
Public Types | |
| typedef Tensor< rank_-1, dim, Number > | value_type |
| typedef numbers::NumberTraits < Number >::real_type | real_type |
| typedef Tensor< rank_-1, dim, Number >::array_type | array_type [dim] |
Public Member Functions | |
| Tensor () | |
| Tensor (const array_type &initializer) | |
| Tensor (const Tensor< 1, dim, Tensor< rank_-1, dim, Number > > &tensor_in) | |
| operator Tensor< 1, dim, Tensor< rank_-1, dim, Number > > () const | |
| Tensor< rank_-1, dim, Number > & | operator[] (const unsigned int i) |
| const Tensor< rank_-1, dim, Number > & | operator[] (const unsigned int i) const |
| Tensor & | operator= (const Tensor< rank_, dim, Number > &) |
| Tensor< rank_, dim, Number > & | operator= (const Number d) |
| bool | operator== (const Tensor< rank_, dim, Number > &) const |
| bool | operator!= (const Tensor< rank_, dim, Number > &) const |
| Tensor< rank_, dim, Number > & | operator+= (const Tensor< rank_, dim, Number > &) |
| Tensor< rank_, dim, Number > & | operator-= (const Tensor< rank_, dim, Number > &) |
| Tensor< rank_, dim, Number > & | operator*= (const Number factor) |
| Tensor< rank_, dim, Number > & | operator/= (const Number factor) |
| Tensor< rank_, dim, Number > | operator+ (const Tensor< rank_, dim, Number > &) const |
| Tensor< rank_, dim, Number > | operator- (const Tensor< rank_, dim, Number > &) const |
| Tensor< rank_, dim, Number > | operator- () const |
| real_type | norm () const |
| real_type | norm_square () const |
| template<typename Number2 > | |
| void | unroll (Vector< Number2 > &result) const |
| void | clear () |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
| static std::size_t | memory_consumption () |
| ::ExceptionBase & | ExcInvalidTensorIndex (int arg1) throw (errortext << "Invalid tensor index " << arg1 ) |
Static Public Attributes | |
| static const unsigned int | dimension = dim |
| static const unsigned int | rank = rank_ |
Private Member Functions | |
| template<typename Number2 > | |
| void | unroll_recursion (Vector< Number2 > &result, unsigned int &start_index) const |
Private Attributes | |
| Tensor< rank_-1, dim, Number > | subtensor [dim] |
Friends | |
| class | Tensor |
Related Functions | |
(Note that these are not member functions.) | |
| template<int rank_, int dim, typename Number > | |
| std::ostream & | operator<< (std::ostream &out, const Tensor< rank_, dim, Number > &p) |
| template<int dim, typename Number > | |
| Number | contract (const Tensor< 1, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Number | operator* (const Tensor< 1, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 1, dim, Number > &dest, const Tensor< 2, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Tensor< 1, dim, Number > | operator* (const Tensor< 2, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 1, dim, Number > &dest, const Tensor< 1, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Tensor< 1, dim, Number > | operator* (const Tensor< 1, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 2, dim, Number > &dest, const Tensor< 2, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Tensor< 2, dim, Number > | operator* (const Tensor< 2, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 2, dim, Number > &dest, const Tensor< 2, dim, Number > &src1, const unsigned int index1, const Tensor< 2, dim, Number > &src2, const unsigned int index2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 2, dim, Number > &dest, const Tensor< 3, dim, Number > &src1, const unsigned int index1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 3, dim, Number > &dest, const Tensor< 3, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 3, dim, Number > &dest, const Tensor< 3, dim, Number > &src1, const unsigned int index1, const Tensor< 2, dim, Number > &src2, const unsigned int index2) |
| template<int dim, typename Number > | |
| Tensor< 3, dim, Number > | operator* (const Tensor< 3, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | contract (Tensor< 3, dim, Number > &dest, const Tensor< 2, dim, Number > &src1, const Tensor< 3, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Tensor< 3, dim, Number > | operator* (const Tensor< 2, dim, Number > &src1, const Tensor< 3, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Tensor< 4, dim, Number > | operator* (const Tensor< 3, dim, Number > &src1, const Tensor< 3, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | double_contract (Tensor< 2, dim, Number > &dest, const Tensor< 4, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Number | contract3 (const Tensor< 1, dim, Number > &u, const Tensor< 2, dim, Number > &A, const Tensor< 1, dim, Number > &v) |
| template<int dim, typename Number > | |
| Number | contract3 (const Tensor< 1, dim, Number > &t1, const Tensor< 3, dim, Number > &t2, const Tensor< 2, dim, Number > &t3) |
| template<int dim, typename Number > | |
| Number | contract3 (const Tensor< 2, dim, Number > &t1, const Tensor< 3, dim, Number > &t2, const Tensor< 1, dim, Number > &t3) |
| template<int dim, typename Number > | |
| Number | contract3 (const Tensor< 2, dim, Number > &t1, const Tensor< 4, dim, Number > &t2, const Tensor< 2, dim, Number > &t3) |
| template<int dim, typename Number > | |
| void | outer_product (Tensor< 2, dim, Number > &dst, const Tensor< 1, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | outer_product (Tensor< 3, dim, Number > &dst, const Tensor< 1, dim, Number > &src1, const Tensor< 2, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | outer_product (Tensor< 3, dim, Number > &dst, const Tensor< 2, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | outer_product (Tensor< 1, dim, Number > &dst, const Number src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| void | outer_product (Tensor< 1, dim, Number > &dst, const Tensor< 1, dim, Number > src1, const Number src2) |
| template<int dim, typename Number > | |
| void | cross_product (Tensor< 1, dim, Number > &dst, const Tensor< 1, dim, Number > &src) |
| template<int dim, typename Number > | |
| void | cross_product (Tensor< 1, dim, Number > &dst, const Tensor< 1, dim, Number > &src1, const Tensor< 1, dim, Number > &src2) |
| template<int dim, typename Number > | |
| Number | scalar_product (const Tensor< 2, dim, Number > &t1, const Tensor< 2, dim, Number > &t2) |
| template<int rank, typename Number > | |
| Number | determinant (const Tensor< rank, 1, Number > &t) |
| template<typename Number > | |
| Number | determinant (const Tensor< 1, 1, Number > &t) |
| template<typename Number > | |
| Number | determinant (const Tensor< 2, 1, Number > &t) |
| template<typename Number > | |
| Number | determinant (const Tensor< 2, 2, Number > &t) |
| template<typename Number > | |
| Number | determinant (const Tensor< 2, 3, Number > &t) |
| template<int dim, typename Number > | |
| Number | determinant (const Tensor< 2, dim, Number > &t) |
| template<int dim, typename Number > | |
| Number | trace (const Tensor< 2, dim, Number > &d) |
| template<int dim, typename Number > | |
| Tensor< 2, dim, Number > | invert (const Tensor< 2, dim, Number > &t) |
| template<int dim, typename Number > | |
| Tensor< 2, dim, Number > | transpose (const Tensor< 2, dim, Number > &t) |
| template<int rank, int dim, typename Number > | |
| Tensor< rank, dim, Number > | operator* (const Tensor< rank, dim, Number > &t, const Number factor) |
| template<int rank, int dim, typename Number > | |
| Tensor< rank, dim, Number > | operator* (const Number factor, const Tensor< rank, dim, Number > &t) |
| template<int rank, int dim, typename Number > | |
| Tensor< rank, dim, Number > | operator/ (const Tensor< rank, dim, Number > &t, const Number factor) |
| template<int rank, int dim> | |
| Tensor< rank, dim > | operator* (const Tensor< rank, dim > &t, const double factor) |
| template<int rank, int dim> | |
| Tensor< rank, dim > | operator* (const double factor, const Tensor< rank, dim > &t) |
| template<int rank, int dim> | |
| Tensor< rank, dim > | operator/ (const Tensor< rank, dim > &t, const double factor) |
| template<int dim, typename Number > | |
| std::ostream & | operator<< (std::ostream &out, const Tensor< 0, dim, Number > &p) |
| template<int dim, typename Number > | |
| std::ostream & | operator<< (std::ostream &out, const Tensor< 1, dim, Number > &p) |
| std::ostream & | operator<< (std::ostream &out, const Tensor< 1, 1, double > &p) |
| template<int dim, typename Number > | |
| Tensor< 1, dim, Number > | operator* (const Tensor< 1, dim, Number > &t, const Number factor) |
| template<int dim, typename Number > | |
| Tensor< 1, dim, Number > | operator* (const Number factor, const Tensor< 1, dim, Number > &t) |
| template<int dim, typename Number > | |
| Tensor< 1, dim, Number > | operator/ (const Tensor< 1, dim, Number > &t, const Number factor) |
| template<int dim> | |
| Tensor< 1, dim > | operator* (const Tensor< 1, dim > &t, const double factor) |
| template<int dim> | |
| Tensor< 1, dim > | operator* (const double factor, const Tensor< 1, dim > &t) |
| template<int dim> | |
| Tensor< 1, dim > | operator/ (const Tensor< 1, dim > &t, const double factor) |
Provide a general tensor class with an arbitrary rank, i.e. with an arbitrary number of indices. The Tensor class provides an indexing operator and a bit of infrastructure, but most functionality is recursively handed down to tensors of rank 1 or put into external templated functions, e.g. the contract family.
Using this tensor class for objects of rank 2 has advantages over matrices in many cases since the dimension is known to the compiler as well as the location of the data. It is therefore possible to produce far more efficient code than for matrices with runtime-dependent dimension.
This class provides an optional template argument for the type of the underlying data. It defaults to double values. It can be used to base tensors on float or complex numbers or any other data type that implements basic arithmetic operations.
Definition at line 46 of file tensor.h.
| typedef Tensor<rank_-1,dim,Number> Tensor< rank_, dim, Number >::value_type |
| typedef numbers::NumberTraits<Number>::real_type Tensor< rank_, dim, Number >::real_type |
Declare a type that has holds real-valued numbers with the same precision as the template argument to this class. For std::complex<number>, this corresponds to type number, and it is equal to Number for all other cases. See also the respective field in Vector<Number>.
This typedef is used to represent the return type of norms.
| typedef Tensor<rank_-1,dim,Number>::array_type Tensor< rank_, dim, Number >::array_type[dim] |
Constructor. Initialize all entries to zero.
| Tensor< rank_, dim, Number >::Tensor | ( | const array_type & | initializer ) |
Copy constructor, where the data is copied from a C-style array.
| Tensor< rank_, dim, Number >::Tensor | ( | const Tensor< 1, dim, Tensor< rank_-1, dim, Number > > & | tensor_in ) |
Conversion operator from tensor of tensors.
| Tensor< rank_, dim, Number >::operator Tensor< 1, dim, Tensor< rank_-1, dim, Number > > | ( | ) | const |
Conversion operator to tensor of tensors.
| Tensor<rank_-1,dim,Number>& Tensor< rank_, dim, Number >::operator[] | ( | const unsigned int | i ) |
Read-Write access operator.
| const Tensor<rank_-1,dim,Number>& Tensor< rank_, dim, Number >::operator[] | ( | const unsigned int | i ) | const |
Read-only access operator.
| Tensor& Tensor< rank_, dim, Number >::operator= | ( | const Tensor< rank_, dim, Number > & | ) |
Assignment operator.
| Tensor<rank_,dim,Number>& Tensor< rank_, dim, Number >::operator= | ( | const Number | d ) |
This operator assigns a scalar to a tensor. To avoid confusion with what exactly it means to assign a scalar value to a tensor, zero is the only value allowed for d, allowing the intuitive notation t=0 to reset all elements of the tensor to zero.
| bool Tensor< rank_, dim, Number >::operator== | ( | const Tensor< rank_, dim, Number > & | ) | const |
Test for equality of two tensors.
| bool Tensor< rank_, dim, Number >::operator!= | ( | const Tensor< rank_, dim, Number > & | ) | const |
Test for inequality of two tensors.
| Tensor<rank_,dim,Number>& Tensor< rank_, dim, Number >::operator+= | ( | const Tensor< rank_, dim, Number > & | ) |
Add another tensor.
| Tensor<rank_,dim,Number>& Tensor< rank_, dim, Number >::operator-= | ( | const Tensor< rank_, dim, Number > & | ) |
Subtract another tensor.
| Tensor<rank_,dim,Number>& Tensor< rank_, dim, Number >::operator*= | ( | const Number | factor ) |
Scale the tensor by factor, i.e. multiply all components by factor.
| Tensor<rank_,dim,Number>& Tensor< rank_, dim, Number >::operator/= | ( | const Number | factor ) |
Scale the vector by 1/factor.
| Tensor<rank_,dim,Number> Tensor< rank_, dim, Number >::operator+ | ( | const Tensor< rank_, dim, Number > & | ) | const |
Add two tensors. If possible, you should use operator += instead since this does not need the creation of a temporary.
| Tensor<rank_,dim,Number> Tensor< rank_, dim, Number >::operator- | ( | const Tensor< rank_, dim, Number > & | ) | const |
Subtract two tensors. If possible, you should use operator -= instead since this does not need the creation of a temporary.
| Tensor<rank_,dim,Number> Tensor< rank_, dim, Number >::operator- | ( | ) | const |
Unary minus operator. Negate all entries of a tensor.
| real_type Tensor< rank_, dim, Number >::norm | ( | ) | const |
Return the Frobenius-norm of a tensor, i.e. the square root of the sum of squares of all entries.
| real_type Tensor< rank_, dim, Number >::norm_square | ( | ) | const |
Return the square of the Frobenius-norm of a tensor, i.e. the square root of the sum of squares of all entries.
This function mainly exists because it makes computing the norm simpler recursively, but may also be useful in other contexts.
| void Tensor< rank_, dim, Number >::unroll | ( | Vector< Number2 > & | result ) | const |
Fill a vector with all tensor elements.
This function unrolls all tensor entries into a single, linearly numbered vector. As usual in C++, the rightmost index of the tensor marches fastest.
| void Tensor< rank_, dim, Number >::clear | ( | ) |
Reset all values to zero.
Note that this is partly inconsistent with the semantics of the clear() member functions of the STL and of several other classes within deal.II which not only reset the values of stored elements to zero, but release all memory and return the object into a virginial state. However, since the size of objects of the present type is determined by its template parameters, resizing is not an option, and indeed the state where all elements have a zero value is the state right after construction of such an object.
Referenced by Tensor< rank_, dim, Number >::contract(), and Tensor< rank_, dim, Number >::double_contract().
| static std::size_t Tensor< rank_, dim, Number >::memory_consumption | ( | ) | [static] |
Determine an estimate for the memory consumption (in bytes) of this object.
| ::ExceptionBase& Tensor< rank_, dim, Number >::ExcInvalidTensorIndex | ( | int | arg1 ) | throw (errortext << "Invalid tensor index " << arg1 ) [static] |
Exception.
| void Tensor< rank_, dim, Number >::serialize | ( | Archive & | ar, |
| const unsigned int | version | ||
| ) |
Read or write the data of this object to or from a stream for the purpose of serialization
| void Tensor< rank_, dim, Number >::unroll_recursion | ( | Vector< Number2 > & | result, |
| unsigned int & | start_index | ||
| ) | const [private] |
Help function for unroll.
friend class Tensor [friend] |
| std::ostream & operator<< | ( | std::ostream & | out, |
| const Tensor< rank_, dim, Number > & | p | ||
| ) | [related] |
| Number contract | ( | const Tensor< 1, dim, Number > & | src1, |
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Contract a tensor of rank 1 with a tensor of rank 1. The result is sum_j src1[j] src2[j].
Definition at line 656 of file tensor.h.
Referenced by Tensor< rank_, dim, Number >::operator*().
| Number operator* | ( | const Tensor< 1, dim, Number > & | src1, |
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
Definition at line 686 of file tensor.h.
References Tensor< rank_, dim, Number >::contract().
| Tensor< 1, dim, Number > operator* | ( | const Tensor< 2, dim, Number > & | src1, |
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
| Tensor< 1, dim, Number > operator* | ( | const Tensor< 1, dim, Number > & | src1, |
| const Tensor< 2, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
| Tensor< 2, dim, Number > operator* | ( | const Tensor< 2, dim, Number > & | src1, |
| const Tensor< 2, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
| void contract | ( | Tensor< 2, dim, Number > & | dest, |
| const Tensor< 2, dim, Number > & | src1, | ||
| const unsigned int | index1, | ||
| const Tensor< 2, dim, Number > & | src2, | ||
| const unsigned int | index2 | ||
| ) | [related] |
Contract a tensor of rank 2 with a tensor of rank 2. The contraction is performed over index index1 of the first tensor, and index2 of the second tensor. Thus, if index1==2, index2==1, the result is the usual contraction, but if for example index1==1, index2==2, then the result is dest[i][k] = sum_j src1[j][i] src2[k][j].
Note that the number of the index is counted from 1 on, not from zero as usual.
Definition at line 873 of file tensor.h.
References Assert, and Tensor< rank_, dim, Number >::clear().
| void contract | ( | Tensor< 2, dim, Number > & | dest, |
| const Tensor< 3, dim, Number > & | src1, | ||
| const unsigned int | index1, | ||
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Contract a tensor of rank 3 with a tensor of rank 1. The contraction is performed over index index1 of the first tensor.
Note that the number of the index is counted from 1 on, not from zero as usual.
Definition at line 943 of file tensor.h.
References Assert, and Tensor< rank_, dim, Number >::clear().
| void contract | ( | Tensor< 3, dim, Number > & | dest, |
| const Tensor< 3, dim, Number > & | src1, | ||
| const Tensor< 2, dim, Number > & | src2 | ||
| ) | [related] |
Contract a tensor of rank 3 with a tensor of rank 2. The result is dest[i][j][l] = sum_k src1[i][j][k] src2[k][l].
Definition at line 988 of file tensor.h.
References Tensor< rank_, dim, Number >::clear().
| void contract | ( | Tensor< 3, dim, Number > & | dest, |
| const Tensor< 3, dim, Number > & | src1, | ||
| const unsigned int | index1, | ||
| const Tensor< 2, dim, Number > & | src2, | ||
| const unsigned int | index2 | ||
| ) | [related] |
Contract a tensor of rank 3 with a tensor of rank 2. The contraction is performed over index index1 of the first tensor, and index2 of the second tensor. Thus, if index1==3, index2==1, the result is the usual contraction, but if for example index1==1, index2==2, then the result is dest[i][j][k] = sum_l src1[l][i][j] src2[k][l].
Note that the number of the index is counted from 1 on, not from zero as usual.
Definition at line 1016 of file tensor.h.
References Assert, and Tensor< rank_, dim, Number >::clear().
| Tensor< 3, dim, Number > operator* | ( | const Tensor< 3, dim, Number > & | src1, |
| const Tensor< 2, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
| void contract | ( | Tensor< 3, dim, Number > & | dest, |
| const Tensor< 2, dim, Number > & | src1, | ||
| const Tensor< 3, dim, Number > & | src2 | ||
| ) | [related] |
Contract a tensor of rank 2 with a tensor of rank 3. The result is dest[i][j][l] = sum_k src1[i][k] src2[k][j][l].
Definition at line 1141 of file tensor.h.
References Tensor< rank_, dim, Number >::clear().
| Tensor< 3, dim, Number > operator* | ( | const Tensor< 2, dim, Number > & | src1, |
| const Tensor< 3, dim, Number > & | src2 | ||
| ) | [related] |
Multiplication operator performing a contraction of the last index of the first argument and the first index of the second argument. This function therefore does the same as the corresponding contract function, but returns the result as a return value, rather than writing it into the reference given as the first argument to the contract function.
Note that for the Tensor class, the multiplication operator only performs a contraction over a single pair of indices. This is in contrast to the multiplication operator for symmetric tensors, which does the double contraction.
| void double_contract | ( | Tensor< 2, dim, Number > & | dest, |
| const Tensor< 4, dim, Number > & | src1, | ||
| const Tensor< 2, dim, Number > & | src2 | ||
| ) | [related] |
Contract the last two indices of src1 with the two indices src2, creating a rank-2 tensor. This is the matrix-vector product analog operation between tensors of rank 4 and rank 2.
Definition at line 1220 of file tensor.h.
References Tensor< rank_, dim, Number >::clear().
| void outer_product | ( | Tensor< 1, dim, Number > & | dst, |
| const Number | src1, | ||
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Form the outer product of two tensors of rank 0 and 1, i.e. dst[i] = src1 * src2[i]. Of course, this is only a scaling of src2, but we consider this an outer product for completeness of these functions and since this is sometimes needed when writing templates that depend on the rank of a tensor, which may sometimes be zero (i.e. a scalar).
| void outer_product | ( | Tensor< 1, dim, Number > & | dst, |
| const Tensor< 1, dim, Number > | src1, | ||
| const Number | src2 | ||
| ) | [related] |
Form the outer product of two tensors of rank 1 and 0, i.e. dst[i] = src1[i] * src2. Of course, this is only a scaling of src1, but we consider this an outer product for completeness of these functions and since this is sometimes needed when writing templates that depend on the rank of a tensor, which may sometimes be zero (i.e. a scalar).
| void cross_product | ( | Tensor< 1, dim, Number > & | dst, |
| const Tensor< 1, dim, Number > & | src | ||
| ) | [related] |
Cross-product in 2d. This is just a rotation by 90 degrees clockwise to compute the outer normal from a tangential vector. This function is defined for all space dimensions to allow for dimension independent programming (e.g. within switches over the space dimenion), but may only be called if the actual dimension of the arguments is two (e.g. from the dim==2 case in the switch).
Definition at line 1439 of file tensor.h.
References Assert, and StandardExceptions::ExcInternalError().
| void cross_product | ( | Tensor< 1, dim, Number > & | dst, |
| const Tensor< 1, dim, Number > & | src1, | ||
| const Tensor< 1, dim, Number > & | src2 | ||
| ) | [related] |
Cross-product of 2 vectors in 3d. This function is defined for all space dimensions to allow for dimension independent programming (e.g. within switches over the space dimenion), but may only be called if the actual dimension of the arguments is three (e.g. from the dim==3 case in the switch).
Definition at line 1462 of file tensor.h.
References Assert, and StandardExceptions::ExcInternalError().
| Number scalar_product | ( | const Tensor< 2, dim, Number > & | t1, |
| const Tensor< 2, dim, Number > & | t2 | ||
| ) | [related] |
Compute the scalar product
between two tensors
of rank 2. We don't use operator* for this operation since the product between two tensors is usually assumed to be the contraction over the last index of the first tensor and the first index of the second tensor, for example
.
| Number determinant | ( | const Tensor< rank, 1, Number > & | t ) | [related] |
Compute the determinant of a tensor of arbitrary rank and dimension one. Since this is a number, the return value is, of course, the number itself.
Definition at line 1508 of file tensor.h.
References SymmetricTensor< rank, dim, Number >::determinant().
| Number determinant | ( | const Tensor< 1, 1, Number > & | t ) | [related] |
| Number determinant | ( | const Tensor< 2, 1, Number > & | t ) | [related] |
| Number determinant | ( | const Tensor< 2, 2, Number > & | t ) | [related] |
| Number determinant | ( | const Tensor< 2, 3, Number > & | t ) | [related] |
| Number determinant | ( | const Tensor< 2, dim, Number > & | t ) | [related] |
Compute the determinant of a tensor or rank 2, here for all dimensions for which no explicit specialization is available above.
Definition at line 1597 of file tensor.h.
References SymmetricTensor< rank, dim, Number >::determinant().
| Number trace | ( | const Tensor< 2, dim, Number > & | d ) | [related] |
| Tensor< 2, dim, Number > invert | ( | const Tensor< 2, dim, Number > & | t ) | [related] |
Compute and return the inverse of the given tensor. Since the compiler can perform the return value optimization, and since the size of the return object is known, it is acceptable to return the result by value, rather than by reference as a parameter.
Definition at line 1657 of file tensor.h.
References AssertThrow, and StandardExceptions::ExcNotImplemented().
| Tensor< 2, dim, Number > transpose | ( | const Tensor< 2, dim, Number > & | t ) | [related] |
Return the transpose of the given tensor. Since the compiler can perform the return value optimization, and since the size of the return object is known, it is acceptable to return the result by value, rather than by reference as a parameter. Note that there are specializations of this function for dim==1,2,3.
| std::ostream & operator<< | ( | std::ostream & | out, |
| const Tensor< 0, dim, Number > & | p | ||
| ) | [related] |
Output operator for tensors of rank 0. Since such tensors are scalars, we simply print this one value.
<0,dim,Number>
Definition at line 1256 of file tensor_base.h.
| std::ostream & operator<< | ( | std::ostream & | out, |
| const Tensor< 1, dim, Number > & | p | ||
| ) | [related] |
Output operator for tensors of rank 1. Print the elements consecutively, with a space in between.
<1,dim,Number>
Definition at line 1272 of file tensor_base.h.
| std::ostream & operator<< | ( | std::ostream & | out, |
| const Tensor< 1, 1, double > & | p | ||
| ) | [related] |
Output operator for tensors of rank 1 and dimension 1. This is implemented specialized from the general template in order to avoid a compiler warning that the loop is empty.
<1,dim,Number>
Definition at line 1291 of file tensor_base.h.
| Tensor< 1, dim, Number > operator* | ( | const Tensor< 1, dim, Number > & | t, |
| const Number | factor | ||
| ) | [related] |
Multiplication of a tensor of rank 1 with a scalar Number from the right.
<1,dim,Number>
Definition at line 1308 of file tensor_base.h.
| Tensor< 1, dim, Number > operator* | ( | const Number | factor, |
| const Tensor< 1, dim, Number > & | t | ||
| ) | [related] |
Multiplication of a tensor of rank 1 with a scalar Number from the left.
<1,dim,Number>
Definition at line 1327 of file tensor_base.h.
| Tensor< 1, dim, Number > operator/ | ( | const Tensor< 1, dim, Number > & | t, |
| const Number | factor | ||
| ) | [related] |
Division of a tensor of rank 1 by a scalar Number.
<1,dim,Number>
Definition at line 1346 of file tensor_base.h.
| Tensor< 1, dim > operator* | ( | const Tensor< 1, dim > & | t, |
| const double | factor | ||
| ) | [related] |
Multiplication of a tensor of rank 1 with a scalar double from the right.
<1,dim,Number>
Definition at line 1365 of file tensor_base.h.
| Tensor< 1, dim > operator* | ( | const double | factor, |
| const Tensor< 1, dim > & | t | ||
| ) | [related] |
Multiplication of a tensor of rank 1 with a scalar double from the left.
<1,dim,Number>
Definition at line 1384 of file tensor_base.h.
| Tensor< 1, dim > operator/ | ( | const Tensor< 1, dim > & | t, |
| const double | factor | ||
| ) | [related] |
Division of a tensor of rank 1 by a scalar double.
<1,dim,Number>
Definition at line 1403 of file tensor_base.h.
const unsigned int Tensor< rank_, dim, Number >::dimension = dim [static] |
Provide a way to get the dimension of an object without explicit knowledge of it's data type. Implementation is this way instead of providing a function dimension() because now it is possible to get the dimension at compile time without the expansion and preevaluation of an inlined function; the compiler may therefore produce more efficient code and you may use this value to declare other data types.
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