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TooN 2.0.0-beta8
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Vector and Matrix classes, and helpers. More...
Classes | |
| struct | Matrix< Rows, Cols, Precision, Layout > |
| A matrix. More... | |
| class | DiagonalMatrix< Size, Precision, Base > |
| A diagonal matrix. More... | |
| class | Vector< Size, Precision, Base > |
| A vector. More... | |
Functions | |
| template<int R, int C, typename Precision , typename Base > | |
| Precision | determinant_gaussian_elimination (const Matrix< R, C, Precision, Base > &A_) |
| template<int R, int C, class P , class B > | |
| P | determinant (const Matrix< R, C, P, B > &A) |
| template<int Size, class Precision , class Base > | |
| TOON_DEPRECATED void | Fill (Vector< Size, Precision, Base > &v, const Precision &p) |
| template<int Rows, int Cols, class Precision , class Base > | |
| TOON_DEPRECATED void | Fill (Matrix< Rows, Cols, Precision, Base > &m, const Precision &p) |
| template<int Size, class Precision , class Base > | |
| Precision | norm (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| Precision | norm_sq (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| Precision | norm_1 (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| Precision | norm_inf (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| Precision | norm_2 (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| Vector< Size, Precision > | unit (const Vector< Size, Precision, Base > &v) |
| template<int Size, class Precision , class Base > | |
| void | normalize (Vector< Size, Precision, Base > v) |
| template<int Size, typename Precision , typename Base > | |
| Vector<(Size==Dynamic?Dynamic:Size-1), Precision > | project (const Vector< Size, Precision, Base > &v) |
| template<int Size, typename Precision , typename Base > | |
| Vector<(Size==Dynamic?Dynamic:Size+1), Precision > | unproject (const Vector< Size, Precision, Base > &v) |
| template<int R, int C, typename P , typename B > | |
| P | norm_fro (const Matrix< R, C, P, B > &m) |
| template<int R, int C, typename P , typename B > | |
| P | norm_inf (const Matrix< R, C, P, B > &m) |
| template<int R, int C, typename P , typename B > | |
| P | norm_1 (const Matrix< R, C, P, B > &m) |
| template<int R, int C, typename P , typename B > | |
| Matrix< R, C, P > | exp (const Matrix< R, C, P, B > &m) |
| template<int R, int C, typename P , typename B > | |
| Matrix< R, C, P > | sqrt (const Matrix< R, C, P, B > &m) |
| template<int R, int C, typename P , typename B > | |
| Matrix< R, C, P > | log (const Matrix< R, C, P, B > &m) |
| template<int S, class P , class B > | |
| bool | isfinite (const Vector< S, P, B > &v) |
| template<int S, class P , class B > | |
| bool | isnan (const Vector< S, P, B > &v) |
| template<int Rows, int Cols, typename Precision , typename Base > | |
| void | Symmetrize (Matrix< Rows, Cols, Precision, Base > &m) |
| template<int Rows, int Cols, typename Precision , typename Base > | |
| Precision | trace (const Matrix< Rows, Cols, Precision, Base > &m) |
| template<int Size, class P , class B > | |
| TooN::Matrix< 3, 3, P > | cross_product_matrix (const Vector< Size, P, B > &vec) |
| template<int R, int C, class Precision , class Base > | |
| Internal::MatrixStartFill< R, C, Precision, Base > | Fill (Matrix< R, C, Precision, Base > &m) |
| template<int Size, class Precision , class Base > | |
| Internal::VectorStartFill < Size, Precision, Base > | Fill (Vector< Size, Precision, Base > &v) |
| Operator< Internal::Data< N, double > > | Data (double a,...) |
| template<typename Precision > | |
| Operator< Internal::Data< N, Precision > > | Data (const Precision &a,...) |
Variables | |
| static const Operator < Internal::Scalars < Internal::One > > | Ones |
| static Operator< Internal::Zero > | Zeros |
| static Operator < Internal::Identity < Internal::One > > | Identity |
| template<int Rows, int Cols> | |
| Matrix< Rows, Cols, double, Reference::RowMajor > | wrapMatrix (double *data) |
| template<int Rows, int Cols> | |
| const Matrix< Rows, Cols, const double, Reference::RowMajor > | wrapMatrix (const double *data) |
| template<int Rows, int Cols, class Precision > | |
| Matrix< Rows, Cols, Precision, Reference::RowMajor > | wrapMatrix (Precision *data) |
| template<int Rows, int Cols, class Precision > | |
| const Matrix< Rows, Cols, const Precision, Reference::RowMajor > | wrapMatrix (const Precision *data) |
| template<int Rows, int Cols> | |
| Matrix< Rows, Cols, double, Reference::RowMajor > | wrapMatrix (double *data, int rows, int cols) |
| template<int Rows, int Cols> | |
| const Matrix< Rows, Cols, const double, Reference::RowMajor > | wrapMatrix (const double *data, int rows, int cols) |
| template<int Rows, int Cols, class Precision > | |
| Matrix< Rows, Cols, Precision, Reference::RowMajor > | wrapMatrix (Precision *data, int rows, int cols) |
| template<int Rows, int Cols, class Precision > | |
| const Matrix< Rows, Cols, const Precision, Reference::RowMajor > | wrapMatrix (const Precision *data, int rows, int cols) |
Vector and Matrix classes, and helpers.
| Precision TooN::determinant_gaussian_elimination | ( | const Matrix< R, C, Precision, Base > & | A_ | ) |
Compute the determinant using Gaussian elimination.
| A_ | The matrix to find the determinant of. |
References TooN::determinant(), Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
Referenced by TooN::determinant().
| P TooN::determinant | ( | const Matrix< R, C, P, B > & | A | ) |
Compute the determinant of a matrix using an appropriate method.
The obvious method is used for 2x2, otherwise determinant_gaussian_elimination() or determinant_LU() is used depending on the value of TOON_DETERMINANT_LAPACK. See also Functions using LAPACK.
| A | The matrix to find the determinant of. |
References TooN::determinant_gaussian_elimination(), Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
Referenced by TooN::determinant_gaussian_elimination().
| TOON_DEPRECATED void TooN::Fill | ( | Vector< Size, Precision, Base > & | v, |
| const Precision & | p | ||
| ) |
References Vector< Size, Precision, Base >::size().
| TOON_DEPRECATED void TooN::Fill | ( | Matrix< Rows, Cols, Precision, Base > & | m, |
| const Precision & | p | ||
| ) |
| Precision TooN::norm | ( | const Vector< Size, Precision, Base > & | v | ) |
Compute the
norm of v.
| v | v |
References TooN::sqrt().
Referenced by DownhillSimplex< N, Precision >::finished(), and TooN::norm_2().
| Precision TooN::norm_sq | ( | const Vector< Size, Precision, Base > & | v | ) |
| Precision TooN::norm_1 | ( | const Vector< Size, Precision, Base > & | v | ) |
| Precision TooN::norm_inf | ( | const Vector< Size, Precision, Base > & | v | ) |
Compute the
norm of v.
| v | v |
References Vector< Size, Precision, Base >::size().
Referenced by TooN::exp(), TooN::log(), and TooN::sqrt().
| Precision TooN::norm_2 | ( | const Vector< Size, Precision, Base > & | v | ) |
| Vector<Size, Precision> TooN::unit | ( | const Vector< Size, Precision, Base > & | v | ) |
Compute a the unit vector
.
| v | v |
References TooN::sqrt().
Referenced by SO3< P >::coerce(), SO2< P >::coerce(), SO3< Precision >::ln(), and SO3< P >::SO3().
| void TooN::normalize | ( | Vector< Size, Precision, Base > | v | ) |
Normalize a vector in place.
| v | Vector to normalize |
References TooN::sqrt().
Referenced by ComputeSymEigen< 3 >::compute(), and TooN::normalize().
| Vector<(Size==Dynamic?Dynamic:Size-1), Precision> TooN::project | ( | const Vector< Size, Precision, Base > & | v | ) |
For a vector v of length i, return
.
| v | v |
References TooN::Dynamic, and Vector< Size, Precision, Base >::size().
| Vector<(Size==Dynamic?Dynamic:Size+1), Precision> TooN::unproject | ( | const Vector< Size, Precision, Base > & | v | ) |
For a vector v of length i, return
.
| v | v |
References TooN::Dynamic, and Vector< Size, Precision, Base >::size().
| P TooN::norm_fro | ( | const Matrix< R, C, P, B > & | m | ) |
Frobenius (root of sum of squares) norm of input matrix m.
| m | m |
References Matrix< Rows, Cols, Precision, Layout >::num_cols(), Matrix< Rows, Cols, Precision, Layout >::num_rows(), and TooN::sqrt().
| Matrix<R, C, P> TooN::exp | ( | const Matrix< R, C, P, B > & | m | ) |
computes the matrix exponential of a matrix m by scaling m by 1/(powers of 2), using Taylor series and squaring again.
| m | input matrix, must be square |
References TooN::norm_inf(), Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
Referenced by SL< N, Precision >::exp().
| Matrix<R, C, P> TooN::sqrt | ( | const Matrix< R, C, P, B > & | m | ) |
computes a matrix square root of a matrix m by the product form of the Denman and Beavers iteration as given in Chen et al.
'Approximating the logarithm of a matrix to specified accuracy', J. Matrix Anal Appl, 2001. This is used for the matrix logarithm function, but is useable by on its own.
| m | input matrix, must be square |
References TooN::gaussian_elimination(), TooN::Identity, TooN::norm_inf(), Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
Referenced by TooN::brent_line_search(), ComputeSymEigen< 3 >::compute(), DownhillSimplex< N, Precision >::DownhillSimplex(), SO3< Precision >::exp(), SymEigen< Size, Precision >::get_isqrtm(), SymEigen< Size, Precision >::get_sqrtm(), TooN::golden_section_search(), ConjugateGradient< Size, Precision >::init(), SO3< Precision >::ln(), TooN::log(), TooN::norm(), TooN::norm_fro(), TooN::normalize(), and TooN::unit().
| Matrix<R, C, P> TooN::log | ( | const Matrix< R, C, P, B > & | m | ) |
computes the matrix logarithm of a matrix m using the inverse scaling and squaring method.
The overall approach is described in Chen et al. 'Approximating the logarithm of a matrix to specified accuracy', J. Matrix Anal Appl, 2001, but this implementation only uses a simple taylor series after the repeated square root operation.
| m | input matrix, must be square |
References TooN::Identity, TooN::norm_inf(), and TooN::sqrt().
Referenced by RobustII< Precision >::objective(), and RobustI< Precision >::objective().
| void TooN::Symmetrize | ( | Matrix< Rows, Cols, Precision, Base > & | m | ) |
Symmetrize a matrix.
| m | m |
References Matrix< Rows, Cols, Precision, Layout >::num_cols(), and Matrix< Rows, Cols, Precision, Layout >::num_rows().
| TooN::Matrix<3, 3, P> TooN::cross_product_matrix | ( | const Vector< Size, P, B > & | vec | ) |
creates an returns a cross product matrix M from a 3 vector v, such that for all vectors w, the following holds: v ^ w = M * w
| vec | the 3 vector input |
References Vector< Size, Precision, Base >::size().
| Internal::MatrixStartFill<R, C, Precision, Base> TooN::Fill | ( | Matrix< R, C, Precision, Base > & | m | ) |
Set up a matrix for filling.
Uses the following syntax:
Matrix<2,2> m;
Fill(m) = 1, 2,
3, 4;
Overfill is detected at compile time if possible, underfill is detected at run-time. The checks can not be optimized out for dynamic matrices, so define TOON_NDEBUG_FILL to prevent the checks from being used.
| m | Matrix to fill |
| Internal::VectorStartFill<Size, Precision, Base> TooN::Fill | ( | Vector< Size, Precision, Base > & | v | ) |
Set up a vector for filling.
Uses the following syntax:
Vector<2> v;
Fill(v) = 1, 2;
Overfill is detected at compile time if possible, underfill is detected at run-time. The checks can not be optimized out for dynamic vectors, so define TOON_NDEBUG_FILL to prevent the checks from being used.
| v | Vector to fill |
| Operator<Internal::Data<N, double> > TooN::Data | ( | double | a, |
| ... | |||
| ) |
Package up the function arguments as some data for filling matrices.
Matrices are filled in row major order. For example:
double theta = 2;
Matrix<2> rotation = data( cos(theta), sin(theta)
-sin(theta), cos(theta));
See also TooN::wrapMatrix().
| a | The first data element. |
| Operator<Internal::Data<N, Precision> > TooN::Data | ( | const Precision & | a, |
| ... | |||
| ) |
Package up the function arguments as some data for filling matrices.
Any type can be uses. Matrices are filled in row-major order.
Matrix<2,2,float> rotation = data(1f, 2f, 3f, 4f);
See also TooN::wrapMatrix().
| a | The first data element. |
const Operator<Internal::Scalars<Internal::One> > Ones [static] |
This function is used to add a scalar to every element of a vector or matrix.
For example:
Vector<3> v; ... ... v += Ones * 3; //Add 3 to every element of v;
Both + and += are supported on vectors,matrices and slices.
For construction of dynamic vectors and matrices, a size needs to be given:
Vector<3> v_static = Ones; Vector<> v_dynamic = Ones(3); //Construct a 3x1 vector full one 1s Matrix<3> m_static = Ones; Matrix<> m_dynamic = Ones(3,4); //Construct a 3x4 matrix
Referenced by ComputeSymEigen< 3 >::compute(), and TooN::unproject().
Operator<Internal::Zero> Zeros [static] |
This function is used to initialize vectors and matrices to zero.
For construction of dynamic vectors and matrices, a size needs to be given. For example:
Vector<3> v_static = Zeros; Vector<> v_dynamic = Zeros(3); //Construct a 3x1 vector Matrix<3> m_static = Zeros; Matrix<> m_dynamic = Zeros(3,4); //Construct a 3x4 matrix
Referenced by TooN::Internal::bracket_minimum_forward(), WLS< Size, Precision >::clear(), IRLS< Size, Precision, Reweight >::clear(), SL< N, Precision >::exp(), DownhillSimplex< N, Precision >::find_next_point(), SO3< P >::generator(), SL< N, Precision >::generator(), SIM2< P >::generator(), SE2< P >::generator(), SIM3< P >::generator_field(), and SE3< P >::generator_field().
Operator<Internal::Identity<Internal::One> > Identity [static] |
This function is used to add a scalar to the diagonal of a matrix, or to construct matrices.
For example:
Matrix<3> v; ... ... Matrix<3> u = v + Identity * 4;
Both + and += are supported. For assignment, if the matrix is non-square, then all elements off the leading diagonal are set to zero. For construction of dynamic matrices, a size needs to be given:
Referenced by Cholesky< Size, Precision >::get_inverse(), TooN::log(), SO3< P >::SO3(), and TooN::sqrt().
1.7.4