0245877
 Example of how to use an adaptive-precision potential is provided in examples/PACKAGES/APIP .
 The pair_style pace/apip requires the installation of lib/pace of the ML-PACE package.
 The installation of lib/pace is described in src/ML-PACE/README .
--- a/src/APIP/fix_apip_atom_weight.cpp
+++ b/src/APIP/fix_apip_atom_weight.cpp
@ -0,0 +1,539 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "fix_apip_atom_weight.h"
 #include "atom.h"
 #include "atom_vec_apip.h"
 #include "comm.h"
 #include "error.h"
 #include "fix_store_atom.h"
 #include "force.h"
 #include "group.h"
 #include "modify.h"
 #include "pair.h"
 #include "timer.h"
 #include "update.h"
 using namespace LAMMPS_NS;
 using namespace FixConst;
 FixApipAtomWeight::FixApipAtomWeight(LAMMPS *lmp, int narg, char **arg) :
    Fix(lmp, narg, arg), fixstore(nullptr), time_simple_extract_name(nullptr),
    time_complex_extract_name(nullptr), time_lambda_extract_name(nullptr),
    time_group_extract_name(nullptr), time_group_name(nullptr), fix_lambda(nullptr),
    ap_timer(nullptr)
 {
  if (narg < 9) error->all(FLERR, "Illegal fix balance command");
  ap_timer = new APIPtimer(lmp);
  // set defaults
  time_simple_atom = time_complex_atom = time_group_atom = time_lambda_atom = -1;
  n_simple = n_complex = n_group = n_lambda = 0;
  nevery = -1;
  rescale_work = true;
  peratom_flag = 1;
  size_peratom_cols = 0;    // vector
  time_group_i = -1;
  time_group_bit = 0;
  vector_flag = 1;
  size_vector = 4;
  extvector = 0;
  for (int i = 0; i < size_vector; i++) avg_time_atom[i] = 0;
  nevery = utils::inumeric(FLERR, arg[3], false, lmp);
  if (strcmp(arg[4], "eam") == 0) {
    time_simple_extract_name = utils::strdup("eam/apip:time_per_atom");
  } else if (strcmp(arg[4], "ace") == 0) {
    time_simple_extract_name = utils::strdup("pace/apip/fast:time_per_atom");
  } else {
    time_simple_atom = utils::numeric(FLERR, arg[4], false, lmp);
    avg_time_atom[0] = time_simple_atom;
  }
  if (strcmp(arg[5], "ace") == 0) {
    time_complex_extract_name = utils::strdup("pace/apip:time_per_atom");
  } else {
    time_complex_atom = utils::numeric(FLERR, arg[5], false, lmp);
    avg_time_atom[1] = time_complex_atom;
  }
  if (strcmp(arg[6], "lambda_input") == 0) {
    time_group_extract_name = utils::strdup("lambda_input:time_per_atom");
  } else {
    time_group_atom = utils::numeric(FLERR, arg[6], false, lmp);
    avg_time_atom[2] = time_group_atom;
  }
  if (strcmp(arg[7], "lambda/zone") == 0) {
    time_lambda_extract_name = utils::strdup("lambda_zone:time_per_atom");
  } else {
    time_lambda_atom = utils::numeric(FLERR, arg[7], false, lmp);
    avg_time_atom[3] = time_lambda_atom;
  }
  // read name of group
  time_group_name = utils::strdup(arg[8]);
  time_group_i = group->find(time_group_name);
  if (time_group_i == -1)
    error->all(FLERR, "apip_atom_weight: group {} does not exist", time_group_name);
  time_group_bit = group->bitmask[time_group_i];
  // parse remaining arguments
  for (int iarg = 9; iarg < narg; iarg++) {
    if (strcmp(arg[iarg], "no_rescale") == 0) {
      rescale_work = false;
    } else {
      error->all(FLERR, "apip_atom_weight: unknown argument {}", arg[iarg]);
    }
  }
  // check arguments
  if (nevery < 1) error->all(FLERR, "apip_atom_weight: nevery > 0 required");
  if (!atom->lambda_required_flag)
    error->all(FLERR, "apip_atom_weight: atomic style with lambda_required required");
  if (time_simple_extract_name || time_complex_extract_name || time_group_extract_name ||
      time_lambda_extract_name) {
    if (force->pair == nullptr)
      error->all(FLERR, "apip_atom_weight: extract requires a defined pair style");
  }
  int useless_dim = -1;
  void *extracted_ptr = nullptr;
  if (time_simple_extract_name) {
    if (force->pair->extract(time_simple_extract_name, useless_dim) == nullptr)
      error->all(FLERR, "apip_atom_weight: simple time cannot be extracted with {} from {}",
                 time_simple_extract_name, force->pair_style);
  } else {
    if (time_simple_atom <= 0)
      error->all(FLERR, "apip_atom_weight: time_simple_atom needs to be positive instead of {}",
                 time_simple_atom);
  }
  if (time_complex_extract_name) {
    if (force->pair->extract(time_complex_extract_name, useless_dim) == nullptr)
      error->all(FLERR, "apip_atom_weight: complex time cannot be extracted with {} from {}",
                 time_complex_extract_name, force->pair_style);
  } else {
    if (time_complex_atom <= 0)
      error->all(FLERR, "apip_atom_weight: time_complex_atom needs to be positive instead of {}",
                 time_complex_atom);
  }
  if (time_group_extract_name) {
    if (force->pair->extract(time_group_extract_name, useless_dim) == nullptr)
      error->all(FLERR, "apip_atom_weight: group time cannot be extracted with {} from {}",
                 time_group_extract_name, force->pair_style);
  } else {
    if (time_group_atom <= 0)
      error->all(FLERR, "apip_atom_weight: time_group_atom needs to be positive instead of {}",
                 time_group_atom);
  }
  if (time_lambda_extract_name) {
    if (force->pair->extract(time_lambda_extract_name, useless_dim) == nullptr)
      error->all(FLERR, "apip_atom_weight: lambda time cannot be extracted with {} from {}",
                 time_lambda_extract_name, force->pair_style);
  } else {
    if (time_lambda_atom <= 0)
      error->all(FLERR, "apip_atom_weight: time_lambda_atom needs to be positive instead of {}",
                 time_lambda_atom);
  }
  if (comm->me == 0) {
    utils::logmesg(lmp, "atomic load lambda:\n");
    if (time_simple_extract_name)
      utils::logmesg(lmp, "\tfast potential: extract {}\n", time_simple_extract_name);
    else
      utils::logmesg(lmp, "\tfast potential: const {}\n", time_simple_atom);
    if (time_complex_extract_name)
      utils::logmesg(lmp, "\tprecise potential: extract {}\n", time_complex_extract_name);
    else
      utils::logmesg(lmp, "\tprecise potential: const {}\n", time_complex_atom);
    if (time_group_extract_name)
      utils::logmesg(lmp, "\tlambda_input: extract {}\n", time_group_extract_name);
    else
      utils::logmesg(lmp, "\tlambda_input: const {}\n", time_group_atom);
    if (time_lambda_extract_name)
      utils::logmesg(lmp, "\tlambda: extract {}\n", time_lambda_extract_name);
    else
      utils::logmesg(lmp, "\tlambda: const {}\n", time_lambda_atom);
  }
  global_freq = nevery;
  peratom_freq = nevery;
 }
 /**
 *  Deconstructor. Delete allocated memory.
 */
 FixApipAtomWeight::~FixApipAtomWeight()
 {
  delete ap_timer;
  delete[] time_simple_extract_name;
  delete[] time_complex_extract_name;
  delete[] time_lambda_extract_name;
  delete[] time_group_extract_name;
  delete[] time_group_name;
  // check nfix in case all fixes have already been deleted
  if (fixstore && modify->nfix) modify->delete_fix(fixstore->id);
  fixstore = nullptr;
 }
 /**
  * allocate per-particle weight storage via FixStoreAtom
  * fix could already be allocated if fix balance is re-specified
  */
 void FixApipAtomWeight::post_constructor()
 {
  std::string cmd;
  cmd = id;
  cmd += "LAMBDA_WEIGHT";
  fixstore = dynamic_cast<FixStoreAtom *>(modify->get_fix_by_id(cmd));
  if (!fixstore)
    fixstore = dynamic_cast<FixStoreAtom *>(modify->add_fix(cmd + " all STORE/ATOM 1 0 0 1"));
  // do not carry weights with atoms during normal atom migration
  fixstore->disable = 1;
  vector_atom = fixstore->vstore;
 }
 /**
 *  For lammps.
 *  @return mask
 */
 int FixApipAtomWeight::setmask()
 {
  int mask = 0;
  mask |= PRE_EXCHANGE;
  mask |= PRE_FORCE;    // for setup_pre_force only
  mask |= END_OF_STEP;
  return mask;
 }
 /**
 *  Initialise calculated variables and setup timer objects.
 */
 void FixApipAtomWeight::init()
 {
  int counter = 0;
  for (int i = 0; i < modify->nfix; i++) {
    if (strcmp(modify->fix[i]->style, "apip_atom_weight") == 0) counter++;
  }
  if (counter > 1) error->all(FLERR, "More than one apip_atom_weight fix");
  // get ptr to fix lambda
  counter = 0;
  for (int i = 0; i < modify->nfix; i++) {
    if (strcmp(modify->fix[i]->style, "lambda") == 0) {
      fix_lambda = modify->fix[i];
      counter++;
    }
  }
  if (counter > 1) error->all(FLERR, "More than one fix lambda");
  // This fix is evaluated in pre_exchange, but needs to be evaluated before load-balancing fixes.
  for (auto ifix : modify->get_fix_list()) {
    if (strcmp(id, ifix->id) == 0) {
      // The remaining fixes are called after fix atom_load_lambda and ,thus, are not of interest.
      break;
    } else if (ifix->box_change == BOX_CHANGE_DOMAIN) {
      error->all(FLERR, "apip_atom_weight: fix {} should come after fix {}", ifix->id, id);
    }
  }
  // check that group for time_group has not been deleted
  if (time_group_name) {
    time_group_i = group->find(time_group_name);
    if (time_group_i == -1)
      error->all(FLERR, "apip_atom_weight: group {} does not exist", time_group_name);
    time_group_bit = group->bitmask[time_group_i];
  }
  ap_timer->init();
  last_calc = -1;
 }
 /**
  * Set 1 as initial weight as no forces have been calculated yet.
  */
 void FixApipAtomWeight::setup_pre_exchange()
 {
  // fix balance rebalances in setup_pre_exchange.
  // setup_pre_exchange is called prior to force-calculations.
  // Thus, there are no measured times yet.
  // Fix balance with weight time 1.0 uses 1.0 as weight for each atom.
  int i, nlocal;
  double *weight;
  nlocal = atom->nlocal;
  weight = fixstore->vstore;
  for (i = 0; i < nlocal; i++) weight[i] = 1;
  // store pointer to weight for lammps
  vector_atom = fixstore->vstore;
  // fix balance can move particles and the weight information is required
  // at the end of the step for the dump output.
  // Thus, weights need to migrate with atoms.
  fixstore->disable = 0;
 }
 /**
  * Initial atom migration is done.
  * The atoms do not need to migrate with atoms any more.
  */
 void FixApipAtomWeight::setup_pre_force(int /*vflag*/)
 {
  fixstore->disable = 1;
  // Atoms are with their weights now.
  // -> update vector_atom
  vector_atom = fixstore->vstore;
 }
 /**
  *  Compute weight of particles for load balancing.
  */
 void FixApipAtomWeight::pre_exchange()
 {
  if (update->ntimestep % peratom_freq != 0) { return; }
  calc_work_per_particle();
 }
 /**
  *  Update output pointer for output.
  */
 void FixApipAtomWeight::end_of_step()
 {
  if (update->ntimestep % peratom_freq != 0) { return; }
  // The work is not calculated twice.
  // Call a second time as pre_exchange is not called when there is no exchange.
  calc_work_per_particle();
  // weights should not migrate with atoms
  fixstore->disable = 1;
  vector_atom = fixstore->vstore;
 }
 /**
 *  Calculate the work for a simple/complex atom.
 *  Times and number of atoms are extracted from pair styles.
 *  @note updates particle number and time variables of this class.
 */
 void FixApipAtomWeight::calc_work_per_particle()
 {
  // calculating twice would destroy time measurements
  if (update->ntimestep == last_calc) { return; }
  last_calc = update->ntimestep;
  char *extract_name[4] = {time_simple_extract_name, time_complex_extract_name,
                           time_group_extract_name, time_lambda_extract_name};
  double *time_pa_ptr[4] = {&time_simple_atom, &time_complex_atom, &time_group_atom,
                            &time_lambda_atom};
  double buffer[8];
  int useless_dim = -1;
  // extract times per atom from pair styles if required
  int counter = 0;
  for (int i = 0; i < 4; i++) {
    if (extract_name[i]) {
      // get time per atom
      *(time_pa_ptr[i]) = *((double *) force->pair->extract(extract_name[i], useless_dim));
      // save time per atom to buffer
      if (*(time_pa_ptr[i]) < 0) {
        // no calculations
        buffer[counter] = buffer[counter + 1] = 0;
      } else {
        // save time per calculation
        buffer[counter] = *(time_pa_ptr[i]);
        buffer[counter + 1] = 1;
      }
      counter += 2;
    }
  }
  if (counter) {
    // do not use averaged values for all processors since they depend on the number of neighbours
    // (which can vary, e.g. at a surface
    // -> only use global value if there is no local one
    MPI_Allreduce(MPI_IN_PLACE, buffer, counter, MPI_DOUBLE, MPI_SUM, world);
    for (int i = 3; i >= 0; i--) {
      if (extract_name[i]) {
        // calculate average over all processors
        avg_time_atom[i] = buffer[counter - 1] > 0 ? buffer[counter - 2] / buffer[counter - 1] : 0;
        // use average if there is no local value
        if (*(time_pa_ptr[i]) < 0) *(time_pa_ptr[i]) = avg_time_atom[i];
        counter -= 2;
      }
    }
  }
  //set weight for each particle
  double work_atom, *weight, **lambda_input_history;
  int dim, *mask, *lambda_required;
  weight = fixstore->vstore;
  mask = atom->mask;
  lambda_required = atom->lambda_required;
  // get lambda(time averaged lambda input)
  lambda_input_history = (double **) fix_lambda->extract("fix_lambda:lambda_input_history", dim);
  const int histlen_lambda_input =
      *((int *) fix_lambda->extract("fix_lambda:lambda_input_history_len", dim));
  if (lambda_input_history == nullptr || histlen_lambda_input < 1)
    error->all(FLERR, "apip_atom_weight: extracting fix_lambda:lambda_input_history failed");
  int nlocal = atom->nlocal;
  // assume a homogeneous time per simple and complex particle
  n_simple = n_complex = n_group = n_lambda = 0;
  for (int i = 0; i < nlocal; i++) {
    work_atom = 0;
    if (lambda_required[i] & LambdaRequired::SIMPLE) {
      work_atom += time_simple_atom;
      n_simple++;
    }
    if (lambda_required[i] & LambdaRequired::COMPLEX) {
      work_atom += time_complex_atom;
      n_complex++;
    }
    if (mask[i] & time_group_bit) {
      work_atom += time_group_atom;
      n_group++;
    }
    if (lambda_input_history[i][histlen_lambda_input + 1] != 1) {
      work_atom += time_lambda_atom;
      n_lambda++;
    }
    weight[i] = work_atom;
  }
  if (rescale_work) {
    // calculate sum of vector work
    double work_atoms = 0;
    for (int i = 0; i < nlocal; i++) work_atoms += weight[i];
    // calculate rescale factor
    double rescale_factor = ap_timer->get_work() / work_atoms;
    // apply rescale factor
    for (int i = 0; i < nlocal; i++) weight[i] *= rescale_factor;
  }
  // store pointer to weight for lammps
  vector_atom = fixstore->vstore;
  // weights need to migrate with atoms
  fixstore->disable = 0;
 }
 /**
  * Provide average compute times for the output.
  * 1st: time per simple atom
  * 2nd: time per complex atom
  * 3rd: time per lambda_input calculation
  * 4th: time per lambda calculation
  */
 double FixApipAtomWeight::compute_vector(int i)
 {
  if (i < size_vector) return avg_time_atom[i];
  return 0;
 }
 /**
 *  Set everything to zero.
 *  @param[in] lmp lammps to get the Pointers class
 */
 APIPtimer::APIPtimer(LAMMPS *lmp) : Pointers(lmp)
 {
  for (int i = 0; i < 4; i++) {
    time[i] = 0;
    time_interval[i] = 0;
  }
 }
 /**
 *  Reset times to zero.
 */
 void APIPtimer::init()
 {
  // do not use set_time();
  // lammps resets the timers to zero, but the timers are not zero at timer initialisation time
  for (int i = 0; i < 4; i++) {
    time[i] = 0;
    time_interval[i] = 0;
  }
 }
 /**
 *  Save values of lammps timers.
 *  @note sets time
 */
 void APIPtimer::set_time()
 {
  time[0] = timer->get_wall(Timer::PAIR);
  time[1] = timer->get_wall(Timer::NEIGH);
  time[2] = timer->get_wall(Timer::BOND);
  time[3] = timer->get_wall(Timer::KSPACE);
 }
 /**
 *  Get time work since last call.
 *  @note sets time and time_interval
 *  @return work
 */
 double APIPtimer::get_work()
 {
  double work = 0;
  // store old times
  for (int i = 0; i < 4; i++) time_interval[i] = -time[i];
  set_time();
  // calculate differences to new times
  for (int i = 0; i < 4; i++) {
    time_interval[i] += time[i];
    work += time_interval[i];
  }
  // add constant time to prevent balancing with numerically zero
  // e.g. (for few atoms per processor and balancing every step)
  return work + 0.1;
 }
--- a/src/APIP/fix_apip_atom_weight.h
+++ b/src/APIP/fix_apip_atom_weight.h
@ -0,0 +1,106 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef FIX_CLASS
 // clang-format off
 FixStyle(apip_atom_weight,FixApipAtomWeight);
 // clang-format on
 #else
 #ifndef LMP_FIX_APIP_ATOM_WEIGHT_H
 #define LMP_FIX_APIP_ATOM_WEIGHT_H
 #include "fix.h"
 #include "pointers.h"
 namespace LAMMPS_NS {
 /**
 *  Small wrapper for the lammps timers to get time intervals.
 */
 class APIPtimer : protected Pointers {
 public:
  APIPtimer(class LAMMPS *);
  void init();
  double get_work();
 private:
  double time[4];             ///< value of lammps timers
  double time_interval[4];    ///< time interval between two calls
  void set_time();
 };
 /**
 *  Fix to compute an atomic wegiht that can be used to load-balance an adaptive-precision potential.
 */
 class FixApipAtomWeight : public Fix {
 public:
  FixApipAtomWeight(class LAMMPS *, int, char **);
  ~FixApipAtomWeight() override;
  int setmask() override;
  void post_constructor() override;
  void init() override;
  void end_of_step() override;
  void pre_exchange() override;
  void setup_pre_exchange() override;
  void setup_pre_force(int) override;
  double compute_vector(int) override;
 private:
  bigint last_calc;    ///< last timestep in which weights were calculated
  // user set variables
  // clang-format off
  bool rescale_work;          ///< rescale total work of all atoms according to our model to the measured total work
  char * time_simple_extract_name;  ///< argument for pair->extract to get the simple per_atom_time
  char * time_complex_extract_name; ///< argument for pair->extract to get the complex per_atom_time
  char * time_group_extract_name;   ///< argument for pair->extract to get the time independent of lambda
  char * time_lambda_extract_name;  ///< argument for pair->extract to get the time for lambda max calculation
  char * time_group_name;     ///< name of group corresponding to time_group_extract_name
  int time_group_i;          ///< id of group corresponding to time_group_extract_name
  int time_group_bit;         ///< groupbit corresponding to time_group_extract_name
  // clang-format on
  // calculated variables
  double time_simple_atom;     ///< time per particle of simple pair style
  double time_complex_atom;    ///< time per particle of precise pair style
  double time_group_atom;      ///< time per particle independent of lambda
  double time_lambda_atom;     ///< time per atom with non-simple lambda_own
  int n_simple;                ///< number of simple particles before load balancing z
  int n_complex;               ///< number of complex particles before load balancing z
  int n_group;                 ///< number of group particles before load balancing z
  int n_lambda;                ///< numebr of own_complex particles before load balancing z
  double avg_time_atom[4];    ///< global average of per atom times per type
  // class pointers
  class FixStoreAtom *fixstore;    ///< per-atom weights are stored in FixStore
  class APIPtimer *ap_timer;       ///< wrapper for lammps timers
  class Fix *fix_lambda;           ///< ptr to fix_lambda to extract information
  void calc_work_per_particle();
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/fix_lambda.cpp
+++ b/src/APIP/fix_lambda.cpp
@ -0,0 +1,782 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "fix_lambda.h"
 #include "atom.h"
 #include "citeme.h"
 #include "comm.h"
 #include "error.h"
 #include "fix_store_atom.h"
 #include "force.h"
 #include "group.h"
 #include "memory.h"
 #include "modify.h"
 #include "pair.h"
 #include "update.h"
 using namespace LAMMPS_NS;
 using namespace FixConst;
 static const char cite_fix_lambda_c[] =
    "fix lambda command: doi.org/10.1063/5.0245877\n\n"
    "@Article{Immel25,\n"
    " author = {Immel, David and Drautz, Ralf and Sutmann, Godehard},\n"
    " title = {Adaptive-precision potentials for large-scale atomistic simulations},\n"
    " journal = {The Journal of Chemical Physics},\n"
    " volume = {162},\n"
    " number = {11},\n"
    " pages = {114119},\n"
    " year = {2025}\n"
    "}\n\n";
 /* ---------------------------------------------------------------------- */
 FixLambda::FixLambda(LAMMPS *lmp, int narg, char **arg) :
    Fix(lmp, narg, arg), peratom_stats(nullptr), group_name_simple(nullptr),
    group_name_complex(nullptr), group_name_ignore_lambda_input(nullptr), fixstore(nullptr),
    fixstore2(nullptr), pair_lambda_input(nullptr), pair_lambda_zone(nullptr)
 {
  if (lmp->citeme) lmp->citeme->add(cite_fix_lambda_c);
  // set defaults
  threshold_lo = threshold_hi = threshold_width = -1;
  cut_lo = 4.0;
  cut_hi = 12.0;
  lambda_non_group = 1;    // simple
  history_last = history2_last = -1;
  history_length = history2_length = 100;
  history_used = history2_used = 0;
  min_delta_lambda = 0;
  group_bit_simple = group_bit_complex = group_bit_ignore_lambda_input = 0;
  // output
  peratom_flag = 0;
  peratom_freq = -1;    // default from fix.cpp
  dump_history_flag = false;
  size_peratom_cols = 5;
  invoked_history_update = invoked_history2_update = -1;
  if (narg < 4) error->all(FLERR, "fix lambda requires two arguments");
  threshold_lo = utils::numeric(FLERR, arg[3], false, lmp);
  threshold_hi = utils::numeric(FLERR, arg[4], false, lmp);
  threshold_width = threshold_hi - threshold_lo;
  // parse remaining arguments
  for (int iarg = 5; iarg < narg; iarg++) {
    if (strcmp(arg[iarg], "time_averaged_zone") == 0) {
      if (iarg + 4 >= narg)
        error->all(FLERR, "fix lambda: time_averaged_zone requires four arguments");
      cut_lo = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
      cut_hi = utils::numeric(FLERR, arg[iarg + 2], false, lmp);
      history_length = utils::inumeric(FLERR, arg[iarg + 3], false, lmp);
      history2_length = utils::inumeric(FLERR, arg[iarg + 4], false, lmp);
      iarg += 4;
    } else if (strcmp(arg[iarg], "min_delta_lambda") == 0) {
      if (iarg + 1 >= narg) error->all(FLERR, "fix lambda: min_delta_lambda requires one argument");
      min_delta_lambda = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
      iarg += 1;
    } else if (strcmp(arg[iarg], "lambda_non_group") == 0) {
      if (iarg + 1 >= narg) error->all(FLERR, "fix lambda: lambda_non_group requires an argument");
      if (strcmp(arg[iarg + 1], "precise") == 0) {
        lambda_non_group = 0;
      } else if (strcmp(arg[iarg + 1], "fast") == 0) {
        lambda_non_group = 1;
      } else {
        lambda_non_group = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
        if (lambda_non_group < 0 || lambda_non_group > 1)
          error->all(FLERR, "fix lambda: Illegal value of lambda_non_group");
      }
      iarg++;
    } else if (strcmp(arg[iarg], "store_atomic_stats") == 0) {
      peratom_flag = 1;
    } else if (strcmp(arg[iarg], "dump_atomic_history") == 0) {
      peratom_flag = 1;
      dump_history_flag = true;
    } else if (strcmp(arg[iarg], "group_fast") == 0) {
      // read name of group
      group_name_simple = utils::strdup(arg[iarg + 1]);
      int tmp = group->find(group_name_simple);
      if (tmp == -1) error->all(FLERR, "fix lambda: group {} does not exist", group_name_simple);
      group_bit_simple = group->bitmask[tmp];
      iarg++;
    } else if (strcmp(arg[iarg], "group_precise") == 0) {
      // read name of group
      group_name_complex = utils::strdup(arg[iarg + 1]);
      int tmp = group->find(group_name_complex);
      if (tmp == -1) error->all(FLERR, "fix lambda: group {} does not exist", group_name_complex);
      group_bit_complex = group->bitmask[tmp];
      iarg++;
    } else if (strcmp(arg[iarg], "group_ignore_lambda_input") == 0) {
      // read name of group
      group_name_ignore_lambda_input = utils::strdup(arg[iarg + 1]);
      int tmp = group->find(group_name_ignore_lambda_input);
      if (tmp == -1)
        error->all(FLERR, "fix lambda: group {} does not exist", group_name_ignore_lambda_input);
      group_bit_ignore_lambda_input = group->bitmask[tmp];
      iarg++;
    } else
      error->all(FLERR, "fix lambda: unknown argument {}", arg[iarg]);
  }
  cut_hi_sq = cut_hi * cut_hi;
  cut_width = cut_hi - cut_lo;
  // verify arguments
  if (threshold_lo > threshold_hi || threshold_lo < 0)
    error->all(FLERR, "fix lambda: Illegal or missing threshold values");
  if (min_delta_lambda < 0)
    error->all(FLERR, "fix lambda: min_delta_lambda >= 0 required instead of {}", min_delta_lambda);
  if (cut_lo < 0 || cut_hi < cut_lo) error->all(FLERR, "fix lambda: Illegal cutoff values");
  if (history_length < 2 || history2_length < 2)
    error->all(FLERR, "fix lambda: history_length > 1 required");
  if (comm->me == 0 && ((group_bit_simple != 0) || (group_bit_complex != 0)) &&
      group_bit_ignore_lambda_input == 0)
    error->warning(FLERR,
                   "group_ignore_lambda_input should be used to prevent the calculation of "
                   "lambda_input for atoms that are in the groups group_fast and group_precise.");
  if (!atom->lambda_const_flag) {
    error->all(FLERR, "fix lambda requires atomic style with lambda_const.");
  }
  if (!atom->lambda_flag) { error->all(FLERR, "fix lambda requires atomic style with lambda."); }
  if (!atom->lambda_input_flag) {
    error->all(FLERR, "fix lambda requires atomic style with lambda_input.");
  }
  comm_forward = 2;    // up to two doubles per atom
  comm_forward_flag = FORWARD_TA;
  restart_global = 1;
  if (peratom_flag) {
    if (dump_history_flag) size_peratom_cols += history_length + history2_length + 2;
    peratom_freq = 1;
    // zero the array since dump may access it on timestep 0
    // zero the array since a variable may access it before first run
    nmax_stats = atom->nmax;
    memory->create(peratom_stats, nmax_stats, size_peratom_cols, "lambda:peratom_stats");
    array_atom = peratom_stats;
    int nlocal = atom->nlocal;
    for (int i = 0; i < nlocal; i++)
      for (int j = 0; j < size_peratom_cols; j++) peratom_stats[i][j] = 0;
  }
 }
 /* ----------------------------------------------------------------------
   modify cutoff setings
 ------------------------------------------------------------------------- */
 int FixLambda::modify_param(int narg, char **arg)
 {
  cut_lo = utils::numeric(FLERR, arg[0], false, lmp);
  cut_hi = utils::numeric(FLERR, arg[1], false, lmp);
  cut_hi_sq = cut_hi * cut_hi;
  cut_width = cut_hi - cut_lo;
  if (cut_lo < 0 || cut_hi < cut_lo) error->all(FLERR, "fix lambda: Illegal cutoff values");
  if (force->pair->cutforce < cut_hi)
    error->all(FLERR, "fix lambda: cutoff of potential smaller than cutoff of switching region");
  return 2;
 }
 /* ---------------------------------------------------------------------- */
 FixLambda::~FixLambda()
 {
  // check nfix in case all fixes have already been deleted
  if (fixstore && modify->nfix) modify->delete_fix(fixstore->id);
  if (fixstore2 && modify->nfix) modify->delete_fix(fixstore2->id);
  fixstore = fixstore2 = nullptr;
  memory->destroy(peratom_stats);
  delete[] group_name_simple;
  delete[] group_name_complex;
  delete[] group_name_ignore_lambda_input;
 }
 /* ---------------------------------------------------------------------- */
 int FixLambda::setmask()
 {
  int mask = 0;
  mask |= POST_INTEGRATE;
  mask |= PRE_FORCE;    // for setup_pre_force only
  if (peratom_flag) mask |= END_OF_STEP;
  return mask;
 }
 /* ---------------------------------------------------------------------- */
 void FixLambda::init()
 {
  if (force->pair == nullptr) error->all(FLERR, "Fix lambda requires a pair style be defined");
  // only one fix lambda
  int count = 0;
  for (int i = 0; i < modify->nfix; i++) {
    if (strcmp(modify->fix[i]->style, "lambda") == 0) count++;
  }
  if (count > 1) error->all(FLERR, "More than one fix lambda.");
  // warn if there is no fix lambda_thermostat
  if (comm->me == 0 && modify->get_fix_by_style("lambda_thermostat").size() == 0)
    error->warning(
        FLERR,
        "The energy is not conserved when lambda changes as fix lambda_thermostat is not used.");
  Pair *pair_tmp;
  // lambda_input
  pair_tmp = force->pair_match("lambda_input/", 0);
  if (!pair_tmp) error->all(FLERR, "fix lambda requires a `pair lambda_input`");
  pair_lambda_input = (PairLambdaInput *) pair_tmp;
  // lambda/zone
  pair_tmp = force->pair_match("lambda/zone", 1);
  if (!pair_tmp) error->all(FLERR, "fix lambda requires a `pair lambda`");
  pair_lambda_zone = (PairLambdaZone *) pair_tmp;
  if (force->pair->cutforce < cut_hi)
    error->all(FLERR, "fix lambda: cutoff of potential smaller than cutoff of switching region");
  if (strcmp(atom->atom_style, "apip")) error->all(FLERR, "fix lambda requires atom style apip");
  // check that groups have not been deleted
  if (group_name_simple) {
    int tmp = group->find(group_name_simple);
    if (tmp == -1) error->all(FLERR, "fix lambda: group {} does not exist", group_name_simple);
    group_bit_simple = group->bitmask[tmp];
  }
  if (group_name_complex) {
    int tmp = group->find(group_name_complex);
    if (tmp == -1) error->all(FLERR, "fix lambda: group {} does not exist", group_name_complex);
    group_bit_complex = group->bitmask[tmp];
  }
  if (group_name_ignore_lambda_input) {
    int tmp = group->find(group_name_ignore_lambda_input);
    if (tmp == -1)
      error->all(FLERR, "fix lambda: group {} does not exist", group_name_ignore_lambda_input);
    group_bit_ignore_lambda_input = group->bitmask[tmp];
  }
 }
 /**
  * allocate per-particle storage for past cs values via FixStoreAtom
  * fix could already be allocated if fix lambda is re-specified
  */
 void FixLambda::post_constructor()
 {
  std::string cmd, cmd2;
  cmd = id;
  cmd2 = id;
  cmd += "LAMBDA_INPUT_HISTORY";
  cmd2 += "LAMBDA_HISTORY";
  // delete existing fix store if existing
  fixstore = dynamic_cast<FixStoreAtom *>(modify->get_fix_by_id(cmd));
  fixstore2 = dynamic_cast<FixStoreAtom *>(modify->get_fix_by_id(cmd2));
  // check nfix in case all fixes have already been deleted
  if (fixstore && modify->nfix) modify->delete_fix(fixstore->id);
  if (fixstore2 && modify->nfix) modify->delete_fix(fixstore2->id);
  fixstore = nullptr;
  // create new FixStoreAtom
  // store history_length of last values and the sum over all values
  char history_length_str[40], history2_length_str[40];
  sprintf(history_length_str, "%d", history_length + 2);      // lambda_input
  sprintf(history2_length_str, "%d", history2_length + 1);    // lambda
  // arguments of peratom:
  // first: 1 -> store in restart file
  // second: number of doubles to store per atom
  cmd += " all STORE/ATOM ";
  cmd2 += " all STORE/ATOM ";
  cmd += history_length_str;      // n1
  cmd2 += history2_length_str;    // n1
  cmd += " 0 0 1";                // n2 gflag rflag
  cmd2 += " 0 0 1";               // n2 gflag rflag
  fixstore = dynamic_cast<FixStoreAtom *>(modify->add_fix(cmd));
  fixstore2 = dynamic_cast<FixStoreAtom *>(modify->add_fix(cmd2));
  // carry weights with atoms during normal atom migration
  fixstore->disable = 0;
  fixstore2->disable = 0;
 }
 /**
  * Calculate lambda for initial atoms if required.
  * If required, this includes communication.
  */
 void FixLambda::setup_pre_force(int /*vflag*/)
 {
  // lambda, lambda_input, lambda_input_ta and lambda_const are written to restart files.
  // Calculate lambda_input in pair style.
  pair_lambda_input->calculate_lambda_input();
  // Update lambda_input_history with lambda_input.
  update_lambda_input_history();
  // calculate and communicate lambda_input_ta to neighbours
  communicate_lambda_input_ta();
  // calculate lambda max with lambda_input_ta of own and ngh atoms
  pair_lambda_zone->calculate_lambda();
  // update lambda_history with calculated lambda_input_ta, set lambda, set lambda_input_ta to lambda(own ta lambda_input)
  post_integrate();
  // set initial lambda_const if required, communicate lambda and lambda_const to neighbours
  comm_forward_lambda();
  // pair_lambda_zone->calculate_lambda is again called as default setup force calculation
  // -> communicate lambda_input_ta again to have an appropriate input for this "force" calculation
  // increase invoked update to prevent double values
  communicate_lambda_input_ta();
  // just to be sure
  write_peratom_stats();
 }
 /**
  * The new lambda is stored for own atoms in lambda_input_ta since the last force calculation.
  * Update lambda and lambda_const with the running average including the new lambda.
  */
 void FixLambda::post_integrate()
 {
  double *lambda, *lambda_const, *lambda_input_ta;
  lambda = atom->lambda;
  lambda_const = atom->lambda_const;
  lambda_input_ta = atom->lambda_input_ta;
  update_lambda_history();    // update running average of lambda with lambda_input_ta
  get_lambda_average();       // and copy running average to lambda_input_ta
  // use lambda_input_ta to set lambda max
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    lambda_const[i] = lambda[i];
    lambda[i] = lambda_input_ta[i];
    // prevent useless fluctuations in the switching zone just due to atomic fluctuations
    // the values 0 and 1 are always permitted to prevent atoms from keeping a lambda of epsilon forever
    if (fabs(lambda[i] - lambda_const[i]) < min_delta_lambda && lambda[i] != 1 && lambda[i] != 0)
      lambda[i] = lambda_const[i];
  }
  // set lambda_input_ta to own lambda for new lambda calculation with pair_lambda_zone.cpp
  calculate_lambda_input_ta();
 }
 /**
  * write stats at end of step
  */
 void FixLambda::end_of_step()
 {
  write_peratom_stats();
 }
 /**
  * The new calculated lambda is stored in lambda.
  * Exchange lambda and lambda_const with neighbours.
  * Use only in setup_pre_force.
  */
 void FixLambda::comm_forward_lambda()
 {
  if (history2_used == 1) {
    // There is only one one calculated lambda.
    // -> This is the first lambda calculation.
    // -> set lambda_const to lambda since there is no previous lambda
    double *lambda, *lambda_const;
    int nlocal;
    lambda = atom->lambda;
    lambda_const = atom->lambda_const;
    nlocal = atom->nlocal;
    for (int i = 0; i < nlocal; i++) { lambda_const[i] = lambda[i]; }
  }
  comm_forward_flag = FORWARD_MAX;
  comm->forward_comm(this);
 }
 /**
  * write per atom stats
  */
 void FixLambda::write_peratom_stats()
 {
  if (!peratom_flag) return;
  int i, j, nlocal;
  double **lambda_input_history, **lambda_history;
  nlocal = atom->nlocal;
  lambda_input_history = fixstore->astore;
  lambda_history = fixstore2->astore;
  // grow stats array if required
  if (atom->nmax > nmax_stats) {
    memory->destroy(peratom_stats);
    nmax_stats = atom->nmax;
    memory->create(peratom_stats, nmax_stats, size_peratom_cols, "lambda:peratom_stats");
    array_atom = peratom_stats;
  }
  for (i = 0; i < nlocal; i++) {
    peratom_stats[i][0] = lambda_input_history[i][history_last];    // lambda_input now
    peratom_stats[i][1] =
        lambda_input_history[i][history_length] / history_used;    // lambda_input averaged
    peratom_stats[i][2] =
        lambda_input_history[i][history_length + 1];           // lambda of own ta lambda_input
    peratom_stats[i][3] = lambda_history[i][history2_last];    // lambda max now
    peratom_stats[i][4] =
        lambda_history[i][history2_length] / history2_used;    // lambda max averaged
  }
  if (dump_history_flag) {
    for (i = 0; i < nlocal; i++) {
      // include lambda_input sum -> <= history_length
      for (j = 0; j <= history_length; j++) {
        peratom_stats[i][j + 5] = lambda_input_history[i][j];    // lambda_input history
      }
      for (j = 0; j <= history2_length; j++) {
        peratom_stats[i][j + 6 + history_length] = lambda_history[i][j];    // lambda_input history
      }
    }
  }
 }
 /**
  * Update running average of lambda_input.
  */
 void FixLambda::update_lambda_input_history()
 {
  if (invoked_history_update == update->ntimestep) return;
  invoked_history_update = update->ntimestep;
  double *lambda_input, **lambda_input_history;
  int *mask;
  int nlocal;
  lambda_input = atom->lambda_input;
  mask = atom->mask;
  lambda_input_history = fixstore->astore;
  nlocal = atom->nlocal;
  // update stats about written values
  history_last = (history_last + 1) % history_length;
  history_used = std::min(history_used + 1, history_length);
  for (int i = 0; i < nlocal; i++) {
    if (!(mask[i] & groupbit)) {
      lambda_input_history[i][history_length + 1] = lambda_non_group;
      continue;
    }
    // lambda_input_history[particle_number][history_number]
    // history_number:
    //     0 - history_length - 1 : single lambda_input of past time step
    //     history_length         : sum of all stored past lambda_input values
    //     history_length + 1     : lambda(time averaged lambda_input)
    // subtract the lambda_input to be overwritten from sum
    lambda_input_history[i][history_length] -= lambda_input_history[i][history_last];
    // store new lambda_input value
    lambda_input_history[i][history_last] = lambda_input[i];
    // add the new lambda_input to sum
    lambda_input_history[i][history_length] += lambda_input_history[i][history_last];
    // calculate lambda of new time average
    if (group_name_complex && (mask[i] & group_bit_complex)) {
      // hard code complex with highest priority
      lambda_input_history[i][history_length + 1] = 0;
    } else if (group_name_simple && (mask[i] & group_bit_simple)) {
      // hard code simple with second highest priority
      lambda_input_history[i][history_length + 1] = 1;
    } else if ((mask[i] & groupbit) &&
               !(group_name_ignore_lambda_input && (mask[i] & group_bit_ignore_lambda_input))) {
      // calculate lambda based on lambda_input
      lambda_input_history[i][history_length + 1] =
          switching_function_poly(lambda_input_history[i][history_length] / history_used);
    } else {
      lambda_input_history[i][history_length + 1] = lambda_non_group;
    }
  }
 }
 /**
  * Update running average of lambda with lambda_input_ta.
  */
 void FixLambda::update_lambda_history()
 {
  if (invoked_history2_update == update->ntimestep) return;
  invoked_history2_update = update->ntimestep;
  double *lambda_input_ta, **lambda_history, **lambda_input_history;
  int *mask;
  int nlocal;
  lambda_input_ta = atom->lambda_input_ta;
  mask = atom->mask;
  lambda_history = fixstore2->astore;
  lambda_input_history = fixstore->astore;
  nlocal = atom->nlocal;
  // update stats about written values
  history2_last = (history2_last + 1) % history2_length;
  history2_used = std::min(history2_used + 1, history2_length);
  int tmp = 0;
  for (int i = 0; i < nlocal; i++) {
    if (!(mask[i] & groupbit)) continue;
    // lambda_history[particle_number][history2_number]
    // history2_number:
    //     0 - history2_length - 1 : lambda of past time step
    //     history2_length         : sum of all stored past lambda values
    // subtract the lambda to be overwritten from sum
    lambda_history[i][history2_length] -= lambda_history[i][history2_last];
    // store new lambda_input value
    lambda_history[i][history2_last] = lambda_input_ta[i];
    // add the new lambda_input to sum
    lambda_history[i][history2_length] += lambda_history[i][history2_last];
  }
 }
 /**
  * Copy running average of lambda to lambda_input_ta.
  */
 void FixLambda::get_lambda_average()
 {
  double *lambda_input_ta, **lambda_history, avg;
  int *mask, nlocal;
  mask = atom->mask;
  nlocal = atom->nlocal;
  lambda_history = fixstore2->astore;
  lambda_input_ta = atom->lambda_input_ta;
  // recalculate history sum to limit floating point issues since only changes of the sum are tracked
  if (history2_last == history2_length - 1) {
    double sum;
    for (int i = 0; i < nlocal; i++) {
      sum = 0;
      for (int j = 0; j < history2_length; j++) sum += lambda_history[i][j];
      lambda_history[i][history2_length] = sum;
    }
  }
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) {
      // avg is a division and not exactly 1 or 0
      // exact values are required otherwise many useless complex calculations follow since avg = 1 - epsilon < 1
      // -> hard code zero and one if required
      avg = lambda_history[i][history2_length] / history2_used;
      if (avg > 0.9999)
        lambda_input_ta[i] = 1;    // simple
      else if (avg < 0.0001)
        lambda_input_ta[i] = 0;    // complex
      else
        lambda_input_ta[i] = avg;    // switching
    }
  }
 }
 /**
  * calculate lambda_input_ta for own atoms
  */
 void FixLambda::calculate_lambda_input_ta()
 {
  int i, nlocal;
  int *mask;
  double *lambda_input_ta = atom->lambda_input_ta;
  nlocal = atom->nlocal;
  mask = atom->mask;
  // store time averaged lambda_input for own atoms
  double **lambda_input_history = fixstore->astore;
  for (i = 0; i < nlocal; i++) { lambda_input_ta[i] = lambda_input_history[i][history_length + 1]; }
 }
 /* ----------------------------------------------------------------------
  Compute temporary lambda for owned atoms based on lambda_input_history of owned atoms.
  Save this temporary lambda as lambda_input_ta and send it to neighbours.
 ------------------------------------------------------------------------- */
 void FixLambda::communicate_lambda_input_ta()
 {
  calculate_lambda_input_ta();
  // lambda_input_ta is known only for own atoms
  // -> exchange lambda_input_ta
  comm_forward_flag = FORWARD_TA;
  comm->forward_comm(this);
 }
 // helper function
 // similar to cutoff_func_poly in ace_radial.cpp
 // compare Phys Rev Mat 6, 013804 (2022) APPENDIX C: RADIAL AND CUTOFF FUNCTIONS 2. Cutoff function
 // the first two derivatives of the switching function lambda vanishes at the boundaries of the switching region
 double FixLambda::switching_function_poly(double input)
 {
  // calculate lambda
  if (input <= threshold_lo) {
    return 1;
  } else if (input >= threshold_hi) {
    return 0;
  } else {
    double deltatmp = 1 - 2 * (1 + (input - threshold_hi) / (threshold_width));
    return 0.5 + 7.5 / 2. * (deltatmp / 4. - pow(deltatmp, 3) / 6. + pow(deltatmp, 5) / 20.);
  }
 }
 /**
  * Send lambda to neighbours.
  */
 int FixLambda::pack_forward_comm(int n, int *list, double *buf, int /*pbc_flag*/, int * /*pbc*/)
 {
  int i, j, m;
  double *lambda_input_ta = atom->lambda_input_ta;
  m = 0;
  if (comm_forward_flag == FORWARD_TA) {
    for (i = 0; i < n; i++) {
      j = list[i];
      buf[m++] = lambda_input_ta[j];
    }
  } else if (comm_forward_flag == FORWARD_MAX) {
    for (i = 0; i < n; i++) {
      j = list[i];
      buf[m++] = atom->lambda[j];
      buf[m++] = atom->lambda_const[j];
    }
  }
  return m;
 }
 /**
  * Recv lambda from neighbours.
  */
 void FixLambda::unpack_forward_comm(int n, int first, double *buf)
 {
  int i, m, last;
  double *lambda_input_ta = atom->lambda_input_ta;
  m = 0;
  last = first + n;
  if (comm_forward_flag == FORWARD_TA) {
    for (i = first; i < last; i++) { lambda_input_ta[i] = buf[m++]; }
  } else if (comm_forward_flag == FORWARD_MAX) {
    for (i = first; i < last; i++) {
      atom->lambda[i] = buf[m++];
      atom->lambda_const[i] = buf[m++];
    }
  }
 }
 /**
   * store scalar history information
   */
 void FixLambda::write_restart(FILE *fp)
 {
  int timesteps_since_invoked_history_update = update->ntimestep - invoked_history_update;
  int timesteps_since_invoked_history2_update = update->ntimestep - invoked_history2_update;
  int n = 0;
  double list[8];
  list[n++] = history_length;
  list[n++] = history_used;
  list[n++] = history_last;
  list[n++] = timesteps_since_invoked_history_update;
  list[n++] = history2_length;
  list[n++] = history2_used;
  list[n++] = history2_last;
  list[n++] = timesteps_since_invoked_history2_update;
  if (comm->me == 0) {
    int size = n * sizeof(double);
    fwrite(&size, sizeof(int), 1, fp);
    fwrite(list, sizeof(double), n, fp);
  }
 }
 /* ----------------------------------------------------------------------
   use state info from restart file to restart the Fix
 ------------------------------------------------------------------------- */
 void FixLambda::restart(char *buf)
 {
  int timesteps_since_invoked_history_update, history_length_br,
      timesteps_since_invoked_history2_update, history2_length_br;
  bigint next_file_write_calculated;
  int n = 0;
  auto list = (double *) buf;
  history_length_br = static_cast<int>(list[n++]);
  history_used = static_cast<int>(list[n++]);
  history_last = static_cast<int>(list[n++]);
  invoked_history_update = update->ntimestep - (static_cast<int>(list[n++]));
  history2_length_br = static_cast<int>(list[n++]);
  history2_used = static_cast<int>(list[n++]);
  history2_last = static_cast<int>(list[n++]);
  invoked_history2_update = update->ntimestep - (static_cast<int>(list[n++]));
  // simple comparisons first
  if (history_length != history_length_br)
    error->all(FLERR, "fix lambda: history_length = {} != {} = history_length_before_restart",
               history_length, history_length_br);
  if (history2_length != history2_length_br)
    error->all(FLERR, "fix lambda: history2_length = {} != {} = history2_length_before_restart",
               history2_length, history2_length_br);
 }
 /**
  * extract lambda(time averaged lambda_input) and lambda_input_history_len
  */
 void *FixLambda::extract(const char *str, int &dim)
 {
  dim = 2;
  if (strcmp(str, "fix_lambda:lambda_input_history") == 0 && fixstore) { return fixstore->astore; }
  dim = 0;
  if (strcmp(str, "fix_lambda:lambda_input_history_len") == 0) { return &history_length; }
  if (strcmp(str, "fix_lambda:cut_lo") == 0) { return &cut_lo; }
  if (strcmp(str, "fix_lambda:cut_hi") == 0) { return &cut_hi; }
  if (strcmp(str, "fix_lambda:cut_hi_sq") == 0) { return &cut_hi_sq; }
  if (strcmp(str, "fix_lambda:cut_width") == 0) { return &cut_width; }
  if (strcmp(str, "fix_lambda:lambda_non_group") == 0) { return &lambda_non_group; }
  return nullptr;
 }
--- a/src/APIP/fix_lambda.h
+++ b/src/APIP/fix_lambda.h
@ -0,0 +1,108 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef FIX_CLASS
 // clang-format off
 FixStyle(lambda,FixLambda);
 // clang-format on
 #else
 #ifndef LMP_FIX_LAMBDA_H
 #define LMP_FIX_LAMBDA_H
 #include "fix.h"
 #include "pair_lambda_input.h"
 #include "pair_lambda_zone.h"
 namespace LAMMPS_NS {
 class FixLambda : public Fix {
  friend class PairLambdaInput;
  friend class PairLambdaZone;
 public:
  FixLambda(class LAMMPS *, int, char **);
  ~FixLambda() override;
  int modify_param(int, char **) override;
  void init() override;
  int setmask() override;
  void post_constructor() override;
  void setup_pre_force(int) override;
  void post_integrate() override;
  void end_of_step() override;
  int pack_forward_comm(int, int *, double *, int, int *) override;
  void unpack_forward_comm(int, int, double *) override;
  void write_restart(FILE *) override;
  void restart(char *) override;
  void *extract(const char *, int &) override;
 private:
  enum { FORWARD_MAX, FORWARD_TA };
  int comm_forward_flag;    // flag that determines which variables are communicated in comm forward
  class PairLambdaInput *pair_lambda_input;
  class PairLambdaZone *pair_lambda_zone;
  double cut_lo;    ///< distance at which the cutoff function of the transition zone decays from 1
  double cut_hi;    ///< distance at which the cutoff function of the transition zone is 0
  double cut_width;           ///< cut_hi - cut_lo
  double cut_hi_sq;           ///< cut_hi_sq * cut_hi_sq
  double threshold_lo;        ///< threshold above which the fast potential starts to be turned off
  double threshold_hi;        ///< threshold above which the fast potential is turned off completely
  double threshold_width;     ///< threshold_hi - threshold_lo
  double min_delta_lambda;    ///< minimum steps size of lambda
  double lambda_non_group;    ///< lambda for atoms that are not in the group of this fix
  int history_length;              ///< number of steps of which lambda_input is sterd at max
  int history_used;                ///< number of steps of which lambda_input is currently stored
  int history_last;                ///< index of last written lambda_input value
  class FixStoreAtom *fixstore;    ///< ptr to stored lambda_input values
  int history2_length;              ///< number of steps of which lambda is stored at max
  int history2_used;                ///< number of steps of which lambda is currently stored
  int history2_last;                ///< index of last written lambda value
  class FixStoreAtom *fixstore2;    ///< ptr to stored lambda values
  double switching_function_poly(double);
  bigint invoked_history_update;     ///< last timestep with stored history
  bigint invoked_history2_update;    ///< last timestep with stored history
  bool dump_history_flag;            ///< dump whole stored history (for debugging)
  int group_bit_simple;                    ///< hard coded simple atoms
  int group_bit_complex;                   ///< hard coded complex atoms
  int group_bit_ignore_lambda_input;       ///< ignore lambda_input of this group
  char *group_name_simple;                 ///< hard coded simple atoms
  char *group_name_complex;                ///< hard coded complex atoms
  char *group_name_ignore_lambda_input;    ///< ignore lambda_input of this group
  int nmax_stats;            ///< number of allocated atoms for peratom_stats
  double **peratom_stats;    ///< returned peratom vector
  void calculate_lambda_input_ta();
  void comm_forward_lambda();
  void write_peratom_stats();
  void update_lambda_input_history();
  void communicate_lambda_input_ta();
  void get_lambda_average();
  void update_lambda_history();
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/fix_lambda_thermostat.cpp
+++ b/src/APIP/fix_lambda_thermostat.cpp
@ -0,0 +1,630 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "fix_lambda_thermostat.h"
 #include "atom.h"
 #include "comm.h"
 #include "error.h"
 #include "force.h"
 #include "memory.h"
 #include "modify.h"
 #include "my_page.h"
 #include "neigh_list.h"
 #include "neighbor.h"
 #include "random_park.h"
 #include "update.h"
 #include <algorithm>
 using namespace LAMMPS_NS;
 using namespace FixConst;
 #define PGDELTA 1
 /* ---------------------------------------------------------------------- */
 FixLambdaThermostat::FixLambdaThermostat(LAMMPS *lmp, int narg, char **arg) :
    Fix(lmp, narg, arg), list(nullptr), energy_change_atom(nullptr), peratom_stats(nullptr),
    local_numneigh(nullptr), local_firstneigh(nullptr), ipage(nullptr), jlist_copy(nullptr)
 {
  // set global options for fix class
  vector_flag = 1;
  size_vector = 6;
  extvector = 0;
  // set default vaues
  dtf = 0;
  update_stats = false;
  int seed = 42;
  rescaling_N_neighbours = 200;
  // output
  peratom_flag = 0;
  peratom_freq = -1;    // default from fix.cpp
  size_peratom_cols = 4;
  // parse arguments
  for (int iarg = 3; iarg < narg; iarg++) {
    if (strcmp(arg[iarg], "seed") == 0) {
      if (iarg + 1 >= narg) error->all(FLERR, "fix lambda_thermostat: seed requires one argument");
      seed = utils::inumeric(FLERR, arg[iarg + 1], false, lmp);
      if (seed <= 0) { error->all(FLERR, "fix lambda_thermostat seed <= 0"); }
      iarg++;
    } else if (strcmp(arg[iarg], "store_atomic_forces") == 0) {
      if (iarg + 1 >= narg)
        error->all(FLERR, "fix lambda_thermostat: store_atomic_forces requires one argument");
      peratom_flag = 1;
      peratom_freq = utils::inumeric(FLERR, arg[iarg + 1], false, lmp);
      if (peratom_freq < 1)
        error->all(FLERR, "fix lambda_thermostat: frequency of store_atomic_forces < 1");
      iarg++;
    } else if (strcmp(arg[iarg], "N_rescaling") == 0) {
      if (iarg + 1 >= narg)
        error->all(FLERR, "fix lambda_thermostat: mode number requires one argument");
      rescaling_N_neighbours = utils::inumeric(FLERR, arg[iarg + 1], false, lmp);
      iarg += 1;
    } else
      error->all(FLERR, "fix lambda_thermostat: unknown argument {}", arg[iarg]);
  }
  // error checks
  if (!atom->e_simple_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with e_simple.");
  }
  if (!atom->e_complex_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with e_complex.");
  }
  if (!atom->lambda_const_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with lambda_const.");
  }
  if (!atom->lambda_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with lambda.");
  }
  if (!atom->f_const_lambda_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with f_const_lambda.");
  }
  if (!atom->f_dyn_lambda_flag) {
    error->all(FLERR, "fix lambda_thermostat requires atomic style with f_dyn_lambda.");
  }
  if (rescaling_N_neighbours <= 1)
    error->all(FLERR, "fix lambda_thermostat: rescaling_N_neighbours <= 1");
  // rng for shuffle
  random_mt = std::mt19937(seed);
  // init output values
  energy_change_kin = energy_change_pot = 0;
  nmax_energy = 0;
  reduceflag = 0;
  for (int i = 0; i < size_vector; i++) { outvec[i] = 0; }
  sum_energy_change = sum_energy_violation = 0;
  n_energy_violation = n_energy_differences = 0;
  if (peratom_flag) {
    // zero the array since dump may access it on timestep 0
    // zero the array since a variable may access it before first run
    nmax_stats = atom->nmax;
    memory->create(peratom_stats, nmax_stats, size_peratom_cols, "lambda_thermostat:peratom_stats");
    array_atom = peratom_stats;
    int nlocal = atom->nlocal;
    for (int i = 0; i < nlocal; i++)
      for (int j = 0; j < size_peratom_cols; j++) peratom_stats[i][j] = 0;
  } else {
    nmax_stats = 0;
  }
  nmax_list = 0;
  pgsize = oneatom = 0;
 }
 /* ---------------------------------------------------------------------- */
 FixLambdaThermostat::~FixLambdaThermostat()
 {
  memory->destroy(energy_change_atom);
  memory->destroy(peratom_stats);
  memory->destroy(local_numneigh);
  memory->sfree(local_firstneigh);
  memory->destroy(jlist_copy);
  delete[] ipage;
 }
 /* ---------------------------------------------------------------------- */
 int FixLambdaThermostat::setmask()
 {
  int mask = 0;
  mask |= POST_FORCE;
  mask |= END_OF_STEP;
  return mask;
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::init()
 {
  dtf = 0.5 * update->dt * force->ftm2v;
  // full neighbour list for thermostating
  neighbor->add_request(this, NeighConst::REQ_FULL);
  int counter = 0;
  for (int i = 0; i < modify->nfix; i++)
    if (strcmp(modify->fix[i]->style, "lambda_thermostat") == 0) counter++;
  if (counter > 1) error->all(FLERR, "fix lambda_thermostat: more than one fix lambda_thermostat");
  // local neighbor list
  // create pages if first time or if neighbor pgsize/oneatom has changed
  int create = 0;
  if (ipage == nullptr) create = 1;
  if (pgsize != neighbor->pgsize) create = 1;
  if (oneatom != neighbor->oneatom) create = 1;
  if (oneatom != neighbor->oneatom || ipage == nullptr) {
    // allocate memory for copy of one ngh list
    memory->destroy(jlist_copy);
    memory->create(jlist_copy, neighbor->oneatom, "lambda_thermostat:jlist_copy");
  }
  if (create) {
    delete[] ipage;
    pgsize = neighbor->pgsize;
    oneatom = neighbor->oneatom;
    int nmypage = comm->nthreads;
    ipage = new MyPage<int>[nmypage];
    for (int i = 0; i < nmypage; i++) ipage[i].init(oneatom, pgsize, PGDELTA);
  }
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::init_list(int /*id*/, NeighList *ptr)
 {
  list = ptr;
 }
 /* ----------------------------------------------------------------------
   Create neighbor list from main neighbor list with local atoms only.
   The velocity updates are dependent on the velocity.
   Thus, one would need to communicate a velocity change of a ghost atom directly to all neighbouring processors.
   This communication would kill the performance.
   Thus, update only local particles.
 ------------------------------------------------------------------------- */
 void FixLambdaThermostat::local_neighbour_list()
 {
  int i, j, ii, jj, n, inum, jnum, nlocal;
  int *ilist, *jlist, *numneigh, **firstneigh;
  int *neighptr;
  int *mask = atom->mask;
  if (atom->nmax > nmax_list) {
    nmax_list = atom->nmax;
    memory->destroy(local_numneigh);
    memory->sfree(local_firstneigh);
    memory->create(local_numneigh, nmax_list, "lambda_thermostat:numneigh");
    local_firstneigh =
        (int **) memory->smalloc(nmax_list * sizeof(int *), "lambda_thermostat:firstneigh");
  }
  nlocal = atom->nlocal;
  inum = list->inum;
  ilist = list->ilist;
  numneigh = list->numneigh;
  firstneigh = list->firstneigh;
  // store all local neighbours of local atoms
  // scan full neighbor list of I
  ipage->reset();
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    n = 0;
    neighptr = ipage->vget();
    jlist = firstneigh[i];
    jnum = numneigh[i];
    for (jj = 0; jj < jnum; jj++) {
      j = jlist[jj];
      j &= NEIGHMASK;
      if (j < nlocal && mask[j] & groupbit) neighptr[n++] = j;
    }
    local_firstneigh[i] = neighptr;
    local_numneigh[i] = n;
    ipage->vgot(n);
    if (ipage->status()) error->one(FLERR, "Neighbor list overflow, boost neigh_modify one");
  }
 }
 /* ---------------------------------------------------------------------- */
 double FixLambdaThermostat::calculate_kinetic_energy(int i)
 {
  double *v = atom->v[i];
  double m = (atom->rmass ? atom->rmass[i] : atom->mass[atom->type[i]]);
  return 0.5 * force->mvv2e * m * (v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::post_force(int /*vflag*/)
 {
  init_peratom_stats();
  calculate_energy_change();
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::end_of_step()
 {
  apply_thermostat();
 }
 /**
  * Init per-atom array with zeros.
  */
 void FixLambdaThermostat::init_peratom_stats()
 {
  if ((!peratom_flag) || (update->ntimestep % peratom_freq != 0)) {
    update_stats = false;
    return;
  }
  update_stats = true;
  int nlocal;
  nlocal = atom->nlocal;
  // grow stats array if required
  if (atom->nmax > nmax_stats) {
    memory->destroy(peratom_stats);
    nmax_stats = atom->nmax;
    memory->create(peratom_stats, nmax_stats, size_peratom_cols, "lambda_thermostat:peratom_stats");
    array_atom = peratom_stats;
  }
  for (int i = 0; i < nlocal; i++)
    peratom_stats[i][0] = peratom_stats[i][1] = peratom_stats[i][2] = peratom_stats[i][3] = 0;
 }
 /**
  * Calculate the energy difference of atoms that needs to be corrected
  * by the local thermostat.
  */
 void FixLambdaThermostat::calculate_energy_change()
 {
  double **v = atom->v;
  double *rmass = atom->rmass;
  double *mass = atom->mass;
  int *type = atom->type;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  if (igroup == atom->firstgroup) nlocal = atom->nfirst;
  double *e_simple = atom->e_simple;
  double *e_complex = atom->e_complex;
  double *lambda_const = atom->lambda_const;
  double *lambda = atom->lambda;
  double **f_const_lambda = atom->f_const_lambda;
  double **f_dyn_lambda = atom->f_dyn_lambda;
  double masstmp, dtfm, changetmp;
  // allocate memory for energy change
  if (atom->nmax > nmax_energy) {
    memory->destroy(energy_change_atom);
    nmax_energy = atom->nmax;
    memory->create(energy_change_atom, nmax_energy, "lambda_thermostat:energy_change_atom");
  }
  // reset calculated changes
  energy_change_pot = 0;
  energy_change_kin = 0;
  for (int i = 0; i < nlocal; i++) { energy_change_atom[i] = 0; }
  // calculate potential energy differences
  for (int i = 0; i < nlocal; i++) {
    if ((!(mask[i] & groupbit)) || lambda_const[i] == lambda[i]) { continue; }
    if (e_simple[i] == 0 || e_complex[i] == 0)
      error->one(FLERR, "lambda = {} != {} = lambda_const and e_simple = {} and e_complex = {}",
                 lambda[i], lambda_const[i], e_simple[i], e_complex[i]);
    changetmp =
        (lambda_const[i] - lambda[i]) * e_simple[i] + (lambda[i] - lambda_const[i]) * e_complex[i];
    energy_change_atom[i] += changetmp;
    energy_change_pot += changetmp;
  }
  // calculate kinetic energy difference
  // consider all local atoms
  for (int i = 0; i < nlocal; i++) {
    if (!(mask[i] & groupbit)) { continue; }
    masstmp = (rmass ? rmass[i] : mass[type[i]]);
    dtfm = dtf / masstmp;
    // dtfm = Delta t / 2 (in corresponding units)
    changetmp = (v[i][0] * 2 * dtfm * (f_const_lambda[i][0] - f_dyn_lambda[i][0]) +
                 dtfm * dtfm *
                     (f_const_lambda[i][0] * f_const_lambda[i][0] -
                      f_dyn_lambda[i][0] * f_dyn_lambda[i][0]) +
                 v[i][1] * 2 * dtfm * (f_const_lambda[i][1] - f_dyn_lambda[i][1]) +
                 dtfm * dtfm *
                     (f_const_lambda[i][1] * f_const_lambda[i][1] -
                      f_dyn_lambda[i][1] * f_dyn_lambda[i][1]) +
                 v[i][2] * 2 * dtfm * (f_const_lambda[i][2] - f_dyn_lambda[i][2]) +
                 dtfm * dtfm *
                     (f_const_lambda[i][2] * f_const_lambda[i][2] -
                      f_dyn_lambda[i][2] * f_dyn_lambda[i][2])) *
        masstmp * force->mvv2e * 0.5;
    energy_change_atom[i] += changetmp;
    energy_change_kin += changetmp;
  }
  if (update_stats) {
    for (int i = 0; i < nlocal; i++) peratom_stats[i][4] = energy_change_atom[i];
  }
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::apply_thermostat()
 {
  double xtmp, ytmp, ztmp, delx, dely, delz, delvx, delvy, delvz, r, dotvu, masstmp, massj, muij,
      delv, delv_m, epsilon, epsilonsq, deltaK, rinv;
  double m_cm, v_cm[3], beta_rescaling, k_rel, v_rel[3], radicand;
  int i, ii, inum, *ilist;
  int j, jj, jnum, *jlist;
  int nlocal = atom->nlocal;
  if (igroup == atom->firstgroup) nlocal = atom->nfirst;
  double **x = atom->x;
  double **v = atom->v;
  double *rmass = atom->rmass;
  double *mass = atom->mass;
  int *type = atom->type;
  int *mask = atom->mask;
  double *e_simple = atom->e_simple;
  double *e_complex = atom->e_complex;
  double *lambda_const = atom->lambda_const;
  double *lambda = atom->lambda;
  // calculate local neighbour list without ghost atoms
  local_neighbour_list();
  inum = list->inum;
  ilist = list->ilist;
  // reset stats
  // outvec has to be calculated again
  reduceflag = 1;
  sum_energy_change = 0;
  n_energy_differences = 0;
  // perform bath collisions
  // consider all local atoms
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    if (!(mask[i] & groupbit)) { continue; }
    if (energy_change_atom[i] == 0) { continue; }
    // update stats
    n_energy_differences++;
    // store constant information of target atom
    masstmp = (rmass ? rmass[i] : mass[type[i]]);
    xtmp = x[i][0];
    ytmp = x[i][1];
    ztmp = x[i][2];
    // get neighbour list
    jlist = local_firstneigh[i];
    jnum = local_numneigh[i];
    if (jnum == 0)
      error->one(FLERR,
                 "fix lambda_thermostat: thermostating required for particle with no local "
                 "particles in neighbour list particle: {} {} {} groupbit {}\n",
                 xtmp, ytmp, ztmp, mask[i] & groupbit);
    int i_collisions = 0;
    double e_remain = energy_change_atom[i];
    // copy ngh list
    for (jj = 0; jj < jnum; jj++) jlist_copy[jj] = jlist[jj];
    // shuffle neighbour list for random rescaling set
    std::shuffle(jlist_copy, jlist_copy + jnum, random_mt);
    // rescale velocities relative to centre of mass velocity
    const int n_ngh = MIN(rescaling_N_neighbours, jnum);
    if (n_ngh < 2)
      error->one(FLERR, "fix lambda_thermostat: rescaling not possible for local ngh list size {}",
                 jnum);
    // 1. calculate centre of mass velocity
    // start with own particle ...
    m_cm = masstmp;
    v_cm[0] = masstmp * v[i][0];
    v_cm[1] = masstmp * v[i][1];
    v_cm[2] = masstmp * v[i][2];
    // ... and include neighbours
    for (jj = 0; jj < n_ngh; jj++) {
      j = jlist_copy[jj];
      j &= NEIGHMASK;
      massj = (rmass ? rmass[j] : mass[type[j]]);
      m_cm += massj;
      v_cm[0] += massj * v[j][0];
      v_cm[1] += massj * v[j][1];
      v_cm[2] += massj * v[j][2];
    }
    // normalisation
    v_cm[0] /= m_cm;
    v_cm[1] /= m_cm;
    v_cm[2] /= m_cm;
    // 2. calculate beta_rescaling
    // calculate kinetic energy of relative velocity for own particle ...
    v_rel[0] = v[i][0] - v_cm[0];
    v_rel[1] = v[i][1] - v_cm[1];
    v_rel[2] = v[i][2] - v_cm[2];
    k_rel = masstmp * (v_rel[0] * v_rel[0] + v_rel[1] * v_rel[1] + v_rel[2] * v_rel[2]);
    // ... and include neighbours
    for (jj = 0; jj < n_ngh; jj++) {
      j = jlist_copy[jj];
      j &= NEIGHMASK;
      massj = (rmass ? rmass[j] : mass[type[j]]);
      v_rel[0] = v[j][0] - v_cm[0];
      v_rel[1] = v[j][1] - v_cm[1];
      v_rel[2] = v[j][2] - v_cm[2];
      k_rel += massj * (v_rel[0] * v_rel[0] + v_rel[1] * v_rel[1] + v_rel[2] * v_rel[2]);
    }
    // normalisation
    k_rel *= force->mvv2e / 2.0;
    radicand = e_remain / k_rel + 1;
    if (radicand < 0) {
      // cooling is not possible
      // e_remain is the requested energy change
      // radicand = 0 <=> e_remain = -k_rel
      // -> save the energy error
      sum_energy_violation += (-e_remain - k_rel);    // > 0
      n_energy_violation++;
      e_remain += k_rel;    // save corrected part
      // use smallest possible radicand
      radicand = 0;
    }
    beta_rescaling = sqrt(radicand) - 1;
    // 3. apply velocity changes
    // start with own particle ...
    v_rel[0] = beta_rescaling * (v[i][0] - v_cm[0]);
    v_rel[1] = beta_rescaling * (v[i][1] - v_cm[1]);
    v_rel[2] = beta_rescaling * (v[i][2] - v_cm[2]);
    v[i][0] += v_rel[0];
    v[i][1] += v_rel[1];
    v[i][2] += v_rel[2];
    if (update_stats) {
      // forces
      peratom_stats[i][0] += v_rel[0] * masstmp / dtf;
      peratom_stats[i][1] += v_rel[1] * masstmp / dtf;
      peratom_stats[i][2] += v_rel[2] * masstmp / dtf;
    }
    // ... continue with neighbours
    for (jj = 0; jj < n_ngh; jj++) {
      j = jlist_copy[jj];
      j &= NEIGHMASK;
      v_rel[0] = beta_rescaling * (v[j][0] - v_cm[0]);
      v_rel[1] = beta_rescaling * (v[j][1] - v_cm[1]);
      v_rel[2] = beta_rescaling * (v[j][2] - v_cm[2]);
      v[j][0] += v_rel[0];
      v[j][1] += v_rel[1];
      v[j][2] += v_rel[2];
      if (update_stats) {
        // forces
        massj = (rmass ? rmass[j] : mass[type[j]]);
        peratom_stats[j][0] += v_rel[0] * massj / dtf;
        peratom_stats[j][1] += v_rel[1] * massj / dtf;
        peratom_stats[j][2] += v_rel[2] * massj / dtf;
      }
    }
    sum_energy_change += fabs(e_remain);
  }
  // lambda_const is used -> reset to lambda
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    if (mask[i] & groupbit) lambda_const[i] = lambda[i];
  }
 }
 /* ---------------------------------------------------------------------- */
 double FixLambdaThermostat::compute_vector(int i)
 {
  // 0 # atoms with energy differences compared to lambda_const
  // 1 # bath collisions
  // 2 total change of potential energy compared to lambda_const (sum over all atoms)
  // 3 total change of kinetic   energy compared to lambda_const (sum over all atoms)
  // 4 total energy change due to thermostat
  if (reduceflag) {
    // perform reduction only once per step (if at all)
    outvec[0] = n_energy_differences;
    outvec[1] = energy_change_pot;
    outvec[2] = energy_change_kin;
    outvec[3] = sum_energy_change;
    outvec[4] = sum_energy_violation;
    outvec[5] = n_energy_violation;
    MPI_Allreduce(MPI_IN_PLACE, &outvec, size_vector, MPI_DOUBLE, MPI_SUM, world);
    reduceflag = 0;
  }
  if (i < size_vector) return outvec[i];
  return 0;
 }
 /* ---------------------------------------------------------------------- */
 void FixLambdaThermostat::reset_dt()
 {
  dtf = 0.5 * update->dt * force->ftm2v;
 }
 /* ----------------------------------------------------------------------
   memory usage of local atom-based arrays
 ------------------------------------------------------------------------- */
 double FixLambdaThermostat::memory_usage()
 {
  double bytes = 0;
  bytes += (double) nmax_energy * sizeof(double);
  bytes += (double) nmax_stats * size_peratom_cols * sizeof(double);
  bytes += (double) nmax_list * sizeof(int);
  bytes += (double) nmax_list * sizeof(int *);
  for (int i = 0; i < comm->nthreads; i++) bytes += ipage[i].size();
  return bytes;
 }
--- a/src/APIP/fix_lambda_thermostat.h
+++ b/src/APIP/fix_lambda_thermostat.h
@ -0,0 +1,88 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef FIX_CLASS
 // clang-format off
 FixStyle(lambda_thermostat,FixLambdaThermostat);
 // clang-format on
 #else
 #ifndef LMP_FIX_LAMBDA_THERMOSTAT_H
 #define LMP_FIX_LAMBDA_THERMOSTAT_H
 #include "fix.h"
 #include <random>
 namespace LAMMPS_NS {
 class FixLambdaThermostat : public Fix {
 public:
  FixLambdaThermostat(class LAMMPS *, int, char **);
  ~FixLambdaThermostat() override;
  int setmask() override;
  void init() override;
  void init_list(int, class NeighList *) override;
  void post_force(int) override;
  void end_of_step() override;
  double memory_usage() override;
  void reset_dt() override;
  double compute_vector(int) override;
 protected:
  void apply_thermostat();
  void calculate_energy_change();
  double calculate_kinetic_energy(int);
  void local_neighbour_list();
  void init_peratom_stats();
  double dtf;    // constant for time integration
  class NeighList *list;
  double *energy_change_atom;    // energy violation compared to const lambda case
  double **peratom_stats;        // peratom output
  int nmax_energy;               // number of atoms for which energy_change_atom is allocated
  int nmax_stats;                // number of atoms for which peratom_stats is allocated
  // own neighbour list
  int pgsize;                // size of neighbor page
  int oneatom;               // max # of neighbors for one atom
  int nmax_list;             // size of numneigh, firstneigh arrays
  int *local_numneigh;       // # of pair neighbors for each atom
  int **local_firstneigh;    // ptr to 1st neighbor of each atom
  MyPage<int> *ipage;        // neighbor list pages
  int *jlist_copy;           // jlist for one atom
  int reduceflag;              // 1/0 calculation of compute_vector required/not required
  double outvec[6];            // vector returned by compute_vector
  double energy_change_pot;    // energy conservation violation of all atoms
  double energy_change_kin;    // energy conservation violation of all atoms
  int n_energy_differences;    // number of atoms whose energy has changed compared to the constant lambda case
  double sum_energy_change;       // absolute value of all energy changes due to rescaling
  double sum_energy_violation;    // energy that could not be compensated, accumulated over time
  int n_energy_violation;    // number of atoms whose energy could not be compensated, accumulated over time
  int rescaling_N_neighbours;    // requested neighbour list size used for rescaling
  std::mt19937 random_mt;    // mersenne twister for shuffle
  bool update_stats;    // true(false) peratom output needs(not) to be calculated
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_eam_apip.cpp
+++ b/src/APIP/pair_eam_apip.cpp
@ -0,0 +1,978 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing authors: Stephen Foiles (SNL), Murray Daw (SNL) (EAM)
     David Immel (d.immel@fz-juelich.de, FZJ, Germany) for APIP
 ------------------------------------------------------------------------- */
 #include "pair_eam_apip.h"
 #include "atom.h"
 #include "atom_vec_apip.h"
 #include "comm.h"
 #include "error.h"
 #include "force.h"
 #include "memory.h"
 #include "modify.h"
 #include "neigh_list.h"
 #include "neighbor.h"
 #include "potential_file_reader.h"
 #include "update.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 PairEAMapip::PairEAMapip(LAMMPS *lmp) : Pair(lmp)
 {
  restartinfo = 0;
  manybody_flag = 1;
  unit_convert_flag = utils::get_supported_conversions(utils::ENERGY);
  nmax = 0;
  rho = nullptr;
  fp = nullptr;
  numforce = nullptr;
  type2frho = nullptr;
  nfuncfl = 0;
  funcfl = nullptr;
  setfl = nullptr;
  fs = nullptr;
  frho = nullptr;
  rhor = nullptr;
  z2r = nullptr;
  scale = nullptr;
  rhomax = rhomin = 0.0;
  frho_spline = nullptr;
  rhor_spline = nullptr;
  z2r_spline = nullptr;
  n_non_complex_accumulated = 0;
  time_per_atom = -1;
  time_wall_accumulated = 0;
  lambda_thermostat = true;
 }
 /* ----------------------------------------------------------------------
   check if allocated, since class can be destructed when incomplete
 ------------------------------------------------------------------------- */
 PairEAMapip::~PairEAMapip()
 {
  if (copymode) return;
  memory->destroy(rho);
  memory->destroy(fp);
  memory->destroy(numforce);
  if (allocated) {
    memory->destroy(setflag);
    memory->destroy(cutsq);
    delete[] type2frho;
    type2frho = nullptr;
    memory->destroy(type2rhor);
    memory->destroy(type2z2r);
    memory->destroy(scale);
  }
  if (funcfl) {
    for (int i = 0; i < nfuncfl; i++) {
      delete[] funcfl[i].file;
      memory->destroy(funcfl[i].frho);
      memory->destroy(funcfl[i].rhor);
      memory->destroy(funcfl[i].zr);
    }
    memory->sfree(funcfl);
    funcfl = nullptr;
  }
  if (setfl) {
    for (int i = 0; i < setfl->nelements; i++) delete[] setfl->elements[i];
    delete[] setfl->elements;
    memory->destroy(setfl->mass);
    memory->destroy(setfl->frho);
    memory->destroy(setfl->rhor);
    memory->destroy(setfl->z2r);
    delete setfl;
    setfl = nullptr;
  }
  if (fs) {
    for (int i = 0; i < fs->nelements; i++) delete[] fs->elements[i];
    delete[] fs->elements;
    memory->destroy(fs->mass);
    memory->destroy(fs->frho);
    memory->destroy(fs->rhor);
    memory->destroy(fs->z2r);
    delete fs;
    fs = nullptr;
  }
  memory->destroy(frho);
  memory->destroy(rhor);
  memory->destroy(z2r);
  memory->destroy(frho_spline);
  memory->destroy(rhor_spline);
  memory->destroy(z2r_spline);
 }
 /* ---------------------------------------------------------------------- */
 void PairEAMapip::compute(int eflag, int vflag)
 {
  // start timers
  double time_wall_start = platform::walltime();
  int n_non_complex = 0;
  int i, j, ii, jj, m, inum, jnum, itype, jtype;
  double xtmp, ytmp, ztmp, delx, dely, delz, evdwl, fpair, lambda_ij, fpair_cl;
  double rsq, r, p, rhoip, rhojp, z2, z2p, recip, phip, psip, phi, psip_cl;
  double *coeff;
  int *ilist, *jlist, *numneigh, **firstneigh;
  evdwl = 0.0;
  ev_init(eflag, vflag);
  // grow energy and fp arrays if necessary
  // need to be atom->nmax in length
  if (atom->nmax > nmax) {
    memory->destroy(rho);
    memory->destroy(fp);
    memory->destroy(numforce);
    nmax = atom->nmax;
    memory->create(rho, nmax, "pair:rho");
    memory->create(fp, nmax, "pair:fp");
    memory->create(numforce, nmax, "pair:numforce");
  }
  double **x = atom->x;
  double **f = atom->f;
  double *lambda = atom->lambda;
  int *lambda_required = atom->lambda_required;
  double **f_const_lambda = nullptr;
  double **f_dyn_lambda = nullptr;
  double *e_simple = nullptr;
  double *lambda_const = nullptr;
  if (lambda_thermostat) {
    f_const_lambda = atom->f_const_lambda;
    f_dyn_lambda = atom->f_dyn_lambda;
    e_simple = atom->e_simple;
    lambda_const = atom->lambda_const;
  }
  int *type = atom->type;
  int nlocal = atom->nlocal;
  int nall = nlocal + atom->nghost;
  int newton_pair = force->newton_pair;
  inum = list->inum;
  ilist = list->ilist;
  numneigh = list->numneigh;
  firstneigh = list->firstneigh;
  // zero out density
  for (i = 0; i < nlocal; i++) rho[i] = 0.0;
  // rho = density at each atom
  // loop over neighbors of my atoms
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    xtmp = x[i][0];
    ytmp = x[i][1];
    ztmp = x[i][2];
    itype = type[i];
    jlist = firstneigh[i];
    jnum = numneigh[i];
    for (jj = 0; jj < jnum; jj++) {
      j = jlist[jj];
      j &= NEIGHMASK;
      // avoid double counting due to full neighbour list for two local particles
      // j < i implies j < nlocal
      if (j < i && i < nlocal) { continue; }
      delx = xtmp - x[j][0];
      dely = ytmp - x[j][1];
      delz = ztmp - x[j][2];
      rsq = delx * delx + dely * dely + delz * delz;
      if (rsq < cutforcesq) {
        jtype = type[j];
        p = sqrt(rsq) * rdr + 1.0;
        m = static_cast<int>(p);
        m = MIN(m, nr - 1);
        p -= m;
        p = MIN(p, 1.0);
        coeff = rhor_spline[type2rhor[jtype][itype]][m];
        rho[i] += ((coeff[3] * p + coeff[4]) * p + coeff[5]) * p + coeff[6];
        // do not calculate rho for ghost atoms
        if (j < nlocal) {
          coeff = rhor_spline[type2rhor[itype][jtype]][m];
          rho[j] += ((coeff[3] * p + coeff[4]) * p + coeff[5]) * p + coeff[6];
        }
      }
    }
  }
  // fp = derivative of embedding energy at each atom
  // phi = embedding energy at each atom
  // if rho > rhomax (e.g. due to close approach of two atoms),
  //   will exceed table, so add linear term to conserve energy
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    p = rho[i] * rdrho + 1.0;
    m = static_cast<int>(p);
    m = MAX(1, MIN(m, nrho - 1));
    p -= m;
    p = MIN(p, 1.0);
    coeff = frho_spline[type2frho[type[i]]][m];
    fp[i] = (coeff[0] * p + coeff[1]) * p + coeff[2];
    if (eflag || e_simple) {
      phi = ((coeff[3] * p + coeff[4]) * p + coeff[5]) * p + coeff[6];
      if (rho[i] > rhomax) phi += fp[i] * (rho[i] - rhomax);
      phi *= scale[type[i]][type[i]];
      ev_tally_full(i, 2.0 * lambda[i] * phi, 0.0, 0.0, 0.0, 0.0, 0.0);
      if (e_simple) { e_simple[i] = phi; }
    }
  }
  // compute forces on each atom
  // loop over neighbors of my atoms
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    xtmp = x[i][0];
    ytmp = x[i][1];
    ztmp = x[i][2];
    itype = type[i];
    jlist = firstneigh[i];
    jnum = numneigh[i];
    numforce[i] = 0;
    // The distances between atoms are not calculated.
    // The neighbour list contains more than the cutoff atoms.
    // The calculation of distances is probably not worth the compute time.
    // lambda_required is used to compute the weight of atoms for load balancing.
    // -> store information about required calculations
    if (lambda_required[i] & LambdaRequired::NO_SIMPLE)
      continue;
    else if (!(lambda_required[i] & LambdaRequired::SIMPLE)) {
      // neither SIMPLE nor NO_SIMPLE set
      // check own atom
      if (lambda[i] != 0 || (lambda_thermostat && lambda_const[i] != 0)) {
        // set own atom
        lambda_required[i] |= LambdaRequired::SIMPLE;
        // set neighbour list
        for (jj = 0; jj < jnum; jj++) {
          j = jlist[jj];
          j &= NEIGHMASK;
          if (j < nlocal) lambda_required[j] |= LambdaRequired::SIMPLE;
        }
      } else {
        // check neighbour list
        for (jj = 0; jj < jnum; jj++) {
          j = jlist[jj];
          j &= NEIGHMASK;
          if (lambda[j] != 0 || (lambda_thermostat && lambda_const[j] != 0)) {
            lambda_required[i] |= LambdaRequired::SIMPLE;
            // set lambda also for non-ghost j
            if (j < nlocal) lambda_required[j] |= LambdaRequired::SIMPLE;
            break;
          }
        }
      }
      // SIMPLE not set -> set NO_SIMPLE
      if (!(lambda_required[i] & LambdaRequired::SIMPLE)) {
        // go to next atom
        lambda_required[i] |= LambdaRequired::NO_SIMPLE;
        continue;
      }
    }
    n_non_complex++;
    for (jj = 0; jj < jnum; jj++) {
      j = jlist[jj];
      j &= NEIGHMASK;
      // avoid double counting due to full neighbour list for two local particles
      // j < i implies j < nlocal
      if (j < i && i < nlocal) { continue; }
      delx = xtmp - x[j][0];
      dely = ytmp - x[j][1];
      delz = ztmp - x[j][2];
      rsq = delx * delx + dely * dely + delz * delz;
      if (rsq < cutforcesq) {
        ++numforce[i];
        jtype = type[j];
        r = sqrt(rsq);
        p = r * rdr + 1.0;
        m = static_cast<int>(p);
        m = MIN(m, nr - 1);
        p -= m;
        p = MIN(p, 1.0);
        // rhoip = derivative of (density at atom j due to atom i)
        // rhojp = derivative of (density at atom i due to atom j)
        // phi = pair potential energy
        // phip = phi'
        // z2 = phi * r
        // z2p = (phi * r)' = (phi' r) + phi
        // psip needs both fp[i] and fp[j] terms since r_ij appears in two
        //   terms of embed eng: Fi(sum rho_ij) and Fj(sum rho_ji)
        //   hence embed' = Fi(sum rho_ij) rhojp + Fj(sum rho_ji) rhoip
        // scale factor can be applied by thermodynamic integration
        coeff = rhor_spline[type2rhor[jtype][itype]][m];
        rhojp = (coeff[0] * p + coeff[1]) * p + coeff[2];
        coeff = z2r_spline[type2z2r[itype][jtype]][m];
        z2p = (coeff[0] * p + coeff[1]) * p + coeff[2];
        z2 = ((coeff[3] * p + coeff[4]) * p + coeff[5]) * p + coeff[6];
        recip = 1.0 / r;
        phi = z2 * recip;
        phip = z2p * recip - phi * recip;
        if (j < nlocal) {
          coeff = rhor_spline[type2rhor[itype][jtype]][m];
          rhoip = (coeff[0] * p + coeff[1]) * p + coeff[2];
          psip = lambda[i] * fp[i] * rhojp + lambda[j] * fp[j] * rhoip +
              phip * (lambda[i] + lambda[j]) / 2;
        } else {
          // processor of j calculates the remaining terms (compared to psip in if case)
          psip = lambda[i] * fp[i] * rhojp + phip * 0.5 * lambda[i];
        }
        fpair = -scale[itype][jtype] * psip * recip;
        f[i][0] += delx * fpair;
        f[i][1] += dely * fpair;
        f[i][2] += delz * fpair;
        f[j][0] -= delx * fpair;
        f[j][1] -= dely * fpair;
        f[j][2] -= delz * fpair;
        if (lambda_thermostat) {
          f_dyn_lambda[i][0] += delx * fpair;
          f_dyn_lambda[i][1] += dely * fpair;
          f_dyn_lambda[i][2] += delz * fpair;
          f_dyn_lambda[j][0] -= delx * fpair;
          f_dyn_lambda[j][1] -= dely * fpair;
          f_dyn_lambda[j][2] -= delz * fpair;
          // psip_const
          if (j < nlocal) {
            psip_cl = lambda_const[i] * fp[i] * rhojp + lambda_const[j] * fp[j] * rhoip +
                phip * (lambda_const[i] + lambda_const[j]) / 2;
          } else {
            psip_cl = lambda_const[i] * fp[i] * rhojp + phip * 0.5 * lambda_const[i];
          }
          // calculate fpair_const
          fpair_cl = -scale[itype][jtype] * psip_cl * recip;
          // update f_const_lambda with fpair_const
          f_const_lambda[i][0] += delx * fpair_cl;
          f_const_lambda[i][1] += dely * fpair_cl;
          f_const_lambda[i][2] += delz * fpair_cl;
          f_const_lambda[j][0] -= delx * fpair_cl;
          f_const_lambda[j][1] -= dely * fpair_cl;
          f_const_lambda[j][2] -= delz * fpair_cl;
        }
        if (eflag || e_simple) {
          evdwl = scale[itype][jtype] * phi;
          if (e_simple) {
            e_simple[i] += 0.5 * evdwl;
            if (j < nlocal) e_simple[j] += 0.5 * evdwl;
          }
          ev_tally_full(i, lambda[i] * evdwl, 0.0, 0.0, 0.0, 0.0, 0.0);
          if (j < nlocal) ev_tally_full(j, lambda[j] * evdwl, 0.0, 0.0, 0.0, 0.0, 0.0);
        }
        if (vflag) ev_tally(i, j, nlocal, newton_pair, 0.0, 0.0, fpair, delx, dely, delz);
      }
    }
  }
  if (vflag_fdotr) virial_fdotr_compute();
  // stop timers
  time_wall_accumulated += platform::walltime() - time_wall_start;
  n_non_complex_accumulated += n_non_complex;
 }
 /* ----------------------------------------------------------------------
   allocate all arrays
 ------------------------------------------------------------------------- */
 void PairEAMapip::allocate()
 {
  allocated = 1;
  int n = atom->ntypes;
  memory->create(setflag, n + 1, n + 1, "pair:setflag");
  for (int i = 1; i <= n; i++)
    for (int j = i; j <= n; j++) setflag[i][j] = 0;
  memory->create(cutsq, n + 1, n + 1, "pair:cutsq");
  delete[] map;
  map = new int[n + 1];
  for (int i = 1; i <= n; i++) map[i] = -1;
  type2frho = new int[n + 1];
  memory->create(type2rhor, n + 1, n + 1, "pair:type2rhor");
  memory->create(type2z2r, n + 1, n + 1, "pair:type2z2r");
  memory->create(scale, n + 1, n + 1, "pair:scale");
 }
 /* ----------------------------------------------------------------------
   global settings
 ------------------------------------------------------------------------- */
 void PairEAMapip::settings(int narg, char ** /*arg*/)
 {
  if (narg > 0) error->all(FLERR, "Illegal pair_style command");
 }
 /* ----------------------------------------------------------------------
   set coeffs for one or more type pairs
   read DYNAMO funcfl file
 ------------------------------------------------------------------------- */
 void PairEAMapip::coeff(int narg, char **arg)
 {
  if (!allocated) allocate();
  if (narg != 3) error->all(FLERR, "Incorrect args for pair coefficients");
  // parse pair of atom types
  int ilo, ihi, jlo, jhi;
  utils::bounds(FLERR, arg[0], 1, atom->ntypes, ilo, ihi, error);
  utils::bounds(FLERR, arg[1], 1, atom->ntypes, jlo, jhi, error);
  // read funcfl file if hasn't already been read
  // store filename in Funcfl data struct
  int ifuncfl;
  for (ifuncfl = 0; ifuncfl < nfuncfl; ifuncfl++)
    if (strcmp(arg[2], funcfl[ifuncfl].file) == 0) break;
  if (ifuncfl == nfuncfl) {
    nfuncfl++;
    funcfl = (Funcfl *) memory->srealloc(funcfl, nfuncfl * sizeof(Funcfl), "pair:funcfl");
    read_file(arg[2]);
    funcfl[ifuncfl].file = utils::strdup(arg[2]);
  }
  // set setflag and map only for i,i type pairs
  // set mass of atom type if i = j
  int count = 0;
  for (int i = ilo; i <= ihi; i++) {
    for (int j = MAX(jlo, i); j <= jhi; j++) {
      if (i == j) {
        setflag[i][i] = 1;
        map[i] = ifuncfl;
        atom->set_mass(FLERR, i, funcfl[ifuncfl].mass);
        count++;
      }
      scale[i][j] = 1.0;
    }
  }
  if (count == 0) error->all(FLERR, "Incorrect args for pair coefficients");
 }
 /* ----------------------------------------------------------------------
   init specific to this pair style
 ------------------------------------------------------------------------- */
 void PairEAMapip::init_style()
 {
  // convert read-in file(s) to arrays and spline them
  if (!atom->lambda_flag)
    error->all(FLERR, "Pair style eam/apip requires an atom style with lambda");
  if (force->newton_pair == 0) error->all(FLERR, "Pair style eam/apip requires newton pair on");
  if (!atom->lambda_required_flag)
    error->all(FLERR, "pair style eam/apip requires an atom style with lambda_required.");
  file2array();
  array2spline();
  // communication during computation should be avoided
  // -> do not exchange the derivative of the embedding function by default
  neighbor->add_request(this, NeighConst::REQ_FULL);
 }
 /* ----------------------------------------------------------------------
   init for one type pair i,j and corresponding j,i
 ------------------------------------------------------------------------- */
 double PairEAMapip::init_one(int i, int j)
 {
  // single global cutoff = max of cut from all files read in
  // for funcfl could be multiple files
  // for setfl or fs, just one file
  if (setflag[i][j] == 0) scale[i][j] = 1.0;
  scale[j][i] = scale[i][j];
  if (funcfl) {
    cutmax = 0.0;
    for (int m = 0; m < nfuncfl; m++) cutmax = MAX(cutmax, funcfl[m].cut);
  } else if (setfl)
    cutmax = setfl->cut;
  else if (fs)
    cutmax = fs->cut;
  cutforcesq = cutmax * cutmax;
  return cutmax;
 }
 /**
  * setup specific to this pair style
  * Determine whether there is a fix lambda_thermostat or not and set
  * lambda_thermostat.
  */
 void PairEAMapip::setup()
 {
  if (modify->get_fix_by_style("^lambda_thermostat$").size() == 0) {
    lambda_thermostat = false;
  } else {
    lambda_thermostat = true;
    if (!atom->lambda_const_flag)
      error->all(
          FLERR,
          "Pair style pace/apip requires an atom style with lambda_const for a local thermostat.");
    if (!atom->e_simple_flag)
      error->all(
          FLERR,
          "Pair style pace/apip requires an atom style with e_simple for a local thermostat.");
    if (!atom->f_const_lambda_flag)
      error->all(FLERR,
                 "Pair style pace/apip requires an atom style with f_const_lambda for a local "
                 "thermostat.");
    if (!atom->f_dyn_lambda_flag)
      error->all(FLERR,
                 "Pair style pace/apip requires an atom style with f_const_lambda for a local "
                 "thermostat.");
  }
 }
 /* ----------------------------------------------------------------------
   read potential values from a DYNAMO single element funcfl file
 ------------------------------------------------------------------------- */
 void PairEAMapip::read_file(char *filename)
 {
  Funcfl *file = &funcfl[nfuncfl - 1];
  // read potential file
  if (comm->me == 0) {
    PotentialFileReader reader(lmp, filename, "eam", unit_convert_flag);
    // transparently convert units for supported conversions
    int unit_convert = reader.get_unit_convert();
    double conversion_factor = utils::get_conversion_factor(utils::ENERGY, unit_convert);
    try {
      reader.skip_line();
      ValueTokenizer values = reader.next_values(2);
      values.next_int();    // ignore
      file->mass = values.next_double();
      values = reader.next_values(5);
      file->nrho = values.next_int();
      file->drho = values.next_double();
      file->nr = values.next_int();
      file->dr = values.next_double();
      file->cut = values.next_double();
      if ((file->nrho <= 0) || (file->nr <= 0) || (file->dr <= 0.0))
        error->one(FLERR, "Invalid EAM potential file");
      memory->create(file->frho, (file->nrho + 1), "pair:frho");
      memory->create(file->rhor, (file->nr + 1), "pair:rhor");
      memory->create(file->zr, (file->nr + 1), "pair:zr");
      reader.next_dvector(&file->frho[1], file->nrho);
      reader.next_dvector(&file->zr[1], file->nr);
      reader.next_dvector(&file->rhor[1], file->nr);
      if (unit_convert) {
        const double sqrt_conv = sqrt(conversion_factor);
        for (int i = 1; i <= file->nrho; ++i) file->frho[i] *= conversion_factor;
        for (int j = 1; j <= file->nr; ++j) file->zr[j] *= sqrt_conv;
      }
    } catch (TokenizerException &e) {
      error->one(FLERR, e.what());
    }
  }
  MPI_Bcast(&file->mass, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->nrho, 1, MPI_INT, 0, world);
  MPI_Bcast(&file->drho, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->nr, 1, MPI_INT, 0, world);
  MPI_Bcast(&file->dr, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->cut, 1, MPI_DOUBLE, 0, world);
  if (comm->me != 0) {
    memory->create(file->frho, (file->nrho + 1), "pair:frho");
    memory->create(file->rhor, (file->nr + 1), "pair:rhor");
    memory->create(file->zr, (file->nr + 1), "pair:zr");
  }
  MPI_Bcast(&file->frho[1], file->nrho, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->zr[1], file->nr, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->rhor[1], file->nr, MPI_DOUBLE, 0, world);
 }
 /* ----------------------------------------------------------------------
   convert read-in funcfl potential(s) to standard array format
   interpolate all file values to a single grid and cutoff
 ------------------------------------------------------------------------- */
 void PairEAMapip::file2array()
 {
  int i, j, k, m, n;
  int ntypes = atom->ntypes;
  double sixth = 1.0 / 6.0;
  // determine max function params from all active funcfl files
  // active means some element is pointing at it via map
  int active;
  double rmax;
  dr = drho = rmax = rhomax = 0.0;
  for (int i = 0; i < nfuncfl; i++) {
    active = 0;
    for (j = 1; j <= ntypes; j++)
      if (map[j] == i) active = 1;
    if (active == 0) continue;
    Funcfl *file = &funcfl[i];
    dr = MAX(dr, file->dr);
    drho = MAX(drho, file->drho);
    rmax = MAX(rmax, (file->nr - 1) * file->dr);
    rhomax = MAX(rhomax, (file->nrho - 1) * file->drho);
  }
  // set nr,nrho from cutoff and spacings
  // 0.5 is for round-off in divide
  nr = static_cast<int>(rmax / dr + 0.5);
  nrho = static_cast<int>(rhomax / drho + 0.5);
  // ------------------------------------------------------------------
  // setup frho arrays
  // ------------------------------------------------------------------
  // allocate frho arrays
  // nfrho = # of funcfl files + 1 for zero array
  nfrho = nfuncfl + 1;
  memory->destroy(frho);
  memory->create(frho, nfrho, nrho + 1, "pair:frho");
  // interpolate each file's frho to a single grid and cutoff
  double r, p, cof1, cof2, cof3, cof4;
  n = 0;
  for (i = 0; i < nfuncfl; i++) {
    Funcfl *file = &funcfl[i];
    for (m = 1; m <= nrho; m++) {
      r = (m - 1) * drho;
      p = r / file->drho + 1.0;
      k = static_cast<int>(p);
      k = MIN(k, file->nrho - 2);
      k = MAX(k, 2);
      p -= k;
      p = MIN(p, 2.0);
      cof1 = -sixth * p * (p - 1.0) * (p - 2.0);
      cof2 = 0.5 * (p * p - 1.0) * (p - 2.0);
      cof3 = -0.5 * p * (p + 1.0) * (p - 2.0);
      cof4 = sixth * p * (p * p - 1.0);
      frho[n][m] = cof1 * file->frho[k - 1] + cof2 * file->frho[k] + cof3 * file->frho[k + 1] +
          cof4 * file->frho[k + 2];
    }
    n++;
  }
  // add extra frho of zeroes for non-EAM types to point to (pair hybrid)
  // this is necessary b/c fp is still computed for non-EAM atoms
  for (m = 1; m <= nrho; m++) frho[nfrho - 1][m] = 0.0;
  // type2frho[i] = which frho array (0 to nfrho-1) each atom type maps to
  // if atom type doesn't point to file (non-EAM atom in pair hybrid)
  // then map it to last frho array of zeroes
  for (i = 1; i <= ntypes; i++)
    if (map[i] >= 0)
      type2frho[i] = map[i];
    else
      type2frho[i] = nfrho - 1;
  // ------------------------------------------------------------------
  // setup rhor arrays
  // ------------------------------------------------------------------
  // allocate rhor arrays
  // nrhor = # of funcfl files
  nrhor = nfuncfl;
  memory->destroy(rhor);
  memory->create(rhor, nrhor, nr + 1, "pair:rhor");
  // interpolate each file's rhor to a single grid and cutoff
  n = 0;
  for (i = 0; i < nfuncfl; i++) {
    Funcfl *file = &funcfl[i];
    for (m = 1; m <= nr; m++) {
      r = (m - 1) * dr;
      p = r / file->dr + 1.0;
      k = static_cast<int>(p);
      k = MIN(k, file->nr - 2);
      k = MAX(k, 2);
      p -= k;
      p = MIN(p, 2.0);
      cof1 = -sixth * p * (p - 1.0) * (p - 2.0);
      cof2 = 0.5 * (p * p - 1.0) * (p - 2.0);
      cof3 = -0.5 * p * (p + 1.0) * (p - 2.0);
      cof4 = sixth * p * (p * p - 1.0);
      rhor[n][m] = cof1 * file->rhor[k - 1] + cof2 * file->rhor[k] + cof3 * file->rhor[k + 1] +
          cof4 * file->rhor[k + 2];
    }
    n++;
  }
  // type2rhor[i][j] = which rhor array (0 to nrhor-1) each type pair maps to
  // for funcfl files, I,J mapping only depends on I
  // OK if map = -1 (non-EAM atom in pair hybrid) b/c type2rhor not used
  for (i = 1; i <= ntypes; i++)
    for (j = 1; j <= ntypes; j++) type2rhor[i][j] = map[i];
  // ------------------------------------------------------------------
  // setup z2r arrays
  // ------------------------------------------------------------------
  // allocate z2r arrays
  // nz2r = N*(N+1)/2 where N = # of funcfl files
  nz2r = nfuncfl * (nfuncfl + 1) / 2;
  memory->destroy(z2r);
  memory->create(z2r, nz2r, nr + 1, "pair:z2r");
  // create a z2r array for each file against other files, only for I >= J
  // interpolate zri and zrj to a single grid and cutoff
  // final z2r includes unit conversion of 27.2 eV/Hartree and 0.529 Ang/Bohr
  double zri, zrj;
  n = 0;
  for (i = 0; i < nfuncfl; i++) {
    Funcfl *ifile = &funcfl[i];
    for (j = 0; j <= i; j++) {
      Funcfl *jfile = &funcfl[j];
      for (m = 1; m <= nr; m++) {
        r = (m - 1) * dr;
        p = r / ifile->dr + 1.0;
        k = static_cast<int>(p);
        k = MIN(k, ifile->nr - 2);
        k = MAX(k, 2);
        p -= k;
        p = MIN(p, 2.0);
        cof1 = -sixth * p * (p - 1.0) * (p - 2.0);
        cof2 = 0.5 * (p * p - 1.0) * (p - 2.0);
        cof3 = -0.5 * p * (p + 1.0) * (p - 2.0);
        cof4 = sixth * p * (p * p - 1.0);
        zri = cof1 * ifile->zr[k - 1] + cof2 * ifile->zr[k] + cof3 * ifile->zr[k + 1] +
            cof4 * ifile->zr[k + 2];
        p = r / jfile->dr + 1.0;
        k = static_cast<int>(p);
        k = MIN(k, jfile->nr - 2);
        k = MAX(k, 2);
        p -= k;
        p = MIN(p, 2.0);
        cof1 = -sixth * p * (p - 1.0) * (p - 2.0);
        cof2 = 0.5 * (p * p - 1.0) * (p - 2.0);
        cof3 = -0.5 * p * (p + 1.0) * (p - 2.0);
        cof4 = sixth * p * (p * p - 1.0);
        zrj = cof1 * jfile->zr[k - 1] + cof2 * jfile->zr[k] + cof3 * jfile->zr[k + 1] +
            cof4 * jfile->zr[k + 2];
        z2r[n][m] = 27.2 * 0.529 * zri * zrj;
      }
      n++;
    }
  }
  // type2z2r[i][j] = which z2r array (0 to nz2r-1) each type pair maps to
  // set of z2r arrays only fill lower triangular Nelement matrix
  // value = n = sum over rows of lower-triangular matrix until reach irow,icol
  // swap indices when irow < icol to stay lower triangular
  // if map = -1 (non-EAM atom in pair hybrid):
  //   type2z2r is not used by non-opt
  //   but set type2z2r to 0 since accessed by opt
  int irow, icol;
  for (i = 1; i <= ntypes; i++) {
    for (j = 1; j <= ntypes; j++) {
      irow = map[i];
      icol = map[j];
      if (irow == -1 || icol == -1) {
        type2z2r[i][j] = 0;
        continue;
      }
      if (irow < icol) {
        irow = map[j];
        icol = map[i];
      }
      n = 0;
      for (m = 0; m < irow; m++) n += m + 1;
      n += icol;
      type2z2r[i][j] = n;
    }
  }
 }
 /* ---------------------------------------------------------------------- */
 void PairEAMapip::array2spline()
 {
  rdr = 1.0 / dr;
  rdrho = 1.0 / drho;
  memory->destroy(frho_spline);
  memory->destroy(rhor_spline);
  memory->destroy(z2r_spline);
  memory->create(frho_spline, nfrho, nrho + 1, 7, "pair:frho");
  memory->create(rhor_spline, nrhor, nr + 1, 7, "pair:rhor");
  memory->create(z2r_spline, nz2r, nr + 1, 7, "pair:z2r");
  for (int i = 0; i < nfrho; i++) interpolate(nrho, drho, frho[i], frho_spline[i]);
  for (int i = 0; i < nrhor; i++) interpolate(nr, dr, rhor[i], rhor_spline[i]);
  for (int i = 0; i < nz2r; i++) interpolate(nr, dr, z2r[i], z2r_spline[i]);
 }
 /* ---------------------------------------------------------------------- */
 void PairEAMapip::interpolate(int n, double delta, double *f, double **spline)
 {
  for (int m = 1; m <= n; m++) spline[m][6] = f[m];
  spline[1][5] = spline[2][6] - spline[1][6];
  spline[2][5] = 0.5 * (spline[3][6] - spline[1][6]);
  spline[n - 1][5] = 0.5 * (spline[n][6] - spline[n - 2][6]);
  spline[n][5] = spline[n][6] - spline[n - 1][6];
  for (int m = 3; m <= n - 2; m++)
    spline[m][5] =
        ((spline[m - 2][6] - spline[m + 2][6]) + 8.0 * (spline[m + 1][6] - spline[m - 1][6])) /
        12.0;
  for (int m = 1; m <= n - 1; m++) {
    spline[m][4] = 3.0 * (spline[m + 1][6] - spline[m][6]) - 2.0 * spline[m][5] - spline[m + 1][5];
    spline[m][3] = spline[m][5] + spline[m + 1][5] - 2.0 * (spline[m + 1][6] - spline[m][6]);
  }
  spline[n][4] = 0.0;
  spline[n][3] = 0.0;
  for (int m = 1; m <= n; m++) {
    spline[m][2] = spline[m][5] / delta;
    spline[m][1] = 2.0 * spline[m][4] / delta;
    spline[m][0] = 3.0 * spline[m][3] / delta;
  }
 }
 /* ----------------------------------------------------------------------
   memory usage of local atom-based arrays
 ------------------------------------------------------------------------- */
 double PairEAMapip::memory_usage()
 {
  double bytes = (double) maxeatom * sizeof(double);
  bytes += (double) maxvatom * 6 * sizeof(double);
  bytes += (double) 2 * nmax * sizeof(double);
  return bytes;
 }
 /* ----------------------------------------------------------------------
   swap fp array with one passed in by caller
 ------------------------------------------------------------------------- */
 void PairEAMapip::swap_eam(double *fp_caller, double **fp_caller_hold)
 {
  double *tmp = fp;
  fp = fp_caller;
  *fp_caller_hold = tmp;
 }
 /* ----------------------------------------------------------------------
   set return values for timers and counted particles
 ------------------------------------------------------------------------- */
 void PairEAMapip::calculate_time_per_atom()
 {
  if (n_non_complex_accumulated > 0)
    time_per_atom = time_wall_accumulated / n_non_complex_accumulated;
  else
    time_per_atom = -1;
  // reset
  time_wall_accumulated = 0;
  n_non_complex_accumulated = 0;
 }
 /* ---------------------------------------------------------------------- */
 void *PairEAMapip::extract(const char *str, int &dim)
 {
  dim = 2;
  if (strcmp(str, "scale") == 0) return (void *) scale;
  dim = 0;
  if (strcmp(str, "eam/apip:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  return nullptr;
 }
--- a/src/APIP/pair_eam_apip.h
+++ b/src/APIP/pair_eam_apip.h
@ -0,0 +1,123 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing authors: Stephen Foiles (SNL), Murray Daw (SNL) (EAM)
     David Immel (d.immel@fz-juelich.de, FZJ, Germany) (APIP)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(eam/apip,PairEAMapip);
 // clang-format on
 #else
 #ifndef LMP_PAIR_EAM_APIP_H
 #define LMP_PAIR_EAM_APIP_H
 #include "pair.h"
 namespace LAMMPS_NS {
 class PairEAMapip : public Pair {
 public:
  friend class FixSemiGrandCanonicalMC;    // Alex Stukowski option
  // public variables so ATC package can access them
  double cutmax;
  // potentials as array data
  int nrho, nr;
  int nfrho, nrhor, nz2r;
  double **frho, **rhor, **z2r;
  int *type2frho, **type2rhor, **type2z2r;
  // potentials in spline form used for force computation
  double dr, rdr, drho, rdrho, rhomax, rhomin;
  double ***rhor_spline, ***frho_spline, ***z2r_spline;
  PairEAMapip(class LAMMPS *);
  ~PairEAMapip() override;
  void compute(int, int) override;
  void settings(int, char **) override;
  void setup() override;
  void coeff(int, char **) override;
  void init_style() override;
  double init_one(int, int) override;
  void *extract(const char *, int &) override;
  double memory_usage() override;
  void swap_eam(double *, double **) override;
 protected:
  int nmax;    // allocated size of per-atom arrays
  double cutforcesq;
  double **scale;
  // per-atom arrays
  double *rho, *fp;
  int *numforce;
  // potentials as file data
  struct Funcfl {
    char *file;
    int nrho, nr;
    double drho, dr, cut, mass;
    double *frho, *rhor, *zr;
  };
  Funcfl *funcfl;
  int nfuncfl;
  struct Setfl {
    char **elements;
    int nelements, nrho, nr;
    double drho, dr, cut;
    double *mass;
    double **frho, **rhor, ***z2r;
  };
  Setfl *setfl;
  struct Fs {
    char **elements;
    int nelements, nrho, nr;
    double drho, dr, cut;
    double *mass;
    double **frho, ***rhor, ***z2r;
  };
  Fs *fs;
  virtual void allocate();
  virtual void array2spline();
  void interpolate(int, double, double *, double **);
  virtual void read_file(char *);
  virtual void file2array();
  // stats required for load balancing
  int n_non_complex_accumulated;    // number of calculated atoms
  double time_wall_accumulated;     // time required for the atom calculation
  double time_per_atom;             // time for one calculation
  void calculate_time_per_atom();
  bool lambda_thermostat;    // true/false there is one/no fix lambda_thermostat
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_eam_fs_apip.cpp
+++ b/src/APIP/pair_eam_fs_apip.cpp
@ -0,0 +1,365 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing authors: Tim Lau (MIT) for EAM/FS
     David Immel (d.immel@fz-juelich.de, FZJ, Germany) for APIP
 ------------------------------------------------------------------------- */
 #include "pair_eam_fs_apip.h"
 #include "atom.h"
 #include "comm.h"
 #include "error.h"
 #include "memory.h"
 #include "potential_file_reader.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 PairEAMFSapip::PairEAMFSapip(LAMMPS *lmp) : PairEAMapip(lmp)
 {
  one_coeff = 1;
  manybody_flag = 1;
  he_flag = 0;
 }
 /* ----------------------------------------------------------------------
   set coeffs for one or more type pairs
   read EAM Finnis-Sinclair file
 ------------------------------------------------------------------------- */
 void PairEAMFSapip::coeff(int narg, char **arg)
 {
  int i, j;
  if (!allocated) allocate();
  if (narg != 3 + atom->ntypes) error->all(FLERR, "Incorrect args for pair coefficients");
  // insure I,J args are * *
  if (strcmp(arg[0], "*") != 0 || strcmp(arg[1], "*") != 0)
    error->all(FLERR, "Incorrect args for pair coefficients");
  // read EAM Finnis-Sinclair file
  if (fs) {
    for (i = 0; i < fs->nelements; i++) delete[] fs->elements[i];
    delete[] fs->elements;
    memory->destroy(fs->mass);
    memory->destroy(fs->frho);
    memory->destroy(fs->rhor);
    memory->destroy(fs->z2r);
    delete fs;
  }
  fs = new Fs();
  read_file(arg[2]);
  // read args that map atom types to elements in potential file
  // map[i] = which element the Ith atom type is, -1 if "NULL"
  for (i = 3; i < narg; i++) {
    if (strcmp(arg[i], "NULL") == 0) {
      map[i - 2] = -1;
      continue;
    }
    for (j = 0; j < fs->nelements; j++)
      if (strcmp(arg[i], fs->elements[j]) == 0) break;
    if (j < fs->nelements)
      map[i - 2] = j;
    else
      error->all(FLERR, "No matching element in EAM potential file");
  }
  // clear setflag since coeff() called once with I,J = * *
  int n = atom->ntypes;
  for (i = 1; i <= n; i++)
    for (j = i; j <= n; j++) setflag[i][j] = 0;
  // set setflag i,j for type pairs where both are mapped to elements
  // set mass of atom type if i = j
  int count = 0;
  for (i = 1; i <= n; i++) {
    for (j = i; j <= n; j++) {
      if (map[i] >= 0 && map[j] >= 0) {
        setflag[i][j] = 1;
        if (i == j) atom->set_mass(FLERR, i, fs->mass[map[i]]);
        count++;
      }
      scale[i][j] = 1.0;
    }
  }
  if (count == 0) error->all(FLERR, "Incorrect args for pair coefficients");
 }
 /* ----------------------------------------------------------------------
   read a multi-element DYNAMO setfl file
 ------------------------------------------------------------------------- */
 void PairEAMFSapip::read_file(char *filename)
 {
  Fs *file = fs;
  // read potential file
  if (comm->me == 0) {
    PotentialFileReader reader(lmp, filename, he_flag ? "eam/he" : "eam/fs", unit_convert_flag);
    // transparently convert units for supported conversions
    int unit_convert = reader.get_unit_convert();
    double conversion_factor = utils::get_conversion_factor(utils::ENERGY, unit_convert);
    try {
      reader.skip_line();
      reader.skip_line();
      reader.skip_line();
      // extract element names from nelements line
      ValueTokenizer values = reader.next_values(1);
      file->nelements = values.next_int();
      if ((int) values.count() != file->nelements + 1)
        error->one(FLERR, "Incorrect element names in EAM potential file");
      file->elements = new char *[file->nelements];
      for (int i = 0; i < file->nelements; i++) {
        const std::string word = values.next_string();
        const int n = word.length() + 1;
        file->elements[i] = new char[n];
        strcpy(file->elements[i], word.c_str());
      }
      //
      if (he_flag)
        values = reader.next_values(6);
      else
        values = reader.next_values(5);
      file->nrho = values.next_int();
      file->drho = values.next_double();
      file->nr = values.next_int();
      file->dr = values.next_double();
      file->cut = values.next_double();
      if (he_flag) rhomax = values.next_double();
      if ((file->nrho <= 0) || (file->nr <= 0) || (file->dr <= 0.0))
        error->one(FLERR, "Invalid EAM potential file");
      memory->create(file->mass, file->nelements, "pair:mass");
      memory->create(file->frho, file->nelements, file->nrho + 1, "pair:frho");
      memory->create(file->rhor, file->nelements, file->nelements, file->nr + 1, "pair:rhor");
      memory->create(file->z2r, file->nelements, file->nelements, file->nr + 1, "pair:z2r");
      for (int i = 0; i < file->nelements; i++) {
        values = reader.next_values(2);
        values.next_int();    // ignore
        file->mass[i] = values.next_double();
        reader.next_dvector(&file->frho[i][1], file->nrho);
        if (unit_convert) {
          for (int j = 1; j <= file->nrho; ++j) file->frho[i][j] *= conversion_factor;
        }
        for (int j = 0; j < file->nelements; j++) {
          reader.next_dvector(&file->rhor[i][j][1], file->nr);
        }
      }
      for (int i = 0; i < file->nelements; i++) {
        for (int j = 0; j <= i; j++) {
          reader.next_dvector(&file->z2r[i][j][1], file->nr);
          if (unit_convert) {
            for (int k = 1; k <= file->nr; ++k) file->z2r[i][j][k] *= conversion_factor;
          }
        }
      }
    } catch (TokenizerException &e) {
      error->one(FLERR, e.what());
    }
  }
  // broadcast potential information
  MPI_Bcast(&file->nelements, 1, MPI_INT, 0, world);
  MPI_Bcast(&file->nrho, 1, MPI_INT, 0, world);
  MPI_Bcast(&file->drho, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->nr, 1, MPI_INT, 0, world);
  MPI_Bcast(&file->dr, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&file->cut, 1, MPI_DOUBLE, 0, world);
  MPI_Bcast(&rhomax, 1, MPI_DOUBLE, 0, world);
  // allocate memory on other procs
  if (comm->me != 0) {
    file->elements = new char *[file->nelements];
    for (int i = 0; i < file->nelements; i++) file->elements[i] = nullptr;
    memory->create(file->mass, file->nelements, "pair:mass");
    memory->create(file->frho, file->nelements, file->nrho + 1, "pair:frho");
    memory->create(file->rhor, file->nelements, file->nelements, file->nr + 1, "pair:rhor");
    memory->create(file->z2r, file->nelements, file->nelements, file->nr + 1, "pair:z2r");
  }
  // broadcast file->elements string array
  for (int i = 0; i < file->nelements; i++) {
    int n;
    if (comm->me == 0) n = strlen(file->elements[i]) + 1;
    MPI_Bcast(&n, 1, MPI_INT, 0, world);
    if (comm->me != 0) file->elements[i] = new char[n];
    MPI_Bcast(file->elements[i], n, MPI_CHAR, 0, world);
  }
  // broadcast file->mass, frho, rhor
  for (int i = 0; i < file->nelements; i++) {
    MPI_Bcast(&file->mass[i], 1, MPI_DOUBLE, 0, world);
    MPI_Bcast(&file->frho[i][1], file->nrho, MPI_DOUBLE, 0, world);
    for (int j = 0; j < file->nelements; j++) {
      MPI_Bcast(&file->rhor[i][j][1], file->nr, MPI_DOUBLE, 0, world);
    }
  }
  // broadcast file->z2r
  for (int i = 0; i < file->nelements; i++) {
    for (int j = 0; j <= i; j++) { MPI_Bcast(&file->z2r[i][j][1], file->nr, MPI_DOUBLE, 0, world); }
  }
 }
 /* ----------------------------------------------------------------------
   copy read-in setfl potential to standard array format
 ------------------------------------------------------------------------- */
 void PairEAMFSapip::file2array()
 {
  int i, j, m, n;
  int ntypes = atom->ntypes;
  // set function params directly from fs file
  nrho = fs->nrho;
  nr = fs->nr;
  drho = fs->drho;
  dr = fs->dr;
  if (he_flag)
    rhomin = rhomax - (nrho - 1) * drho;
  else
    rhomax = (nrho - 1) * drho;
  // ------------------------------------------------------------------
  // setup frho arrays
  // ------------------------------------------------------------------
  // allocate frho arrays
  // nfrho = # of fs elements + 1 for zero array
  nfrho = fs->nelements + 1;
  memory->destroy(frho);
  memory->create(frho, nfrho, nrho + 1, "pair:frho");
  // copy each element's frho to global frho
  for (i = 0; i < fs->nelements; i++)
    for (m = 1; m <= nrho; m++) frho[i][m] = fs->frho[i][m];
  // add extra frho of zeroes for non-EAM types to point to (pair hybrid)
  // this is necessary b/c fp is still computed for non-EAM atoms
  for (m = 1; m <= nrho; m++) frho[nfrho - 1][m] = 0.0;
  // type2frho[i] = which frho array (0 to nfrho-1) each atom type maps to
  // if atom type doesn't point to element (non-EAM atom in pair hybrid)
  // then map it to last frho array of zeroes
  for (i = 1; i <= ntypes; i++)
    if (map[i] >= 0)
      type2frho[i] = map[i];
    else
      type2frho[i] = nfrho - 1;
  // ------------------------------------------------------------------
  // setup rhor arrays
  // ------------------------------------------------------------------
  // allocate rhor arrays
  // nrhor = square of # of fs elements
  nrhor = fs->nelements * fs->nelements;
  memory->destroy(rhor);
  memory->create(rhor, nrhor, nr + 1, "pair:rhor");
  // copy each element pair rhor to global rhor
  n = 0;
  for (i = 0; i < fs->nelements; i++)
    for (j = 0; j < fs->nelements; j++) {
      for (m = 1; m <= nr; m++) rhor[n][m] = fs->rhor[i][j][m];
      n++;
    }
  // type2rhor[i][j] = which rhor array (0 to nrhor-1) each type pair maps to
  // for fs files, there is a full NxN set of rhor arrays
  // OK if map = -1 (non-EAM atom in pair hybrid) b/c type2rhor not used
  for (i = 1; i <= ntypes; i++)
    for (j = 1; j <= ntypes; j++) type2rhor[i][j] = map[i] * fs->nelements + map[j];
  // ------------------------------------------------------------------
  // setup z2r arrays
  // ------------------------------------------------------------------
  // allocate z2r arrays
  // nz2r = N*(N+1)/2 where N = # of fs elements
  nz2r = fs->nelements * (fs->nelements + 1) / 2;
  memory->destroy(z2r);
  memory->create(z2r, nz2r, nr + 1, "pair:z2r");
  // copy each element pair z2r to global z2r, only for I >= J
  n = 0;
  for (i = 0; i < fs->nelements; i++)
    for (j = 0; j <= i; j++) {
      for (m = 1; m <= nr; m++) z2r[n][m] = fs->z2r[i][j][m];
      n++;
    }
  // type2z2r[i][j] = which z2r array (0 to nz2r-1) each type pair maps to
  // set of z2r arrays only fill lower triangular Nelement matrix
  // value = n = sum over rows of lower-triangular matrix until reach irow,icol
  // swap indices when irow < icol to stay lower triangular
  // if map = -1 (non-EAM atom in pair hybrid):
  //   type2z2r is not used by non-opt
  //   but set type2z2r to 0 since accessed by opt
  int irow, icol;
  for (i = 1; i <= ntypes; i++) {
    for (j = 1; j <= ntypes; j++) {
      irow = map[i];
      icol = map[j];
      if (irow == -1 || icol == -1) {
        type2z2r[i][j] = 0;
        continue;
      }
      if (irow < icol) {
        irow = map[j];
        icol = map[i];
      }
      n = 0;
      for (m = 0; m < irow; m++) n += m + 1;
      n += icol;
      type2z2r[i][j] = n;
    }
  }
 }
--- a/src/APIP/pair_eam_fs_apip.h
+++ b/src/APIP/pair_eam_fs_apip.h
@ -0,0 +1,48 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: Tim Lau (MIT) for EAM/FS
     David Immel (d.immel@fz-juelich.de, FZJ, Germany) for APIP
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(eam/fs/apip,PairEAMFSapip);
 // clang-format on
 #else
 #ifndef LMP_PAIR_EAM_FS_APIP_H
 #define LMP_PAIR_EAM_FS_APIP_H
 #include "pair_eam_apip.h"
 namespace LAMMPS_NS {
 // need virtual public b/c of how eam/fs/opt inherits from it
 class PairEAMFSapip : virtual public PairEAMapip {
 public:
  PairEAMFSapip(class LAMMPS *);
  void coeff(int, char **) override;
 protected:
  void read_file(char *) override;
  void file2array() override;
  int he_flag;
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_lambda_input.cpp
+++ b/src/APIP/pair_lambda_input.cpp
@ -0,0 +1,218 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "pair_lambda_input.h"
 #include "atom.h"
 #include "comm.h"
 #include "error.h"
 #include "force.h"
 #include "memory.h"
 #include "modify.h"
 #include "neigh_list.h"
 #include "neighbor.h"
 #include "update.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 PairLambdaInput::PairLambdaInput(LAMMPS *lmp) : Pair(lmp), fix_lambda(nullptr), cut(nullptr)
 {
  cut_global = -1;
  ignore_group_bit = 0;
  timer = 0;
  n_calculations = 0;
  time_per_atom = -1;
 }
 /* ---------------------------------------------------------------------- */
 PairLambdaInput::~PairLambdaInput()
 {
  if (copymode) return;
  if (allocated) {
    memory->destroy(setflag);
    memory->destroy(cutsq);
    memory->destroy(cut);
  }
 }
 /* ---------------------------------------------------------------------- */
 void PairLambdaInput::coeff(int narg, char **arg)
 {
  if (narg != 2) error->all(FLERR, "Incorrect args for pair coefficients");
  if (!allocated) allocate();
  int ilo, ihi, jlo, jhi;
  utils::bounds(FLERR, arg[0], 1, atom->ntypes, ilo, ihi, error);
  utils::bounds(FLERR, arg[1], 1, atom->ntypes, jlo, jhi, error);
  int count = 0;
  for (int i = ilo; i <= ihi; i++) {
    for (int j = MAX(jlo, i); j <= jhi; j++) {
      setflag[i][j] = 1;
      cut[i][j] = cut_global;
      count++;
    }
  }
  if (count == 0) error->all(FLERR, "Incorrect args for pair coefficients");
 }
 /* ----------------------------------------------------------------------
   allocate all arrays
 ------------------------------------------------------------------------- */
 void PairLambdaInput::allocate()
 {
  allocated = 1;
  int n = atom->ntypes + 1;
  memory->create(setflag, n, n, "pair:setflag");
  for (int i = 1; i < n; i++)
    for (int j = i; j < n; j++) setflag[i][j] = 0;
  memory->create(cutsq, n, n, "pair:cutsq");
  memory->create(cut, n, n, "pair:cut");
 }
 /* ---------------------------------------------------------------------- */
 void PairLambdaInput::compute(int eflag, int vflag)
 {
  // basic stuff (see pair_zero)
  ev_init(eflag, vflag);
  if (vflag_fdotr) virial_fdotr_compute();
  double timer_start = platform::walltime();
  n_calculations += calculate_lambda_input();
  timer += platform::walltime() - timer_start;
  fix_lambda->update_lambda_input_history();
 }
 /* ----------------------------------------------------------------------
   global settings
 ------------------------------------------------------------------------- */
 void PairLambdaInput::settings(int narg, char **arg)
 {
  if (narg < 1) utils::missing_cmd_args(FLERR, "pair_style lambda_input", error);
  cut_global = utils::numeric(FLERR, arg[0], false, lmp);
  // reset cutoffs that have been explicitly set
  if (allocated) {
    int i, j;
    for (i = 1; i <= atom->ntypes; i++)
      for (j = i; j <= atom->ntypes; j++)
        if (setflag[i][j]) cut[i][j] = cut_global;
  }
 }
 /* ----------------------------------------------------------------------
   init specific to this pair style
 ------------------------------------------------------------------------- */
 void PairLambdaInput::init_style()
 {
  if (!atom->lambda_input_flag)
    error->all(FLERR, "pair_lambda input requires an atom style with lambda_input");
  // find fix lambda
  int count = 0;
  for (int i = 0; i < modify->nfix; i++) {
    if (strcmp(modify->fix[i]->style, "lambda") == 0) {
      fix_lambda = (FixLambda *) modify->fix[i];
      count++;
    }
  }
  if (count != 1) error->all(FLERR, "Exact one fix lambda required");
  // get group whose input is ignored from fix lambda
  ignore_group_bit = fix_lambda->group_bit_ignore_lambda_input;
  neighbor->add_request(this, NeighConst::REQ_FULL);
 }
 /* ----------------------------------------------------------------------
   init for one type pair i,j and corresponding j,i
 ------------------------------------------------------------------------- */
 double PairLambdaInput::init_one(int i, int j)
 {
  if (setflag[i][j] == 0) { cut[i][j] = mix_distance(cut[i][i], cut[j][j]); }
  return cut[i][j];
 }
 /**
  * Compute lambda_input and write it to atom->lambda_input.
  * Count the number of computations and measure the compute time for
  * fix apip_atom_weight.
  */
 int PairLambdaInput::calculate_lambda_input()
 {
  int i, ii, inum;
  int *ilist;
  inum = list->inum;
  ilist = list->ilist;
  double *lambda_input = atom->lambda_input;
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    // "compute" and set lambda input
    lambda_input[i] = 0;
  }
  // return number of calculations
  return inum;
 }
 /* ----------------------------------------------------------------------
   set return values for timers and counted particles
 ------------------------------------------------------------------------- */
 void PairLambdaInput::calculate_time_per_atom()
 {
  if (n_calculations > 0)
    time_per_atom = timer / n_calculations;
  else
    time_per_atom = -1;
  // reset
  timer = 0;
  n_calculations = 0;
 }
 /* ---------------------------------------------------------------------- */
 void *PairLambdaInput::extract(const char *str, int &dim)
 {
  dim = 0;
  if (strcmp(str, "lambda_input:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  return nullptr;
 }
--- a/src/APIP/pair_lambda_input.h
+++ b/src/APIP/pair_lambda_input.h
@ -0,0 +1,64 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(lambda_input,PairLambdaInput);
 // clang-format on
 #else
 #ifndef LMP_PAIR_LAMBDA_INPUT_H
 #define LMP_PAIR_LAMBDA_INPUT_H
 #include "fix_lambda.h"
 #include "pair.h"
 namespace LAMMPS_NS {
 class PairLambdaInput : public Pair {
  friend class FixLambda;
 public:
  PairLambdaInput(class LAMMPS *);
  ~PairLambdaInput() override;
  void compute(int, int) override;
  virtual void settings(int, char **) override;
  void coeff(int, char **) override;
  void init_style() override;
  double init_one(int, int) override;
  void *extract(const char *, int &) override;
 protected:
  class FixLambda *fix_lambda;    // ptr to fix lambda to store the calculated lambda_input
  // pro forma pair style variables
  double cut_global;
  double **cut;
  double timer;            // accumulated compute time
  double time_per_atom;    // compute time of one calculaiton
  int n_calculations;      // number of accumulated calculations
  int ignore_group_bit;    // groupbit of the group that must not be calculated
  void allocate();
  void calculate_time_per_atom();
  virtual int calculate_lambda_input();
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_lambda_input_csp.cpp
+++ b/src/APIP/pair_lambda_input_csp.cpp
@ -0,0 +1,319 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "pair_lambda_input_csp.h"
 #include "atom.h"
 #include "error.h"
 #include "memory.h"
 #include "neigh_list.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 PairLambdaInputCsp::PairLambdaInputCsp(LAMMPS *lmp) :
    PairLambdaInput(lmp), distsq(nullptr), nearest(nullptr)
 {
  // set defaults
  nnn = 0;
  nnn_buffer = 0;
  maxneigh = 0;
  cut_csp_sq = -1;
 }
 /* ---------------------------------------------------------------------- */
 PairLambdaInputCsp::~PairLambdaInputCsp()
 {
  if (copymode) return;
  memory->destroy(distsq);
  memory->destroy(nearest);
 }
 /* ----------------------------------------------------------------------
   global settings
 ------------------------------------------------------------------------- */
 void PairLambdaInputCsp::settings(int narg, char **arg)
 {
  double cut_csp = 5;
  // parse arguments
  if (narg < 1) error->all(FLERR, "pair lambda_input/csp: lattice requires one argument");
  if (strcmp(arg[0], "fcc") == 0)
    nnn = 12;
  else if (strcmp(arg[0], "bcc") == 0)
    nnn = 8;
  else
    nnn = utils::inumeric(FLERR, arg[0], false, lmp);
  int iarg = 1;
  while (iarg < narg) {
    if (strcmp(arg[iarg], "cutoff") == 0) {
      if (iarg + 1 >= narg)
        error->all(FLERR, "pair lambda_input/csp: threshold requires an argument");
      cut_csp = utils::numeric(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else if (strcmp(arg[iarg], "N_buffer") == 0) {
      if (iarg + 1 >= narg)
        error->all(FLERR, "pair lambda_input/csp: N_buffer requires an argument");
      nnn_buffer = utils::inumeric(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else
      error->all(FLERR, "pair_lambda_input_csp: unknown argument {}", arg[iarg]);
  }
  if (nnn <= 1 || nnn % 2)
    error->all(FLERR,
               "pair_lambda_input_csp: even number of neighbours > 1 for csp calculation required");
  if (cut_csp <= 0) error->all(FLERR, "pair_lambda_input_csp: cut_csp <= 0");
  if (nnn_buffer < 0) error->all(FLERR, "pair_lambda_input_csp: N_buffer negative");
  cut_global = cut_csp;
  cut_csp_sq = cut_csp * cut_csp;
  // reset cutoffs that have been explicitly set
  if (allocated) {
    int i, j;
    for (i = 1; i <= atom->ntypes; i++)
      for (j = i; j <= atom->ntypes; j++)
        if (setflag[i][j]) cut[i][j] = cut_global;
  }
 }
 /**
  * Compute CSP and write it to atom->lambda_input.
  * Count the number of computations and measure the compute time for
  * fix apip_atom_weight.
  */
 int PairLambdaInputCsp::calculate_lambda_input()
 {
  int i, j, k, ii, jj, kk, n, n_cutoff, inum, jnum;
  double xtmp, ytmp, ztmp, delx, dely, delz, rsq, value;
  int *ilist, *jlist, *numneigh, **firstneigh, *mask;
  inum = list->inum;
  ilist = list->ilist;
  numneigh = list->numneigh;
  firstneigh = list->firstneigh;
  mask = atom->mask;
  // npairs = number of unique pairs
  int nhalf = nnn / 2;
  int nnn_all = nnn + nnn_buffer;
  int npairs = nnn_all * (nnn_all - 1) / 2;
  auto pairs = new double[npairs];
  double **x = atom->x;
  double *lambda_input = atom->lambda_input;
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    if (mask[i] & ignore_group_bit) {
      // do not calculate the input as it is not used later
      lambda_input[i] = 0;
      continue;
    }
    xtmp = x[i][0];
    ytmp = x[i][1];
    ztmp = x[i][2];
    jlist = firstneigh[i];
    jnum = numneigh[i];
    // ensure distsq and nearest arrays are long enough
    if (jnum > maxneigh) {
      memory->destroy(distsq);
      memory->destroy(nearest);
      maxneigh = jnum;
      memory->create(distsq, maxneigh, "pair lambda_input/csp:distsq");
      memory->create(nearest, maxneigh, "pair lambda_input/csp:nearest");
    }
    // loop over list of all neighbors within force cutoff
    // distsq[] = distance sq to each
    // nearest[] = atom indices of neighbors
    n_cutoff = 0;
    for (jj = 0; jj < jnum; jj++) {
      j = jlist[jj];
      j &= NEIGHMASK;
      delx = xtmp - x[j][0];
      dely = ytmp - x[j][1];
      delz = ztmp - x[j][2];
      rsq = delx * delx + dely * dely + delz * delz;
      // do not use cutsq since cutsq may be quite large due to the maximum search of lambda
      if (rsq < cut_csp_sq) {
        distsq[n_cutoff] = rsq;
        nearest[n_cutoff++] = j;
      }
    }
    if (n_cutoff >= nnn_all) {
      // calculate the values of the centro symmetry parameter for this atom
      // store nnn_all nearest neighs in 1st nnn_all locations of distsq and nearest
      select2(nnn_all, n_cutoff, distsq, nearest);
      // R = Ri + Rj for each of npairs i,j pairs among nnn_all neighbors
      // pairs = squared length of each R
      n = 0;
      for (j = 0; j < nnn_all; j++) {
        jj = nearest[j];
        for (k = j + 1; k < nnn_all; k++) {
          kk = nearest[k];
          delx = x[jj][0] + x[kk][0] - 2.0 * xtmp;
          dely = x[jj][1] + x[kk][1] - 2.0 * ytmp;
          delz = x[jj][2] + x[kk][2] - 2.0 * ztmp;
          pairs[n++] = delx * delx + dely * dely + delz * delz;
        }
      }
      // store nhalf smallest pair distances in 1st nhalf locations of pairs
      select(nhalf, npairs, pairs);
      // centrosymmetry = sum of nhalf smallest squared values
      // calculate centro symmetry parameter of this atom
      value = 0.0;
      for (j = 0; j < nhalf; j++) value += pairs[j];
    } else {
      // cannot calculate nnn/2 neighbour pairs
      // -> just set a high value
      value = 1000.0;
    }
    // store cs for this atom
    lambda_input[i] = value;
  }
  delete[] pairs;
  // return number of calculations
  return inum;
 }
 /* ----------------------------------------------------------------------
   2 select routines from Numerical Recipes (slightly modified)
   find k smallest values in array of length n
   2nd routine sorts auxiliary array at same time
 ------------------------------------------------------------------------- */
 void PairLambdaInputCsp::select(int k, int n, double *arr)
 {
  int i, ir, j, l, mid;
  double a;
  arr--;
  l = 1;
  ir = n;
  for (;;) {
    if (ir <= l + 1) {
      if (ir == l + 1 && arr[ir] < arr[l]) { std::swap(arr[l], arr[ir]); }
      return;
    } else {
      mid = (l + ir) >> 1;
      std::swap(arr[mid], arr[l + 1]);
      if (arr[l] > arr[ir]) { std::swap(arr[l], arr[ir]); }
      if (arr[l + 1] > arr[ir]) { std::swap(arr[l + 1], arr[ir]); }
      if (arr[l] > arr[l + 1]) { std::swap(arr[l], arr[l + 1]); }
      i = l + 1;
      j = ir;
      a = arr[l + 1];
      for (;;) {
        do i++;
        while (arr[i] < a);
        do j--;
        while (arr[j] > a);
        if (j < i) break;
        std::swap(arr[i], arr[j]);
      }
      arr[l + 1] = arr[j];
      arr[j] = a;
      if (j >= k) ir = j - 1;
      if (j <= k) l = i;
    }
  }
 }
 /* ---------------------------------------------------------------------- */
 void PairLambdaInputCsp::select2(int k, int n, double *arr, int *iarr)
 {
  int i, ir, j, l, mid, ia, itmp;
  double a;
  arr--;
  iarr--;
  l = 1;
  ir = n;
  for (;;) {
    if (ir <= l + 1) {
      if (ir == l + 1 && arr[ir] < arr[l]) {
        std::swap(arr[l], arr[ir]);
        std::swap(iarr[l], iarr[ir]);
      }
      return;
    } else {
      mid = (l + ir) >> 1;
      std::swap(arr[mid], arr[l + 1]);
      std::swap(iarr[mid], iarr[l + 1]);
      if (arr[l] > arr[ir]) {
        std::swap(arr[l], arr[ir]);
        std::swap(iarr[l], iarr[ir]);
      }
      if (arr[l + 1] > arr[ir]) {
        std::swap(arr[l + 1], arr[ir]);
        std::swap(iarr[l + 1], iarr[ir]);
      }
      if (arr[l] > arr[l + 1]) {
        std::swap(arr[l], arr[l + 1]);
        std::swap(iarr[l], iarr[l + 1]);
      }
      i = l + 1;
      j = ir;
      a = arr[l + 1];
      ia = iarr[l + 1];
      for (;;) {
        do i++;
        while (arr[i] < a);
        do j--;
        while (arr[j] > a);
        if (j < i) break;
        std::swap(arr[i], arr[j]);
        std::swap(iarr[i], iarr[j]);
      }
      arr[l + 1] = arr[j];
      arr[j] = a;
      iarr[l + 1] = iarr[j];
      iarr[j] = ia;
      if (j >= k) ir = j - 1;
      if (j <= k) l = i;
    }
  }
 }
--- a/src/APIP/pair_lambda_input_csp.h
+++ b/src/APIP/pair_lambda_input_csp.h
@ -0,0 +1,54 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(lambda_input/csp,PairLambdaInputCsp);
 // clang-format on
 #else
 #ifndef LMP_PAIR_LAMBDA_INPUT_CSP_H
 #define LMP_PAIR_LAMBDA_INPUT_CSP_H
 #include "pair_lambda_input.h"
 namespace LAMMPS_NS {
 class PairLambdaInputCsp : virtual public PairLambdaInput {
 public:
  PairLambdaInputCsp(class LAMMPS *);
  ~PairLambdaInputCsp();
  void settings(int, char **) override;
 protected:
  // csp variables
  double cut_csp_sq;    ///< squared cutoff
  int maxneigh;         ///< number of atoms for which distsq and nearest are allocated
  int nnn;              ///< number of nearest neighbours that are used in the csp calculation
  int nnn_buffer;       ///< number of additional (to nnn) stored nearest neighbours
  double *distsq;       ///< distance sq to each neighbor
  int *nearest;         ///< atom indices of neighbors
  int calculate_lambda_input() override;
  void select(int, int, double *);
  void select2(int, int, double *, int *);
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_lambda_zone.cpp
+++ b/src/APIP/pair_lambda_zone.cpp
@ -0,0 +1,309 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "pair_lambda_zone.h"
 #include "atom.h"
 #include "error.h"
 #include "memory.h"
 #include "modify.h"
 #include "neigh_list.h"
 #include "neighbor.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 PairLambdaZone::PairLambdaZone(LAMMPS *lmp) :
    Pair(lmp), fix_lambda(nullptr), lambda_ta(nullptr), cut(nullptr)
 {
  // set defaults
  cut_global = cut_lo = cut_hi = cut_hi_sq = cut_width = lambda_non_group = -1;
  groupbit = -1;
  nmax_ta = 0;
  timer = 0;
  n_calculations = 0;
  time_per_atom = -1;
 }
 /* ---------------------------------------------------------------------- */
 PairLambdaZone::~PairLambdaZone()
 {
  if (copymode) return;
  if (allocated) {
    memory->destroy(setflag);
    memory->destroy(cutsq);
    memory->destroy(cut);
  }
  if (nmax_ta > 0) memory->destroy(lambda_ta);
 }
 /* ---------------------------------------------------------------------- */
 void PairLambdaZone::coeff(int narg, char **arg)
 {
  if (narg != 2) error->all(FLERR, "Incorrect args for pair coefficients");
  if (!allocated) allocate();
  int ilo, ihi, jlo, jhi;
  utils::bounds(FLERR, arg[0], 1, atom->ntypes, ilo, ihi, error);
  utils::bounds(FLERR, arg[1], 1, atom->ntypes, jlo, jhi, error);
  int count = 0;
  for (int i = ilo; i <= ihi; i++) {
    for (int j = MAX(jlo, i); j <= jhi; j++) {
      setflag[i][j] = 1;
      cut[i][j] = cut_global;
      count++;
    }
  }
  if (count == 0) error->all(FLERR, "Incorrect args for pair coefficients");
 }
 /* ----------------------------------------------------------------------
   allocate all arrays
 ------------------------------------------------------------------------- */
 void PairLambdaZone::allocate()
 {
  allocated = 1;
  int n = atom->ntypes + 1;
  memory->create(setflag, n, n, "pair:setflag");
  for (int i = 1; i < n; i++)
    for (int j = i; j < n; j++) setflag[i][j] = 0;
  memory->create(cutsq, n, n, "pair:cutsq");
  memory->create(cut, n, n, "pair:cut");
 }
 /* ---------------------------------------------------------------------- */
 void PairLambdaZone::compute(int eflag, int vflag)
 {
  // basic stuff (see pair_zero)
  ev_init(eflag, vflag);
  if (vflag_fdotr) virial_fdotr_compute();
  calculate_lambda();
 }
 /* ----------------------------------------------------------------------
   global settings
 ------------------------------------------------------------------------- */
 void PairLambdaZone::settings(int narg, char **arg)
 {
  // parse arguments
  if (narg != 1) error->all(FLERR, "pair_lambda_zone: expected 1 instead of {} arguments", narg);
  cut_global = utils::numeric(FLERR, arg[0], false, lmp);
  if (cut_global <= 0) error->all(FLERR, "pair_lambda_zone: cut_global = {} <= 0", cut_global);
  // reset cutoffs that have been explicitly set
  if (allocated) {
    int i, j;
    for (i = 1; i <= atom->ntypes; i++)
      for (j = i; j <= atom->ntypes; j++)
        if (setflag[i][j]) cut[i][j] = cut_global;
  }
 }
 /* ----------------------------------------------------------------------
   init specific to this pair style
 ------------------------------------------------------------------------- */
 void PairLambdaZone::init_style()
 {
  if (!atom->lambda_input_ta_flag)
    error->all(FLERR, "pair_lambda_zone requires an atom style with lambda_input_ta");
  // find thermo style
  int count = 0;
  for (int i = 0; i < modify->nfix; i++) {
    if (strcmp(modify->fix[i]->style, "lambda") == 0) {
      fix_lambda = modify->fix[i];
      count++;
    }
  }
  if (count != 1) error->all(FLERR, "Exact one fix lambda required");
  int dim = 0;
  cut_lo = *((double *) fix_lambda->extract("fix_lambda:cut_lo", dim));
  cut_hi = *((double *) fix_lambda->extract("fix_lambda:cut_hi", dim));
  cut_hi_sq = *((double *) fix_lambda->extract("fix_lambda:cut_hi_sq", dim));
  cut_width = *((double *) fix_lambda->extract("fix_lambda:cut_width", dim));
  lambda_non_group = *((double *) fix_lambda->extract("fix_lambda:lambda_non_group", dim));
  groupbit = fix_lambda->groupbit;
  if (cut_hi > cut_global) error->all(FLERR, "The r_lambda_hi > neighbour_list_cutoff.");
  neighbor->add_request(this, NeighConst::REQ_FULL | NeighConst::REQ_GHOST);
 }
 /* ----------------------------------------------------------------------
   init for one type pair i,j and corresponding j,i
 ------------------------------------------------------------------------- */
 double PairLambdaZone::init_one(int i, int j)
 {
  if (setflag[i][j] == 0) { cut[i][j] = mix_distance(cut[i][i], cut[j][j]); }
  return cut[i][j];
 }
 /**
  * calculate new lambda with lambda_input_ta of own and ghost atoms.
  * Search local maximum of neighbouring atoms for each atom.
  * input: lambda_input_ta of own + ghost particles
  * output: lambda_input_ta of own particles
  */
 void PairLambdaZone::calculate_lambda()
 {
  double timer_start = platform::walltime();
  double xtmp, ytmp, ztmp, delx, dely, delz, lambda_tmp, rsq, lambda_new;
  double **x, *lambda_input_ta;
  int allnum, ii, i, nlocal, nall, jnum, j, jj, loop_iterations;
  int *ilist, *mask, *jlist, *numneigh, **firstneigh;
  mask = atom->mask;
  x = atom->x;
  lambda_input_ta = atom->lambda_input_ta;
  nlocal = atom->nlocal;
  nall = nlocal + atom->nghost;
  if (nlocal > nmax_ta) {
    memory->destroy(lambda_ta);
    nmax_ta = nlocal;
    memory->create(lambda_ta, nmax_ta, "pair/lambda:lambda_ta");
  }
  // 1 set lambda for own particles
  for (i = 0; i < nlocal; i++) {
    lambda_ta[i] = (mask[i] & groupbit) ? lambda_input_ta[i] : lambda_non_group;
  }
  // 2 loop over all atoms with non-simple lambda
  loop_iterations = 0;
  if (cut_hi_sq > 0) {
    ilist = list->ilist;
    allnum = list->inum + list->gnum;
    numneigh = list->numneigh;
    firstneigh = list->firstneigh;
    for (ii = 0; ii < allnum; ii++) {
      i = ilist[ii];
      // skip simple atoms and non-group atoms
      // which do not influence the lambda_ta of neighbouring atoms
      if (lambda_input_ta[i] == 1 || (!(mask[i] & groupbit))) { continue; }
      xtmp = x[i][0];
      ytmp = x[i][1];
      ztmp = x[i][2];
      lambda_tmp = 1 - lambda_input_ta[i];
      jlist = firstneigh[i];
      jnum = numneigh[i];
      loop_iterations++;
      // 3 loop over neighbours to set their lambda_ta
      for (jj = 0; jj < jnum; jj++) {
        j = jlist[jj];
        j &= NEIGHMASK;
        // it is not required to set lambda_ta of ghosts or non-group atoms
        if (j >= nlocal || (!(mask[j] & groupbit))) { continue; }
        // the neighbour j is already complex -> skip
        if (lambda_ta[j] == 0) { continue; }
        delx = xtmp - x[j][0];
        dely = ytmp - x[j][1];
        delz = ztmp - x[j][2];
        rsq = delx * delx + dely * dely + delz * delz;
        if (rsq >= cut_hi_sq) { continue; }
        lambda_new = 1 - lambda_tmp * switching_function_poly_distance(sqrt(rsq));
        // more complex lambda_ta found ? set lambda_ta for ngh
        if (lambda_new < lambda_ta[j]) lambda_ta[j] = lambda_new;
      }
    }
  }
  // copy calculated lambda max back to lambda_ta
  for (i = 0; i < nlocal; i++) lambda_input_ta[i] = lambda_ta[i];
  timer += platform::walltime() - timer_start;
  n_calculations += loop_iterations;
 }
 // helper function
 // similar to cutoff_func_poly in ace_radial.cpp
 // compare Phys Rev Mat 6, 013804 (2022) APPENDIX C: RADIAL AND CUTOFF FUNCTIONS 2. Cutoff function
 // the first two derivatives of the switching function lambda vanishes at the boundaries of the switching region
 double PairLambdaZone::switching_function_poly_distance(double input)
 {
  // calculate lambda
  if (input <= cut_lo) {
    return 1;
  } else if (input >= cut_hi) {
    return 0;
  } else {
    double deltatmp = 1 - 2 * (1 + (input - cut_hi) / (cut_width));
    return 0.5 + 7.5 / 2. * (deltatmp / 4. - pow(deltatmp, 3) / 6. + pow(deltatmp, 5) / 20.);
  }
 }
 /* ----------------------------------------------------------------------
   set return values for timers and counted particles
 ------------------------------------------------------------------------- */
 void PairLambdaZone::calculate_time_per_atom()
 {
  if (n_calculations > 0)
    time_per_atom = timer / n_calculations;
  else
    time_per_atom = -1;
  // reset
  timer = 0;
  n_calculations = 0;
 }
 /* ---------------------------------------------------------------------- */
 void *PairLambdaZone::extract(const char *str, int &dim)
 {
  dim = 0;
  if (strcmp(str, "lambda_zone:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  return nullptr;
 }
--- a/src/APIP/pair_lambda_zone.h
+++ b/src/APIP/pair_lambda_zone.h
@ -0,0 +1,76 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(lambda/zone,PairLambdaZone);
 // clang-format on
 #else
 #ifndef LMP_PAIR_LAMBDA_ZONE_H
 #define LMP_PAIR_LAMBDA_ZONE_H
 #include "fix.h"
 #include "pair.h"
 namespace LAMMPS_NS {
 class PairLambdaZone : public Pair {
  friend class FixLambda;
 public:
  PairLambdaZone(class LAMMPS *);
  ~PairLambdaZone() override;
  void compute(int, int) override;
  void settings(int, char **) override;
  void coeff(int, char **) override;
  void init_style() override;
  double init_one(int, int) override;
  void *extract(const char *, int &) override;
 protected:
  class Fix *fix_lambda;
  // pro forma pair style variables
  double **cut;
  // lambda calculation variables
  double timer;            ///< accumulated compute time
  double time_per_atom;    ///< compute time for one atom
  int n_calculations;      ///< number of accumulated computations
  double cut_global;    ///< used cutoff
  double cut_lo;    ///< distance at which the cutoff function of the transition zone decays from 1
  double cut_hi;    ///< distance at which the cutoff function of the transition zone is 0
  double cut_width;           ///< cut_hi - cut_lo
  double cut_hi_sq;           ///< cut_hi_sq * cut_hi_sq
  double lambda_non_group;    ///< lambda for atoms that are not in the group of this fix
  int groupbit;               ///< group for which lambda is calculated
  // variables for calculation
  double *lambda_ta;    ///< time averaged lambda input
  int nmax_ta;          ///< size of lambda_ta
  virtual void allocate();
  void calculate_time_per_atom();
  void calculate_lambda();
  double switching_function_poly_distance(double);
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_pace_apip.cpp
+++ b/src/APIP/pair_pace_apip.cpp
@ -0,0 +1,609 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /*
 This file is a modified version of src/ML-PACE/pair_pace.cpp.
 Original copyright:
 Copyright 2021 Yury Lysogorskiy^1, Cas van der Oord^2, Anton Bochkarev^1,
 Sarath Menon^1, Matteo Rinaldi^1, Thomas Hammerschmidt^1, Matous Mrovec^1,
 Aidan Thompson^3, Gabor Csanyi^2, Christoph Ortner^4, Ralf Drautz^1
 ^1: Ruhr-University Bochum, Bochum, Germany
 ^2: University of Cambridge, Cambridge, United Kingdom
 ^3: Sandia National Laboratories, Albuquerque, New Mexico, USA
 ^4: University of British Columbia, Vancouver, BC, Canada
 */
 //
 // Originally created by Lysogorskiy Yury on 27.02.20.
 // Adaptive precision added by David Immel in 2025
 // (d.immel@fz-juelich.de, FZJ, Germany).
 //
 #include "pair_pace_apip.h"
 #include "atom.h"
 #include "atom_vec_apip.h"
 #include "comm.h"
 #include "error.h"
 #include "force.h"
 #include "math_const.h"
 #include "memory.h"
 #include "modify.h"
 #include "neigh_list.h"
 #include "neighbor.h"
 #include "update.h"
 #include <exception>
 #include "ace-evaluator/ace_c_basis.h"
 #include "ace-evaluator/ace_evaluator.h"
 #include "ace-evaluator/ace_recursive.h"
 #include "ace-evaluator/ace_version.h"
 #include "ace/ace_b_basis.h"
 namespace LAMMPS_NS {
 struct ACEImpl {
  ACEImpl() : basis_set(nullptr), ace(nullptr) {}
  ~ACEImpl()
  {
    delete basis_set;
    delete ace;
  }
  ACECTildeBasisSet *basis_set;
  ACERecursiveEvaluator *ace;
 };
 }    // namespace LAMMPS_NS
 using namespace LAMMPS_NS;
 using namespace MathConst;
 static char const *const elements_pace[] = {
    "X",  "H",  "He", "Li", "Be", "B",  "C",  "N",  "O",  "F",  "Ne", "Na", "Mg", "Al", "Si",
    "P",  "S",  "Cl", "Ar", "K",  "Ca", "Sc", "Ti", "V",  "Cr", "Mn", "Fe", "Co", "Ni", "Cu",
    "Zn", "Ga", "Ge", "As", "Se", "Br", "Kr", "Rb", "Sr", "Y",  "Zr", "Nb", "Mo", "Tc", "Ru",
    "Rh", "Pd", "Ag", "Cd", "In", "Sn", "Sb", "Te", "I",  "Xe", "Cs", "Ba", "La", "Ce", "Pr",
    "Nd", "Pm", "Sm", "Eu", "Gd", "Tb", "Dy", "Ho", "Er", "Tm", "Yb", "Lu", "Hf", "Ta", "W",
    "Re", "Os", "Ir", "Pt", "Au", "Hg", "Tl", "Pb", "Bi", "Po", "At", "Rn", "Fr", "Ra", "Ac",
    "Th", "Pa", "U",  "Np", "Pu", "Am", "Cm", "Bk", "Cf", "Es", "Fm", "Md", "No", "Lr"};
 static constexpr int elements_num_pace = sizeof(elements_pace) / sizeof(const char *);
 static int AtomicNumberByName_pace(char *elname)
 {
  for (int i = 1; i < elements_num_pace; i++)
    if (strcmp(elname, elements_pace[i]) == 0) return i;
  return -1;
 }
 /* ---------------------------------------------------------------------- */
 PairPACEapip::PairPACEapip(LAMMPS *lmp) : Pair(lmp)
 {
  single_enable = 0;
  restartinfo = 0;
  one_coeff = 1;
  manybody_flag = 1;
  nmax_corerep = 0;
  flag_corerep_factor = 0;
  corerep_factor = nullptr;
  aceimpl = new ACEImpl;
  recursive = false;
  scale = nullptr;
  chunksize = 4096;
  // start of adaptive-precision modifications by DI
  lambda_thermostat = true;
  n_computations_accumulated = 0;
  time_wall_accumulated = 0;
  time_per_atom = -1;
  // end of adaptive-precision modifications by DI
 }
 /* ----------------------------------------------------------------------
   check if allocated, since class can be destructed when incomplete
 ------------------------------------------------------------------------- */
 PairPACEapip::~PairPACEapip()
 {
  if (copymode) return;
  delete aceimpl;
  if (allocated) {
    memory->destroy(setflag);
    memory->destroy(cutsq);
    memory->destroy(scale);
    memory->destroy(corerep_factor);
  }
 }
 /**
  * Set lambda_required based on lambda and lambda_const
  * @return true if this calculation is not required
  */
 // written by DI. This function is required for the adaptive-precision.
 int PairPACEapip::check_abort_condition(double *lambda, double *lambda_const, int *lambda_required,
                                        int i)
 {
  if ((lambda[i] == 1) && ((!lambda_thermostat) || (lambda_thermostat && lambda_const[i] == 1))) {
    lambda_required[i] |= LambdaRequired::NO_COMPLEX;
    return 1;
  }
  lambda_required[i] |= LambdaRequired::COMPLEX;
  return 0;
 }
 /**
  * @return prefactor 1-lambda which is used for a precise ACE potential
  */
 // written by DI. This function is required for the adaptive-precision.
 double PairPACEapip::compute_factor_lambda(double lambda)
 {
  return 1 - lambda;
 }
 /**
  * @return atom->e_complex which is used for a precise ACE potential
  */
 // written by DI. This function is required for the adaptive-precision.
 double *PairPACEapip::get_e_ref_ptr()
 {
  return atom->e_complex;
 }
 /* ---------------------------------------------------------------------- */
 void PairPACEapip::compute(int eflag, int vflag)
 {
  // start of adaptive-precision modifications by DI
  // start timers
  double time_wall_start = platform::walltime();
  double *lambda = atom->lambda;
  int *lambda_required = atom->lambda_required;
  double **f_const_lambda = nullptr;
  double **f_dyn_lambda = nullptr;
  double *e_ref = nullptr;
  double *lambda_const = nullptr;
  if (lambda_thermostat) {
    f_const_lambda = atom->f_const_lambda;
    f_dyn_lambda = atom->f_dyn_lambda;
    e_ref = get_e_ref_ptr();
    lambda_const = atom->lambda_const;
  }
  int n_computations = 0;
  // end of adaptive-precision modifications by DI
  int i, j, ii, jj, inum, jnum;
  double delx, dely, delz, evdwl;
  double fij[3];
  int *ilist, *jlist, *numneigh, **firstneigh;
  ev_init(eflag, vflag);
  double **x = atom->x;
  double **f = atom->f;
  int *type = atom->type;
  // number of atoms in cell
  int nlocal = atom->nlocal;
  int newton_pair = force->newton_pair;
  // inum: length of the neighborlists list
  inum = list->inum;
  // ilist: list of "i" atoms for which neighbor lists exist
  ilist = list->ilist;
  //numneigh: the length of each these neigbor list
  numneigh = list->numneigh;
  // the pointer to the list of neighbors of "i"
  firstneigh = list->firstneigh;
  if (flag_corerep_factor && atom->nlocal > nmax_corerep) {
    memory->destroy(corerep_factor);
    nmax_corerep = atom->nlocal;
    memory->create(corerep_factor, nmax_corerep, "pace/atom:corerep_factor");
    //zeroify array
    memset(corerep_factor, 0, nmax_corerep * sizeof(*corerep_factor));
  }
  //determine the maximum number of neighbours
  int max_jnum = 0;
  int nei = 0;
  for (ii = 0; ii < inum; ii++) {
    i = ilist[ii];
    jnum = numneigh[i];
    nei = nei + jnum;
    if (jnum > max_jnum) max_jnum = jnum;
  }
  aceimpl->ace->resize_neighbours_cache(max_jnum);
  //loop over atoms
  for (ii = 0; ii < inum; ii++) {
    i = list->ilist[ii];
    const int itype = type[i];
    const double xtmp = x[i][0];
    const double ytmp = x[i][1];
    const double ztmp = x[i][2];
    jlist = firstneigh[i];
    jnum = numneigh[i];
    // start of adaptive-precision modifications by DI
    // Abort calculation when ace is not required for this atom.
    // All force and energy contributions calculated in the following are weighted with
    // 1-lambda when ace is used as precise potential (and with lambda if ace is used as simple potential).
    // As this weighting factor can be 0, i.e. there is no contribution, one can abort the calculation
    // of this atom in this case.
    if (check_abort_condition(lambda, lambda_const, lambda_required, i)) { continue; }
    n_computations++;
    // set factor required for forces and for energy summation
    // fast potential: lambda
    // precise potential: 1-lambda
    const double factor_lambda_i = compute_factor_lambda(lambda[i]);
    const double factor_lambdaconst_i =
        (lambda_thermostat ? compute_factor_lambda(lambda_const[i]) : 0);
    // end of adaptive-precision modifications by DI
    // checking if neighbours are actually within cutoff range is done inside compute_atom
    // mapping from LAMMPS atom types ('type' array) to ACE species is done inside compute_atom
    //      by using 'aceimpl->ace->element_type_mapping' array
    // x: [r0 ,r1, r2, ..., r100]
    // i = 0 ,1
    // jnum(0) = 50
    // jlist(neigh ind of 0-atom) = [1,2,10,7,99,25, .. 50 element in total]
    try {
      aceimpl->ace->compute_atom(i, x, type, jnum, jlist);
    } catch (std::exception &e) {
      error->one(FLERR, e.what());
    }
    if (flag_corerep_factor) corerep_factor[i] = 1 - aceimpl->ace->ace_fcut;
    // 'compute_atom' will update the `aceimpl->ace->e_atom` and `aceimpl->ace->neighbours_forces(jj, alpha)` arrays
    for (jj = 0; jj < jnum; jj++) {
      j = jlist[jj];
      j &= NEIGHMASK;
      delx = x[j][0] - xtmp;
      dely = x[j][1] - ytmp;
      delz = x[j][2] - ztmp;
      fij[0] = scale[itype][itype] * aceimpl->ace->neighbours_forces(jj, 0);
      fij[1] = scale[itype][itype] * aceimpl->ace->neighbours_forces(jj, 1);
      fij[2] = scale[itype][itype] * aceimpl->ace->neighbours_forces(jj, 2);
      // start of adaptive-precision modifications by DI
      // The force contributions fij need to be weighted with 1-lambda[i]
      // (or lambda[i] in case of a fast ace potential).
      f[i][0] += factor_lambda_i * fij[0];
      f[i][1] += factor_lambda_i * fij[1];
      f[i][2] += factor_lambda_i * fij[2];
      f[j][0] -= factor_lambda_i * fij[0];
      f[j][1] -= factor_lambda_i * fij[1];
      f[j][2] -= factor_lambda_i * fij[2];
      if (lambda_thermostat) {
        f_dyn_lambda[i][0] += factor_lambda_i * fij[0];
        f_dyn_lambda[i][1] += factor_lambda_i * fij[1];
        f_dyn_lambda[i][2] += factor_lambda_i * fij[2];
        f_dyn_lambda[j][0] -= factor_lambda_i * fij[0];
        f_dyn_lambda[j][1] -= factor_lambda_i * fij[1];
        f_dyn_lambda[j][2] -= factor_lambda_i * fij[2];
        f_const_lambda[i][0] += factor_lambdaconst_i * fij[0];
        f_const_lambda[i][1] += factor_lambdaconst_i * fij[1];
        f_const_lambda[i][2] += factor_lambdaconst_i * fij[2];
        f_const_lambda[j][0] -= factor_lambdaconst_i * fij[0];
        f_const_lambda[j][1] -= factor_lambdaconst_i * fij[1];
        f_const_lambda[j][2] -= factor_lambdaconst_i * fij[2];
      }
      // end of adaptive-precision modifications by DI
      // tally per-atom virial contribution
      if (vflag_either)
        // following line of code modified by DI
        ev_tally_xyz(i, j, nlocal, newton_pair, 0.0, 0.0, factor_lambda_i * fij[0],
                     factor_lambda_i * fij[1], factor_lambda_i * fij[2], -delx, -dely, -delz);
    }
    // tally energy contribution
    // start of adaptive-precision modifications by DI
    if (eflag_either || lambda_thermostat) {
      // The potential energy needs to be stored to apply the
      // energy correction with the local thermostat.
      if (e_ref) e_ref[i] = scale[itype][itype] * aceimpl->ace->e_atom;
      // evdwl = energy of atom I
      // The potential energy is weighted with lambda[i] as well.
      evdwl = factor_lambda_i * scale[itype][itype] * aceimpl->ace->e_atom;
      // end of adaptive-precision modifications by DI
      ev_tally_full(i, 2.0 * evdwl, 0.0, 0.0, 0.0, 0.0, 0.0);
    }
  }
  if (vflag_fdotr) virial_fdotr_compute();
  // end modifications YL
  // start of adaptive-precision modifications by DI
  // stop timers
  time_wall_accumulated += platform::walltime() - time_wall_start;
  n_computations_accumulated += n_computations;
  // end of adaptive-precision modifications by DI
 }
 /* ---------------------------------------------------------------------- */
 void PairPACEapip::allocate()
 {
  allocated = 1;
  int n = atom->ntypes + 1;
  memory->create(setflag, n, n, "pair:setflag");
  memory->create(cutsq, n, n, "pair:cutsq");
  memory->create(scale, n, n, "pair:scale");
  map = new int[n];
 }
 /* ----------------------------------------------------------------------
   global settings
 ------------------------------------------------------------------------- */
 void PairPACEapip::settings(int narg, char **arg)
 {
  if (narg > 3) utils::missing_cmd_args(FLERR, "pair_style pace", error);
  // ACE potentials are parameterized in metal units
  if (strcmp("metal", update->unit_style) != 0)
    error->all(FLERR, "ACE potentials require 'metal' units");
  recursive = true;    // default evaluator style: RECURSIVE
  int iarg = 0;
  while (iarg < narg) {
    if (strcmp(arg[iarg], "recursive") == 0) {
      recursive = true;
      iarg += 1;
    } else if (strcmp(arg[iarg], "product") == 0) {
      recursive = false;
      iarg += 1;
    } else if (strcmp(arg[iarg], "chunksize") == 0) {
      chunksize = utils::inumeric(FLERR, arg[iarg + 1], false, lmp);
      iarg += 2;
    } else
      error->all(FLERR, "Unknown pair_style pace keyword: {}", arg[iarg]);
  }
  if (comm->me == 0) {
    utils::logmesg(lmp, "ACE version: {}.{}.{}\n", VERSION_YEAR, VERSION_MONTH, VERSION_DAY);
    if (recursive)
      utils::logmesg(lmp, "Recursive evaluator is used by ACE\n");
    else
      utils::logmesg(lmp, "Product evaluator is used by ACE\n");
  }
 }
 /* ----------------------------------------------------------------------
   set coeffs for one or more type pairs
 ------------------------------------------------------------------------- */
 void PairPACEapip::coeff(int narg, char **arg)
 {
  if (!allocated) allocate();
  map_element2type(narg - 3, arg + 3);
  auto potential_file_name = utils::get_potential_file_path(arg[2]);
  //load potential file
  delete aceimpl->basis_set;
  if (comm->me == 0) utils::logmesg(lmp, "Loading {}\n", potential_file_name);
  // if potential is in ACEBBasisSet (YAML) format, then convert to ACECTildeBasisSet automatically
  if (utils::strmatch(potential_file_name, ".*\\.yaml$")) {
    ACEBBasisSet bBasisSet = ACEBBasisSet(potential_file_name);
    ACECTildeBasisSet cTildeBasisSet = bBasisSet.to_ACECTildeBasisSet();
    aceimpl->basis_set = new ACECTildeBasisSet(cTildeBasisSet);
  } else {
    aceimpl->basis_set = new ACECTildeBasisSet(potential_file_name);
  }
  if (comm->me == 0) {
    utils::logmesg(lmp, "Total number of basis functions\n");
    for (SPECIES_TYPE mu = 0; mu < aceimpl->basis_set->nelements; mu++) {
      int n_r1 = aceimpl->basis_set->total_basis_size_rank1[mu];
      int n = aceimpl->basis_set->total_basis_size[mu];
      utils::logmesg(lmp, "\t{}: {} (r=1) {} (r>1)\n", aceimpl->basis_set->elements_name[mu], n_r1,
                     n);
    }
  }
  // read args that map atom types to PACE elements
  // map[i] = which element the Ith atom type is, -1 if not mapped
  // map[0] is not used
  delete aceimpl->ace;
  aceimpl->ace = new ACERecursiveEvaluator();
  aceimpl->ace->set_recursive(recursive);
  aceimpl->ace->element_type_mapping.init(atom->ntypes + 1);
  const int n = atom->ntypes;
  for (int i = 1; i <= n; i++) {
    char *elemname = arg[2 + i];
    if (strcmp(elemname, "NULL") == 0) {
      // species_type=-1 value will not reach ACE Evaluator::compute_atom,
      // but if it will ,then error will be thrown there
      aceimpl->ace->element_type_mapping(i) = -1;
      map[i] = -1;
      if (comm->me == 0) utils::logmesg(lmp, "Skipping LAMMPS atom type #{}(NULL)\n", i);
    } else {
      int atomic_number = AtomicNumberByName_pace(elemname);
      if (atomic_number == -1) error->all(FLERR, "'{}' is not a valid element\n", elemname);
      SPECIES_TYPE mu = aceimpl->basis_set->get_species_index_by_name(elemname);
      if (mu != -1) {
        if (comm->me == 0)
          utils::logmesg(lmp, "Mapping LAMMPS atom type #{}({}) -> ACE species type #{}\n", i,
                         elemname, mu);
        map[i] = mu;
        // set up LAMMPS atom type to ACE species  mapping for ace evaluator
        aceimpl->ace->element_type_mapping(i) = mu;
      } else {
        error->all(FLERR, "Element {} is not supported by ACE-potential from file {}", elemname,
                   potential_file_name);
      }
    }
  }
  // initialize scale factor
  for (int i = 1; i <= n; i++) {
    for (int j = i; j <= n; j++) scale[i][j] = 1.0;
  }
  aceimpl->ace->set_basis(*aceimpl->basis_set, 1);
 }
 /* ----------------------------------------------------------------------
   init specific to this pair style
 ------------------------------------------------------------------------- */
 void PairPACEapip::init_style()
 {
  if (atom->tag_enable == 0) error->all(FLERR, "Pair style pace requires atom IDs");
  if (force->newton_pair == 0) error->all(FLERR, "Pair style pace requires newton pair on");
  // start of adaptive-precision modifications by DI
  if (!atom->lambda_required_flag)
    error->all(FLERR, "pair style pace/apip requires an atom style with lambda_required.");
  if (!atom->lambda_flag)
    error->all(FLERR, "Pair style pace/apip requires an atom style with lambda");
  // end of adaptive-precision modifications by DI
  // request a full neighbor list
  neighbor->add_request(this, NeighConst::REQ_FULL);
 }
 /* ----------------------------------------------------------------------
   init for one type pair i,j and corresponding j,i
 ------------------------------------------------------------------------- */
 double PairPACEapip::init_one(int i, int j)
 {
  if (setflag[i][j] == 0) error->all(FLERR, "All pair coeffs are not set");
  //cutoff from the basis set's radial functions settings
  scale[j][i] = scale[i][j];
  return aceimpl->basis_set->radial_functions->cut(map[i], map[j]);
 }
 /**
  * setup specific to this pair style
  * Determine whether there is a fix lambda_thermostat or not and set
  * lambda_thermostat.
  */
 // written by DI. This function is required for the adaptive-precision.
 void PairPACEapip::setup()
 {
  if (modify->get_fix_by_style("^lambda_thermostat$").size() == 0) {
    lambda_thermostat = false;
  } else {
    lambda_thermostat = true;
    if (!atom->lambda_const_flag)
      error->all(
          FLERR,
          "Pair style pace/apip requires an atom style with lambda_const for a local thermostat.");
    if (!atom->e_simple_flag)
      error->all(
          FLERR,
          "Pair style pace/apip requires an atom style with e_simple for a local thermostat.");
    if (!atom->e_complex_flag)
      error->all(
          FLERR,
          "Pair style pace/apip requires an atom style with e_complex for a local thermostat.");
    if (!atom->f_const_lambda_flag)
      error->all(FLERR,
                 "Pair style pace/apip requires an atom style with f_const_lambda for a local "
                 "thermostat.");
    if (!atom->f_dyn_lambda_flag)
      error->all(FLERR,
                 "Pair style pace/apip requires an atom style with f_const_lambda for a local "
                 "thermostat.");
  }
 }
 /**
  * set return values for timers and number of computed particles
  */
 // written by DI. This function is required for the adaptive-precision.
 void PairPACEapip::calculate_time_per_atom()
 {
  if (n_computations_accumulated > 0)
    time_per_atom = time_wall_accumulated / n_computations_accumulated;
  else
    time_per_atom = -1;
  // reset
  time_wall_accumulated = 0;
  n_computations_accumulated = 0;
 }
 /* ----------------------------------------------------------------------
    extract method for extracting value of scale variable
 ---------------------------------------------------------------------- */
 void *PairPACEapip::extract(const char *str, int &dim)
 {
  dim = 0;
  //check if str=="corerep_flag" then compute extrapolation grades on this iteration
  if (strcmp(str, "corerep_flag") == 0) return (void *) &flag_corerep_factor;
  // DI: The following option is required for the adaptive precision.
  if (strcmp(str, "pace/apip:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  dim = 2;
  if (strcmp(str, "scale") == 0) return (void *) scale;
  return nullptr;
 }
 /* ----------------------------------------------------------------------
   peratom requests from FixPair
   return ptr to requested data
   also return ncol = # of quantites per atom
     0 = per-atom vector
     1 or more = # of columns in per-atom array
   return NULL if str is not recognized
 ---------------------------------------------------------------------- */
 void *PairPACEapip::extract_peratom(const char *str, int &ncol)
 {
  if (strcmp(str, "corerep") == 0) {
    ncol = 0;
    return (void *) corerep_factor;
  }
  return nullptr;
 }
--- a/src/APIP/pair_pace_apip.h
+++ b/src/APIP/pair_pace_apip.h
@ -0,0 +1,90 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   This software is distributed under the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /*
 This file is a modified version of src/ML-PACE/pair_pace.h.
 Original copyright:
 Copyright 2021 Yury Lysogorskiy^1, Cas van der Oord^2, Anton Bochkarev^1,
 Sarath Menon^1, Matteo Rinaldi^1, Thomas Hammerschmidt^1, Matous Mrovec^1,
 Aidan Thompson^3, Gabor Csanyi^2, Christoph Ortner^4, Ralf Drautz^1
 ^1: Ruhr-University Bochum, Bochum, Germany
 ^2: University of Cambridge, Cambridge, United Kingdom
 ^3: Sandia National Laboratories, Albuquerque, New Mexico, USA
 ^4: University of British Columbia, Vancouver, BC, Canada
 */
 //
 // Originally created by Lysogorskiy Yury on 27.02.20.
 // Adaptive precision added by David Immel in 2025
 // (d.immel@fz-juelich.de, FZJ, Germany).
 //
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(pace/apip,PairPACEapip);
 // clang-format on
 #else
 #ifndef LMP_PAIR_PACE_APIP_H
 #define LMP_PAIR_PACE_APIP_H
 #include "pair.h"
 namespace LAMMPS_NS {
 class PairPACEapip : public Pair {
 public:
  PairPACEapip(class LAMMPS *);
  ~PairPACEapip() override;
  void compute(int, int) override;
  void settings(int, char **) override;
  void coeff(int, char **) override;
  void init_style() override;
  double init_one(int, int) override;
  void setup() override;
  void *extract(const char *, int &) override;
  void *extract_peratom(const char *, int &) override;
 protected:
  struct ACEImpl *aceimpl;
  int nmax_corerep;
  virtual void allocate();
  double *corerep_factor;    //per-atom core-rep factor (= 1 - fcut)
  int flag_corerep_factor;
  double **scale;
  bool recursive;    // "recursive" option for ACERecursiveEvaluator
  int chunksize;
  // start of adaptive-precision modifications by DI
  virtual double *get_e_ref_ptr();
  virtual double compute_factor_lambda(double);
  virtual int check_abort_condition(double *, double *, int *, int);
  bool lambda_thermostat;    // true/false there is one/no fix lambda_thermostat
  void calculate_time_per_atom();
  // stats required for load balancing
  int n_computations_accumulated;    // number of accumulated computations
  double time_wall_accumulated;      // accumulated compute time
  double time_per_atom;              // average time of one computation
  // end of adaptive-precision modifications by DI
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_pace_apip_fast.cpp
+++ b/src/APIP/pair_pace_apip_fast.cpp
@ -0,0 +1,73 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "pair_pace_apip_fast.h"
 #include "atom.h"
 #include "atom_vec_apip.h"
 using namespace LAMMPS_NS;
 PairPACEapipFast::PairPACEapipFast(LAMMPS *lmp) : PairPACEapip(lmp) {}
 /**
  * Set lambda_required based on lambda and lambda_const
  * @return true if this calculation is not required
  */
 int PairPACEapipFast::check_abort_condition(double *lambda, double *lambda_const,
                                            int *lambda_required, int i)
 {
  if ((lambda[i] == 0) && ((!lambda_thermostat) || (lambda_thermostat && lambda_const[i] == 0))) {
    lambda_required[i] |= LambdaRequired::NO_SIMPLE;
    return 1;
  }
  lambda_required[i] |= LambdaRequired::SIMPLE;
  return 0;
 }
 /**
  * @return prefactor lambda which is used for a fast ACE potential
  */
 double PairPACEapipFast::compute_factor_lambda(double lambda)
 {
  return lambda;
 }
 /**
  * @return atom->e_simple which is used for a fast ACE potential
  */
 double *PairPACEapipFast::get_e_ref_ptr()
 {
  return atom->e_simple;
 }
 /* ----------------------------------------------------------------------
    extract method for extracting value of scale variable
 ---------------------------------------------------------------------- */
 void *PairPACEapipFast::extract(const char *str, int &dim)
 {
  dim = 2;
  if (strcmp(str, "scale") == 0) return (void *) scale;
  dim = 0;
  if (strcmp(str, "pace/apip/fast:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  return nullptr;
 }
--- a/src/APIP/pair_pace_apip_fast.h
+++ b/src/APIP/pair_pace_apip_fast.h
@ -0,0 +1,44 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(pace/apip/fast,PairPACEapipFast);
 // clang-format on
 #else
 #ifndef LMP_PAIR_PACE_APIP_FAST_H
 #define LMP_PAIR_PACE_APIP_FAST_H
 #include "pair_pace_apip.h"
 namespace LAMMPS_NS {
 class PairPACEapipFast : public PairPACEapip {
 public:
  PairPACEapipFast(class LAMMPS *);
  void *extract(const char *, int &) override;
 protected:
  double *get_e_ref_ptr() override;
  double compute_factor_lambda(double) override;
  int check_abort_condition(double *, double *, int *, int) override;
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/APIP/pair_pace_apip_precise.cpp
+++ b/src/APIP/pair_pace_apip_precise.cpp
@ -0,0 +1,73 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #include "pair_pace_apip_precise.h"
 #include "atom.h"
 #include "atom_vec_apip.h"
 using namespace LAMMPS_NS;
 PairPACEapipPrecise::PairPACEapipPrecise(LAMMPS *lmp) : PairPACEapip(lmp) {}
 /**
  * Set lambda_required based on lambda and lambda_const
  * @return true if this calculation is not required
  */
 int PairPACEapipPrecise::check_abort_condition(double *lambda, double *lambda_const,
                                               int *lambda_required, int i)
 {
  if ((lambda[i] == 1) && ((!lambda_thermostat) || (lambda_thermostat && lambda_const[i] == 1))) {
    lambda_required[i] |= LambdaRequired::NO_COMPLEX;
    return 1;
  }
  lambda_required[i] |= LambdaRequired::COMPLEX;
  return 0;
 }
 /**
  * @return prefactor 1-lambda which is used for a precise ACE potential
  */
 double PairPACEapipPrecise::compute_factor_lambda(double lambda)
 {
  return 1 - lambda;
 }
 /**
  * @return atom->e_complex which is used for a precise ACE potential
  */
 double *PairPACEapipPrecise::get_e_ref_ptr()
 {
  return atom->e_complex;
 }
 /* ----------------------------------------------------------------------
    extract method for extracting value of scale variable
 ---------------------------------------------------------------------- */
 void *PairPACEapipPrecise::extract(const char *str, int &dim)
 {
  dim = 2;
  if (strcmp(str, "scale") == 0) return (void *) scale;
  dim = 0;
  if (strcmp(str, "pace/apip:time_per_atom") == 0) {
    calculate_time_per_atom();
    return (void *) &time_per_atom;
  }
  return nullptr;
 }
--- a/src/APIP/pair_pace_apip_precise.h
+++ b/src/APIP/pair_pace_apip_precise.h
@ -0,0 +1,44 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 /* ----------------------------------------------------------------------
   Contributing author: David Immel (d.immel@fz-juelich.de, FZJ, Germany)
 ------------------------------------------------------------------------- */
 #ifdef PAIR_CLASS
 // clang-format off
 PairStyle(pace/apip/precise,PairPACEapipPrecise);
 // clang-format on
 #else
 #ifndef LMP_PAIR_PACE_APIP_PRECISE_H
 #define LMP_PAIR_PACE_APIP_PRECISE_H
 #include "pair_pace_apip.h"
 namespace LAMMPS_NS {
 class PairPACEapipPrecise : public PairPACEapip {
 public:
  PairPACEapipPrecise(class LAMMPS *);
  void *extract(const char *, int &) override;
 protected:
  double *get_e_ref_ptr() override;
  double compute_factor_lambda(double) override;
  int check_abort_condition(double *, double *, int *, int) override;
 };
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/ML-PACE/Install.sh
+++ b/src/ML-PACE/Install.sh
@ -32,6 +32,7 @@ for file in *.cpp *.h; do
  test -f ${file} && action $file
 done
 # edit 2 Makefile.package files to include/exclude package info
 if (test $1 = 1) then
@ -53,6 +54,12 @@ include ..\/..\/lib\/pace\/Makefile.lammps
 elif (test $1 = 0) then
  # The APIP package depends also on the pace library.
  # Remove in Makefiles only if there are no remaining includes from APIP.
  # grep searches also in kspace.cpp and thus returns no error.
  if (test $(grep '#include "ace' ../*pace*.cpp | wc -l) = 0) then
    # update Makefiles
    if (test -e ../Makefile.package) then
      sed -i -e 's/[^ \t]*pace[^ \t]* //' ../Makefile.package
    fi
@ -62,3 +69,5 @@ elif (test $1 = 0) then
    fi
  fi
 fi
--- a/src/Makefile
+++ b/src/Makefile
@ -59,6 +59,7 @@ PACKAGE = \
 	kspace \
 	adios \
 	amoeba \
 	apip \
 	asphere \
 	awpmd \
 	bocs \
@ -225,6 +226,7 @@ PACKLIB = \
 	python \
 	voronoi \
 	adios \
 	apip \
 	atc \
 	awpmd \
 	colvars \
@ -252,6 +254,7 @@ PACKINT = atc awpmd colvars electrode gpu kokkos lepton ml-pod poems
 PACKEXT = \
 	adios \
 	apip \
 	h5md \
 	kim \
 	machdyn \
--- a/src/atom.cpp
+++ b/src/atom.cpp
@ -220,6 +220,11 @@ Atom::Atom(LAMMPS *_lmp) : Pointers(_lmp), atom_style(nullptr), avec(nullptr), a
  area = ed = em = epsilon = curvature = q_scaled = nullptr;
  // APIP package
  lambda_const = lambda = lambda_input = lambda_input_ta = e_simple = e_complex = nullptr;
  lambda_required = nullptr;
  f_const_lambda = f_dyn_lambda = nullptr;
  // end of customization section
  // --------------------------------------------------------------------
@ -575,6 +580,17 @@ void Atom::peratom_create()
  add_peratom("curvature",&curvature,DOUBLE,0);
  add_peratom("q_scaled",&q_scaled,DOUBLE,0);
  // APIP package
  add_peratom("lambda",&lambda,DOUBLE,0);
  add_peratom("lambda_required",&lambda_required,INT,0);
  add_peratom("lambda_input",&lambda_input,DOUBLE,0);
  add_peratom("lambda_input_ta",&lambda_input_ta,DOUBLE,0);
  add_peratom("e_simple",&e_simple,DOUBLE,0);
  add_peratom("e_complex",&e_complex,DOUBLE,0);
  add_peratom("lambda_const",&lambda_const,DOUBLE,0);
  add_peratom("f_const_lambda",&f_const_lambda,DOUBLE,3,1);
  add_peratom("f_dyn_lambda",&f_dyn_lambda,DOUBLE,3,1);
  // end of customization section
  // --------------------------------------------------------------------
 }
@ -658,6 +674,7 @@ void Atom::set_atomflag_defaults()
  contact_radius_flag = smd_data_9_flag = smd_stress_flag = 0;
  eff_plastic_strain_flag = eff_plastic_strain_rate_flag = 0;
  nspecial15_flag = 0;
  lambda_flag = e_simple_flag = e_complex_flag = lambda_input_flag = lambda_input_ta_flag = lambda_required_flag = f_const_lambda_flag = f_dyn_lambda_flag = lambda_const_flag = 0;
  pdscale = 1.0;
 }
@ -3116,6 +3133,18 @@ void *Atom::extract(const char *name)
  if (strcmp(name,"curvature") == 0) return (void *) curvature;
  if (strcmp(name,"q_scaled") == 0) return (void *) q_scaled;
  // APIP package
  if (strcmp(name,"lambda") == 0) return (void *) lambda;
  if (strcmp(name,"lambda_required") == 0) return (void *) lambda_required;
  if (strcmp(name,"lambda_input") == 0) return (void *) lambda_input;
  if (strcmp(name,"lambda_input_ta") == 0) return (void *) lambda_input_ta;
  if (strcmp(name,"e_simple") == 0) return (void *) e_simple;
  if (strcmp(name,"e_complex") == 0) return (void *) e_complex;
  if (strcmp(name,"f_const_lambda") == 0) return (void *) f_const_lambda;
  if (strcmp(name,"f_dyn_lambda") == 0) return (void *) f_dyn_lambda;
  if (strcmp(name,"lambda_const") == 0) return (void *) lambda_const;
  // end of customization section
  // --------------------------------------------------------------------
@ -3247,6 +3276,17 @@ int Atom::extract_datatype(const char *name)
  if (strcmp(name,"curvature") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"q_unscaled") == 0) return LAMMPS_DOUBLE;
  // PACE package
  if (strcmp(name,"lambda") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"lambda_required") == 0) return LAMMPS_INT;
  if (strcmp(name,"lambda_input") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"lambda_input_ta") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"e_simple") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"e_complex") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"lambda_const") == 0) return LAMMPS_DOUBLE;
  if (strcmp(name,"f_const_lambda") == 0) return LAMMPS_DOUBLE_2D;
  if (strcmp(name,"f_dyn_lambda") == 0) return LAMMPS_DOUBLE_2D;
  // end of customization section
  // --------------------------------------------------------------------
@ -3383,6 +3423,18 @@ int Atom::extract_size(const char *name, int type)
      if (strcmp(name, "smd_data_9") == 0) return 9;
      if (strcmp(name, "smd_stress") == 0) return 6;
      // APIP package
      if (strcmp(name, "lambda") == 0) return nlocal;
      if (strcmp(name, "lambda_required") == 0) return nlocal;
      if (strcmp(name, "lambda_input") == 0) return nlocal;
      if (strcmp(name, "lambda_input_ta") == 0) return nlocal;
      if (strcmp(name, "e_simple") == 0) return nlocal;
      if (strcmp(name, "e_complex") == 0) return nlocal;
      if (strcmp(name, "lambda_const") == 0) return nlocal;
      if (strcmp(name, "f_const_lambda") == 0) return nall;
      if (strcmp(name, "f_dyn_lambda") == 0) return nall;
    }
    // custom arrays
--- a/src/atom.h
+++ b/src/atom.h
@ -177,6 +177,11 @@ class Atom : protected Pointers {
  double *area, *ed, *em, *epsilon, *curvature, *q_scaled;
  // APIP package
  double *lambda, *lambda_input, *lambda_input_ta, *e_simple, *e_complex, **f_const_lambda, **f_dyn_lambda, *lambda_const;
  int *lambda_required;
  // end of customization section
  // --------------------------------------------------------------------
@ -225,6 +230,10 @@ class Atom : protected Pointers {
  int dielectric_flag;
  // APIP package
  int lambda_flag, e_simple_flag, e_complex_flag, lambda_input_flag, lambda_input_ta_flag, lambda_required_flag, f_const_lambda_flag, f_dyn_lambda_flag, lambda_const_flag;
  // end of customization section
  // --------------------------------------------------------------------
--- a/src/atom_vec_apip.cpp
+++ b/src/atom_vec_apip.cpp
@ -0,0 +1,96 @@
 /* ----------------------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 #include "atom_vec_apip.h"
 #include "atom.h"
 using namespace LAMMPS_NS;
 /* ---------------------------------------------------------------------- */
 AtomVecApip::AtomVecApip(LAMMPS *lmp) : AtomVec(lmp)
 {
  molecular = Atom::ATOMIC;
  mass_type = PER_TYPE;
  forceclearflag = 1;
  double *lambda, *lambda_input, *lambda_input_ta, *lambda_const, *e_simple, *e_complex,
      **f_const_lambda, **f_dyn_lambda;
  int *lambda_required;
  atom->lambda_flag = 1;
  atom->lambda_input_flag = 1;
  atom->lambda_input_ta_flag = 1;
  atom->lambda_const_flag = 1;
  atom->lambda_required_flag = 1;
  atom->e_simple_flag = 1;
  atom->e_complex_flag = 1;
  atom->f_const_lambda_flag = 1;
  atom->f_dyn_lambda_flag = 1;
  // strings with peratom variables to include in each AtomVec method
  // strings cannot contain fields in corresponding AtomVec default strings
  // order of fields in a string does not matter
  // except: fields_data_atom & fields_data_vel must match data file
  // The full list of fields is in atom_vec.cpp
  fields_copy = {"lambda", "lambda_required", "lambda_input", "lambda_input_ta", "lambda_const"};
  fields_comm = {"lambda", "lambda_required", "lambda_input_ta", "lambda_const"};
  fields_comm_vel = {};
  fields_border = {"lambda", "lambda_required", "lambda_input_ta", "lambda_const"};
  fields_border_vel = {};
  fields_exchange = {"lambda", "lambda_required", "lambda_input_ta", "lambda_const"};
  fields_restart = {"lambda", "lambda_required", "lambda_input", "lambda_input_ta", "lambda_const"};
  fields_create = {};
  fields_grow = {
      "lambda",   "lambda_required", "lambda_input",   "lambda_input_ta", "lambda_const",
      "e_simple", "e_complex",       "f_const_lambda", "f_dyn_lambda"};    // allocates memory
  fields_reverse = {"f_const_lambda",
                    "f_dyn_lambda"};    // communication of force after calculation
  fields_data_atom = {"id", "type", "x"};
  fields_data_vel = {"id", "v"};
  setup_fields();
 }
 /* ----------------------------------------------------------------------
   set local copies of all grow ptrs used by this class, except defaults
   needed in replicate when 2 atom classes exist and it calls pack_restart()
 ------------------------------------------------------------------------- */
 void AtomVecApip::grow_pointers()
 {
  lambda = atom->lambda;
  lambda_required = atom->lambda_required;
  lambda_input = atom->lambda_input;
  lambda_input_ta = atom->lambda_input_ta;
  lambda_const = atom->lambda_const;
  e_simple = atom->e_simple;
  e_complex = atom->e_complex;
  f_const_lambda = atom->f_const_lambda;
  f_dyn_lambda = atom->f_dyn_lambda;
 }
 /* ----------------------------------------------------------------------
   clear extra forces starting at atom n
   natoms = # of atoms to clear
   nbytes = natoms * sizeof(double)
   requires forceclearflag = 1 to be called
 ------------------------------------------------------------------------- */
 void AtomVecApip::force_clear(int n, size_t nbytes)
 {
  memset(&f_const_lambda[n][0], 0, 3 * nbytes);
  memset(&f_dyn_lambda[n][0], 0, 3 * nbytes);
  memset(&lambda_required[n], 0, nbytes / sizeof(double) * sizeof(int));
 }
--- a/src/atom_vec_apip.h
+++ b/src/atom_vec_apip.h
@ -0,0 +1,58 @@
 /* -*- c++ -*- ----------------------------------------------------------
   LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
   https://www.lammps.org/, Sandia National Laboratories
   LAMMPS development team: developers@lammps.org
   Copyright (2003) Sandia Corporation.  Under the terms of Contract
   DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
   certain rights in this software.  This software is distributed under
   the GNU General Public License.
   See the README file in the top-level LAMMPS directory.
 ------------------------------------------------------------------------- */
 #ifdef ATOM_CLASS
 // clang-format off
 AtomStyle(apip,AtomVecApip);
 // clang-format on
 #else
 #ifndef LMP_ATOM_VEC_APIP_H
 #define LMP_ATOM_VEC_APIP_H
 #include "atom_vec.h"
 namespace LAMMPS_NS {
 class AtomVecApip : public AtomVec {
 public:
  AtomVecApip(class LAMMPS *);
  void grow_pointers();
  void force_clear(int, size_t) override;
 protected:
  double *lambda, *lambda_input, *lambda_const, *lambda_input_ta, *e_simple, *e_complex,
      **f_const_lambda, **f_dyn_lambda;
  int *lambda_required;
 };
 #ifndef LMP_ATOM_LAMBDA_REQUIRED
 #define LMP_ATOM_LAMBDA_REQUIRED
 namespace LambdaRequired {
  enum {
    UNKNOWN = 0,
    SIMPLE = 1 << 0,
    NO_SIMPLE = 1 << 1,
    COMPLEX = 1 << 2,
    NO_COMPLEX = 1 << 3,
  };
 }    // namespace LambdaRequired
 #endif
 }    // namespace LAMMPS_NS
 #endif
 #endif
--- a/src/compute_property_atom.cpp
+++ b/src/compute_property_atom.cpp
@ -331,6 +331,27 @@ ComputePropertyAtom::ComputePropertyAtom(LAMMPS *lmp, int narg, char **arg) :
        error->all(FLERR,"Compute property/atom {} requires atom style tri", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_corner3z;
    } else if (strcmp(arg[iarg],"lambda") == 0) {
      if (!atom->lambda_flag)
        error->all(FLERR,"Compute property/atom {} is not available", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_lambda;
    } else if (strcmp(arg[iarg],"lambda_input") == 0) {
      if (!atom->lambda_input_flag)
        error->all(FLERR,"Compute property/atom {} is not available", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_lambda_input;
    } else if (strcmp(arg[iarg],"lambda_required") == 0) {
      if (!atom->lambda_required_flag)
        error->all(FLERR,"Compute property/atom {} is not available", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_lambda_required;
    } else if (strcmp(arg[iarg],"e_simple") == 0) {
      if (!atom->e_simple_flag)
        error->all(FLERR,"Compute property/atom {} is not available", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_e_simple;
    } else if (strcmp(arg[iarg],"e_complex") == 0) {
      if (!atom->e_complex_flag)
        error->all(FLERR,"Compute property/atom {} is not available", arg[iarg]);
      pack_choice[i] = &ComputePropertyAtom::pack_e_complex;
    // custom per-atom vector or array
    } else if (utils::strmatch(arg[iarg],"^[id]2?_")) {
@ -1564,6 +1585,81 @@ void ComputePropertyAtom::pack_tqz(int n)
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_lambda(int n)
 {
  double *lambda = atom->lambda;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) buf[n] = lambda[i];
    else buf[n] = 0.0;
    n += nvalues;
  }
 }
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_lambda_input(int n)
 {
  double *lambda_input = atom->lambda_input;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) buf[n] = lambda_input[i];
    else buf[n] = 0.0;
    n += nvalues;
  }
 }
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_lambda_required(int n)
 {
  int *lambda_required = atom->lambda_required;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) buf[n] = lambda_required[i];
    else buf[n] = 0.0;
    n += nvalues;
  }
 }
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_e_simple(int n)
 {
  double *e_simple = atom->e_simple;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) buf[n] = e_simple[i];
    else buf[n] = 0.0;
    n += nvalues;
  }
 }
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_e_complex(int n)
 {
  double *e_complex = atom->e_complex;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) buf[n] = e_complex[i];
    else buf[n] = 0.0;
    n += nvalues;
  }
 }
 /* ---------------------------------------------------------------------- */
 void ComputePropertyAtom::pack_end1x(int n)
 {
  AtomVecLine::Bonus *bonus = avec_line->bonus;
--- a/src/compute_property_atom.h
+++ b/src/compute_property_atom.h
@ -137,6 +137,12 @@ class ComputePropertyAtom : public Compute {
  void pack_d2name(int);
  void pack_atom_style(int);
  void pack_lambda(int);
  void pack_lambda_required(int);
  void pack_lambda_input(int);
  void pack_e_simple(int);
  void pack_e_complex(int);
 };
 }    // namespace LAMMPS_NS
--- a/src/dump_custom.cpp
+++ b/src/dump_custom.cpp
@ -45,6 +45,7 @@ enum{ID,MOL,PROC,PROCP1,TYPE,TYPELABEL,ELEMENT,MASS,
     Q,MUX,MUY,MUZ,MU,RADIUS,DIAMETER,
     OMEGAX,OMEGAY,OMEGAZ,ANGMOMX,ANGMOMY,ANGMOMZ,
     TQX,TQY,TQZ,
     LAMBDA,LAMBDA_INPUT,LAMBDA_REQUIRED,ESIMPLE,ECOMPLEX, // APIP package
     COMPUTE,FIX,VARIABLE,IVEC,DVEC,IARRAY,DARRAY};
 enum{LT,LE,GT,GE,EQ,NEQ,XOR};
@ -1223,6 +1224,25 @@ int DumpCustom::count()
        double **darray = atom->darray[iwhich];
        ptr = &darray[0][argindex[i]-1];
        nstride = atom->dcols[iwhich];
      // APIP package
      } else if (thresh_array[ithresh] == LAMBDA) {
        ptr = &atom->lambda[0];
        nstride = 1;
      } else if (thresh_array[ithresh] == LAMBDA_INPUT) {
        ptr = &atom->lambda_input[0];
        nstride = 1;
      } else if (thresh_array[ithresh] == LAMBDA_REQUIRED) {
        int *lambda_required = atom->lambda_required;
        for (i = 0; i < nlocal; i++) dchoose[i] = lambda_required[i];
        ptr = dchoose;
        nstride = 1;
      } else if (thresh_array[ithresh] == ESIMPLE) {
        ptr = &atom->e_simple[0];
        nstride = 1;
      } else if (thresh_array[ithresh] == ECOMPLEX) {
        ptr = &atom->e_complex[0];
        nstride = 1;
      }
      // unselect atoms that don't meet threshold criterion
@ -1624,6 +1644,33 @@ int DumpCustom::parse_fields(int narg, char **arg)
      pack_choice[iarg] = &DumpCustom::pack_tqz;
      vtype[iarg] = Dump::DOUBLE;
    // APIP package
    } else if (strcmp(arg[iarg],"lambda") == 0) {
      if (!atom->lambda_flag)
        error->all(FLERR,"Dumping an atom property that isn't allocated");
      pack_choice[iarg] = &DumpCustom::pack_lambda;
      vtype[iarg] = Dump::DOUBLE;
    } else if (strcmp(arg[iarg],"lambda_input") == 0) {
      if (!atom->lambda_input_flag)
        error->all(FLERR,"Dumping an atom property that isn't allocated");
      pack_choice[iarg] = &DumpCustom::pack_lambda_input;
      vtype[iarg] = Dump::DOUBLE;
    } else if (strcmp(arg[iarg],"lambda_required") == 0) {
      if (!atom->lambda_required_flag)
        error->all(FLERR,"Dumping an atom property that isn't allocated");
      pack_choice[iarg] = &DumpCustom::pack_lambda_required;
      vtype[iarg] = Dump::INT;
    } else if (strcmp(arg[iarg],"e_simple") == 0) {
      if (!atom->e_simple_flag)
        error->all(FLERR,"Dumping an atom property that isn't allocated");
      pack_choice[iarg] = &DumpCustom::pack_e_simple;
      vtype[iarg] = Dump::DOUBLE;
    } else if (strcmp(arg[iarg],"e_complex") == 0) {
      if (!atom->e_complex_flag)
        error->all(FLERR,"Dumping an atom property that isn't allocated");
      pack_choice[iarg] = &DumpCustom::pack_e_complex;
      vtype[iarg] = Dump::DOUBLE;
    // compute or fix or variable or custom vector/array
    } else {
@ -2067,6 +2114,13 @@ int DumpCustom::modify_param(int narg, char **arg)
    else if (strcmp(arg[1],"tqy") == 0) thresh_array[nthresh] = TQY;
    else if (strcmp(arg[1],"tqz") == 0) thresh_array[nthresh] = TQZ;
    // APIP package
    else if (strcmp(arg[1],"lambda") == 0) thresh_array[nthresh] = LAMBDA;
    else if (strcmp(arg[1],"lambda_input") == 0) thresh_array[nthresh] = LAMBDA_INPUT;
    else if (strcmp(arg[1],"lambda_required") == 0) thresh_array[nthresh] = LAMBDA_REQUIRED;
    else if (strcmp(arg[1],"e_simple") == 0) thresh_array[nthresh] = ESIMPLE;
    else if (strcmp(arg[1],"e_complex") == 0) thresh_array[nthresh] = ECOMPLEX;
    // compute or fix or variable or custom vector/array
    // must grow field2index and argindex arrays, since access is beyond nfield
@ -3448,3 +3502,63 @@ void DumpCustom::pack_tqz_triclinic_general(int n)
    n += size_one;
  }
 }
 /* ---------------------------------------------------------------------- */
 void DumpCustom::pack_lambda(int n)
 {
  double *lambda = atom->lambda;
  for (int i = 0; i < nchoose; i++) {
    buf[n] = lambda[clist[i]];
    n += size_one;
  }
 }
 /* ---------------------------------------------------------------------- */
 void DumpCustom::pack_lambda_input(int n)
 {
  double *lambda_input = atom->lambda_input;
  for (int i = 0; i < nchoose; i++) {
    buf[n] = lambda_input[clist[i]];
    n += size_one;
  }
 }
 /* ---------------------------------------------------------------------- */
 void DumpCustom::pack_lambda_required(int n)
 {
  int *lambda_required = atom->lambda_required;
  for (int i = 0; i < nchoose; i++) {
    buf[n] = lambda_required[clist[i]];
    n += size_one;
  }
 }
 /* ---------------------------------------------------------------------- */
 void DumpCustom::pack_e_simple(int n)
 {
  double *e_simple = atom->e_simple;
  for (int i = 0; i < nchoose; i++) {
    buf[n] = e_simple[clist[i]];
    n += size_one;
  }
 }
 /* ---------------------------------------------------------------------- */
 void DumpCustom::pack_e_complex(int n)
 {
  double *e_complex = atom->e_complex;
  for (int i = 0; i < nchoose; i++) {
    buf[n] = e_complex[clist[i]];
    n += size_one;
  }
 }
--- a/src/dump_custom.h
+++ b/src/dump_custom.h
@ -235,6 +235,12 @@ class DumpCustom : public Dump {
  void pack_tqx_triclinic_general(int);
  void pack_tqy_triclinic_general(int);
  void pack_tqz_triclinic_general(int);
  void pack_lambda(int);
  void pack_lambda_input(int);
  void pack_lambda_required(int);
  void pack_e_simple(int);
  void pack_e_complex(int);
 };
 }    // namespace LAMMPS_NS
--- a/src/fix_store_state.cpp
+++ b/src/fix_store_state.cpp
@ -141,6 +141,11 @@ FixStoreState::FixStoreState(LAMMPS *lmp, int narg, char **arg) :
        error->all(FLERR, "Cannot use fix store/state {} for atom style {}",
                   arg[iarg], atom->get_style());
      val.pack_choice = &FixStoreState::pack_q;
    } else if (strcmp(arg[iarg],"lambda") == 0) {
      if (!atom->lambda_flag)
        error->all(FLERR, "Cannot use fix store/state {} for atom style {}",
                   arg[iarg], atom->get_style());
      val.pack_choice = &FixStoreState::pack_lambda;
    } else if (strcmp(arg[iarg],"mux") == 0) {
      if (!atom->mu_flag)
        error->all(FLERR, "Cannot use fix store/state {} for atom style {}",
@ -1269,6 +1274,21 @@ void FixStoreState::pack_q(int n)
 /* ---------------------------------------------------------------------- */
 void FixStoreState::pack_lambda(int n)
 {
  double *lambda = atom->lambda;
  int *mask = atom->mask;
  int nlocal = atom->nlocal;
  for (int i = 0; i < nlocal; i++) {
    if (mask[i] & groupbit) vbuf[n] = lambda[i];
    else vbuf[n] = 0.0;
    n += values.size();
  }
 }
 /* ---------------------------------------------------------------------- */
 void FixStoreState::pack_mux(int n)
 {
  double **mu = atom->mu;
--- a/src/fix_store_state.h
+++ b/src/fix_store_state.h
@ -106,6 +106,7 @@ class FixStoreState : public Fix {
  void pack_fy(int);
  void pack_fz(int);
  void pack_q(int);
  void pack_lambda(int);
  void pack_mux(int);
  void pack_muy(int);
  void pack_muz(int);
--- a/src/read_dump.cpp
+++ b/src/read_dump.cpp
@ -813,6 +813,7 @@ void ReadDump::process_atoms()
  double **x = atom->x;
  double **v = atom->v;
  double *q = atom->q;
  double *lambda = atom->lambda;
  double **f = atom->f;
  tagint *tag = atom->tag;
  imageint *image = atom->image;
@ -862,6 +863,9 @@ void ReadDump::process_atoms()
        case Reader::Q:
          q[m] = fields[i][ifield];
          break;
        case Reader::LAMBDA:
          lambda[m] = fields[i][ifield];
          break;
        case Reader::VY:
          v[m][1] = fields[i][ifield];
          break;
@ -977,6 +981,7 @@ void ReadDump::process_atoms()
    tag = atom->tag;
    v = atom->v;
    q = atom->q;
    lambda = atom->lambda;
    image = atom->image;
    // set atom attributes from other dump file fields
@ -1001,6 +1006,9 @@ void ReadDump::process_atoms()
      case Reader::Q:
        q[m] = fields[i][ifield];
        break;
      case Reader::LAMBDA:
        lambda[m] = fields[i][ifield];
        break;
      case Reader::IX:
        xbox = static_cast<int> (fields[i][ifield]);
        break;
@ -1163,6 +1171,8 @@ int ReadDump::fields_and_keywords(int narg, char **arg)
    if (type < 0) break;
    if (type == Reader::Q && !atom->q_flag)
      error->all(FLERR,"Read dump of charge property that isn't supported by atom style");
    if (type == Reader::LAMBDA && !atom->lambda_flag)
      error->all(FLERR,"Read dump of lambda property that isn't supported by atom style");
    fieldtype[nfield++] = type;
    iarg++;
  }
@ -1288,6 +1298,7 @@ int ReadDump::whichtype(char *str)
  else if (strcmp(str,"vy") == 0) type = Reader::VY;
  else if (strcmp(str,"vz") == 0) type = Reader::VZ;
  else if (strcmp(str,"q") == 0) type = Reader::Q;
  else if (strcmp(str,"lambda") == 0) type = Reader::LAMBDA;
  else if (strcmp(str,"ix") == 0) type = Reader::IX;
  else if (strcmp(str,"iy") == 0) type = Reader::IY;
  else if (strcmp(str,"iz") == 0) type = Reader::IZ;
--- a/src/reader.h
+++ b/src/reader.h
@ -22,7 +22,7 @@ namespace LAMMPS_NS {
 class Reader : protected Pointers {
 public:
-  enum { ID, TYPE, X, Y, Z, VX, VY, VZ, Q, IX, IY, IZ, FX, FY, FZ };
+  enum { ID, TYPE, X, Y, Z, VX, VY, VZ, Q, LAMBDA, IX, IY, IZ, FX, FY, FZ };
  enum { UNSET, NOSCALE_NOWRAP, NOSCALE_WRAP, SCALE_NOWRAP, SCALE_WRAP };
  Reader(class LAMMPS *);
--- a/src/reader_native.cpp
+++ b/src/reader_native.cpp
@ -413,6 +413,9 @@ bigint ReaderNative::read_header(double box[3][3], int &boxinfo, int &triclinic,
    else if (fieldtype[i] == Q)
      fieldindex[i] = find_label("q", labels);
    else if (fieldtype[i] == LAMBDA)
      fieldindex[i] = find_label("lambda", labels);
    else if (fieldtype[i] == IX)
      fieldindex[i] = find_label("ix", labels);
    else if (fieldtype[i] == IY)
--- a/src/variable.cpp
+++ b/src/variable.cpp
@ -4992,6 +4992,30 @@ void Variable::peratom2global(int flag, char *word, double *vector, int nstride,
        if (!atom->q_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->q[index];
      } else if (strcmp(word,"lambda") == 0) {
        if (!atom->lambda_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->lambda[index];
      } else if (strcmp(word,"lambda_required") == 0) {
        if (!atom->lambda_required_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->lambda_required[index];
      } else if (strcmp(word,"lambda_input") == 0) {
        if (!atom->lambda_input_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->lambda_input[index];
      } else if (strcmp(word,"lambda_const") == 0) {
        if (!atom->lambda_const_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->lambda_const[index];
      } else if (strcmp(word,"e_simple") == 0) {
        if (!atom->e_simple_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->e_simple[index];
      } else if (strcmp(word,"e_complex") == 0) {
        if (!atom->e_complex_flag)
          error->one(FLERR,"Variable uses atom property that isn't allocated");
        mine = atom->e_complex[index];
      }
      else if (strcmp(word,"x") == 0) mine = atom->x[index][0];
@ -5087,6 +5111,12 @@ int Variable::is_atom_vector(char *word)
  if (strcmp(word,"fx") == 0) return 1;
  if (strcmp(word,"fy") == 0) return 1;
  if (strcmp(word,"fz") == 0) return 1;
  if (strcmp(word,"lambda") == 0) return 1;
  if (strcmp(word,"lambda_input") == 0) return 1;
  if (strcmp(word,"lambda_required") == 0) return 1;
  if (strcmp(word,"lambda_const") == 0) return 1;
  if (strcmp(word,"e_simple") == 0) return 1;
  if (strcmp(word,"e_complex") == 0) return 1;
  return 0;
 }
@ -5155,6 +5185,37 @@ void Variable::atom_vector(char *word, Tree **tree, Tree **treestack, int &ntree
      error->one(FLERR,"Variable uses atom property 'q' that isn't allocated");
    newtree->array = atom->q;
    newtree->nstride = 1;
  } else if (strcmp(word,"lambda") == 0) {
    if (!atom->lambda_flag)
      error->one(FLERR,"Variable uses atom property 'lambda' that isn't allocated");
    newtree->array = atom->lambda;
    newtree->nstride = 1;
  } else if (strcmp(word,"lambda_required") == 0) {
    if (!atom->lambda_required_flag)
      error->one(FLERR,"Variable uses atom property 'lambda_required' that isn't allocated");
    newtree->type = INTARRAY;
    newtree->nstride = 1;
    newtree->iarray = atom->lambda_required;
  } else if (strcmp(word,"lambda_input") == 0) {
    if (!atom->lambda_input_flag)
      error->one(FLERR,"Variable uses atom property 'lambda_input' that isn't allocated");
    newtree->array = atom->lambda_input;
    newtree->nstride = 1;
  } else if (strcmp(word,"lambda_const") == 0) {
    if (!atom->lambda_const_flag)
      error->one(FLERR,"Variable uses atom property 'lambda_const' that isn't allocated");
    newtree->array = atom->lambda_const;
    newtree->nstride = 1;
  } else if (strcmp(word,"e_simple") == 0) {
    if (!atom->e_simple_flag)
      error->one(FLERR,"Variable uses atom property 'e_simple' that isn't allocated");
    newtree->array = atom->e_simple;
    newtree->nstride = 1;
  } else if (strcmp(word,"e_complex") == 0) {
    if (!atom->e_complex_flag)
      error->one(FLERR,"Variable uses atom property 'e_complex' that isn't allocated");
    newtree->array = atom->e_complex;
    newtree->nstride = 1;
  }
  else if (strcmp(word,"x") == 0) newtree->array = &atom->x[0][0];