Provided by: librheolef-dev_6.6-1build2_amd64

#### NAME

```       tensor - a N*N tensor, N=1,2,3

```

#### SYNOPSYS

```       The  tensor  class  defines  a 3*3 tensor, as the value of a tensorial valued field. Basic
algebra with scalars, vectors of R^3  (i.e.  the  point  class)  and  tensor  objects  are
supported.

```

#### IMPLEMENTATION

```       template<class T>
class tensor_basic {
public:

typedef size_t size_type;
typedef T      element_type;
typedef T      float_type;

// allocators:

tensor_basic (const T& init_val = 0);
tensor_basic (T x[3][3]);
tensor_basic (const tensor_basic<T>& a);
static tensor_basic<T> eye (size_type d = 3);

#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
tensor_basic (const std::initializer_list<std::initializer_list<T> >& il);
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST

// affectation:

tensor_basic<T>& operator = (const tensor_basic<T>& a);
tensor_basic<T>& operator = (const T& val);

// modifiers:

void fill (const T& init_val);
void reset ();
void set_row    (const point_basic<T>& r, size_t i, size_t d = 3);
void set_column (const point_basic<T>& c, size_t j, size_t d = 3);

// accessors:

T& operator()(size_type i, size_type j);
const T& operator()(size_type i, size_type j) const;
point_basic<T>  row(size_type i) const;
point_basic<T>  col(size_type i) const;
size_t nrow() const; // = 3, for template matrix compatibility
size_t ncol() const;

// inputs/outputs:

std::ostream& put (std::ostream& s, size_type d = 3) const;
std::istream& get (std::istream&);

// algebra:

bool operator== (const tensor_basic<T>&) const;
bool operator!= (const tensor_basic<T>& b) const { return ! operator== (b); }
point_basic<T>  trans_mult (const point_basic<T>& x) const;

// metric and geometric transformations:

template <class U>
friend U ddot (const tensor_basic<U>&, const tensor_basic<U>&);
T determinant (size_type d = 3) const;

// spectral:
// eigenvalues & eigenvectors:
// a = q*d*q^T
// a may be symmetric
// where q=(q1,q2,q3) are eigenvectors in rows (othonormal matrix)
// and   d=(d1,d2,d3) are eigenvalues, sorted in decreasing order d1 >= d2 >= d3
// return d
point_basic<T> eig (tensor_basic<T>& q, size_t dim = 3) const;
point_basic<T> eig (size_t dim = 3) const;

// singular value decomposition:
// a = u*s*v^T
// a can be unsymmetric
// where u=(u1,u2,u3) are left pseudo-eigenvectors in rows (othonormal matrix)
//       v=(v1,v2,v3) are right pseudo-eigenvectors in rows (othonormal matrix)
// and   s=(s1,s2,s3) are eigenvalues, sorted in decreasing order s1 >= s2 >= s3
// return s
point_basic<T> svd (tensor_basic<T>& u, tensor_basic<T>& v, size_t dim = 3) const;

// data:
T _x[3][3];
};
typedef tensor_basic<Float> tensor;

// algebra (cont.)

template <class U>
tensor_basic<U> operator- (const tensor_basic<U>&);
template <class U>
tensor_basic<U> operator+ (const tensor_basic<U>&, const tensor_basic<U>&);
template <class U>
tensor_basic<U> operator- (const tensor_basic<U>&, const tensor_basic<U>&);
template <class U>
tensor_basic<U> operator* (const U& k, const tensor_basic<U>& a);
template <class U>
tensor_basic<U> operator* (const tensor_basic<U>& a, const U& k);
template <class U>
tensor_basic<U> operator/ (const tensor_basic<U>& a, const U& k);
template <class U>
point_basic<U>  operator* (const tensor_basic<U>&, const point_basic<U>&);
template <class U>
point_basic<U>  operator* (const point_basic<U>& yt, const tensor_basic<U>& a);
template <class U>
tensor_basic<U> operator* (const tensor_basic<U>& a, const tensor_basic<U>& b);
template <class U>
tensor_basic<U> trans (const tensor_basic<U>& a, size_t d = 3);
template <class U>
void prod (const tensor_basic<U>& a, const tensor_basic<U>& b, tensor_basic<U>& result,
size_t di=3, size_t dj=3, size_t dk=3);
// tr(a) = a00 + a11 + a22
template <class U>
U tr (const tensor_basic<U>& a, size_t d=3);
// a = u otimes v <==> aij = ui*vj
template <class U>
tensor_basic<U> otimes (const point_basic<U>& u, const point_basic<U>& v, size_t d=3);
template <class U>
tensor_basic<U> inv  (const tensor_basic<U>& a, size_t d = 3);
template <class U>
tensor_basic<U> diag (const point_basic<U>& d);
template <class U>
point_basic<U> diag (const tensor_basic<U>& a);
template <class U>
U determinant (const tensor_basic<U>& A, size_t d = 3);
template <class U>
bool invert_3x3 (const tensor_basic<U>& A, tensor_basic<U>& result);

// nonlinear algebra:
template<class T>
tensor_basic<T> exp (const tensor_basic<T>& a, size_t d = 3);

// inputs/outputs:
template<class T>
inline
std::istream& operator>> (std::istream& in, tensor_basic<T>& a)
{
return a.get (in);
}
template<class T>
inline
std::ostream& operator<< (std::ostream& out, const tensor_basic<T>& a)
{
return a.put (out);
}
// t += a otimes b
template<class T>
void cumul_otimes (tensor_basic<T>& t, const point_basic<T>& a, const point_basic<T>& b, size_t na = 3);
template<class T>
void cumul_otimes (tensor_basic<T>& t, const point_basic<T>& a, const point_basic<T>& b, size_t na, size_t nb);
```