Functions
Eigen::internal Namespace Reference

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 Scalar, int Flags, typename Index>
MappedSparseMatrix< Scalar, Flags, Index > map_superlu (SluMatrix &sluMat)
 
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

This is defined in the Jacobi module.

#include <Eigen/Jacobi>

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

◆ computeProductBlockingSizes()

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.

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

◆ map_superlu()

template<typename Scalar, int Flags, typename Index>
MappedSparseMatrix< Scalar, Flags, Index > map_superlu ( SluMatrix & sluMat)

View a Super LU matrix as an Eigen expression

References Eigen::ColMajor, and Eigen::RowMajor.

◆ tridiagonalization_inplace()

template<typename MatrixType, typename DiagonalType, typename SubDiagonalType>
void 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&)):

MatrixXd X = MatrixXd::Random(5,5);
MatrixXd A = X + X.transpose();
cout << "Here is a random symmetric 5x5 matrix:" << endl << A << endl << endl;
VectorXd diag(5);
VectorXd subdiag(4);
internal::tridiagonalization_inplace(A, diag, subdiag, true);
cout << "The orthogonal matrix Q is:" << endl << A << endl;
cout << "The diagonal of the tridiagonal matrix T is:" << endl << diag << endl;
cout << "The subdiagonal of the tridiagonal matrix T is:" << endl << subdiag << endl;
Eigen::MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::transpose
Eigen::Transpose< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > transpose()
Definition Transpose.h:199
Eigen::Matrix< double, Dynamic, Dynamic >::Random
static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, Matrix< double, _Rows, _Cols, _Options, _MaxRows, _MaxCols > > Random(Index rows, Index cols)
Definition Random.h:49

Output: 

Here is a random symmetric 5x5 matrix:
  1.36 -0.816  0.521   1.43 -0.144
-0.816 -0.659  0.794 -0.173 -0.406
 0.521  0.794 -0.541  0.461  0.179
  1.43 -0.173  0.461  -1.43  0.822
-0.144 -0.406  0.179  0.822  -1.37

The orthogonal matrix Q is:
       1        0        0        0        0
       0   -0.471    0.127   -0.671   -0.558
       0    0.301   -0.195    0.437   -0.825
       0    0.825   0.0459   -0.563 -0.00872
       0  -0.0832   -0.971   -0.202   0.0922
The diagonal of the tridiagonal matrix T is:
1.36
-1.2
-1.28
-1.69
0.164
The subdiagonal of the tridiagonal matrix T is:
1.73
-0.966
0.214
0.345
See also
class Tridiagonalization