chi_meshtensor_rank2_dim3.h

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#ifndef _chi_meshtensor_rank2_dim3_h
#define _chi_meshtensor_rank2_dim3_h
 
#include "chi_meshvector.h"
 
//###################################################################
/**General rank 2 tensor to be used with Vector3*/
struct chi_mesh::TensorRank2Dim3
{
  std::vector<chi_mesh::Vector3> t; ///< Tensor entries.
 
  /**Default constructor.*/
  TensorRank2Dim3()
  {
    t.resize(3,chi_mesh::Vector3(0.0,0.0,0.0));
  }
  /**Constructor with specified value.
   * \f$ T_{ii} = \alpha \f$*/
  explicit TensorRank2Dim3(const double value)
  {
    t.resize(3,chi_mesh::Vector3(value,value,value));
  }
 
  /**Copy constructor.*/
  TensorRank2Dim3(const TensorRank2Dim3& that)
  {
    this->t = that.t;
  }
 
  /**Component-wise copy*/
  TensorRank2Dim3& operator=(const TensorRank2Dim3& that)
  {
    this->t = that.t;
 
    return *this;
  }
 
  /**Element access.*/
  chi_mesh::Vector3& operator[](int index)
  {
    return t[index];
  }
 
  //============================================= Addition
  /**Component-wise addition.
   * \f$ \vec{\vec{W}} = \vec{\vec{X}} + \vec{\vec{Y}} \f$*/
  TensorRank2Dim3 operator+(const TensorRank2Dim3& that) const
  {
    TensorRank2Dim3 new_t;
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        new_t[i](j) = this->t[i][j] + that.t[i][j];
 
    return new_t;
  }
 
  /**In-place component-wise addition.
   * \f$ \vec{\vec{X}} = \vec{\vec{X}} + \vec{\vec{Y}} \f$*/
  TensorRank2Dim3& operator+=(const TensorRank2Dim3& that)
  {
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        this->t[i](j) += that.t[i][j];
 
    return *this;
  }
 
  //============================================= Subtraction
  /**Component-wise subtraction.
   * \f$ \vec{\vec{W}} = \vec{\vec{X}} - \vec{\vec{Y}} \f$*/
  TensorRank2Dim3 operator-(const TensorRank2Dim3& that) const
  {
    TensorRank2Dim3 new_t;
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        new_t[i](j) = this->t[i][j] - that.t[i][j];
 
    return new_t;
  }
 
  /**In-place component-wise subtraction.
   * \f$ \vec{\vec{X}} = \vec{\vec{X}} - \vec{\vec{Y}} \f$*/
  TensorRank2Dim3& operator-=(const TensorRank2Dim3& that)
  {
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        this->t[i](j) -= that.t[i][j];
 
    return *this;
  }
 
  //============================================= Multiplication
  /**Component-wise multiplication by scalar.
   * \f$ \vec{\vec{W}} = \vec{\vec{X}}\alpha \f$ */
  TensorRank2Dim3 operator*(const double value) const
  {
    TensorRank2Dim3 new_t;
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        new_t[i](j) = this->t[i][j]*value;
 
    return new_t;
  }
 
  /**In-place component-wise multiplication by scalar.
   *  \f$ \vec{\vec{X}} = \vec{\vec{X}}\alpha \f$*/
  TensorRank2Dim3& operator*=(const double value)
  {
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        this->t[i](j) *= value;
 
    return *this;
  }
 
  //============================================= Division
  /**Component-wise division by scalar.
   *  \f$ \vec{\vec{W}} = \vec{\vec{X}}\frac{1}{\alpha} \f$*/
  TensorRank2Dim3 operator/(const double value) const
  {
    TensorRank2Dim3 new_t;
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        new_t[i](j) = this->t[i][j]/value;
 
    return new_t;
  }
 
  /**In-place component-wise division by scalar.
   * \f$ \vec{\vec{X}} = \vec{\vec{X}}\frac{1}{\alpha} \f$*/
  TensorRank2Dim3& operator/=(const double value)
  {
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        this->t[i](j) /= value;
 
    return *this;
  }
 
  //============================================= Transpose
  /**Classical transpose of the tensor.
   * \f$ W_{ij} = T_{ji} \f$*/
  TensorRank2Dim3 Transpose()
  {
    TensorRank2Dim3 new_t;
    for (int i=0; i<3; ++i)
      for (int j=0; j<3; ++j)
        new_t[i](j) = this->t[j][i];
 
    return new_t;
  }
 
  //============================================= Tensor dot product
  //Defined in chi_mesh_utilities.cc
  Vector3 Dot(const chi_mesh::Vector3& v) const;
 
  //============================================= Get Diagonal
  //Defined in chi_mesh_utilities.cc
  chi_mesh::Vector3 Diag() const;
 
  /**Returns the sum of the diagonal. Sometimes useful to get
   * divergence of a vector given its gradient.*/
  double DiagSum() const
  {
    double val = 0.0;
    for (int i=0; i<3; ++i)
      val += t[i][i];
 
    return val;
  }
 
  //============================================= Printing
  /**Prints the vector to a string and then returns the string.*/
  std::string PrintS()
  {
    std::stringstream out;
    out << "[";
    for (int i=0;i<3;i++)
    {
      for (int j=0;j<3;j++)
      {
        out << t[i][j] << " ";
      }
      if (i!=2)
        out << "\n ";
      else
        out << "]";
    }
 
    return out.str();
  }
};
 
//The following functions are defined in chi_mesh_utilities.cc
//Left multiplcation by scalar
chi_mesh::TensorRank2Dim3
  operator*(const double value, const chi_mesh::TensorRank2Dim3& that);
 
#endif