Eigen  3.2.9
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Eigen::internal Namespace Reference

Functions

template<typename Index >
Index colamd_recommended (Index nnz, Index n_row, Index n_col)
 Returns the recommended value of Alen. More...
 
template<typename MatrixType , typename IndexVector >
int coletree (const MatrixType &mat, IndexVector &parent, IndexVector &firstRowElt, typename MatrixType::Index *perm=0)
 
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. More...
 
template<typename Index , typename IndexVector >
Index etree_find (Index i, IndexVector &pp)
 
template<typename Scalar , int Flags, typename Index >
MappedSparseMatrix< Scalar,
Flags, Index > 
map_superlu (SluMatrix &sluMat)
 
template<typename Index , typename IndexVector >
void nr_etdfs (Index n, IndexVector &parent, IndexVector &first_kid, IndexVector &next_kid, IndexVector &post, Index postnum)
 
template<typename Index , typename IndexVector >
void treePostorder (Index n, IndexVector &parent, IndexVector &post)
 Post order a tree. More...
 
template<typename MatrixType , typename DiagonalType , typename SubDiagonalType >
void tridiagonalization_inplace (MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ)
 Performs a full tridiagonalization in place. More...
 

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

Index Eigen::internal::colamd_recommended ( Index  nnz,
Index  n_row,
Index  n_col 
)
inline

Returns the recommended value of Alen.

Returns recommended value of Alen for use by colamd. Returns -1 if any input argument is negative. The use of this routine or macro is optional. Note that the macro uses its arguments more than once, so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED.

Parameters
nnznonzeros in A
n_rownumber of rows in A
n_colnumber of columns in A
Returns
recommended value of Alen for use by colamd

Referenced by COLAMDOrdering< Index >::operator()().

int Eigen::internal::coletree ( const MatrixType &  mat,
IndexVector &  parent,
IndexVector &  firstRowElt,
typename MatrixType::Index *  perm = 0 
)

Compute the column elimination tree of a sparse matrix

Parameters
matThe matrix in column-major format.
parentThe elimination tree
firstRowEltThe column index of the first element in each row
permThe permutation to apply to the column of mat

References etree_find().

Referenced by SparseQR< MatrixType, OrderingType >::analyzePattern(), SparseLU< _MatrixType, _OrderingType >::analyzePattern(), and SparseQR< MatrixType, OrderingType >::factorize().

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
Index Eigen::internal::etree_find ( Index  i,
IndexVector &  pp 
)

Find the root of the tree/set containing the vertex i : Use Path halving

Referenced by coletree().

MappedSparseMatrix<Scalar,Flags,Index> Eigen::internal::map_superlu ( SluMatrix &  sluMat)

View a Super LU matrix as an Eigen expression

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

void Eigen::internal::nr_etdfs ( Index  n,
IndexVector &  parent,
IndexVector &  first_kid,
IndexVector &  next_kid,
IndexVector &  post,
Index  postnum 
)

Depth-first search from vertex n. No recursion. This routine was contributed by C├ędric Doucet, CEDRAT Group, Meylan, France.

Referenced by treePostorder().

void Eigen::internal::treePostorder ( Index  n,
IndexVector &  parent,
IndexVector &  post 
)

Post order a tree.

Parameters
nthe number of nodes
parentInput tree
postpostordered tree

References nr_etdfs().

Referenced by SparseLU< _MatrixType, _OrderingType >::analyzePattern().

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&)):

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;

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