mat2 Class Template Reference
Matrix class (2x2). More...
#include <mat2.h>
Public Types | |
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typedef af::tiny_plain < NumType, 4 > | base_type |
Public Member Functions | |
| mat2 () | |
| Default constructor. Elements are not initialized. | |
| mat2 (NumType const &e00, NumType const &e01, NumType const &e10, NumType const &e11) | |
| Constructor. | |
| mat2 (base_type const &a) | |
| Constructor. | |
| mat2 (const NumType *a) | |
| Constructor. | |
| mat2 (NumType const &diag) | |
| Constructor for diagonal matrix. | |
| mat2 (af::tiny_plain< NumType, 2 > const &diag) | |
| Constructor for diagonal matrix. | |
| mat2 (sym_mat2< NumType > const &m) | |
| Construction from symmetric matrix. | |
| NumType const & | operator() (std::size_t r, std::size_t c) const |
| Access elements with 2-dimensional indices. | |
| NumType & | operator() (std::size_t r, std::size_t c) |
| Access elements with 2-dimensional indices. | |
| vec2< NumType > | get_row (std::size_t i) const |
| Return a row. | |
| void | set_row (std::size_t i, af::tiny_plain< NumType, 2 > const &v) |
| Set a row. | |
| void | swap_rows (std::size_t i1, std::size_t i2) |
| Swap two rows in place. | |
| vec2< NumType > | get_column (std::size_t i) const |
| Return a column. | |
| void | set_column (std::size_t i, af::tiny_plain< NumType, 2 > const &v) |
| Set a column. | |
| void | swap_columns (std::size_t i1, std::size_t i2) |
| Swap two columns in place. | |
| vec2< NumType > | diagonal () const |
| Return diagonal elements. | |
| mat2 | transpose () const |
| Return the transposed matrix. | |
| NumType | trace () const |
| Return trace (sum of diagonal elements). | |
| NumType | determinant () const |
| Return determinant. | |
| NumType | max_abs () const |
| Maximum of the absolute values of the elements of this matrix. | |
| bool | is_symmetric () const |
| Test for symmetric matrix. | |
| bool | is_symmetric (NumType const &relative_tolerance) const |
| Test for symmetric matrix. | |
| mat2 | co_factor_matrix_transposed () const |
| Return the transposed of the co-factor matrix. | |
| mat2 | inverse () const |
| Return the inverse matrix. | |
| mat2 | error_minimizing_inverse (std::size_t iterations) const |
| Returns the inverse matrix, after minimizing the error numerically. | |
| mat2 & | scale (af::tiny_plain< NumType, 2 > const &v) |
| Scale matrix in place. | |
| mat2 | ortho () const |
| Return a matrix with orthogonal base vectors. | |
| std::pair< mat2, vec2< NumType > > | decompose () const |
| Decomposes the matrix into a rotation and scaling part. | |
| sym_mat2< NumType > | self_times_self_transpose () const |
| (*this) * this->transpose(). | |
| sym_mat2< NumType > | self_transpose_times_self () const |
| this->transpose() * (*this). | |
| NumType | dot (mat2 const &other) |
| Sum of element-wise products. | |
Detailed Description
template<typename NumType>
class scitbx::mat2< NumType >
Matrix class (2x2).
This class represents a 2x2 matrix that can be used to store linear transformations.
A 2D adaptation of the scitbx::mat3 class
Member Function Documentation
| bool is_symmetric | ( | ) | const [inline] |
Test for symmetric matrix.
Returns false iff the absolute value of the difference between any pair of off-diagonal elements is different from zero.
Referenced by sym_mat2< FloatType >::sym_mat2().
| bool is_symmetric | ( | NumType const & | relative_tolerance | ) | const [inline] |
Test for symmetric matrix.
Returns false iff the absolute value of the difference between any pair of off-diagonal elements is larger than max_abs()*relative_tolerance.
References mat2::max_abs().
| mat2 co_factor_matrix_transposed | ( | ) | const [inline] |
Return the transposed of the co-factor matrix.
The inverse matrix is obtained by dividing the result by the determinant().
References mat2::mat2().
Referenced by mat2::inverse().
| mat2 inverse | ( | ) | const [inline] |
Return the inverse matrix.
An exception is thrown if the matrix is not invertible, i.e. if the determinant() is zero.
References mat2::co_factor_matrix_transposed(), and mat2::determinant().
Referenced by mat2::error_minimizing_inverse().
| mat2 error_minimizing_inverse | ( | std::size_t | iterations | ) | const [inline] |
Returns the inverse matrix, after minimizing the error numerically.
Here's the theory: M*M^-1 = I-E, where E is the error M*M^-1*(I+E) = (I-E)*(I+E) M*(M^-1*(I+E)) = I^2-E^2 M*(M^-1*(I+E)) = I-E^2 let M^-1*(I+E) = M1 let E^2 = E2 M*M1*(I+E2) = (I-E2)*(I+E2) M*M2 = I-E4 M*Mi = I-E2^i Supposedly this will drive the error pretty low after only a few repetitions. The error rate should be ~E^(2^iterations), which I think is pretty good. This assumes that E is "<< 1", whatever that means. Attributed to Judah I. Rosenblatt.
2*I - (I-E) ==> 2*I - I + E = I + E
References mat2::inverse().
| mat2& scale | ( | af::tiny_plain< NumType, 2 > const & | v | ) | [inline] |
Scale matrix in place.
Each row of this is multiplied element-wise with v.
The documentation for this class was generated from the following files:
- scitbx/mat2.h
- scitbx/sym_mat2.h
