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//=============================================================================

/*! calculate inverse */

inline dgemat1 inv(const dgemat1& A)

{CPPL_VERBOSE_REPORT;

  dgemat1 Ainv;

  Ainv(0,0) =1./A(0,0);

  return Ainv;

}



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//=============================================================================

/*! calculate determinant */

inline double det(const dgemat2& A)

{CPPL_VERBOSE_REPORT;

  return A(0,0)*A(1,1)-A(0,1)*A(1,0);

}



//=============================================================================

/*! calculate inverse */

inline dgemat2 inv(const dgemat2& A)

{CPPL_VERBOSE_REPORT;

  const double Adet( det(A) );

  dgemat2 Ainv;

  Ainv(0,0)= A(1,1)/Adet;  Ainv(0,1)=-A(0,1)/Adet;

  Ainv(1,0)=-A(1,0)/Adet;  Ainv(1,1)= A(0,0)/Adet;

  return Ainv;

}



//=============================================================================

/*! return rotated tensor */

inline dgemat2 rotate(const dgemat2& m, const double& theta)

{CPPL_VERBOSE_REPORT;

  //dgemat2 R(t2m(theta)); return R*m*t(R);//too slow

  double c(std::cos(theta)), s(std::sin(theta));

  double cc(c*c), cs(c*s), ss(s*s);

  dgemat2 mat;

  mat(0,0) =m(0,0)*cc -(m(0,1)+m(1,0))*cs +m(1,1)*ss;

  mat(0,1) =m(0,1)*cc +(m(0,0)-m(1,1))*cs -m(1,0)*ss;

  mat(1,0) =m(1,0)*cc +(m(0,0)-m(1,1))*cs -m(0,1)*ss;

  mat(1,1) =m(1,1)*cc +(m(0,1)+m(1,0))*cs +m(0,0)*ss;

  return mat;

}



//=============================================================================

/*! convert theta to 2x2 rotational matrix */

inline dgemat2 t2m(const double& theta)

{CPPL_VERBOSE_REPORT;

  dgemat2 R;

  R(0,0)=std::cos(theta); R(0,1)=-std::sin(theta);

  R(1,0)=std::sin(theta); R(1,1)= std::cos(theta);

  return R;

}



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///////////////////////////////////////////////////////////////////////////////



//=============================================================================

/*! calculate determinant */

inline double det(const dgemat3& A)

{CPPL_VERBOSE_REPORT;

  return

    +A(0,0)*A(1,1)*A(2,2) -A(0,0)*A(1,2)*A(2,1)

    +A(0,1)*A(1,2)*A(2,0) -A(0,1)*A(1,0)*A(2,2)

    +A(0,2)*A(1,0)*A(2,1) -A(0,2)*A(1,1)*A(2,0);

}



//=============================================================================

/*! calculate the 2nd invariant */

inline double II(const dgemat3& A)

{CPPL_VERBOSE_REPORT;

  return

    +A(0,0)*A(1,1) +A(1,1)*A(2,2) +A(2,2)*A(0,0)

    -A(0,1)*A(1,0) -A(1,2)*A(2,1) -A(2,0)*A(0,2);

}



//=============================================================================

/*! calculate inverse */

inline dgemat3 inv(const dgemat3& A)

{CPPL_VERBOSE_REPORT;

  const double Adet( det(A) );

  dgemat3 Ainv;

  Ainv(0,0) =(A(1,1)*A(2,2)-A(1,2)*A(2,1))/Adet;

  Ainv(0,1) =(A(0,2)*A(2,1)-A(0,1)*A(2,2))/Adet;

  Ainv(0,2) =(A(0,1)*A(1,2)-A(0,2)*A(1,1))/Adet;

  Ainv(1,0) =(A(1,2)*A(2,0)-A(1,0)*A(2,2))/Adet;

  Ainv(1,1) =(A(0,0)*A(2,2)-A(0,2)*A(2,0))/Adet;

  Ainv(1,2) =(A(0,2)*A(1,0)-A(0,0)*A(1,2))/Adet;

  Ainv(2,0) =(A(1,0)*A(2,1)-A(1,1)*A(2,0))/Adet;

  Ainv(2,1) =(A(0,1)*A(2,0)-A(0,0)*A(2,1))/Adet;

  Ainv(2,2) =(A(0,0)*A(1,1)-A(0,1)*A(1,0))/Adet;

  return Ainv;

}



//=============================================================================

/*! rotate 3D matrix by quaternion */

inline dgemat3 rotate(const dgemat3& m, const dquater& q)

{CPPL_VERBOSE_REPORT;

  dgemat3 R(q2m(q));

  return R*m*t(R);

}



//=============================================================================

/*! convert 3D rotational matrix to quaternion */

inline dquater m2q(const dgemat3& m)

{CPPL_VERBOSE_REPORT;

  dcovec3 v( m(2,1)-m(1,2), m(0,2)-m(2,0), m(1,0)-m(0,1) );

  double t( std::acos(0.5*(m(0,0)+m(1,1)+m(2,2)-1.)) );

  return vt2q(v,t);

}



///////////////////////////////////////////////////////////////////////////////

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//=============================================================================

/*! calculate determinant */

inline double det(const dgemat4& A)

{CPPL_VERBOSE_REPORT;

  return

    ((A(0,0)*A(1,1)-A(0,1)*A(1,0))*A(2,2)+(A(0,2)*A(1,0)-A(0,0)*A(1,2))*A(2,1)+(A(0,1)*A(1,2)-A(0,2)*A(1,1))*A(2,0))*A(3,3)

    +((A(0,1)*A(1,0)-A(0,0)*A(1,1))*A(2,3)+(A(0,0)*A(1,3)-A(0,3)*A(1,0))*A(2,1)+(A(0,3)*A(1,1)-A(0,1)*A(1,3))*A(2,0))*A(3,2)

    +((A(0,0)*A(1,2)-A(0,2)*A(1,0))*A(2,3)+(A(0,3)*A(1,0)-A(0,0)*A(1,3))*A(2,2)+(A(0,2)*A(1,3)-A(0,3)*A(1,2))*A(2,0))*A(3,1)

    +((A(0,2)*A(1,1)-A(0,1)*A(1,2))*A(2,3)+(A(0,1)*A(1,3)-A(0,3)*A(1,1))*A(2,2)+(A(0,3)*A(1,2)-A(0,2)*A(1,3))*A(2,1))*A(3,0);

}



//=============================================================================

/*! calculate inverse */

inline dgemat4 inv(const dgemat4& A)

{CPPL_VERBOSE_REPORT;

  const double Adet =det(A);

  

  dgemat4 Ainv;

  Ainv(0,0) =(A(1,1)*A(2,2)-A(1,2)*A(2,1))*A(3,3)+(A(1,3)*A(2,1)-A(1,1)*A(2,3))*A(3,2)+(A(1,2)*A(2,3)-A(1,3)*A(2,2))*A(3,1);

  Ainv(0,1) =(A(0,2)*A(2,1)-A(0,1)*A(2,2))*A(3,3)+(A(0,1)*A(2,3)-A(0,3)*A(2,1))*A(3,2)+(A(0,3)*A(2,2)-A(0,2)*A(2,3))*A(3,1);

  Ainv(0,2) =(A(0,1)*A(1,2)-A(0,2)*A(1,1))*A(3,3)+(A(0,3)*A(1,1)-A(0,1)*A(1,3))*A(3,2)+(A(0,2)*A(1,3)-A(0,3)*A(1,2))*A(3,1);

  Ainv(0,3) =(A(0,2)*A(1,1)-A(0,1)*A(1,2))*A(2,3)+(A(0,1)*A(1,3)-A(0,3)*A(1,1))*A(2,2)+(A(0,3)*A(1,2)-A(0,2)*A(1,3))*A(2,1);

  Ainv(1,0) =(A(1,2)*A(2,0)-A(1,0)*A(2,2))*A(3,3)+(A(1,0)*A(2,3)-A(1,3)*A(2,0))*A(3,2)+(A(1,3)*A(2,2)-A(1,2)*A(2,3))*A(3,0);

  Ainv(1,1) =(A(0,0)*A(2,2)-A(0,2)*A(2,0))*A(3,3)+(A(0,3)*A(2,0)-A(0,0)*A(2,3))*A(3,2)+(A(0,2)*A(2,3)-A(0,3)*A(2,2))*A(3,0);

  Ainv(1,2) =(A(0,2)*A(1,0)-A(0,0)*A(1,2))*A(3,3)+(A(0,0)*A(1,3)-A(0,3)*A(1,0))*A(3,2)+(A(0,3)*A(1,2)-A(0,2)*A(1,3))*A(3,0);

  Ainv(1,3) =(A(0,0)*A(1,2)-A(0,2)*A(1,0))*A(2,3)+(A(0,3)*A(1,0)-A(0,0)*A(1,3))*A(2,2)+(A(0,2)*A(1,3)-A(0,3)*A(1,2))*A(2,0);

  Ainv(2,0) =(A(1,0)*A(2,1)-A(1,1)*A(2,0))*A(3,3)+(A(1,3)*A(2,0)-A(1,0)*A(2,3))*A(3,1)+(A(1,1)*A(2,3)-A(1,3)*A(2,1))*A(3,0);

  Ainv(2,1) =(A(0,1)*A(2,0)-A(0,0)*A(2,1))*A(3,3)+(A(0,0)*A(2,3)-A(0,3)*A(2,0))*A(3,1)+(A(0,3)*A(2,1)-A(0,1)*A(2,3))*A(3,0);

  Ainv(2,2) =(A(0,0)*A(1,1)-A(0,1)*A(1,0))*A(3,3)+(A(0,3)*A(1,0)-A(0,0)*A(1,3))*A(3,1)+(A(0,1)*A(1,3)-A(0,3)*A(1,1))*A(3,0);

  Ainv(2,3) =(A(0,1)*A(1,0)-A(0,0)*A(1,1))*A(2,3)+(A(0,0)*A(1,3)-A(0,3)*A(1,0))*A(2,1)+(A(0,3)*A(1,1)-A(0,1)*A(1,3))*A(2,0);

  Ainv(3,0) =(A(1,1)*A(2,0)-A(1,0)*A(2,1))*A(3,2)+(A(1,0)*A(2,2)-A(1,2)*A(2,0))*A(3,1)+(A(1,2)*A(2,1)-A(1,1)*A(2,2))*A(3,0);

  Ainv(3,1) =(A(0,0)*A(2,1)-A(0,1)*A(2,0))*A(3,2)+(A(0,2)*A(2,0)-A(0,0)*A(2,2))*A(3,1)+(A(0,1)*A(2,2)-A(0,2)*A(2,1))*A(3,0);

  Ainv(3,2) =(A(0,1)*A(1,0)-A(0,0)*A(1,1))*A(3,2)+(A(0,0)*A(1,2)-A(0,2)*A(1,0))*A(3,1)+(A(0,2)*A(1,1)-A(0,1)*A(1,2))*A(3,0);

  Ainv(3,3) =(A(0,0)*A(1,1)-A(0,1)*A(1,0))*A(2,2)+(A(0,2)*A(1,0)-A(0,0)*A(1,2))*A(2,1)+(A(0,1)*A(1,2)-A(0,2)*A(1,1))*A(2,0);

  

  Ainv /=Adet;

  return Ainv;

}
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