// ******************************************************************************
   //
   // Title:       Force Field X.
   // Description: Force Field X - Software for Molecular Biophysics.
   // Copyright:   Copyright (c) Michael J. Schnieders 2001-2025.
   //
   // This file is part of Force Field X.
   //
   // Force Field X is free software; you can redistribute it and/or modify it
  // under the terms of the GNU General Public License version 3 as published by
  // the Free Software Foundation.
  //
  // Force Field X is distributed in the hope that it will be useful, but WITHOUT
  // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  // FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
  // details.
  //
  // You should have received a copy of the GNU General Public License along with
  // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
  // Place, Suite 330, Boston, MA 02111-1307 USA
  //
  // Linking this library statically or dynamically with other modules is making a
  // combined work based on this library. Thus, the terms and conditions of the
  // GNU General Public License cover the whole combination.
  //
  // As a special exception, the copyright holders of this library give you
  // permission to link this library with independent modules to produce an
  // executable, regardless of the license terms of these independent modules, and
  // to copy and distribute the resulting executable under terms of your choice,
  // provided that you also meet, for each linked independent module, the terms
  // and conditions of the license of that module. An independent module is a
  // module which is not derived from or based on this library. If you modify this
  // library, you may extend this exception to your version of the library, but
  // you are not obligated to do so. If you do not wish to do so, delete this
  // exception statement from your version.
  //
  // ******************************************************************************
  package ffx.xray.scatter;
  
  import ffx.crystal.HKL;
  import ffx.potential.bonded.Atom;
  import ffx.xray.refine.RefinementMode;
  
  import java.util.HashMap;
  import java.util.logging.Logger;
  
  import static ffx.numerics.math.DoubleMath.dot;
  import static ffx.numerics.math.DoubleMath.length;
  import static ffx.numerics.math.DoubleMath.sub;
  import static ffx.numerics.math.MatrixMath.determinant3;
  import static ffx.numerics.math.MatrixMath.mat3Inverse;
  import static ffx.numerics.math.MatrixMath.mat3Mat3;
  import static ffx.numerics.math.MatrixMath.scalarMat3Mat3;
  import static ffx.numerics.math.MatrixMath.vec3Mat3;
  import static ffx.numerics.math.ScalarMath.b2u;
  import static ffx.numerics.math.ScalarMath.quadForm;
  import static ffx.numerics.math.ScalarMath.u2b;
  import static java.lang.String.format;
  import static java.lang.System.arraycopy;
  import static java.util.Arrays.fill;
  import static org.apache.commons.math3.util.FastMath.PI;
  import static org.apache.commons.math3.util.FastMath.exp;
  import static org.apache.commons.math3.util.FastMath.pow;
  import static org.apache.commons.math3.util.FastMath.sqrt;
  
  /**
   * This implementation uses the coefficients from International Tables, Vol. C, chapter 4.4.4.
   *
   * @author Timothy D. Fenn
   * @see <a href="http://dx.doi.org/10.1107/97809553602060000594" target="_blank"> V. F. Sears, Int.
   *     Tables Vol. C (2006). Table 4.4.4.1</a>
   * @see <a href="http://dx.doi.org/10.1107/97809553602060000600" target="_blank"> B. T. M. Willis,
   *     Int. Tables Vol. C (2006). Chapter 6.1.3</a>
   * @see <a href="http://dx.doi.org/10.1107/S0907444909022707" target="_blank"> M. J. Schnieders, T.
   *     D. Fenn, V. S. Pande and A. T. Brunger, Acta Cryst. (2009). D65 952-965.</a>
   * @since 1.0
   */
  public final class NeutronFormFactor implements FormFactor {
  
    private static final Logger logger = Logger.getLogger(NeutronFormFactor.class.getName());
  
    private static final double twoPI2 = 2.0 * PI * PI;
    private static final double inverseTwoPI32 = pow(2.0 * PI, -1.5);
    private static final double oneThird = 1.0 / 3.0;
    private static final double[] vx = {1.0, 0.0, 0.0};
    private static final double[] vy = {0.0, 1.0, 0.0};
    private static final double[] vz = {0.0, 0.0, 1.0};
    private static final double[][] u11 = {{1.0, 0.0, 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
    private static final double[][] u22 = {{0.0, 0.0, 0.0}, {0.0, 1.0, 0.0}, {0.0, 0.0, 0.0}};
    private static final double[][] u33 = {{0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}, {0.0, 0.0, 1.0}};
    private static final double[][] u12 = {{0.0, 1.0, 0.0}, {1.0, 0.0, 0.0}, {0.0, 0.0, 0.0}};
    private static final double[][] u13 = {{0.0, 0.0, 1.0}, {0.0, 0.0, 0.0}, {1.0, 0.0, 0.0}};
    private static final double[][] u23 = {{0.0, 0.0, 0.0}, {0.0, 0.0, 1.0}, {0.0, 1.0, 0.0}};
    private static final HashMap<String, double[][]> formfactors = new HashMap<>();
    private static final String[] atomNames = {
        "H", "D", "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", "Sm", "Eu", "Gd", "Tb", "Dy",
       "Ho", "Er", "Tm", "Yb", "Lu", "Hf", "Ta", "W", "Re", "Os", "Ir", "Pt", "Au", "Hg", "Tl", "Pb",
       "Bi", "Th", "U"
   };
   private static final String[] atomicNumbers = {
       "1_1", "1_2", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16",
       "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32",
       "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49",
       "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "62", "63", "64", "65", "66",
       "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", "80", "81", "82",
       "83", "90", "92"
   };
   private static final double[][][] neutronFormFactors = {
       {{0}, {-3.7390, 0.0}},  // H
       {{1}, {6.671, 0.0}},    // D
       {{2}, {3.26, 0.0}},     // He
       {{3}, {-1.90, 0.0}},    // Li
       {{4}, {7.79, 0.0}},     // Be
       {{5}, {5.30, 0.213}},   // B
       {{6}, {6.6460, 0.0}},   // C
       {{7}, {9.36, 0.0}},     // N
       {{8}, {5.803, 0.0}},    // O
       {{9}, {5.654, 0.0}},    // F
       {{10}, {4.566, 0.0}},   // Ne
       {{11}, {3.63, 0.0}},    // Na
       {{12}, {5.375, 0.0}},   // Mg
       {{13}, {3.449, 0.0}},   // Al
       {{14}, {4.1491, 0.0}},  // Si
       {{15}, {5.13, 0.0}},    // P
       {{16}, {2.847, 0.0}},   // S
       {{17}, {9.5770, 0.0}},  // Cl
       {{18}, {1.909, 0.0}},   // Ar
       {{19}, {3.67, 0.0}},    // K
       {{20}, {4.70, 0.0}},    // Ca
       {{21}, {12.29, 0.0}},   // Sc
       {{22}, {-3.370, 0.0}},  // Ti
       {{23}, {-0.3824, 0.0}}, // V
       {{24}, {3.635, 0.0}},   // Cr
       {{25}, {-3.750, 0.0}},  // Mn
       {{26}, {9.45, 0.0}},    // Fe
       {{27}, {2.49, 0.0}},    // Co
       {{28}, {10.3, 0.0}},    // Ni
       {{29}, {7.718, 0.0}},   // Cu
       {{30}, {5.60, 0.0}},    // Zn
       {{31}, {7.288, 0.0}},   // Ga
       {{32}, {8.185, 0.0}},   // Ge
       {{33}, {6.58, 0.0}},    // As
       {{34}, {7.970, 0.0}},   // Se
       {{35}, {6.795, 0.0}},   // Br
       {{36}, {7.81, 0.0}},    // Kr
       {{37}, {7.09, 0.0}},    // Rb
       {{38}, {7.02, 0.0}},    // Sr
       {{39}, {7.75, 0.0}},    // Y
       {{40}, {7.16, 0.0}},    // Zr
       {{41}, {7.054, 0.0}},   // Nb
       {{42}, {6.715, 0.0}},   // Mo
       {{43}, {6.80, 0.0}},    // Tc
       {{44}, {7.03, 0.0}},    // Ru
       {{45}, {5.88, 0.0}},    // Rh
       {{46}, {5.91, 0.0}},    // Pd
       {{47}, {5.922, 0.0}},   // Ag
       {{48}, {4.87, -0.70}},  // Cd
       {{49}, {2.08, -0.0539}},// In; nCNS 4.065
       {{50}, {6.225, 0.0}},   // Sn
       {{51}, {5.57, 0.0}},    // Sb
       {{52}, {5.80, 0.0}},    // Te; nCNS 5.68
       {{53}, {5.28, 0.0}},    // I
       {{54}, {4.92, 0.0}},    // Xe
       {{55}, {5.42, 0.0}},    // Cs
       {{56}, {5.07, 0.0}},    // Ba
       {{57}, {8.24, 0.0}},    // La
       {{58}, {4.84, 0.0}},    // Ce
       {{59}, {4.58, 0.0}},    // Pr
       {{60}, {7.69, 0.0}},    // Nd
                               // No PM
       {{61}, {0.80, -1.65}},  // Sm cCNS 0.0
       {{62}, {7.22, -1.26}},  // Eu nCNS 5.3
       {{63}, {6.5, -13.82}},  // Gd nCNS 9.5
       {{64}, {7.38, 0.0}},    // Tb
       {{65}, {16.9, -0.276}}, // Dy
       {{66}, {8.01, 0.0}},    // Ho
       {{67}, {7.79, 0.0}},    // Er
       {{68}, {7.07, 0.0}},    // Tm
       {{69}, {12.43, 0.0}},   // Yb
       {{70}, {7.21, 0.0}},    // Lu
       {{71}, {7.77, 0.0}},    // Hf
       {{72}, {6.91, 0.0}},    // Ta
       {{73}, {4.86, 0.0}},    // W
       {{74}, {9.2, 0.0}},     // Re
       {{75}, {10.7, 0.0}},    // Os
       {{76}, {10.6, 0.0}},    // Ir
       {{77}, {9.60, 0.0}},    // Pt
       {{78}, {7.63, 0.0}},    // Au
       {{79}, {12.692, 0.0}},  // Hg
       {{80}, {8.776, 0.0}},   // Tl
       {{81}, {9.405, 0.0}},   // Pb
       {{82}, {8.532, 0.0}},   // Bi
       {{83}, {10.31, 0.0}},   // Th
       {{84}, {8.417, 0.0}}    // U
   };
 
   static {
     for (int i = 0; i < atomNames.length; i++) {
       formfactors.put(atomicNumbers[i], neutronFormFactors[i]);
     }
   }
 
   private final Atom atom;
   private final double[] xyz = new double[3];
   private final double[] dxyz = new double[3];
   private final double[] a = new double[2];
   private final double[] ainv = new double[1];
   private final double[] binv = new double[1];
   private final double[][][] u = new double[1][3][3];
   private final double[][][] uinv = new double[1][3][3];
   private final double[][][] jmat = new double[6][3][3];
   private final double[] gradp = new double[6];
   private final double[] gradu = new double[6];
   private final double[] resv = new double[3];
   private final double[][] resm = new double[3][3];
   private double uadd;
   private double occ;
   private boolean hasAnisou;
   private double[] uaniso = null;
 
   /**
    * Constructor for NeutronFormFactor.
    *
    * @param atom a {@link ffx.potential.bonded.Atom} object.
    */
   public NeutronFormFactor(Atom atom) {
     this(atom, 0.0, atom.getXYZ(null));
   }
 
   /**
    * Constructor for NeutronFormFactor.
    *
    * @param atom a {@link ffx.potential.bonded.Atom} object.
    * @param badd a double.
    */
   public NeutronFormFactor(Atom atom, double badd) {
     this(atom, badd, atom.getXYZ(null));
   }
 
   /**
    * Constructor for NeutronFormFactor.
    *
    * @param atom a {@link ffx.potential.bonded.Atom} object.
    * @param badd a double.
    * @param xyz an array of double.
    */
   public NeutronFormFactor(Atom atom, double badd, double[] xyz) {
     this.atom = atom;
     this.uadd = b2u(badd);
     double[][] ffactor;
 
     String key;
     if (atom.getAtomicNumber() == 1) {
       if (atom.isDeuterium()) {
         key = atom.getAtomicNumber() + "_2";
       } else {
         key = atom.getAtomicNumber() + "_1";
       }
     } else {
       key = "" + atom.getAtomicNumber();
     }
 
     ffactor = getFormFactor(key);
     arraycopy(ffactor[1], 0, a, 0, ffactor[1].length);
     if (a[1] != 0.0) {
       logger.severe(" Complex neutron form factor method not supported");
     }
 
     occ = atom.getOccupancy();
 
     if (occ <= 0.0) {
       StringBuilder sb = new StringBuilder();
       sb.append(" Zero occupancy: ").append(atom);
       logger.fine(sb.toString());
     }
 
     update(xyz, uadd);
   }
 
   /**
    * Returns the string representation of the NeutronFormFactor object.
    * The string includes details about the associated atom and its neutron
    * scattering magnitude.
    *
    * @return A formatted string containing the atom's information and its
    * neutron scattering magnitude.
    */
   @Override
   public String toString() {
     return atom.toString() + format(" Neutron mag: %9.6f", a[0]);
   }
 
   /**
    * getFormFactorA
    *
    * @param atom a {@link java.lang.String} object.
    * @return an array of double.
    */
   public static double[] getFormFactorA(String atom) {
     double[][] ffactor = getFormFactor(atom);
     if (ffactor != null) {
       return ffactor[1];
     } else {
       return null;
     }
   }
 
   /**
    * getFormFactorIndex
    *
    * @param atom a {@link java.lang.String} object.
    * @return a int.
    */
   public static int getFormFactorIndex(String atom) {
     double[][] ffactor = getFormFactor(atom);
     if (ffactor != null) {
       return (int) ffactor[0][0];
     } else {
       return -1;
     }
   }
 
   /**
    * getFormFactor
    *
    * @param atom a {@link java.lang.String} object.
    * @return an array of double.
    */
   private static double[][] getFormFactor(String atom) {
     double[][] ffactor = null;
 
     if (formfactors.containsKey(atom)) {
       ffactor = formfactors.get(atom);
     } else {
       String message = " Form factor for atom: " + atom + " not found!";
       logger.severe(message);
     }
 
     return ffactor;
   }
 
   /**
    * f
    *
    * @param hkl a {@link ffx.crystal.HKL} object.
    * @return a double.
    */
   public double f(HKL hkl) {
     double sum = a[0] * exp(-twoPI2 * hkl.quadForm(u[0]));
     return occ * sum;
   }
 
   /** {@inheritDoc} */
   @Override
   public double rho(double f, double lambda, double[] xyz) {
     sub(this.xyz, xyz, xyz);
     double r = length(xyz);
     if (r > atom.getFormFactorWidth()) {
       return f;
     }
     double sum = ainv[0] * exp(-0.5 * quadForm(xyz, uinv[0]));
     return f + (lambda * occ * inverseTwoPI32 * sum);
   }
 
   /** {@inheritDoc} */
   @Override
   public void rhoGrad(double[] xyz, double dfc, RefinementMode refinementmode) {
     sub(this.xyz, xyz, dxyz);
     double r = length(dxyz);
     double r2 = r * r;
     fill(gradp, 0.0);
     fill(gradu, 0.0);
 
     if (r > atom.getFormFactorWidth()) {
       return;
     }
 
     boolean refinexyz = false;
     boolean refineb = false;
     boolean refineanisou = false;
     boolean refineocc = false;
     if (refinementmode == RefinementMode.COORDINATES
         || refinementmode == RefinementMode.COORDINATES_AND_BFACTORS
         || refinementmode == RefinementMode.COORDINATES_AND_OCCUPANCIES
         || refinementmode == RefinementMode.COORDINATES_AND_BFACTORS_AND_OCCUPANCIES) {
       refinexyz = true;
     }
     if (refinementmode == RefinementMode.BFACTORS
         || refinementmode == RefinementMode.BFACTORS_AND_OCCUPANCIES
         || refinementmode == RefinementMode.COORDINATES_AND_BFACTORS
         || refinementmode == RefinementMode.COORDINATES_AND_BFACTORS_AND_OCCUPANCIES) {
       refineb = true;
       if (hasAnisou) {
         refineanisou = true;
       }
     }
     if (refinementmode == RefinementMode.OCCUPANCIES
         || refinementmode == RefinementMode.BFACTORS_AND_OCCUPANCIES
         || refinementmode == RefinementMode.COORDINATES_AND_OCCUPANCIES
         || refinementmode == RefinementMode.COORDINATES_AND_BFACTORS_AND_OCCUPANCIES) {
       refineocc = true;
     }
 
     double aex = ainv[0] * exp(-0.5 * quadForm(dxyz, uinv[0]));
 
     if (refinexyz) {
       vec3Mat3(dxyz, uinv[0], resv);
       gradp[0] += aex * dot(resv, vx);
       gradp[1] += aex * dot(resv, vy);
       gradp[2] += aex * dot(resv, vz);
     }
 
     if (refineocc) {
       gradp[3] += aex;
     }
 
     if (refineb) {
       gradp[4] += aex * 0.5 * (r2 * binv[0] * binv[0] - 3.0 * binv[0]);
 
       if (refineanisou) {
         scalarMat3Mat3(-1.0, uinv[0], u11, resm);
         mat3Mat3(resm, uinv[0], jmat[0]);
         scalarMat3Mat3(-1.0, uinv[0], u22, resm);
         mat3Mat3(resm, uinv[0], jmat[1]);
         scalarMat3Mat3(-1.0, uinv[0], u33, resm);
         mat3Mat3(resm, uinv[0], jmat[2]);
         scalarMat3Mat3(-1.0, uinv[0], u12, resm);
         mat3Mat3(resm, uinv[0], jmat[3]);
         scalarMat3Mat3(-1.0, uinv[0], u13, resm);
         mat3Mat3(resm, uinv[0], jmat[4]);
         scalarMat3Mat3(-1.0, uinv[0], u23, resm);
         mat3Mat3(resm, uinv[0], jmat[5]);
 
         gradu[0] += aex * 0.5 * (-quadForm(dxyz, jmat[0]) - uinv[0][0][0]);
         gradu[1] += aex * 0.5 * (-quadForm(dxyz, jmat[1]) - uinv[0][1][1]);
         gradu[2] += aex * 0.5 * (-quadForm(dxyz, jmat[2]) - uinv[0][2][2]);
         gradu[3] += aex * 0.5 * (-quadForm(dxyz, jmat[3]) - uinv[0][0][1] * 2.0);
         gradu[4] += aex * 0.5 * (-quadForm(dxyz, jmat[4]) - uinv[0][0][2] * 2.0);
         gradu[5] += aex * 0.5 * (-quadForm(dxyz, jmat[5]) - uinv[0][1][2] * 2.0);
       }
     }
 
     // double rho = occ * inverseTwoPI32 * gradp[3];
     // x, y, z
     if (refinexyz) {
       atom.addToXYZGradient(
           dfc * occ * -inverseTwoPI32 * gradp[0],
           dfc * occ * -inverseTwoPI32 * gradp[1],
           dfc * occ * -inverseTwoPI32 * gradp[2]);
     }
 
     // occ
     if (refineocc) {
       atom.addToOccupancyGradient(dfc * inverseTwoPI32 * gradp[3]);
     }
 
     // Biso
     if (refineb) {
       atom.addToTempFactorGradient(dfc * b2u(occ * inverseTwoPI32 * gradp[4]));
       // Uaniso
       if (hasAnisou) {
         for (int i = 0; i < 6; i++) {
           gradu[i] = dfc * occ * inverseTwoPI32 * gradu[i];
         }
         atom.addToAnisouGradient(gradu);
       }
     }
   }
 
   /** {@inheritDoc} */
   @Override
   public void update(double[] xyz) {
     update(xyz, u2b(uadd));
   }
 
   /** {@inheritDoc} */
   @Override
   public void update(double[] xyz, double badd) {
     this.xyz[0] = xyz[0];
     this.xyz[1] = xyz[1];
     this.xyz[2] = xyz[2];
     double biso = atom.getTempFactor();
     uadd = b2u(badd);
     occ = atom.getOccupancy();
 
     // Check occ is valid.
     if (occ < 0.0) {
       StringBuilder sb = new StringBuilder();
       sb.append(" Negative occupancy for atom: ").append(atom).append("\n");
       sb.append(" Resetting to 0.0\n");
       logger.warning(sb.toString());
       occ = 0.0;
       atom.setOccupancy(0.0);
     }
 
     // Check if anisou changed.
     if (atom.getAnisou(null) == null) {
       if (uaniso == null) {
         uaniso = new double[6];
       }
       hasAnisou = false;
     } else {
       hasAnisou = true;
     }
 
     if (hasAnisou) {
       // first check the ANISOU is valid
       uaniso = atom.getAnisou(null);
       double det = determinant3(uaniso);
       if (det <= 1e-14) {
         StringBuilder sb = new StringBuilder();
         sb.append(" Non-positive definite ANISOU for atom: ").append(atom).append("\n");
         sb.append(" Resetting ANISOU based on isotropic B: (").append(biso).append(")\n");
         logger.warning(sb.toString());
         double val = b2u(biso);
         uaniso[0] = val;
         uaniso[1] = val;
         uaniso[2] = val;
         uaniso[3] = 0.0;
         uaniso[4] = 0.0;
         uaniso[5] = 0.0;
         atom.setAnisou(uaniso);
       }
     } else {
       if (biso < 0.0) {
         StringBuilder sb = new StringBuilder();
         sb.append("negative B factor for atom: ").append(atom).append("\n");
         sb.append("resetting B to 0.01\n");
         logger.warning(sb.toString());
         atom.setTempFactor(0.01);
         double val = b2u(0.01);
         uaniso[0] = val;
         uaniso[1] = val;
         uaniso[2] = val;
       } else {
         double val = b2u(biso);
         uaniso[0] = val;
         uaniso[1] = val;
         uaniso[2] = val;
       }
       uaniso[3] = 0.0;
       uaniso[4] = 0.0;
       uaniso[5] = 0.0;
     }
 
     u[0][0][0] = uaniso[0] + uadd;
     u[0][1][1] = uaniso[1] + uadd;
     u[0][2][2] = uaniso[2] + uadd;
     u[0][0][1] = uaniso[3];
     u[0][1][0] = uaniso[3];
     u[0][0][2] = uaniso[4];
     u[0][2][0] = uaniso[4];
     u[0][1][2] = uaniso[5];
     u[0][2][1] = uaniso[5];
     mat3Inverse(u[0], uinv[0]);
 
     double det = determinant3(u[0]);
     ainv[0] = a[0] / sqrt(det);
     det = determinant3(uinv[0]);
     binv[0] = pow(det,  oneThird);
   }
 }