Yoji KURODA / Eigen

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Dependents:   Eigen_test Odometry_test AttitudeEstimation_usingTicker MPU9250_Quaternion_Binary_Serial ... more

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Eigen::internal Namespace Reference
Namespaces | Data Structures | Functions

Eigen::internal Namespace Reference

Applies the clock wise 2D rotation j to the set of 2D vectors of cordinates x and y: $ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) $ More...

Namespaces

namespace  anonymous_namespace{Macros.h}

Data Structures

class  BandMatrix
 Represents a rectangular matrix with a banded storage. More...
class  TridiagonalMatrix
 Represents a tridiagonal matrix with a compact banded storage. More...
struct  dense_xpr_base_dispatcher_for_doxygen< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >
 This class is just a workaround for Doxygen and it does not not actually exist. More...
struct  dense_xpr_base_dispatcher_for_doxygen< Array< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >
 This class is just a workaround for Doxygen and it does not not actually exist. More...
struct  HessenbergDecompositionMatrixHReturnType
  More...
struct  FullPivHouseholderQRMatrixQReturnType
 Expression type for return value of FullPivHouseholderQR::matrixQ() More...

Functions

template<typename LhsScalar , typename RhsScalar , int KcFactor, typename SizeType >
void computeProductBlockingSizes (SizeType &k, SizeType &m, SizeType &n)
 Computes the blocking parameters for a m x k times k x n matrix product.
template<typename MatrixType , typename DiagonalType , typename SubDiagonalType >
void tridiagonalization_inplace (MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ)
 Performs a full tridiagonalization in place.

Detailed Description

Applies the clock wise 2D rotation j to the set of 2D vectors of cordinates x and y: $ \left ( \begin{array}{cc} x \\ y \end{array} \right ) = J \left ( \begin{array}{cc} x \\ y \end{array} \right ) $

See also:
MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Function Documentation

void Eigen::internal::computeProductBlockingSizes ( SizeType &  k,
SizeType &  m,
SizeType &  n 
)

Computes the blocking parameters for a m x k times k x n matrix product.

Parameters:
[in,out]kInput: the third dimension of the product. Output: the blocking size along the same dimension.
[in,out]mInput: the number of rows of the left hand side. Output: the blocking size along the same dimension.
[in,out]nInput: the number of columns of the right hand side. Output: the blocking size along the same dimension.

Given a m x k times k x n matrix product of scalar types LhsScalar and RhsScalar, this function computes the blocking size parameters along the respective dimensions for matrix products and related algorithms. The blocking sizes depends on various parameters:

  • the L1 and L2 cache sizes,
  • the register level blocking sizes defined by gebp_traits,
  • the number of scalars that fit into a packet (when vectorization is enabled).
See also:
setCpuCacheSizes

Definition at line 73 of file GeneralBlockPanelKernel.h.

void Eigen::internal::tridiagonalization_inplace ( MatrixType &  mat,
DiagonalType &  diag,
SubDiagonalType &  subdiag,
bool  extractQ 
)

Performs a full tridiagonalization in place.

Parameters:
[in,out]matOn input, the selfadjoint matrix whose tridiagonal decomposition is to be computed. Only the lower triangular part referenced. The rest is left unchanged. On output, the orthogonal matrix Q in the decomposition if extractQ is true.
[out]diagThe diagonal of the tridiagonal matrix T in the decomposition.
[out]subdiagThe subdiagonal of the tridiagonal matrix T in the decomposition.
[in]extractQIf true, the orthogonal matrix Q in the decomposition is computed and stored in mat.

Computes the tridiagonal decomposition of the selfadjoint matrix mat in place such that $ mat = Q T Q^* $ where $ Q $ is unitary and $ T $ a real symmetric tridiagonal matrix.

The tridiagonal matrix T is passed to the output parameters diag and subdiag. If extractQ is true, then the orthogonal matrix Q is passed to mat. Otherwise the lower part of the matrix mat is destroyed.

The vectors diag and subdiag are not resized. The function assumes that they are already of the correct size. The length of the vector diag should equal the number of rows in mat, and the length of the vector subdiag should be one left.

This implementation contains an optimized path for 3-by-3 matrices which is especially useful for plane fitting.

Note:
Currently, it requires two temporary vectors to hold the intermediate Householder coefficients, and to reconstruct the matrix Q from the Householder reflectors.

Example (this uses the same matrix as the example in Tridiagonalization::Tridiagonalization(const MatrixType&)): 

 Output: 


See also:
class Tridiagonalization 



Definition at line 427 of file Tridiagonalization.h.









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