Square matrix template class. More...
Public Types | |
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typedef util::sequence < value_type > ::const_reference | const_reference |
| Type of reference to constant element. | |
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typedef util::sequence < value_type >::reference | reference |
| Type of reference to element. | |
| typedef value_t | value_type |
| Type of elements. | |
Public Member Functions | |
| matrix () | |
| Default constructor. | |
| matrix (const matrix &a) | |
| Copy constructor. | |
| matrix (temporary< matrix > &a) | |
| Move constructor from temporary object. | |
| template<typename expr_t , typename tag > | |
| matrix (const shaped_expression< value_type, expr_t, tag, shape > &a) | |
| Copy constructor from matrix expression. | |
| matrix (size_t size) | |
| Constructor with size initialization. | |
| matrix (size_t size, const_reference value) | |
| Constructor with size and value initialization. | |
| ~matrix () | |
| Destructor. | |
| template<typename expr_t , typename tag > | |
| void | assign (const shaped_expression< value_type, expr_t, tag, shape > &rhs) |
| Assigns symmetric matrix expression to this object. | |
| size_t | cols () const |
| Returns number of columns. | |
| reference | operator() (size_t row, size_t column) |
| Subscript operator. | |
| const_reference | operator() (size_t row, size_t column) const |
| Subscript operator. | |
| row_ref | operator() (size_t row) |
| Subscript operator. | |
| const_row_ref | operator() (size_t row) const |
| Subscript operator. | |
| matrix & | operator= (const matrix &a) |
| Assignment operator. | |
| template<typename expr_t , typename tag > | |
| matrix & | operator= (const shaped_expression< value_type, expr_t, tag, shape > &a) |
| Assignment operator. | |
| matrix & | operator= (temporary< matrix > &a) |
| Move assignment operator. | |
| row_ref | operator[] (size_t row) |
| Subscript operator. | |
| const_row_ref | operator[] (size_t row) const |
| Subscript operator. | |
| void | resize (size_t size) |
| Resizes matrix. | |
| void | resize (size_t size, const_reference value) |
| Resizes matrix. | |
| size_t | rows () const |
| Returns number of rows. | |
| void | swap (matrix &a) |
| Swaps contents of two matrices. | |
Detailed Description
template<typename value_t, typename shape>
class nabla::matrix< value_t, shape >
Square matrix template class.
See matrix<value_t, rectangular> specialization for information about general matrix template class.
All square matrices share a restriction: matrices can not be resized to rectangular shape, i.e. can not have size other than n by n elements. This is ensured by the design and one will have to make an effort to brake this constraint. To stick to this policy all user-defined types related to square matrices in any way should also ensure this design constraint.
Depending on the specified shape there are different space optimizations, implementation details and guarantees. The remaining sections discuss that in detail. For more information about shapes consult Matrix Shape.
Symmetrically Shaped matrix
Such a matrix is invoked like
- Additional guarantees:
- Elements of a
matrix<value_t, symmetric>are stored in memory continuously row by row. Only lower triangular part elements are stored. This implies
&m(i, j)==&m(0, 0) + (i1*(i1 + 1)/2 + j1))
is always satisfied for non-empty matrix andi1 = max(i, j); j1 = min(i, j); i<m.rows() && j<m.cols().
Lower Triangular Shaped matrix
Such a matrix is invoked like
or, using a typedef for lower_triangular,
- Additional guarantees:
- Elements of a
matrix<value_t, lower_triangular>are stored in memory continuously row by row. Only lower triangular part elements are stored. This implies
&m(i, j)==&m(0, 0) + ((i*(i + 1))/2 + j)
is always satisfied for non-empty matrix andi<m.rows() && j<m.cols() && j<=i.
Upper Triangular Shaped matrix
Such a matrix is invoked like
or, using a typedef for upper_triangular,
- Additional guarantees:
- Elements of a
matrix<value_t, upper_triangular>are stored in memory continuously row by row. Only upper triangular part elements are stored. This implies
&m(i, j)==&m(0, 0) + ((i*(2*m.rows() - i - 1))/2 + j)
is always satisfied for non-empty matrix andi<m.rows() && j<m.cols() && j>=i.
Member Function Documentation
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Assigns symmetric matrix expression to this object.
- Warning
- This function may produce suprising results. Equivalent effect of this function is if this object were erased and then assigned the rhs.
This function assigns rhs in the most efficient way. It means that no temporary is introduced to store intermediate result. This circumstance can cause suprising results as stated above.Like in the STL this function doesn't care about object's previous state. The function discards all the contents (which may immediately invalidate all references to this object) and copies the result of rhs expression to this object's new contents.In other words this object should not be involved in the argument expression rhs. Otherwise this function may produce unexpected result or even crash the program.
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Subscript operator.
Returns a reference to an element (row, column).
Since for lower and upper triangular matrices some elements are zero by definition (and hence not stored) an attempt to modify such elements will fail.
access_error is thrown under the following circumstances:
- if an element (i, j) of a lower triangular matrix with i<j (i.e. super diagonal element) is to be modified;
- if an element (i, j) of an upper triangular matrix with i>j (i.e. sub diagonal element) is to be modified.
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The documentation for this class was generated from the following file:
