libgmsh-dev 2.10.1+dfsg1-1ubuntu4 / usr / include / gmsh / STensor43.h

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// Gmsh - Copyright (C) 1997-2015 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
//
// Contributor(s):
//   Eric Bechet
//

#ifndef _STENSOR43_H_
#define _STENSOR43_H_

#include "STensor33.h"
#include "fullMatrix.h"
#include "Numeric.h"

// concrete class for general 3rd-order tensor in three-dimensional space

class STensor43 {
 protected:
  // 0000 0001 0002 0010 ... 2211 2212 2220 2221 2222
  double _val[81];
 public:
  inline int getIndex(int i, int j, int k, int l) const
  {
    static int _index[3][3][3][3] = {{{{0,1,2},{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},{60,61,62}},{{63,64,65},{66,67,68},{69,70,71}},{{72,73,74},{75,76,77},{78,79,80}}}};
    return _index[i][j][k][l];
  }
  STensor43(const STensor43& other)
  {
    for (int i = 0; i < 81; i++) _val[i] = other._val[i];
  }
  // default constructor, null tensor
  STensor43(const double v = 0.0)
  {
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        for (int k = 0; k < 3; k++)
          for (int l = 0; l < 3; l++)
            if ((i==k)&&(j==l))
              _val[getIndex(i, j, k, l)]=v;
            else
              _val[getIndex(i, j, k, l)]=0.0;
  }
  // Symmetric identity tensor
  STensor43(const double vik, const double vil)
  {
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        for (int k = 0; k < 3; k++)
          for (int l = 0; l < 3; l++)
          {
            _val[getIndex(i, j, k, l)]= 0.;
            if ((i==k)&&(j==l))
              _val[getIndex(i, j, k, l)]+=0.5*vik;
            if ((i==l)&&(j==k))
              _val[getIndex(i, j, k, l)]+=0.5*vil;
          }
  }
  inline double &operator()(int i, int j,int k, int l)
  {
    return _val[getIndex(i, j, k, l)];
  }
  inline double operator()(int i, int j, int k, int l) const
  {
    return _val[getIndex(i, j, k ,l)];
  }
  STensor43 operator + (const STensor43 &other) const
  {
    STensor43 res(*this);
    for (int i = 0; i < 81; i++) res._val[i] += other._val[i];
    return res;
  }
  STensor43& operator += (const STensor43 &other)
  {
    for (int i = 0; i < 81; i++) _val[i] += other._val[i];
    return *this;
  }
  STensor43& operator -= (const STensor43 &other)
  {
    for (int i = 0; i < 81; i++) _val[i] -= other._val[i];
    return *this;
  }
  STensor43& operator *= (const double &other)
  {
    for (int i = 0; i < 81; i++) _val[i] *= other;
    return *this;
  }
  STensor43 transpose (int n, int m) const
  {
    STensor43 ithis;
    if ((n==0 && m==1) || (n==1 && m==0))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(j,i,k,l);
      return ithis;
    }
    if ((n==0 && m==2) || (n==2 && m==0))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(k,j,i,l);
      return ithis;
    }
    if ((n==0 && m==3) || (n==3 && m==0))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(l,j,k,i);
      return ithis;
    }
    if ((n==1 && m==2) || (n==2 && m==1))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(i,k,j,l);
      return ithis;
    }
    if ((n==1 && m==3) || (n==3 && m==1))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(i,l,k,j);
      return ithis;
    }
    if ((n==2 && m==3) || (n==3 && m==2))
    {
      for (int i = 0; i < 3; i++)
        for (int j = 0; j < 3; j++)
          for (int k = 0; k < 3; k++)
            for (int l = 0; l < 3; l++)
              ithis(i,j,k,l) = (*this)(i,j,l,k);
      return ithis;
    }
    return ithis+=(*this);
  }
/*  STensor43& operator *= (const STensor43 &other)
  {
// to be implemented
    return *this;
  }*/
  void print(const char *) const;
  const double* data() const {return _val;}
  double* data() {return _val;}
};

// tensor product
inline void tensprod(const STensor3 &a, const STensor3 &b, STensor43 &c)
{
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        for (int k = 0; k < 3; k++)
          for (int l = 0; l < 3; l++)
            c(i,j,k,l)=a(i,j)*b(k,l);
}

inline void tensprod(const SVector3 &a, const STensor33 &b, STensor43 &c)
{
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        for (int k = 0; k < 3; k++)
          for (int l = 0; l < 3; l++)
            c(i,j,k,l)=a(i)*b(j,k,l);
}
inline void tensprod(const STensor33 &a, const SVector3 &b, STensor43 &c)
{
    for (int i = 0; i < 3; i++)
      for (int j = 0; j < 3; j++)
        for (int k = 0; k < 3; k++)
          for (int l = 0; l < 3; l++)
            c(i,j,k,l)=a(i,j,k)*b(l);
}

inline double dot(const STensor43 &a, const STensor43 &b)
{
  double prod=0;
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
      prod+=a(i,j,k,l)*b(i,j,k,l);
  return prod;
}

// full contracted product
inline STensor43 operator*(const STensor43 &t, double m)
{
  STensor43 val(t);
  val *= m;
  return val;
}
inline STensor43 operator*(double m,const STensor43 &t)
{
  STensor43 val(t);
  val *= m;
  return val;
}

inline STensor33 operator*(const STensor43 &t, const SVector3 &m)
{
  STensor33 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(i,j,k)+=t(i,j,k,l)*m(l);
  return val;
}
inline STensor33 operator*( const SVector3 &m , const STensor43 &t)
{
  STensor33 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(j,k,l)+=m(i)*t(i,j,k,l);
  return val;
}

inline STensor3 operator*(const STensor43 &t, const STensor3 &m)
{
  STensor3 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(i,j)+=t(i,j,k,l)*m(l,k);
  return val;
}
inline STensor3 operator*( const STensor3 &m , const STensor43 &t)
{
  STensor3 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(k,l)+=m(j,i)*t(i,j,k,l);
  return val;
}

inline SVector3 operator*(const STensor43 &t, const STensor33 &m)
{
  SVector3 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(i)+=t(i,j,k,l)*m(l,k,j);
  return val;
}
inline SVector3 operator*( const STensor33 &m , const STensor43 &t)
{
  SVector3 val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val(l)+=m(k,j,i)*t(i,j,k,l);
  return val;
}

inline double operator*( const STensor43 &m , const STensor43 &t)
{
  double val(0.);
  for (int i = 0; i < 3; i++)
    for (int j = 0; j < 3; j++)
      for (int k = 0; k < 3; k++)
        for (int l = 0; l < 3; l++)
          val+=m(i,j,k,l)*t(l,k,j,i);
  return val;
}

#endif

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