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About template constraints
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tensor(2rheolef) rheolef-6.1 tensor(2rheolef) 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; // allocators: tensor_basic (const T& init_val = 0); tensor_basic (T x[3][3]); tensor_basic (const tensor_basic<T>& a); // 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); 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); } template <class U> friend tensor_basic<U> operator- (const tensor_basic<U>&); template <class U> friend tensor_basic<U> operator+ (const tensor_basic<U>&, const tensor_basic<U>&); template <class U> friend tensor_basic<U> operator- (const tensor_basic<U>&, const tensor_basic<U>&); template <class U> friend tensor_basic<U> operator* (int k, const tensor_basic<U>& a); template <class U> friend tensor_basic<U> operator* (const U& k, const tensor_basic<U>& a); template <class U> friend tensor_basic<U> operator* (const tensor_basic<U>& a, int k); template <class U> friend tensor_basic<U> operator* (const tensor_basic<U>& a, const U& k); template <class U> friend tensor_basic<U> operator/ (const tensor_basic<U>& a, int k); template <class U> friend tensor_basic<U> operator/ (const tensor_basic<U>& a, const U& k); template <class U> friend point_basic<U> operator* (const tensor_basic<U>&, const point_basic<U>&); template <class U> friend point_basic<U> operator* (const point_basic<U>& yt, const tensor_basic<U>& a); point_basic<T> trans_mult (const point_basic<T>& x) const; template <class U> friend tensor_basic<U> trans (const tensor_basic<U>& a, size_t d = 3); template <class U> friend tensor_basic<U> operator* (const tensor_basic<U>& a, const tensor_basic<U>& b); template <class U> friend 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); template <class U> friend tensor_basic<U> inv (const tensor_basic<U>& a, size_t d = 3); template <class U> friend tensor_basic<U> diag (const point_basic<U>& d); template <class U> friend tensor_basic<U> identity (size_t d=3); template <class U> friend tensor_basic<U> dyadic (const point_basic<U>& u, const point_basic<U>& v, size_t d=3); // metric and geometric transformations: template <class U> friend U dotdot (const tensor_basic<U>&, const tensor_basic<U>&); template <class U> friend U norm2 (const tensor_basic<U>& a) { return dotdot(a,a); } template <class U> friend U dist2 (const tensor_basic<U>& a, const tensor_basic<U>& b) { return norm2(a-b); } template <class U> friend U norm (const tensor_basic<U>& a) { return ::sqrt(norm2(a)); } template <class U> friend U dist (const tensor_basic<U>& a, const tensor_basic<U>& b) { return norm(a-b); } T determinant (size_type d = 3) const; template <class U> friend U determinant (const tensor_basic<U>& A, size_t d = 3); template <class U> friend bool invert_3x3 (const tensor_basic<U>& A, tensor_basic<U>& result); // 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; // 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> tensor_basic<T> otimes (const point_basic<T>& a, const point_basic<T>& b, size_t na = 3); // 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); rheolef-6.1 rheolef-6.1 tensor(2rheolef)
