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Searched
refs:schur
(Results
1 - 7
of
7
) sorted by null
/external/eigen/doc/snippets/
ComplexSchur_compute.cpp
2
ComplexSchur<MatrixXcf>
schur
(4);
3
schur
.compute(A);
4
cout << "The matrix T in the decomposition of A is:" << endl <<
schur
.matrixT() << endl;
5
schur
.compute(A.inverse());
6
cout << "The matrix T in the decomposition of A^(-1) is:" << endl <<
schur
.matrixT() << endl;
RealSchur_compute.cpp
2
RealSchur<MatrixXf>
schur
(4);
3
schur
.compute(A, /* computeU = */ false);
4
cout << "The matrix T in the decomposition of A is:" << endl <<
schur
.matrixT() << endl;
5
schur
.compute(A.inverse(), /* computeU = */ false);
6
cout << "The matrix T in the decomposition of A^(-1) is:" << endl <<
schur
.matrixT() << endl;
RealSchur_RealSchur_MatrixType.cpp
4
RealSchur<MatrixXd>
schur
(A);
5
cout << "The orthogonal matrix U is:" << endl <<
schur
.matrixU() << endl;
6
cout << "The quasi-triangular matrix T is:" << endl <<
schur
.matrixT() << endl << endl;
8
MatrixXd U =
schur
.matrixU();
9
MatrixXd T =
schur
.matrixT();
/external/eigen/test/
schur_complex.cpp
14
template<typename MatrixType> void
schur
(int size = MatrixType::ColsAtCompileTime)
function
67
CALL_SUBTEST_1((
schur
<Matrix4cd>() ));
68
CALL_SUBTEST_2((
schur
<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
69
CALL_SUBTEST_3((
schur
<Matrix<std::complex<float>, 1, 1> >() ));
70
CALL_SUBTEST_4((
schur
<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
schur_real.cpp
40
template<typename MatrixType> void
schur
(int size = MatrixType::ColsAtCompileTime)
function
86
CALL_SUBTEST_1((
schur
<Matrix4f>() ));
87
CALL_SUBTEST_2((
schur
<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
88
CALL_SUBTEST_3((
schur
<Matrix<float, 1, 1> >() ));
89
CALL_SUBTEST_4((
schur
<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
/external/ceres-solver/docs/
changes.tex
10
options.ordering_type = ceres::
SCHUR
65
\item Change LOG(ERROR) to LOG(WARNING) in \texttt{
schur
\_complement\_solver.cc}.
71
\item
Schur
ordering was operating on the wrong object (Ricardo Martin)
142
Schur
eliminator.
147
\item Fix how static structure detection for the
Schur
eliminator logs
244
\item Fixed a strict weak ordering bug in the
schur
ordering.
solving.tex
290
\left[B - EC^{-1}E^\top\right] \Delta y = v - EC^{-1}w\ . \label{eq:
schur
}
296
is the
Schur
complement of $C$ in $H$. It is also known as the {\em reduced camera matrix}, because the only variables participating in~\eqref{eq:
schur
} are the ones corresponding to the cameras. $S \in \reals^{pc\times pc}$ is a block structured symmetric positive definite matrix, with blocks of size $c\times c$. The block $S_{ij}$ corresponding to the pair of images $i$ and $j$ is non-zero if and only if the two images observe at least one common point.
299
Thus, the solution of what was an $n\times n$, $n=pc+qs$ linear system is reduced to the inversion of the block diagonal matrix $C$, a few matrix-matrix and matrix-vector multiplies, and the solution of block sparse $pc\times pc$ linear system~\eqref{eq:
schur
}. For almost all problems, the number of cameras is much smaller than the number of points, $p \ll q$, thus solving~\eqref{eq:
schur
} is significantly cheaper than solving~\eqref{eq:linear2}. This is the {\em
Schur
complement trick}~\cite{brown-58}.
301
This still leaves open the question of solving~\eqref{eq:
schur
}. The
318
Sparse direct methods, depending on the exact sparsity structure of the
Schur
complement,
332
The cost of forming and storing the
Schur
complement $S$ can be prohibitive for large problems. Indeed, for an inexact Newton solver that computes $S$ and runs PCG on it, almost all of its time is spent in constructing $S$; the time spent inside the PCG algorithm is negligible in comparison. Because PCG only needs access to $S$ via its product with a vector, one way to evaluate $Sx$ is to observe that
342
Equation~\eqref{eq:schurtrick1} is closely related to {\em Domain Decomposition methods} for solving large linear systems that arise in structural engineering and partial differential equations. In the language of Domain Decomposition, each point in a bundle adjustment problem is a domain, and the cameras form the interface between these domains. The iterative solution of the
Schur
complement then falls within the sub-category of techniques known as Iterative Sub-structuring~\ci (…)
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