/**********************************************************************
matrix3x3.cpp - Handle 3D rotation matrix.
 
Copyright (C) 1998-2001 by OpenEye Scientific Software, Inc.
Some portions Copyright (C) 2001-2006 by Geoffrey R. Hutchison
Some portions Copyright (C) 2006 by Benoit Jacob

This file is part of the Open Babel project.
For more information, see <http://openbabel.sourceforge.net/>
 
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation version 2 of the License.
 
This program 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.
***********************************************************************/
#include <openbabel/babelconfig.h>

#include <openbabel/math/matrix3x3.h>
#include <openbabel/obutil.h>

using namespace std;

namespace OpenBabel
{

  /** \class matrix3x3 matrix3x3.h <openbabel/math/matrix3x3.h>
      \brief Represents a real 3x3 matrix.
 
      Rotating points in space can be performed by a vector-matrix
      multiplication. The matrix3x3 class is designed as a helper to the
      vector3 class for rotating points in space. The rotation matrix may be
      initialised by passing in the array of floating point values, by
      passing euler angles, or a rotation vector and angle of rotation about
      that vector. Once set, the matrix3x3 class can be used to rotate
      vectors by the overloaded multiplication operator. The following
      demonstrates the usage of the matrix3x3 class:
 
      \code
      matrix3x3 mat;
      mat.SetupRotMat(0.0,180.0,0.0); //rotate theta by 180 degrees
      vector3 v = VX;
      v *= mat; //apply the rotation
      \endcode
 
  */

  /*! The axis of the rotation will be uniformly distributed on
    the unit sphere and the angle will be uniformly distributed in
    the interval 0..360 degrees. */
  void matrix3x3::randomRotation(OBRandom &rnd)
  {
    double rotAngle;
    vector3 v1;

    v1.randomUnitVector(&rnd);
    rotAngle = 360.0 * rnd.NextFloat();
    this->RotAboutAxisByAngle(v1,rotAngle);
  }

  void matrix3x3::SetupRotMat(double phi,double theta,double psi)
  {
    double p  = phi * DEG_TO_RAD;
    double h  = theta * DEG_TO_RAD;
    double b  = psi * DEG_TO_RAD;

    double cx = cos(p);
    double sx = sin(p);
    double cy = cos(h);
    double sy = sin(h);
    double cz = cos(b);
    double sz = sin(b);

    ele[0][0] = cy*cz;
    ele[0][1] = cy*sz;
    ele[0][2] = -sy;

    ele[1][0] = sx*sy*cz-cx*sz;
    ele[1][1] = sx*sy*sz+cx*cz;
    ele[1][2] = sx*cy;

    ele[2][0] = cx*sy*cz+sx*sz;
    ele[2][1] = cx*sy*sz-sx*cz;
    ele[2][2] = cx*cy;
  }

  /*! Replaces *this with a matrix that represents reflection on
    the plane through 0 which is given by the normal vector norm.
	
    \warning If the vector norm has length zero, this method will
    generate the 0-matrix. If the length of the axis is close to
    zero, but not == 0.0, this method may behave in unexpected
    ways and return almost random results; details may depend on
    your particular floating point implementation. The use of this
    method is therefore highly discouraged, unless you are certain
    that the length is in a reasonable range, away from 0.0
    (Stefan Kebekus)
	
    \deprecated This method will probably replaced by a safer
    algorithm in the future.
	
    \todo Replace this method with a more fool-proof version.
	
    @param norm specifies the normal to the plane
  */
  void matrix3x3::PlaneReflection(const vector3 &norm)
  {
    //@@@ add a safety net

    vector3 normtmp = norm;
    normtmp.normalize();

    SetColumn(0, vector3(1,0,0) - 2*normtmp.x()*normtmp);
    SetColumn(1, vector3(0,1,0) - 2*normtmp.y()*normtmp);
    SetColumn(2, vector3(0,0,1) - 2*normtmp.z()*normtmp);
  }

  /*! Replaces *this with a matrix that represents rotation about the
    axis by a an angle. 
	
    \warning If the vector axis has length zero, this method will
    generate the 0-matrix. If the length of the axis is close to
    zero, but not == 0.0, this method may behave in unexpected ways
    and return almost random results; details may depend on your
    particular floating point implementation. The use of this method
    is therefore highly discouraged, unless you are certain that the
    length is in a reasonable range, away from 0.0 (Stefan
    Kebekus)
	
    \deprecated This method will probably replaced by a safer
    algorithm in the future.
	
    \todo Replace this method with a more fool-proof version.
	
    @param v specifies the axis of the rotation
    @param angle angle in degrees (0..360)
  */
  void matrix3x3::RotAboutAxisByAngle(const vector3 &v,const double angle)
  {
    double theta = angle*DEG_TO_RAD;
    double s = sin(theta);
    double c = cos(theta);
    double t = 1 - c;

    vector3 vtmp = v;
    vtmp.normalize();

    double x = vtmp.x(),
           y = vtmp.y(),
           z = vtmp.z();

    ele[0][0] = t*x*x + c;
    ele[0][1] = t*x*y + s*z;
    ele[0][2] = t*x*z - s*y;

    ele[1][0] = t*x*y - s*z;
    ele[1][1] = t*y*y + c;
    ele[1][2] = t*y*z + s*x;

    ele[2][0] = t*x*z + s*y;
    ele[2][1] = t*y*z - s*x;
    ele[2][2] = t*z*z + c;
  }

  void matrix3x3::SetColumn(int col, const vector3 &v)
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
#ifdef OB_OLD_MATH_CHECKS
    if (col > 2)
      {
        OBError er("matrix3x3::SetColumn(int col, const vector3 &v)",
                   "The method was called with col > 2.",
                   "This is a programming error in your application.");
        throw er;
      }
#endif

    ele[0][col] = v.x();
    ele[1][col] = v.y();
    ele[2][col] = v.z();
  }

  void matrix3x3::SetRow(int row, const vector3 &v)
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
#ifdef OB_OLD_MATH_CHECKS
    if (row > 2)
      {
        OBError er("matrix3x3::SetRow(int row, const vector3 &v)",
                   "The method was called with row > 2.",
                   "This is a programming error in your application.");
        throw er;
      }
#endif

    ele[row][0] = v.x();
    ele[row][1] = v.y();
    ele[row][2] = v.z();
  }

  vector3 matrix3x3::GetColumn(unsigned int col) const
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
#ifdef OB_OLD_MATH_CHECKS
    if (col > 2)
      {
        OBError er("matrix3x3::GetColumn(unsigned int col) const",
                   "The method was called with col > 2.",
                   "This is a programming error in your application.");
        throw er;
      }
#endif

    return vector3(ele[0][col], ele[1][col], ele[2][col]);
  }

  vector3 matrix3x3::GetRow(unsigned int row) const
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
#ifdef OB_OLD_MATH_CHECKS
    if (row > 2)
      {
        OBError er("matrix3x3::GetRow(unsigned int row) const",
                   "The method was called with row > 2.",
                   "This is a programming error in your application.");
        throw er;
      }
#endif

    return vector3(ele[row][0], ele[row][1], ele[row][2]);
  }

  /*! Calculates the product m*v of the matrix m and the column
    vector represented by v
  */
  vector3 operator *(const matrix3x3 &m,const vector3 &v)
  {
    vector3 vv;

    vv.x() = v.x()*m.ele[0][0] + v.y()*m.ele[0][1] + v.z()*m.ele[0][2];
    vv.y() = v.x()*m.ele[1][0] + v.y()*m.ele[1][1] + v.z()*m.ele[1][2];
    vv.z() = v.x()*m.ele[2][0] + v.y()*m.ele[2][1] + v.z()*m.ele[2][2];

    return(vv);
  }

  matrix3x3 operator *(const matrix3x3 &A,const matrix3x3 &B)
  {
    matrix3x3 result;

    result.ele[0][0] = A.ele[0][0]*B.ele[0][0] + A.ele[0][1]*B.ele[1][0] + A.ele[0][2]*B.ele[2][0];
    result.ele[0][1] = A.ele[0][0]*B.ele[0][1] + A.ele[0][1]*B.ele[1][1] + A.ele[0][2]*B.ele[2][1];
    result.ele[0][2] = A.ele[0][0]*B.ele[0][2] + A.ele[0][1]*B.ele[1][2] + A.ele[0][2]*B.ele[2][2];

    result.ele[1][0] = A.ele[1][0]*B.ele[0][0] + A.ele[1][1]*B.ele[1][0] + A.ele[1][2]*B.ele[2][0];
    result.ele[1][1] = A.ele[1][0]*B.ele[0][1] + A.ele[1][1]*B.ele[1][1] + A.ele[1][2]*B.ele[2][1];
    result.ele[1][2] = A.ele[1][0]*B.ele[0][2] + A.ele[1][1]*B.ele[1][2] + A.ele[1][2]*B.ele[2][2];

    result.ele[2][0] = A.ele[2][0]*B.ele[0][0] + A.ele[2][1]*B.ele[1][0] + A.ele[2][2]*B.ele[2][0];
    result.ele[2][1] = A.ele[2][0]*B.ele[0][1] + A.ele[2][1]*B.ele[1][1] + A.ele[2][2]*B.ele[2][1];
    result.ele[2][2] = A.ele[2][0]*B.ele[0][2] + A.ele[2][1]*B.ele[1][2] + A.ele[2][2]*B.ele[2][2];

    return(result);
  }

  /*! calculates the product m*(*this) of the matrix m and the
    column vector represented by *this
  */
  vector3 &vector3::operator *= (const matrix3x3 &m)
  {
    vector3 vv;

    vv.SetX(x()*m.Get(0,0) + y()*m.Get(0,1) + z()*m.Get(0,2));
    vv.SetY(x()*m.Get(1,0) + y()*m.Get(1,1) + z()*m.Get(1,2));
    vv.SetZ(x()*m.Get(2,0) + y()*m.Get(2,1) + z()*m.Get(2,2));
    x() = vv.x();
    y() = vv.y();
    z() = vv.z();

    return(*this);
  }

  /*! This method checks if the absolute value of the determinant is smaller than 1e-6. If
    so, nothing is done and an exception is thrown. Otherwise, the
    inverse matrix is calculated and returned. *this is not changed.
	
    \warning If the determinant is close to zero, but not == 0.0,
    this method may behave in unexpected ways and return almost
    random results; details may depend on your particular floating
    point implementation. The use of this method is therefore highly
    discouraged, unless you are certain that the determinant is in a
    reasonable range, away from 0.0 (Stefan Kebekus)
  */
  matrix3x3 matrix3x3::inverse(void) const
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
    double det = determinant();

#ifdef OB_OLD_MATH_CHECKS
    if (fabs(det) <= 1e-6)
      {
        OBError er("matrix3x3::invert(void)",
                   "The method was called on a matrix with |determinant| <= 1e-6.",
                   "This is a runtime or a programming error in your application.");
        throw er;
      }
#endif

    matrix3x3 returnValue;
    returnValue.ele[0][0] = ele[1][1]*ele[2][2] - ele[1][2]*ele[2][1];
    returnValue.ele[1][0] = ele[1][2]*ele[2][0] - ele[1][0]*ele[2][2];
    returnValue.ele[2][0] = ele[1][0]*ele[2][1] - ele[1][1]*ele[2][0];
    returnValue.ele[0][1] = ele[2][1]*ele[0][2] - ele[2][2]*ele[0][1];
    returnValue.ele[1][1] = ele[2][2]*ele[0][0] - ele[2][0]*ele[0][2];
    returnValue.ele[2][1] = ele[2][0]*ele[0][1] - ele[2][1]*ele[0][0];
    returnValue.ele[0][2] = ele[0][1]*ele[1][2] - ele[0][2]*ele[1][1];
    returnValue.ele[1][2] = ele[0][2]*ele[1][0] - ele[0][0]*ele[1][2];
    returnValue.ele[2][2] = ele[0][0]*ele[1][1] - ele[0][1]*ele[1][0];

    returnValue /= det;

    return(returnValue);
  }

  /* This method returns the transpose of a matrix. The original
     matrix remains unchanged. */
  matrix3x3 matrix3x3::transpose(void) const
  {
    matrix3x3 returnValue;

    for(unsigned int i=0; i<3; i++)
      for(unsigned int j=0; j<3; j++)
        returnValue.ele[i][j] = ele[j][i];

    return(returnValue);
  }

  double matrix3x3::determinant(void) const
  {
    return( ele[0][0] * (ele[1][1] * ele[2][2] - ele[1][2] * ele[2][1])
          + ele[0][1] * (ele[1][2] * ele[2][0] - ele[1][0] * ele[2][2])
          + ele[0][2] * (ele[1][0] * ele[2][1] - ele[1][1] * ele[2][0]) );
  }

  /*! \return False if there are indices i,j such that
    fabs(*this[i][j]-*this[j][i]) > 1e-6. Otherwise, it returns
    true. */
  bool matrix3x3::isSymmetric(void) const
  {
    return( IsApprox( ele[0][1], ele[1][0], 1e-6 )
         && IsApprox( ele[0][2], ele[2][0], 1e-6 )
         && IsApprox( ele[1][2], ele[2][1], 1e-6 ) );
  }

  /*! This method returns true if and only if the matrix is
   * (approximately) a diagonal matrix. The precision used
   * by this function is 1e-6. */
  bool matrix3x3::isDiagonal(void) const
  {
    return( IsNegligible( ele[1][0], ele[0][0], 1e-6 )
         && IsNegligible( ele[2][0], ele[0][0], 1e-6 )
         && IsNegligible( ele[0][1], ele[1][1], 1e-6 )
         && IsNegligible( ele[2][1], ele[1][1], 1e-6 )
         && IsNegligible( ele[0][2], ele[2][2], 1e-6 )
         && IsNegligible( ele[1][2], ele[2][2], 1e-6 ) );
  }

  /*! This method returns true if and only if the matrix is
   * (approximately) equal to the identity matrix. The precision used
   * by this function is 1e-6. */
  bool matrix3x3::isUnitMatrix(void) const
  {
    return ( isDiagonal()
          && IsApprox( ele[0][0], 1.0, 1e-6 )
          && IsApprox( ele[1][1], 1.0, 1e-6 )
          && IsApprox( ele[2][2], 1.0, 1e-6 ) );
  }

  /*! This method employs the static method matrix3x3::jacobi(...)
    to find the eigenvalues and eigenvectors of a symmetric
    matrix. On entry it is checked if the matrix really is
    symmetric: if isSymmetric() returns 'false', an OBError is
    thrown.
 
    \note The jacobi algorithm is should work great for all
    symmetric 3x3 matrices. If you need to find the eigenvectors
    of a non-symmetric matrix, you might want to resort to the
    sophisticated routines of LAPACK.
 
    @param eigenvals a reference to a vector3 where the
    eigenvalues will be stored. The eigenvalues are ordered so
    that eigenvals[0] <= eigenvals[1] <= eigenvals[2].
 
    @return an orthogonal matrix whose ith column is an
    eigenvector for the eigenvalue eigenvals[i]. Here 'orthogonal'
    means that all eigenvectors have length one and are mutually
    orthogonal. The ith eigenvector can thus be conveniently
    accessed by the GetColumn() method, as in the following
    example.
    \code
    // Calculate eigenvectors and -values
    vector3 eigenvals;
    matrix3x3 eigenmatrix = somematrix.findEigenvectorsIfSymmetric(eigenvals);
  
    // Print the 2nd eigenvector
    cout << eigenmatrix.GetColumn(1) << endl;
    \endcode
    With these conventions, a matrix is diagonalized in the following way:
    \code
    // Diagonalize the matrix
    matrix3x3 diagonalMatrix = eigenmatrix.inverse() * somematrix * eigenmatrix;
    \endcode
  
  */
  matrix3x3 matrix3x3::findEigenvectorsIfSymmetric(vector3 &eigenvals) const
#ifdef OB_OLD_MATH_CHECKS
  throw(OBError)
#endif
  {
    matrix3x3 result;

#ifdef OB_OLD_MATH_CHECKS
    if (!isSymmetric())
      {
        OBError er("matrix3x3::findEigenvectorsIfSymmetric(vector3 &eigenvals) const throw(OBError)",
                   "The method was called on a matrix that was not symmetric, i.e. where isSymetric() == false.",
                   "This is a runtime or a programming error in your application.");
        throw er;
      }
#endif

    double d[3];
    matrix3x3 copyOfThis = *this;

    jacobi(3, copyOfThis.ele[0], d, result.ele[0]);
    eigenvals.Set(d);

    return result;
  }

  static inline double SQUARE( double x ) { return x*x; }

  void matrix3x3::FillOrth(double Alpha,double Beta, double Gamma,
                           double A, double B, double C)
  {
    double V;

    Alpha *= DEG_TO_RAD;
    Beta  *= DEG_TO_RAD;
    Gamma *= DEG_TO_RAD;

    // from the PDB specification:
    //  http://www.rcsb.org/pdb/docs/format/pdbguide2.2/part_75.html


    // since we'll ultimately divide by (a * b), we've factored those out here
    V = C * sqrt(1 - SQUARE(cos(Alpha)) - SQUARE(cos(Beta)) - SQUARE(cos(Gamma))
                 + 2 * cos(Alpha) * cos(Beta) * cos(Gamma));

    ele[0][0] = A;
    ele[0][1] = B*cos(Gamma);
    ele[0][2] = C*cos(Beta);

    ele[1][0] = 0.0;
    ele[1][1] = B*sin(Gamma);
    ele[1][2] = C*(cos(Alpha)-cos(Beta)*cos(Gamma))/sin(Gamma);

    ele[2][0] = 0.0;
    ele[2][1] = 0.0;
    ele[2][2] = V / (sin(Gamma)); // again, we factored out A * B when defining V
  }

  /** Print a text representation of the matrix in the standardized form:
      [ a, b, c ] <br>
      [ d, e, f ] <br>
      [ g, h, i ] <br>
      where the letters represent the appropriate entries in the matrix.
      Uses the standard output format for the individual entries, separated
      by ", " for each column, and [ ] indicating each row.
   **/
  ostream& operator<< ( ostream& co, const matrix3x3& m )

  {
    co << "[ "
       << m.ele[0][0]
       << ", "
       << m.ele[0][1]
       << ", "
       << m.ele[0][2]
       << " ]" << endl;

    co << "[ "
       << m.ele[1][0]
       << ", "
       << m.ele[1][1]
       << ", "
       << m.ele[1][2]
       << " ]" << endl;

    co << "[ "
       << m.ele[2][0]
       << ", "
       << m.ele[2][1]
       << ", "
       << m.ele[2][2]
       << " ]" << endl;

    return co ;
  }

  /*! This static function computes the eigenvalues and
    eigenvectors of a SYMMETRIC nxn matrix. This method is used
    internally by OpenBabel, but may be useful as a general
    eigenvalue finder.
  
    The algorithm uses Jacobi transformations. It is described
    e.g. in Wilkinson, Reinsch "Handbook for automatic computation,
    Volume II: Linear Algebra", part II, contribution II/1. The
    implementation is also similar to the implementation in this
    book. This method is adequate to solve the eigenproblem for
    small matrices, of size perhaps up to 10x10. For bigger
    problems, you might want to resort to the sophisticated routines
    of LAPACK.
  
    \note If you plan to find the eigenvalues of a symmetric 3x3
    matrix, you will probably prefer to use the more convenient
    method findEigenvectorsIfSymmetric()
  
    @param n the size of the matrix that should be diagonalized
  
    @param a array of size n^2 which holds the symmetric matrix
    whose eigenvectors are to be computed. The convention is that
    the entry in row r and column c is addressed as a[n*r+c] where,
    of course, 0 <= r < n and 0 <= c < n. There is no check that the
    matrix is actually symmetric. If it is not, the behaviour of
    this function is undefined.  On return, the matrix is
    overwritten with junk.
  
    @param d pointer to a field of at least n doubles which will be
    overwritten. On return of this function, the entries d[0]..d[n-1]
    will contain the eigenvalues of the matrix.
  
    @param v an array of size n^2 where the eigenvectors will be
    stored. On return, the columns of this matrix will contain the
    eigenvectors. The eigenvectors are normalized and mutually
    orthogonal.
  */
  void matrix3x3::jacobi(unsigned int n, double *a, double *d, double *v)
  {
    double onorm, dnorm;
    double b, dma, q, t, c, s;
    double  atemp, vtemp, dtemp;
    register int i, j, k, l;
    int nrot;

    int MAX_SWEEPS=50;

    // Set v to the identity matrix, set the vector d to contain the
    // diagonal elements of the matrix a
    for (j = 0; j < static_cast<int>(n); j++)
      {
        for (i = 0; i < static_cast<int>(n); i++)
          v[n*i+j] = 0.0;
        v[n*j+j] = 1.0;
        d[j] = a[n*j+j];
      }

    nrot = MAX_SWEEPS;
    for (l = 1; l <= nrot; l++)
      {
        // Set dnorm to be the maximum norm of the diagonal elements, set
        // onorm to the maximum norm of the off-diagonal elements
        dnorm = 0.0;
        onorm = 0.0;
        for (j = 0; j < static_cast<int>(n); j++)
          {
            dnorm += (double)fabs(d[j]);
            for (i = 0; i < j; i++)
              onorm += (double)fabs(a[n*i+j]);
          }
        // Normal end point of this algorithm.
        if((onorm/dnorm) <= 1.0e-12)
          goto Exit_now;

        for (j = 1; j < static_cast<int>(n); j++)
          {
            for (i = 0; i <= j - 1; i++)
              {

                b = a[n*i+j];
                if(fabs(b) > 0.0)
                  {
                    dma = d[j] - d[i];
                    if((fabs(dma) + fabs(b)) <=  fabs(dma))
                      t = b / dma;
                    else
                      {
                        q = 0.5 * dma / b;
                        t = 1.0/((double)fabs(q) + (double)sqrt(1.0+q*q));
                        if (q < 0.0)
                          t = -t;
                      }

                    c = 1.0/(double)sqrt(t*t + 1.0);
                    s = t * c;
                    a[n*i+j] = 0.0;

                    for (k = 0; k <= i-1; k++)
                      {
                        atemp = c * a[n*k+i] - s * a[n*k+j];
                        a[n*k+j] = s * a[n*k+i] + c * a[n*k+j];
                        a[n*k+i] = atemp;
                      }

                    for (k = i+1; k <= j-1; k++)
                      {
                        atemp = c * a[n*i+k] - s * a[n*k+j];
                        a[n*k+j] = s * a[n*i+k] + c * a[n*k+j];
                        a[n*i+k] = atemp;
                      }

                    for (k = j+1; k < static_cast<int>(n); k++)
                      {
                        atemp = c * a[n*i+k] - s * a[n*j+k];
                        a[n*j+k] = s * a[n*i+k] + c * a[n*j+k];
                        a[n*i+k] = atemp;
                      }

                    for (k = 0; k < static_cast<int>(n); k++)
                      {
                        vtemp = c * v[n*k+i] - s * v[n*k+j];
                        v[n*k+j] = s * v[n*k+i] + c * v[n*k+j];
                        v[n*k+i] = vtemp;
                      }

                    dtemp = c*c*d[i] + s*s*d[j] - 2.0*c*s*b;
                    d[j] = s*s*d[i] + c*c*d[j] +  2.0*c*s*b;
                    d[i] = dtemp;
                  } /* end if */
              } /* end for i */
          } /* end for j */
      } /* end for l */

  Exit_now:

    // Now sort the eigenvalues (and the eigenvectors) so that the
    // smallest eigenvalues come first.
    nrot = l;

    for (j = 0; j < static_cast<int>(n)-1; j++)
      {
        k = j;
        dtemp = d[k];
        for (i = j+1; i < static_cast<int>(n); i++)
          if(d[i] < dtemp)
            {
              k = i;
              dtemp = d[k];
            }

        if(k > j)
          {
            d[k] = d[j];
            d[j] = dtemp;
            for (i = 0; i < static_cast<int>(n); i++)
              {
                dtemp = v[n*i+k];
                v[n*i+k] = v[n*i+j];
                v[n*i+j] = dtemp;
              }
          }
      }
  }

} // end namespace OpenBabel

//! \file matrix3x3.cpp
//! \brief Handle 3D rotation matrix.

