content: /*
  * Copyright (c) 1997 - 2016
  * Actelion Pharmaceuticals Ltd.
  * Gewerbestrasse 16
  * CH-4123 Allschwil, Switzerland
  *
  * All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are met:
  *
  * 1. Redistributions of source code must retain the above copyright notice, this
  *    list of conditions and the following disclaimer.
  * 2. Redistributions in binary form must reproduce the above copyright notice,
  *    this list of conditions and the following disclaimer in the documentation
  *    and/or other materials provided with the distribution.
  * 3. Neither the name of the the copyright holder nor the
  *    names of its contributors may be used to endorse or promote products
  *    derived from this software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
  * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
  * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  *
  */
  
  package com.actelion.research.chem.forcefield.mmff;
  
  import com.actelion.research.util.DoubleFormat;
  
  import java.util.ArrayList;
  import java.util.List;
  
  /**
   * Angle bending energy term class. This energy term represents the
   * angle bending energy associated with three bonded atoms A1--A2--A3
   * with an angle at A2.
   */
  public class AngleBend implements EnergyTerm {
      private final MMFFMolecule mol;
      public final int a1;
      public final int a2; // Central atom.
      public final int a3;
      public final boolean isLinear;
  
      public final double ka;     // Force constant.
      public final double theta0; // Ideal angle.
  
      /**
       * Construct a new angle bend energy term.
       *  @param table The tables parameter object.
       *  @param mol The molecule.
       *  @param a1 Index of atom 1 in mol.
       *  @param a2 Index of atom 2 (the central atom) in mol.
       *  @param a3 Index of atom 3 in mol.
       */
      public AngleBend(Tables table, MMFFMolecule mol, int a1, int a2, int a3) {
          this.mol = mol;
          this.a1 = a1;
          this.a2 = a2;
          this.a3 = a3;
          isLinear = table.atom.linear(mol.getAtomType(a2));
  
          theta0 = table.angle.theta(mol, a1, a2, a3);
          ka = table.angle.ka(mol, a1, a2, a3);
      }
  
      /**
       * Calculates the angle energy.
       *  @param pos The atoms current positions array.
       *  @return The energy.
       */
      @Override
      public double getEnergy(double[] pos) {
          return getEnergy(pos, null, null, false);
      }
  
      /**
       * Calculates the angle energy.
       *  @param pos The atoms current positions array.
       *  @return The energy.
       */
      @Override
      public double getEnergy(double[] pos, StringBuilder detail, String detailID, boolean skipHydrogen) {
          if (skipHydrogen && (mol.getAtomicNo(a1) == 1 || mol.getAtomicNo(a3) == 1))
              return 0.0;
  
          double theta = new Vector3(pos, a2, a1).angle(new Vector3(pos, a2, a3));
          double angle = Math.toDegrees(theta) - theta0;
  
          final double cb = -0.006981317;
          final double c2 = Constants.MDYNE_A_TO_KCAL_MOL * Constants.DEG2RAD * Constants.DEG2RAD;
  
          // isLinear is a property of the central atom and can be found in the prop table.
          double e = (isLinear) ? Constants.MDYNE_A_TO_KCAL_MOL * ka * (1.0 + Math.cos(theta))
                  : 0.5*c2*ka*angle*angle*(1.0 + cb*angle);
  
          if (detail != null)
              detail.append(detailID+"\tangleBend\t"+DoubleFormat.toString(Math.toDegrees(theta))+"\t"+DoubleFormat.toString(theta0)
                      +"\t"+a1+","+a2+","+a3+"\t"+ DoubleFormat.toString(e)+"\n");
  
          return e;
      }
  
      /**
       * Calculates the gradient and adds it to the gradients array.
       *  @param pos The atoms current positions array.
       *  @param grad the atoms current gradients array.
       */
      @Override
      public void getGradient(double[] pos, double[] grad) {
          Vector3 r0 = new Vector3(pos, a2, a1).normalise();
          Vector3 r1 = new Vector3(pos, a2, a3).normalise();
  
          double dist0 = new Vector3(pos, a2, a1).length();
          double dist1 = new Vector3(pos, a2, a3).length();
  
          double cosTheta = r0.cosAngle(r1);
  
          double sinThetaSq = 1.0 - cosTheta*cosTheta;
          double sinTheta = 1.0e-8;
          if (sinThetaSq > 0.0)
              sinTheta = Math.sqrt(sinThetaSq);
  
          double angleTerm = Constants.RAD2DEG * Math.acos(cosTheta) - theta0;
          double cb = -0.006981317;
          double c2 = Constants.MDYNE_A_TO_KCAL_MOL * Constants.DEG2RAD
              * Constants.DEG2RAD;
  
          double dE_dTheta = Constants.RAD2DEG*c2*ka*angleTerm
              * (1.0 + 1.5*cb*angleTerm);
          if (isLinear)
              dE_dTheta = -Constants.MDYNE_A_TO_KCAL_MOL * ka * sinTheta;
  
          double dCos_dS[] = new double[]{
              1.0/dist0*(r1.x - cosTheta*r0.x),
              1.0/dist0*(r1.y - cosTheta*r0.y),
              1.0/dist0*(r1.z - cosTheta*r0.z),
              1.0/dist1*(r0.x - cosTheta*r1.x),
              1.0/dist1*(r0.y - cosTheta*r1.y),
              1.0/dist1*(r0.z - cosTheta*r1.z)
          };
  
          grad[3*a1    ] += dE_dTheta*dCos_dS[0]/(-sinTheta);
          grad[3*a1 + 1] += dE_dTheta*dCos_dS[1]/(-sinTheta);
          grad[3*a1 + 2] += dE_dTheta*dCos_dS[2]/(-sinTheta);
  
          grad[3*a2    ] += dE_dTheta*(-dCos_dS[0] - dCos_dS[3])/(-sinTheta);
          grad[3*a2 + 1] += dE_dTheta*(-dCos_dS[1] - dCos_dS[4])/(-sinTheta);
          grad[3*a2 + 2] += dE_dTheta*(-dCos_dS[2] - dCos_dS[5])/(-sinTheta);
  
          grad[3*a3    ] += dE_dTheta*dCos_dS[3]/(-sinTheta);
          grad[3*a3 + 1] += dE_dTheta*dCos_dS[4]/(-sinTheta);
          grad[3*a3 + 2] += dE_dTheta*dCos_dS[5]/(-sinTheta);
      }
  
      /**
       * Helper function that builds a list of AngleBends for a molecule.
       *  @param t The tables object.
       *  @param mol The molecule to generate angles for.
       *  @return Am array of AngleBends.
       */
      public static List<AngleBend> findIn(Tables t, MMFFMolecule mol) {
          ArrayList<AngleBend> angles = new ArrayList<AngleBend>();
  
          for (int atom=0; atom<mol.getAllAtoms(); atom++) {
              if (mol.getAllConnAtoms(atom) > 1) {
                  for (int i=0; i<mol.getAllConnAtoms(atom); i++) {
                      int nbr_i = mol.getConnAtom(atom, i);
                      for (int k=i+1; k<mol.getAllConnAtoms(atom); k++) {
                          int nbr_k = mol.getConnAtom(atom, k);
                          angles.add(new AngleBend(t, mol, nbr_i, atom, nbr_k));
                      }
                  }
              }
          }
  
          return angles;
      }
  }
  