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Date: 2024-10-18 13:59:31 Functions: 17 20 85.0 %

          Line data    Source code
       1             : /* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
       2             : Copyright (c) 2017 of Glen Hocky and Andrew White
       3             : 
       4             : The eds module is free software: you can redistribute it and/or modify
       5             : it under the terms of the GNU Lesser General Public License as published by
       6             : the Free Software Foundation, either version 3 of the License, or
       7             : (at your option) any later version.
       8             : 
       9             : The eds module is distributed in the hope that it will be useful,
      10             : but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
      12             : GNU Lesser General Public License for more details.
      13             : 
      14             : You should have received a copy of the GNU Lesser General Public License
      15             : along with plumed.  If not, see <http://www.gnu.org/licenses/>.
      16             : +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ */
      17             : #include "bias/Bias.h"
      18             : #include "bias/ReweightBase.h"
      19             : #include "core/ActionAtomistic.h"
      20             : #include "core/ActionRegister.h"
      21             : #include "core/PlumedMain.h"
      22             : #include "tools/File.h"
      23             : #include "tools/Matrix.h"
      24             : #include "tools/Random.h"
      25             : 
      26             : #include <iostream>
      27             : 
      28             : using namespace PLMD;
      29             : using namespace bias;
      30             : 
      31             : // namespace is lowercase to match
      32             : // module names being all lowercase
      33             : 
      34             : namespace PLMD
      35             : {
      36             : namespace eds
      37             : {
      38             : 
      39             : //+PLUMEDOC EDSMOD_BIAS EDS
      40             : /*
      41             : Add a linear bias on a set of observables.
      42             : 
      43             : This force is the same as the linear part of the bias in \ref
      44             : RESTRAINT, but this bias has the ability to compute the prefactors
      45             : adaptively using the scheme of White and Voth \cite white2014efficient
      46             : in order to match target observable values for a set of CVs.
      47             : Further updates to the algorithm are described in \cite hocky2017cgds
      48             : and you can read a review on the method and its applications here: \cite Amirkulova2019Recent.
      49             : 
      50             : You can
      51             : see a tutorial on EDS specifically for biasing coordination number at
      52             : <a
      53             : href="http://thewhitelab.org/blog/tutorial/2017/05/10/lammps-coordination-number-tutorial/">
      54             : Andrew White's webpage</a>.
      55             : 
      56             : The addition to the potential is of the form
      57             : \f[
      58             :   \sum_i \frac{\alpha_i}{s_i} x_i
      59             : \f]
      60             : 
      61             : where for CV \f$x_i\f$, a coupling constant \f${\alpha}_i\f$ is determined
      62             : adaptively or set by the user to match a target value for
      63             : \f$x_i\f$. \f$s_i\f$ is a scale parameter, which by default is set to
      64             : the target value. It may also be set separately.
      65             : 
      66             : \warning
      67             : It is not possible to set the target value of the observable
      68             : to zero with the default value of \f$s_i\f$ as this will cause a
      69             : divide-by-zero error. Instead, set \f$s_i=1\f$ or modify the CV so the
      70             : desired target value is no longer zero.
      71             : 
      72             : Notice that a similar method is available as \ref MAXENT, although with different features and using a different optimization algorithm.
      73             : 
      74             : \par Virial
      75             : 
      76             : The bias forces modify the virial and this can change your simulation density if the bias is used in an NPT simulation.
      77             : One way to avoid changing the virial contribution from the bias is to add the keyword VIRIAL=1.0, which changes how the bias
      78             : is computed to minimize its contribution to the virial. This can also lead to smaller magnitude biases that are more robust if
      79             : transferred to other systems.  VIRIAL=1.0 can be a reasonable starting point and increasing the value changes the balance between matching
      80             : the set-points and minimizing the virial. See \cite Amirkulova2019Recent for details on the equations. Since the coupling constants
      81             : are unique with a single CV, VIRIAL is not applicable with a single CV. When used with multiple CVs, the CVs should be correlated
      82             : which is almost always the case.
      83             : 
      84             : \par Weighting
      85             : 
      86             : EDS computes means and variances as part of its algorithm. If you are
      87             : also using a biasing method like metadynamics, you may wish to remove
      88             : the effect of this bias in your EDS computations so that EDS works on
      89             : the canonical values (reweighted to be unbiased).  For example, you may be using
      90             : metadynamics to bias a dihedral angle to enhance sampling and be using
      91             : EDS to set the average distance between two particular atoms. Specifically:
      92             : 
      93             : \plumedfile
      94             : # set-up metadynamics
      95             : t: TORSION ATOMS=1,2,3,4
      96             : md: METAD ARG=d SIGMA=0.2 HEIGHT=0.3 PACE=500 TEMP=300
      97             : # compute bias weights
      98             : bias: REWEIGHT_METAD TEMP=300
      99             : # now do EDS on distance while removing effect of metadynamics
     100             : d: DISTANCE ATOMS=4,7
     101             : eds: EDS ARG=d CENTER=3.0 PERIOD=100 TEMP=300 LOGWEIGHTS=bias
     102             : \endplumedfile
     103             : 
     104             : This is an approximation though because EDS uses a finite samples while running to get means/variances.
     105             : At the end of a run,
     106             : you should ensure this approach worked and indeed your reweighted CV matches the target value.
     107             : 
     108             : \par Examples
     109             : 
     110             : The following input for a harmonic oscillator of two beads will
     111             : adaptively find a linear bias to change the mean and variance to the
     112             : target values. The PRINT line shows how to access the value of the
     113             : coupling constants.
     114             : 
     115             : \plumedfile
     116             : dist: DISTANCE ATOMS=1,2
     117             : # this is the squared of the distance
     118             : dist2: COMBINE ARG=dist POWERS=2 PERIODIC=NO
     119             : 
     120             : # bias mean and variance
     121             : eds: EDS ARG=dist,dist2 CENTER=2.0,1.0 PERIOD=100 TEMP=1.0
     122             : PRINT ARG=dist,dist2,eds.dist_coupling,eds.dist2_coupling,eds.bias,eds.force2 FILE=colvars.dat STRIDE=100
     123             : \endplumedfile
     124             : 
     125             : <hr>
     126             : 
     127             : Rather than trying to find the coupling constants adaptively, one can ramp up to a constant value.
     128             : \plumedfile
     129             : dist: DISTANCE ATOMS=1,2
     130             : dist2: COMBINE ARG=dist POWERS=2 PERIODIC=NO
     131             : 
     132             : # ramp couplings from 0,0 to -1,1 over 50000 steps
     133             : eds: EDS ARG=dist,dist2 CENTER=2.0,1.0 FIXED=-1,1 RAMP PERIOD=50000 TEMP=1.0
     134             : 
     135             : # same as above, except starting at -0.5,0.5 rather than default of 0,0
     136             : eds2: EDS ARG=dist,dist2 CENTER=2.0,1.0 FIXED=-1,1 INIT=-0.5,0.5 RAMP PERIOD=50000 TEMP=1.0
     137             : \endplumedfile
     138             : 
     139             : <hr>
     140             : A restart file can be added to dump information needed to restart/continue simulation using these parameters every PERIOD.
     141             : \plumedfile
     142             : dist: DISTANCE ATOMS=1,2
     143             : dist2: COMBINE ARG=dist POWERS=2 PERIODIC=NO
     144             : 
     145             : # add the option to write to a restart file
     146             : eds: EDS ARG=dist,dist2 CENTER=2.0,1.0 PERIOD=100 TEMP=1.0 OUT_RESTART=checkpoint.eds
     147             : \endplumedfile
     148             : 
     149             : The first few lines of the restart file that is output if we run a calculation with one CV will look something like this:
     150             : 
     151             : \auxfile{restart.eds}
     152             : #! FIELDS time d1_center d1_set d1_target d1_coupling d1_maxrange d1_maxgrad d1_accum d1_mean d1_std
     153             : #! SET adaptive  1
     154             : #! SET update_period  1
     155             : #! SET seed  0
     156             : #! SET kbt    2.4943
     157             :    0.0000   1.0000   0.0000   0.0000   0.0000   7.4830   0.1497   0.0000   0.0000   0.0000
     158             :    1.0000   1.0000   0.0000   0.0000   0.0000   7.4830   0.1497   0.0000   0.0000   0.0000
     159             :    2.0000   1.0000  -7.4830   0.0000   0.0000   7.4830   0.1497   0.0224   0.0000   0.0000
     160             :    3.0000   1.0000  -7.4830   0.0000  -7.4830   7.4830   0.1497   0.0224   0.0000   0.0000
     161             :    4.0000   1.0000  -7.4830   0.0000  -7.4830   7.4830   0.1497   0.0224   0.0000   0.0000
     162             : \endauxfile
     163             : 
     164             : <hr>
     165             : 
     166             : Read in a previous restart file. Adding RESTART flag makes output append
     167             : \plumedfile
     168             : d1: DISTANCE ATOMS=1,2
     169             : 
     170             : eds: EDS ARG=d1 CENTER=2.0 PERIOD=100 TEMP=1.0 IN_RESTART=restart.eds RESTART=YES
     171             : \endplumedfile
     172             : 
     173             : <hr>
     174             : 
     175             : Read in a previous restart file and freeze the bias at the final level from the previous simulation
     176             : \plumedfile
     177             : d1: DISTANCE ATOMS=1,2
     178             : 
     179             : eds: EDS ARG=d1 CENTER=2.0 TEMP=1.0 IN_RESTART=restart.eds FREEZE
     180             : \endplumedfile
     181             : 
     182             : <hr>
     183             : 
     184             : Read in a previous restart file and freeze the bias at the mean from the previous simulation
     185             : \plumedfile
     186             : d1: DISTANCE ATOMS=1,2
     187             : 
     188             : eds: EDS ARG=d1 CENTER=2.0 TEMP=1.0 IN_RESTART=restart.eds FREEZE MEAN
     189             : \endplumedfile
     190             : 
     191             : 
     192             : */
     193             : //+ENDPLUMEDOC
     194             : 
     195             : class EDS : public Bias
     196             : {
     197             : 
     198             : private:
     199             :   /*We will get this and store it once, since on-the-fly changing number of CVs will be fatal*/
     200             :   const unsigned int ncvs_;
     201             :   std::vector<double> center_;
     202             :   std::vector<Value *> center_values_;
     203             :   ReweightBase *logweights_; // weights to use if reweighting averages
     204             :   std::vector<double> scale_;
     205             :   std::vector<double> current_coupling_;   // actually current coupling
     206             :   std::vector<double> set_coupling_;       // what our coupling is ramping up to. Equal to current_coupling when gathering stats
     207             :   std::vector<double> target_coupling_;    // used when loaded to reach a value
     208             :   std::vector<double> max_coupling_range_; // used for adaptive range
     209             :   std::vector<double> max_coupling_grad_;  // maximum allowed gradient
     210             :   std::vector<double> coupling_rate_;
     211             :   std::vector<double> coupling_accum_;
     212             :   std::vector<double> means_;
     213             :   std::vector<double> differences_;
     214             :   std::vector<double> alpha_vector_;
     215             :   std::vector<double> alpha_vector_2_;
     216             :   std::vector<double> ssds_;
     217             :   std::vector<double> step_size_;
     218             :   std::vector<double> pseudo_virial_;
     219             :   std::vector<Value *> out_coupling_;
     220             :   Matrix<double> covar_;
     221             :   Matrix<double> covar2_;
     222             :   Matrix<double> lm_inv_;
     223             :   std::string in_restart_name_;
     224             :   std::string out_restart_name_;
     225             :   std::string fmt_;
     226             :   OFile out_restart_;
     227             :   IFile in_restart_;
     228             :   bool b_c_values_;
     229             :   bool b_adaptive_;
     230             :   bool b_freeze_;
     231             :   bool b_equil_;
     232             :   bool b_ramp_;
     233             :   bool b_covar_;
     234             :   bool b_restart_;
     235             :   bool b_write_restart_;
     236             :   bool b_lm_;
     237             :   bool b_virial_;
     238             :   bool b_update_virial_;
     239             :   bool b_weights_;
     240             :   int seed_;
     241             :   int update_period_;
     242             :   int avg_coupling_count_;
     243             :   int update_calls_;
     244             :   double kbt_;
     245             :   double multi_prop_;
     246             :   double lm_mixing_par_;
     247             :   double virial_scaling_;
     248             :   double pseudo_virial_sum_; // net virial for all cvs in current period
     249             :   double max_logweight_;     // maximum observed max logweight for period
     250             :   double wsum_;              // sum of weights thus far
     251             :   Random rand_;
     252             :   Value *value_force2_;
     253             :   Value *value_pressure_;
     254             : 
     255             :   /*read input restart. b_mean sets if we use mean or final value for freeze*/
     256             :   void readInRestart(const bool b_mean);
     257             :   /*setup output restart*/
     258             :   void setupOutRestart();
     259             :   /*write output restart*/
     260             :   void writeOutRestart();
     261             :   void update_statistics();
     262             :   void update_pseudo_virial();
     263             :   void calc_lm_step_size();
     264             :   void calc_covar_step_size();
     265             :   void calc_ssd_step_size();
     266             :   void reset_statistics();
     267             :   void update_bias();
     268             :   void apply_bias();
     269             : 
     270             : public:
     271             :   explicit EDS(const ActionOptions &);
     272             :   void calculate();
     273             :   void update();
     274             :   void turnOnDerivatives();
     275             :   static void registerKeywords(Keywords &keys);
     276             :   ~EDS();
     277             : };
     278             : 
     279             : PLUMED_REGISTER_ACTION(EDS, "EDS")
     280             : 
     281          10 : void EDS::registerKeywords(Keywords &keys)
     282             : {
     283          10 :   Bias::registerKeywords(keys);
     284          20 :   keys.add("optional", "CENTER", "The desired centers (equilibrium values) which will be sought during the adaptive linear biasing. This is for fixed centers");
     285          20 :   keys.addInputKeyword("optional", "CENTER_ARG", "scalar", "The desired centers (equilibrium values) which will be sought during the adaptive linear biasing. "
     286             :                        "CENTER_ARG is for calculated centers, e.g. from a CV or analysis. ");
     287             : 
     288          20 :   keys.add("optional", "PERIOD", "Steps over which to adjust bias for adaptive or ramping");
     289          20 :   keys.add("compulsory", "RANGE", "25.0", "The (starting) maximum increase in coupling constant per PERIOD (in k_B T/[BIAS_SCALE unit]) for each CV biased");
     290          20 :   keys.add("compulsory", "SEED", "0", "Seed for random order of changing bias");
     291          20 :   keys.add("compulsory", "INIT", "0", "Starting value for coupling constant");
     292          20 :   keys.add("compulsory", "FIXED", "0", "Fixed target values for coupling constant. Non-adaptive.");
     293          20 :   keys.add("optional", "BIAS_SCALE", "A divisor to set the units of the bias. "
     294             :            "If not set, this will be the CENTER value by default (as is done in White and Voth 2014).");
     295          20 :   keys.add("optional", "TEMP", "The system temperature. If not provided will be taken from MD code (if available)");
     296          20 :   keys.add("optional", "MULTI_PROP", "What proportion of dimensions to update at each step. "
     297             :            "Must be in interval [1,0), where 1 indicates all and any other indicates a stochastic update. "
     298             :            "If not set, default is 1 / N, where N is the number of CVs. ");
     299          20 :   keys.add("optional", "VIRIAL", "Add an update penalty for having non-zero virial contributions. Only makes sense with multiple correlated CVs.");
     300          20 :   keys.addInputKeyword("optional", "LOGWEIGHTS", "scalar", "Add weights to use for computing statistics. For example, if biasing with metadynamics.");
     301          20 :   keys.addFlag("LM", false, "Use Levenberg-Marquadt algorithm along with simultaneous keyword. Otherwise use gradient descent.");
     302          20 :   keys.add("compulsory", "LM_MIXING", "1", "Initial mixing parameter when using Levenberg-Marquadt minimization.");
     303          20 :   keys.add("optional", "RESTART_FMT", "the format that should be used to output real numbers in EDS restarts");
     304          20 :   keys.add("optional", "OUT_RESTART", "Output file for all information needed to continue EDS simulation. "
     305             :            "If you have the RESTART directive set (global or for EDS), this file will be appended to. "
     306             :            "Note that the header will be printed again if appending.");
     307          20 :   keys.add("optional", "IN_RESTART", "Read this file to continue an EDS simulation. "
     308             :            "If same as OUT_RESTART and you have not set the RESTART directive, the file will be backed-up and overwritten with new output. "
     309             :            "If you do have the RESTART flag set and it is the same name as OUT_RESTART, this file will be appended.");
     310             : 
     311          20 :   keys.addFlag("RAMP", false, "Slowly increase bias constant to a fixed value");
     312          20 :   keys.addFlag("COVAR", false, "Utilize the covariance matrix when updating the bias. Default Off, but may be enabled due to other options");
     313          20 :   keys.addFlag("FREEZE", false, "Fix bias at current level (only used for restarting).");
     314          20 :   keys.addFlag("MEAN", false, "Instead of using final bias level from restart, use average. Can only be used in conjunction with FREEZE");
     315             : 
     316          10 :   keys.use("RESTART");
     317             : 
     318          20 :   keys.addOutputComponent("force2", "default", "scalar", "squared value of force from the bias");
     319          20 :   keys.addOutputComponent("pressure", "default", "scalar", "If using virial keyword, this is the current sum of virial terms. It is in units of pressure (energy / vol^3)");
     320          20 :   keys.addOutputComponent("_coupling", "default", "scalar", "For each named CV biased, there will be a corresponding output CV_coupling storing the current linear bias prefactor.");
     321          10 : }
     322             : 
     323           8 : EDS::EDS(const ActionOptions &ao) : PLUMED_BIAS_INIT(ao),
     324           8 :   ncvs_(getNumberOfArguments()),
     325           8 :   scale_(ncvs_, 0.0),
     326           8 :   current_coupling_(ncvs_, 0.0),
     327           8 :   set_coupling_(ncvs_, 0.0),
     328           8 :   target_coupling_(ncvs_, 0.0),
     329           8 :   max_coupling_range_(ncvs_, 25.0),
     330           8 :   max_coupling_grad_(ncvs_, 0.0),
     331           8 :   coupling_rate_(ncvs_, 1.0),
     332           8 :   coupling_accum_(ncvs_, 0.0),
     333           8 :   means_(ncvs_, 0.0),
     334           8 :   step_size_(ncvs_, 0.0),
     335           8 :   pseudo_virial_(ncvs_),
     336           8 :   out_coupling_(ncvs_, NULL),
     337           8 :   in_restart_name_(""),
     338           8 :   out_restart_name_(""),
     339           8 :   fmt_("%f"),
     340           8 :   b_adaptive_(true),
     341           8 :   b_freeze_(false),
     342           8 :   b_equil_(true),
     343           8 :   b_ramp_(false),
     344           8 :   b_covar_(false),
     345           8 :   b_restart_(false),
     346           8 :   b_write_restart_(false),
     347           8 :   b_lm_(false),
     348           8 :   b_virial_(false),
     349           8 :   b_weights_(false),
     350           8 :   seed_(0),
     351           8 :   update_period_(0),
     352           8 :   avg_coupling_count_(1),
     353           8 :   update_calls_(0),
     354           8 :   kbt_(0.0),
     355           8 :   multi_prop_(-1.0),
     356           8 :   lm_mixing_par_(0.1),
     357           8 :   virial_scaling_(0.),
     358           8 :   pseudo_virial_sum_(0.0),
     359           8 :   max_logweight_(0.0),
     360           8 :   wsum_(0.0),
     361          32 :   value_force2_(NULL)
     362             : {
     363             :   double temp = -1.0;
     364           8 :   bool b_mean = false;
     365             :   std::vector<Value *> wvalues;
     366             : 
     367          16 :   addComponent("force2");
     368           8 :   componentIsNotPeriodic("force2");
     369           8 :   value_force2_ = getPntrToComponent("force2");
     370             : 
     371          20 :   for (unsigned int i = 0; i < ncvs_; ++i)
     372             :   {
     373          12 :     std::string comp = getPntrToArgument(i)->getName() + "_coupling";
     374          12 :     addComponent(comp);
     375          12 :     componentIsNotPeriodic(comp);
     376          12 :     out_coupling_[i] = getPntrToComponent(comp);
     377             :   }
     378             : 
     379           8 :   parseVector("CENTER", center_);
     380           8 :   parseArgumentList("CENTER_ARG", center_values_);
     381           8 :   parseArgumentList("LOGWEIGHTS", wvalues);
     382           8 :   parseVector("BIAS_SCALE", scale_);
     383           8 :   parseVector("RANGE", max_coupling_range_);
     384           8 :   parseVector("FIXED", target_coupling_);
     385           8 :   parseVector("INIT", set_coupling_);
     386           8 :   parse("PERIOD", update_period_);
     387           8 :   kbt_ = getkBT();
     388           8 :   parse("SEED", seed_);
     389           8 :   parse("MULTI_PROP", multi_prop_);
     390           8 :   parse("LM_MIXING", lm_mixing_par_);
     391           8 :   parse("RESTART_FMT", fmt_);
     392           8 :   parse("VIRIAL", virial_scaling_);
     393           8 :   fmt_ = " " + fmt_; // add space since parse strips them
     394           8 :   parse("OUT_RESTART", out_restart_name_);
     395           8 :   parseFlag("LM", b_lm_);
     396           8 :   parseFlag("RAMP", b_ramp_);
     397           8 :   parseFlag("FREEZE", b_freeze_);
     398           8 :   parseFlag("MEAN", b_mean);
     399           8 :   parseFlag("COVAR", b_covar_);
     400           8 :   parse("IN_RESTART", in_restart_name_);
     401           8 :   checkRead();
     402             : 
     403             :   /*
     404             :    * Things that are different when using changing centers:
     405             :    * 1. Scale
     406             :    * 2. The log file
     407             :    * 3. Reading Restarts
     408             :    */
     409             : 
     410           8 :   if (center_.size() == 0)
     411             :   {
     412           1 :     if (center_values_.size() == 0)
     413           0 :       error("Must set either CENTER or CENTER_ARG");
     414           1 :     else if (center_values_.size() != ncvs_)
     415           0 :       error("CENTER_ARG must contain the same number of variables as ARG");
     416           1 :     b_c_values_ = true;
     417           1 :     center_.resize(ncvs_);
     418           1 :     log.printf("  EDS will use possibly varying centers\n");
     419             :   }
     420             :   else
     421             :   {
     422           7 :     if (center_.size() != ncvs_)
     423           0 :       error("Must have same number of CENTER arguments as ARG arguments");
     424           7 :     else if (center_values_.size() != 0)
     425           0 :       error("You can only set CENTER or CENTER_ARG. Not both");
     426           7 :     b_c_values_ = false;
     427           7 :     log.printf("  EDS will use fixed centers\n");
     428             :   }
     429             : 
     430             :   // check for weights
     431           8 :   if (wvalues.size() > 1)
     432             :   {
     433           0 :     error("LOGWEIGHTS can only support one weight set. Please only pass one action");
     434             :   }
     435           8 :   else if (wvalues.size() == 1)
     436             :   {
     437           1 :     logweights_ = dynamic_cast<ReweightBase *>(wvalues[0]->getPntrToAction());
     438           1 :     b_weights_ = true;
     439             :   }
     440             : 
     441           8 :   log.printf("  setting scaling:");
     442           8 :   if (scale_.size() > 0 && scale_.size() < ncvs_)
     443             :   {
     444           0 :     error("the number of BIAS_SCALE values be the same as number of CVs");
     445             :   }
     446           8 :   else if (scale_.size() == 0 && b_c_values_)
     447             :   {
     448           0 :     log.printf(" Setting SCALE to be 1 for all CVs\n");
     449           0 :     scale_.resize(ncvs_);
     450           0 :     for (unsigned int i = 0; i < ncvs_; ++i)
     451           0 :       scale_[i] = 1;
     452             :   }
     453           8 :   else if (scale_.size() == 0 && !b_c_values_)
     454             :   {
     455           2 :     log.printf(" (default) ");
     456             : 
     457           2 :     scale_.resize(ncvs_);
     458           6 :     for (unsigned int i = 0; i < scale_.size(); ++i)
     459             :     {
     460           4 :       if (center_[i] == 0)
     461           0 :         error("BIAS_SCALE parameter has been set to CENTER value of 0 (as is default). This will divide by 0, so giving up. See doc for EDS bias");
     462           4 :       scale_[i] = center_[i];
     463             :     }
     464             :   }
     465             :   else
     466             :   {
     467          14 :     for (unsigned int i = 0; i < scale_.size(); ++i)
     468           8 :       log.printf(" %f", scale_[i]);
     469             :   }
     470           8 :   log.printf("\n");
     471             : 
     472           8 :   if (b_lm_)
     473             :   {
     474           1 :     log.printf("  EDS will perform Levenberg-Marquardt minimization with mixing parameter = %f\n", lm_mixing_par_);
     475           1 :     differences_.resize(ncvs_);
     476           1 :     alpha_vector_.resize(ncvs_);
     477           1 :     alpha_vector_2_.resize(ncvs_);
     478           1 :     covar_.resize(ncvs_, ncvs_);
     479           1 :     covar2_.resize(ncvs_, ncvs_);
     480           1 :     lm_inv_.resize(ncvs_, ncvs_);
     481           1 :     covar2_ *= 0;
     482           1 :     lm_inv_ *= 0;
     483           1 :     if (multi_prop_ != 1)
     484           0 :       log.printf("     WARNING - doing LM minimization but MULTI_PROP!=1\n");
     485             :   }
     486           7 :   else if (b_covar_)
     487             :   {
     488           1 :     log.printf("  EDS will utilize covariance matrix for update steps\n");
     489           1 :     covar_.resize(ncvs_, ncvs_);
     490             :   }
     491             :   else
     492             :   {
     493           6 :     log.printf("  EDS will utilize variance for update steps\n");
     494           6 :     ssds_.resize(ncvs_);
     495             :   }
     496             : 
     497           8 :   b_virial_ = virial_scaling_;
     498             : 
     499           8 :   if (b_virial_)
     500             :   {
     501           1 :     if (ncvs_ == 1)
     502           0 :       error("Minimizing the virial is only valid with multiply correlated collective variables.");
     503             :     // check that the CVs can be used to compute pseudo-virial
     504           1 :     log.printf("  EDS will compute virials of CVs and penalize with scale of %f. Checking CVs are valid...", virial_scaling_);
     505           4 :     for (unsigned int i = 0; i < ncvs_; ++i)
     506             :     {
     507           3 :       auto a = dynamic_cast<ActionAtomistic *>(getPntrToArgument(i)->getPntrToAction());
     508           3 :       if (!a)
     509           0 :         error("If using VIRIAL keyword, you must have normal CVs as arguments to EDS. Offending action: " + getPntrToArgument(i)->getPntrToAction()->getName());
     510             :       // cppcheck-suppress nullPointerRedundantCheck
     511           3 :       if (!(a->getPbc().isOrthorombic()))
     512           3 :         log.printf("  WARNING: EDS Virial should have a orthorombic cell\n");
     513             :     }
     514           1 :     log.printf("done.\n");
     515           2 :     addComponent("pressure");
     516           1 :     componentIsNotPeriodic("pressure");
     517           1 :     value_pressure_ = getPntrToComponent("pressure");
     518             :   }
     519             : 
     520           8 :   if (b_mean && !b_freeze_)
     521             :   {
     522           0 :     error("EDS keyword MEAN can only be used along with keyword FREEZE");
     523             :   }
     524             : 
     525           8 :   if (in_restart_name_ != "")
     526             :   {
     527           2 :     b_restart_ = true;
     528           2 :     log.printf("  reading simulation information from file: %s\n", in_restart_name_.c_str());
     529           2 :     readInRestart(b_mean);
     530             :   }
     531             :   else
     532             :   {
     533             : 
     534             :     // in driver, this results in kbt of 0
     535           6 :     if (kbt_ == 0)
     536             :     {
     537           0 :       error("  Unable to determine valid kBT. "
     538             :             "Could be because you are runnning from driver or MD didn't give temperature.\n"
     539             :             "Consider setting temperature manually with the TEMP keyword.");
     540             :       kbt_ = 1;
     541             :     }
     542             : 
     543           6 :     log.printf("  kBT = %f\n", kbt_);
     544           6 :     log.printf("  Updating every %i steps\n", update_period_);
     545             : 
     546           6 :     if (!b_c_values_)
     547             :     {
     548           5 :       log.printf("  with centers:");
     549          14 :       for (unsigned int i = 0; i < ncvs_; ++i)
     550             :       {
     551           9 :         log.printf(" %f ", center_[i]);
     552             :       }
     553             :     }
     554             :     else
     555             :     {
     556           1 :       log.printf("  with actions centers:");
     557           2 :       for (unsigned int i = 0; i < ncvs_; ++i)
     558             :       {
     559           1 :         log.printf(" %s ", center_values_[i]->getName().c_str());
     560             :         // add dependency on these actions
     561           1 :         addDependency(center_values_[i]->getPntrToAction());
     562             :       }
     563             :     }
     564             : 
     565           6 :     log.printf("\n  with initial ranges / rates:\n");
     566          16 :     for (unsigned int i = 0; i < max_coupling_range_.size(); ++i)
     567             :     {
     568             :       // this is just an empirical guess. Bigger range, bigger grads. Less frequent updates, bigger changes
     569             :       //
     570             :       // using the current maxing out scheme, max_coupling_range is the biggest step that can be taken in any given interval
     571          10 :       max_coupling_range_[i] *= kbt_;
     572          10 :       max_coupling_grad_[i] = max_coupling_range_[i];
     573          10 :       log.printf("    %f / %f\n", max_coupling_range_[i], max_coupling_grad_[i]);
     574             :     }
     575             : 
     576           6 :     if (seed_ > 0)
     577             :     {
     578           2 :       log.printf("  setting random seed = %i", seed_);
     579           2 :       rand_.setSeed(seed_);
     580             :     }
     581             : 
     582          16 :     for (unsigned int i = 0; i < ncvs_; ++i)
     583          10 :       if (target_coupling_[i] != 0.0)
     584           1 :         b_adaptive_ = false;
     585             : 
     586           6 :     if (!b_adaptive_)
     587             :     {
     588           1 :       if (b_ramp_)
     589             :       {
     590           1 :         log.printf("  ramping up coupling constants over %i steps\n", update_period_);
     591             :       }
     592             : 
     593           1 :       log.printf("  with starting coupling constants");
     594           2 :       for (unsigned int i = 0; i < set_coupling_.size(); ++i)
     595           1 :         log.printf(" %f", set_coupling_[i]);
     596           1 :       log.printf("\n");
     597           1 :       log.printf("  and final coupling constants");
     598           2 :       for (unsigned int i = 0; i < target_coupling_.size(); ++i)
     599           1 :         log.printf(" %f", target_coupling_[i]);
     600           1 :       log.printf("\n");
     601             :     }
     602             : 
     603             :     // now do setup
     604           6 :     if (b_ramp_)
     605             :     {
     606           1 :       update_period_ *= -1;
     607             :     }
     608             : 
     609          16 :     for (unsigned int i = 0; i < set_coupling_.size(); ++i)
     610          10 :       current_coupling_[i] = set_coupling_[i];
     611             : 
     612             :     // if b_adaptive_, then first half will be used for equilibrating and second half for statistics
     613           6 :     if (update_period_ > 0)
     614             :     {
     615           5 :       update_period_ /= 2;
     616             :     }
     617             :   }
     618             : 
     619           8 :   if (b_freeze_)
     620             :   {
     621           1 :     b_adaptive_ = false;
     622           1 :     update_period_ = 0;
     623           1 :     if (b_mean)
     624             :     {
     625           1 :       log.printf("  freezing bias at the average level from the restart file\n");
     626             :     }
     627             :     else
     628             :     {
     629           0 :       log.printf("  freezing bias at current level\n");
     630             :     }
     631             :   }
     632             : 
     633           8 :   if (multi_prop_ == -1.0)
     634             :   {
     635           5 :     log.printf("  Will update each dimension stochastically with probability 1 / number of CVs\n");
     636           5 :     multi_prop_ = 1.0 / ncvs_;
     637             :   }
     638           3 :   else if (multi_prop_ > 0 && multi_prop_ <= 1.0)
     639             :   {
     640           3 :     log.printf("  Will update each dimension stochastically with probability %f\n", multi_prop_);
     641             :   }
     642             :   else
     643             :   {
     644           0 :     error("  MULTI_PROP must be between 0 and 1\n");
     645             :   }
     646             : 
     647           8 :   if (out_restart_name_.length() > 0)
     648             :   {
     649           8 :     log.printf("  writing restart information every %i steps to file %s with format %s\n", abs(update_period_), out_restart_name_.c_str(), fmt_.c_str());
     650           8 :     b_write_restart_ = true;
     651           8 :     setupOutRestart();
     652             :   }
     653             : 
     654          16 :   log << "  Bibliography " << plumed.cite("White and Voth, J. Chem. Theory Comput. 10 (8), 3023-3030 (2014)") << "\n";
     655          16 :   log << "  Bibliography " << plumed.cite("G. M. Hocky, T. Dannenhoffer-Lafage, G. A. Voth, J. Chem. Theory Comput. 13 (9), 4593-4603 (2017)") << "\n";
     656           8 : }
     657             : 
     658           2 : void EDS::readInRestart(const bool b_mean)
     659             : {
     660           2 :   int adaptive_i = 0;
     661             : 
     662           2 :   in_restart_.open(in_restart_name_);
     663             : 
     664           4 :   if (in_restart_.FieldExist("kbt"))
     665             :   {
     666           2 :     in_restart_.scanField("kbt", kbt_);
     667             :   }
     668             :   else
     669             :   {
     670           0 :     error("No field 'kbt' in restart file");
     671             :   }
     672           2 :   log.printf("  with kBT = %f\n", kbt_);
     673             : 
     674           4 :   if (in_restart_.FieldExist("update_period"))
     675             :   {
     676           2 :     in_restart_.scanField("update_period", update_period_);
     677             :   }
     678             :   else
     679             :   {
     680           0 :     error("No field 'update_period' in restart file");
     681             :   }
     682           2 :   log.printf("  Updating every %i steps\n", update_period_);
     683             : 
     684           4 :   if (in_restart_.FieldExist("adaptive"))
     685             :   {
     686             :     // note, no version of scanField for boolean
     687           2 :     in_restart_.scanField("adaptive", adaptive_i);
     688             :   }
     689             :   else
     690             :   {
     691           0 :     error("No field 'adaptive' in restart file");
     692             :   }
     693           2 :   b_adaptive_ = bool(adaptive_i);
     694             : 
     695           4 :   if (in_restart_.FieldExist("seed"))
     696             :   {
     697           2 :     in_restart_.scanField("seed", seed_);
     698             :   }
     699             :   else
     700             :   {
     701           0 :     error("No field 'seed' in restart file");
     702             :   }
     703           2 :   if (seed_ > 0)
     704             :   {
     705           0 :     log.printf("  setting random seed = %i", seed_);
     706           0 :     rand_.setSeed(seed_);
     707             :   }
     708             : 
     709             :   double time, tmp;
     710           2 :   std::vector<double> avg_bias = std::vector<double>(center_.size());
     711             :   unsigned int N = 0;
     712             :   std::string cv_name;
     713             : 
     714          24 :   while (in_restart_.scanField("time", time))
     715             :   {
     716             : 
     717          20 :     for (unsigned int i = 0; i < ncvs_; ++i)
     718             :     {
     719             :       cv_name = getPntrToArgument(i)->getName();
     720          20 :       in_restart_.scanField(cv_name + "_center", set_coupling_[i]);
     721          20 :       in_restart_.scanField(cv_name + "_set", set_coupling_[i]);
     722          20 :       in_restart_.scanField(cv_name + "_target", target_coupling_[i]);
     723          20 :       in_restart_.scanField(cv_name + "_coupling", current_coupling_[i]);
     724          20 :       in_restart_.scanField(cv_name + "_maxrange", max_coupling_range_[i]);
     725          20 :       in_restart_.scanField(cv_name + "_maxgrad", max_coupling_grad_[i]);
     726          20 :       in_restart_.scanField(cv_name + "_accum", coupling_accum_[i]);
     727          10 :       in_restart_.scanField(cv_name + "_mean", means_[i]);
     728          20 :       if (in_restart_.FieldExist(cv_name + "_pseudovirial"))
     729             :       {
     730           0 :         if (b_virial_)
     731           0 :           in_restart_.scanField(cv_name + "_pseudovirial", pseudo_virial_[i]);
     732             :         else // discard the field
     733           0 :           in_restart_.scanField(cv_name + "_pseudovirial", tmp);
     734             :       }
     735             :       // unused due to difference between covar/nocovar
     736          20 :       in_restart_.scanField(cv_name + "_std", tmp);
     737             : 
     738          10 :       avg_bias[i] += current_coupling_[i];
     739             :     }
     740          10 :     N++;
     741             : 
     742          10 :     in_restart_.scanField();
     743             :   }
     744             : 
     745           2 :   log.printf("  with centers:");
     746           4 :   for (unsigned int i = 0; i < center_.size(); ++i)
     747             :   {
     748           2 :     log.printf(" %f", center_[i]);
     749             :   }
     750           2 :   log.printf("\n  and scaling:");
     751           4 :   for (unsigned int i = 0; i < scale_.size(); ++i)
     752             :   {
     753           2 :     log.printf(" %f", scale_[i]);
     754             :   }
     755             : 
     756           2 :   log.printf("\n  with initial ranges / rates:\n");
     757           4 :   for (unsigned int i = 0; i < max_coupling_range_.size(); ++i)
     758             :   {
     759           2 :     log.printf("    %f / %f\n", max_coupling_range_[i], max_coupling_grad_[i]);
     760             :   }
     761             : 
     762           2 :   if (!b_adaptive_ && update_period_ < 0)
     763             :   {
     764           0 :     log.printf("  ramping up coupling constants over %i steps\n", -update_period_);
     765             :   }
     766             : 
     767           2 :   if (b_mean)
     768             :   {
     769           1 :     log.printf("Loaded in averages for coupling constants...\n");
     770           2 :     for (unsigned int i = 0; i < current_coupling_.size(); ++i)
     771           1 :       current_coupling_[i] = avg_bias[i] / N;
     772           2 :     for (unsigned int i = 0; i < current_coupling_.size(); ++i)
     773           1 :       set_coupling_[i] = avg_bias[i] / N;
     774             :   }
     775             : 
     776           2 :   log.printf("  with current coupling constants:\n    ");
     777           4 :   for (unsigned int i = 0; i < current_coupling_.size(); ++i)
     778           2 :     log.printf(" %f", current_coupling_[i]);
     779           2 :   log.printf("\n");
     780           2 :   log.printf("  with initial coupling constants:\n    ");
     781           4 :   for (unsigned int i = 0; i < set_coupling_.size(); ++i)
     782           2 :     log.printf(" %f", set_coupling_[i]);
     783           2 :   log.printf("\n");
     784           2 :   log.printf("  and final coupling constants:\n    ");
     785           4 :   for (unsigned int i = 0; i < target_coupling_.size(); ++i)
     786           2 :     log.printf(" %f", target_coupling_[i]);
     787           2 :   log.printf("\n");
     788             : 
     789           2 :   in_restart_.close();
     790           2 : }
     791             : 
     792           8 : void EDS::setupOutRestart()
     793             : {
     794           8 :   out_restart_.link(*this);
     795           8 :   out_restart_.fmtField(fmt_);
     796           8 :   out_restart_.open(out_restart_name_);
     797             :   out_restart_.setHeavyFlush();
     798             : 
     799          16 :   out_restart_.addConstantField("adaptive").printField("adaptive", b_adaptive_);
     800          16 :   out_restart_.addConstantField("update_period").printField("update_period", update_period_);
     801          16 :   out_restart_.addConstantField("seed").printField("seed", seed_);
     802          16 :   out_restart_.addConstantField("kbt").printField("kbt", kbt_);
     803           8 : }
     804             : 
     805          27 : void EDS::writeOutRestart()
     806             : {
     807             :   std::string cv_name;
     808          27 :   out_restart_.printField("time", getTimeStep() * getStep());
     809             : 
     810          66 :   for (unsigned int i = 0; i < ncvs_; ++i)
     811             :   {
     812             :     cv_name = getPntrToArgument(i)->getName();
     813          78 :     out_restart_.printField(cv_name + "_center", center_[i]);
     814          78 :     out_restart_.printField(cv_name + "_set", set_coupling_[i]);
     815          78 :     out_restart_.printField(cv_name + "_target", target_coupling_[i]);
     816          78 :     out_restart_.printField(cv_name + "_coupling", current_coupling_[i]);
     817          78 :     out_restart_.printField(cv_name + "_maxrange", max_coupling_range_[i]);
     818          78 :     out_restart_.printField(cv_name + "_maxgrad", max_coupling_grad_[i]);
     819          78 :     out_restart_.printField(cv_name + "_accum", coupling_accum_[i]);
     820          39 :     out_restart_.printField(cv_name + "_mean", means_[i]);
     821          39 :     if (b_virial_)
     822          18 :       out_restart_.printField(cv_name + "_pseudovirial", pseudo_virial_[i]);
     823          39 :     if (!b_covar_ && !b_lm_)
     824          42 :       out_restart_.printField(cv_name + "_std", ssds_[i] / (fmax(1, update_calls_ - 1)));
     825             :     else
     826          36 :       out_restart_.printField(cv_name + "_std", covar_(i, i) / (fmax(1, update_calls_ - 1)));
     827             :   }
     828          27 :   out_restart_.printField();
     829          27 : }
     830             : 
     831          40 : void EDS::calculate()
     832             : {
     833             : 
     834             :   // get center values from action if necessary
     835          40 :   if (b_c_values_)
     836          10 :     for (unsigned int i = 0; i < ncvs_; ++i)
     837           5 :       center_[i] = center_values_[i]->get();
     838             : 
     839          40 :   apply_bias();
     840          40 : }
     841             : 
     842          40 : void EDS::apply_bias()
     843             : {
     844             :   // Compute linear force as in "restraint"
     845             :   double ene = 0, totf2 = 0, cv, m, f;
     846             : 
     847         100 :   for (unsigned int i = 0; i < ncvs_; ++i)
     848             :   {
     849          60 :     cv = difference(i, center_[i], getArgument(i));
     850          60 :     m = current_coupling_[i];
     851          60 :     f = -m;
     852          60 :     ene += m * cv;
     853          60 :     setOutputForce(i, f);
     854          60 :     totf2 += f * f;
     855             :   }
     856             : 
     857          40 :   setBias(ene);
     858          40 :   value_force2_->set(totf2);
     859          40 : }
     860             : 
     861          12 : void EDS::update_statistics()
     862             : {
     863             :   double s, N, w = 1.0;
     864          12 :   std::vector<double> deltas(ncvs_);
     865             : 
     866             :   // update weight max, if necessary
     867          12 :   if (b_weights_)
     868             :   {
     869           2 :     w = logweights_->getLogWeight();
     870           2 :     if (max_logweight_ < w)
     871             :     {
     872             :       // we have new max. Need to shift existing values
     873           0 :       wsum_ *= exp(max_logweight_ - w);
     874           0 :       max_logweight_ = w;
     875             :     }
     876             :     // convert to weight
     877           2 :     w = exp(w - max_logweight_);
     878           2 :     wsum_ += w;
     879             :     N = wsum_;
     880             :   }
     881             :   else
     882             :   {
     883          10 :     N = fmax(1, update_calls_);
     884             :   }
     885             : 
     886             :   // Welford, West, and Hanso online variance method
     887             :   // with weights (default =  1.0)
     888          32 :   for (unsigned int i = 0; i < ncvs_; ++i)
     889             :   {
     890          20 :     deltas[i] = difference(i, means_[i], getArgument(i)) * w;
     891          20 :     means_[i] += deltas[i] / N;
     892          20 :     if (!b_covar_ && !b_lm_)
     893           8 :       ssds_[i] += deltas[i] * difference(i, means_[i], getArgument(i));
     894             :   }
     895          12 :   if (b_covar_ || b_lm_)
     896             :   {
     897          16 :     for (unsigned int i = 0; i < ncvs_; ++i)
     898             :     {
     899          36 :       for (unsigned int j = i; j < ncvs_; ++j)
     900             :       {
     901          24 :         s = (N - 1) * deltas[i] * deltas[j] / N / N - covar_(i, j) / N;
     902          24 :         covar_(i, j) += s;
     903             :         // do this so we don't double count
     904          24 :         covar_(j, i) = covar_(i, j);
     905             :       }
     906             :     }
     907             :   }
     908          12 :   if (b_virial_)
     909           2 :     update_pseudo_virial();
     910          12 : }
     911             : 
     912           8 : void EDS::reset_statistics()
     913             : {
     914          20 :   for (unsigned int i = 0; i < ncvs_; ++i)
     915             :   {
     916          12 :     means_[i] = 0;
     917          12 :     if (!b_covar_ && !b_lm_)
     918           6 :       ssds_[i] = 0;
     919             :   }
     920           8 :   if (b_covar_ || b_lm_)
     921           8 :     for (unsigned int i = 0; i < ncvs_; ++i)
     922          24 :       for (unsigned int j = 0; j < ncvs_; ++j)
     923          18 :         covar_(i, j) = 0;
     924           8 :   if (b_virial_)
     925             :   {
     926           4 :     for (unsigned int i = 0; i < ncvs_; ++i)
     927           3 :       pseudo_virial_[i] = 0;
     928           1 :     pseudo_virial_sum_ = 0;
     929             :   }
     930           8 :   if (b_weights_)
     931             :   {
     932           2 :     wsum_ = 0;
     933           2 :     max_logweight_ = 0;
     934             :   }
     935           8 : }
     936             : 
     937           1 : void EDS::calc_lm_step_size()
     938             : {
     939             :   // calulcate step size
     940             :   // uses scale here, which by default is center
     941             : 
     942           1 :   mult(covar_, covar_, covar2_);
     943           4 :   for (unsigned int i = 0; i < ncvs_; ++i)
     944             :   {
     945           3 :     differences_[i] = difference(i, center_[i], means_[i]);
     946           3 :     covar2_[i][i] += lm_mixing_par_ * covar2_[i][i];
     947             :   }
     948             : 
     949             :   // "step_size_vec" = 2*inv(covar*covar+ lambda diag(covar*covar))*covar*(mean-center)
     950           1 :   mult(covar_, differences_, alpha_vector_);
     951           1 :   Invert(covar2_, lm_inv_);
     952           1 :   mult(lm_inv_, alpha_vector_, alpha_vector_2_);
     953             : 
     954           4 :   for (unsigned int i = 0; i < ncvs_; ++i)
     955             :   {
     956           3 :     step_size_[i] = 2 * alpha_vector_2_[i] / kbt_ / scale_[i];
     957             :   }
     958           1 : }
     959             : 
     960           1 : void EDS::calc_covar_step_size()
     961             : {
     962             :   // calulcate step size
     963             :   // uses scale here, which by default is center
     964             :   double tmp;
     965           4 :   for (unsigned int i = 0; i < ncvs_; ++i)
     966             :   {
     967             :     tmp = 0;
     968          12 :     for (unsigned int j = 0; j < ncvs_; ++j)
     969           9 :       tmp += difference(i, center_[i], means_[i]) * covar_(i, j);
     970           3 :     step_size_[i] = 2 * tmp / kbt_ / scale_[i] * update_calls_ / fmax(1, update_calls_ - 1);
     971             :   }
     972           1 : }
     973             : 
     974           6 : void EDS::calc_ssd_step_size()
     975             : {
     976             :   double tmp;
     977          12 :   for (unsigned int i = 0; i < ncvs_; ++i)
     978             :   {
     979           6 :     tmp = 2. * difference(i, center_[i], means_[i]) * ssds_[i] / fmax(1, update_calls_ - 1);
     980           6 :     step_size_[i] = tmp / kbt_ / scale_[i];
     981             :   }
     982           6 : }
     983             : 
     984           2 : void EDS::update_pseudo_virial()
     985             : {
     986             :   // We want to compute the bias force on each atom times the position
     987             :   //  of the atoms.
     988             :   double p, netp = 0, netpv = 0;
     989             :   double volume = 0;
     990           8 :   for (unsigned int i = 0; i < ncvs_; ++i)
     991             :   {
     992             :     // checked in setup to ensure this cast is valid.
     993           6 :     ActionAtomistic *cv = dynamic_cast<ActionAtomistic *>(getPntrToArgument(i)->getPntrToAction());
     994           6 :     Tensor v(cv->getVirial());
     995           6 :     Tensor box(cv->getBox());
     996             :     const unsigned int natoms = cv->getNumberOfAtoms();
     997           6 :     if (!volume)
     998           2 :       volume = box.determinant();
     999             : 
    1000             :     // pressure contribution is -dBias / dV
    1001             :     // dBias / dV = alpha / w * dCV / dV
    1002             :     // to get partial of CV wrt to volume
    1003             :     // dCV/dV = sum dCV/dvij * vij / V
    1004             :     // where vij is box element
    1005             :     // add diagonal of virial tensor to get net pressure
    1006             :     // TODO: replace this with adjugate (Jacobi's Formula)   for non-orthorombic case(?)
    1007           6 :     p = v(0, 0) * box(0, 0) + v(1, 1) * box(1, 1) + v(2, 2) * box(2, 2);
    1008           6 :     p /= volume;
    1009             : 
    1010           6 :     netp += p;
    1011             : 
    1012             :     // now scale for correct units in EDS algorithm
    1013           6 :     p *= (volume) / (kbt_ * natoms);
    1014             : 
    1015             :     // compute running mean of scaled
    1016           6 :     if (set_coupling_[i] != 0)
    1017           0 :       pseudo_virial_[i] = (p - pseudo_virial_[i]) / (fmax(1, update_calls_));
    1018             :     else
    1019           6 :       pseudo_virial_[i] = 0;
    1020             :     // update net pressure
    1021           6 :     netpv += pseudo_virial_[i];
    1022             :   }
    1023             :   // update pressure
    1024           2 :   value_pressure_->set(netp);
    1025           2 :   pseudo_virial_sum_ = netpv;
    1026           2 : }
    1027             : 
    1028           8 : void EDS::update_bias()
    1029             : {
    1030           8 :   log.flush();
    1031           8 :   if (b_lm_)
    1032           1 :     calc_lm_step_size();
    1033           7 :   else if (b_covar_)
    1034           1 :     calc_covar_step_size();
    1035             :   else
    1036           6 :     calc_ssd_step_size();
    1037             : 
    1038          20 :   for (unsigned int i = 0; i < ncvs_; ++i)
    1039             :   {
    1040             : 
    1041             :     // multidimesional stochastic step
    1042          12 :     if (ncvs_ == 1 || (rand_.RandU01() < (multi_prop_)))
    1043             :     {
    1044             : 
    1045          12 :       if (b_virial_)
    1046             :       {
    1047             :         // apply virial regularization
    1048             :         //  P * dP/dcoupling
    1049             :         //  coupling is already included in virial term due to plumed propogating from bias to forces
    1050             :         //  thus we need to divide by it to get the derivative (since force is linear in coupling)
    1051           3 :         if (fabs(set_coupling_[i]) > 0.000000001) // my heuristic for if EDS has started to prevent / 0
    1052             :           // scale^2 here is to align units
    1053           0 :           step_size_[i] -= 2 * scale_[i] * scale_[i] * virial_scaling_ * pseudo_virial_sum_ * pseudo_virial_sum_ / set_coupling_[i];
    1054             :       }
    1055          12 :       if (step_size_[i] == 0)
    1056           4 :         continue;
    1057             : 
    1058             :       // clip gradient
    1059           8 :       step_size_[i] = copysign(fmin(fabs(step_size_[i]), max_coupling_grad_[i]), step_size_[i]);
    1060           8 :       coupling_accum_[i] += step_size_[i] * step_size_[i];
    1061             : 
    1062             :       // equation 5 in White and Voth, JCTC 2014
    1063             :       // no negative sign because it's in step_size
    1064           8 :       set_coupling_[i] += step_size_[i] * max_coupling_range_[i] / sqrt(coupling_accum_[i]);
    1065           8 :       coupling_rate_[i] = (set_coupling_[i] - current_coupling_[i]) / update_period_;
    1066             :     }
    1067             :     else
    1068             :     {
    1069             :       // do not change the bias
    1070           0 :       coupling_rate_[i] = 0;
    1071             :     }
    1072             :   }
    1073             : 
    1074             :   // reset means/vars
    1075           8 :   reset_statistics();
    1076           8 : }
    1077             : 
    1078          40 : void EDS::update()
    1079             : {
    1080             :   // adjust parameters according to EDS recipe
    1081          40 :   update_calls_++;
    1082             : 
    1083             :   // if we aren't wating for the bias to equilibrate, set flag to collect data
    1084             :   // want statistics before writing restart
    1085          40 :   if (!b_equil_ && update_period_ > 0)
    1086          12 :     update_statistics();
    1087             : 
    1088             :   // write restart with correct statistics before bias update
    1089             :   // check if we're ramping or doing normal updates and then restart if needed. The ramping check
    1090             :   // is complicated because we could be frozen, finished ramping or not ramping.
    1091             :   // The + 2 is so we have an extra line showing that the bias isn't changing (for my sanity and yours)
    1092          40 :   if (b_write_restart_)
    1093             :   {
    1094          40 :     if (getStep() == 0 ||
    1095          32 :         ((update_period_ < 0 && !b_freeze_ && update_calls_ <= fabs(update_period_) + 2) ||
    1096          24 :          (update_period_ > 0 && update_calls_ % update_period_ == 0)))
    1097          27 :       writeOutRestart();
    1098             :   }
    1099             : 
    1100             :   int b_finished_equil_flag = 1;
    1101             : 
    1102             :   // assume forces already applied and saved
    1103             :   // are we ramping to a constant value and not done equilibrating?
    1104          40 :   if (update_period_ < 0)
    1105             :   {
    1106           5 :     if (update_calls_ <= fabs(update_period_) && !b_freeze_)
    1107             :     {
    1108           4 :       for (unsigned int i = 0; i < ncvs_; ++i)
    1109           2 :         current_coupling_[i] += (target_coupling_[i] - set_coupling_[i]) / fabs(update_period_);
    1110             :     }
    1111             :     // make sure we don't reset update calls
    1112             :     b_finished_equil_flag = 0;
    1113             :   }
    1114          35 :   else if (update_period_ == 0)
    1115             :   { // do we have a no-update case?
    1116             :     // not updating
    1117             :     // pass
    1118             :   }
    1119          30 :   else if (b_equil_)
    1120             :   {
    1121             :     // equilibrating
    1122             :     // check if we've reached the setpoint
    1123          48 :     for (unsigned int i = 0; i < ncvs_; ++i)
    1124             :     {
    1125          30 :       if (coupling_rate_[i] == 0 || pow(current_coupling_[i] - set_coupling_[i], 2) < pow(coupling_rate_[i], 2))
    1126             :       {
    1127          14 :         b_finished_equil_flag &= 1;
    1128             :       }
    1129             :       else
    1130             :       {
    1131          16 :         current_coupling_[i] += coupling_rate_[i];
    1132             :         b_finished_equil_flag = 0;
    1133             :       }
    1134             :     }
    1135             :   }
    1136             : 
    1137             :   // reduce all the flags
    1138          40 :   if (b_equil_ && b_finished_equil_flag)
    1139             :   {
    1140          11 :     b_equil_ = false;
    1141          11 :     update_calls_ = 0;
    1142             :   }
    1143             : 
    1144             :   // Now we update coupling constant, if necessary
    1145          40 :   if (!b_equil_ && update_period_ > 0 && update_calls_ == update_period_ && !b_freeze_)
    1146             :   {
    1147           8 :     update_bias();
    1148           8 :     update_calls_ = 0;
    1149           8 :     avg_coupling_count_++;
    1150           8 :     b_equil_ = true; // back to equilibration now
    1151             :   }                  // close update if
    1152             : 
    1153             :   // pass couplings out so they are accessible
    1154         100 :   for (unsigned int i = 0; i < ncvs_; ++i)
    1155             :   {
    1156          60 :     out_coupling_[i]->set(current_coupling_[i]);
    1157             :   }
    1158          40 : }
    1159             : 
    1160          16 : EDS::~EDS()
    1161             : {
    1162           8 :   out_restart_.close();
    1163          24 : }
    1164             : 
    1165           0 : void EDS::turnOnDerivatives()
    1166             : {
    1167             :   // do nothing
    1168             :   // this is to avoid errors triggered when a bias is used as a CV
    1169             :   // (This is done in ExtendedLagrangian.cpp)
    1170           0 : }
    1171             : 
    1172             : }
    1173             : } // close the 2 namespaces

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