Two-sided Jacobi SVD decomposition of a square matrix.
MatrixType | the type of the matrix of which we are computing the SVD decomposition | |
QRPreconditioner | this optional parameter allows to specify the type of QR decomposition that will be used internally for the R-SVD step for non-square matrices. See discussion of possible values below. |
SVD decomposition consists in decomposing any n-by-p matrix A as a product
where U is a n-by-n unitary, V is a p-by-p unitary, and S is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively.
Singular values are always sorted in decreasing order.
This JacobiSVD decomposition computes only the singular values by default. If you want U or V, you need to ask for them explicitly.
You can ask for only thin U or V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting m be the smaller value among n and p, there are only m singular vectors; the remaining columns of U and V do not correspond to actual singular vectors. Asking for thin U or V means asking for only their m first columns to be formed. So U is then a n-by-m matrix, and V is then a p-by-m matrix. Notice that thin U and V are all you need for (least squares) solving.
Here's an example demonstrating basic usage:
Output:
This JacobiSVD class is a two-sided Jacobi R-SVD decomposition, ensuring optimal reliability and accuracy. The downside is that it's slower than bidiagonalizing SVD algorithms for large square matrices; however its complexity is still where n is the smaller dimension and p is the greater dimension, meaning that it is still of the same order of complexity as the faster bidiagonalizing R-SVD algorithms. In particular, like any R-SVD, it takes advantage of non-squareness in that its complexity is only linear in the greater dimension.
If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time.
The possible values for QRPreconditioner are:
Definition at line 343 of file JacobiSVD.h.
#include <src/SVD/JacobiSVD.h>
Public Types | |
enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime), MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime), MatrixOptions = MatrixType::Options } |
typedef _MatrixType | MatrixType |
typedef MatrixType::Scalar | Scalar |
typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixUType |
typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime > | MatrixVType |
typedef internal::plain_diag_type < MatrixType, RealScalar > ::type | SingularValuesType |
typedef internal::plain_row_type < MatrixType >::type | RowType |
typedef internal::plain_col_type < MatrixType >::type | ColType |
typedef Matrix< Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime > | WorkMatrixType |
Public Member Functions | |
JacobiSVD () | |
Default Constructor. | |
JacobiSVD (Index rows, Index cols, unsigned int computationOptions=0) | |
Default Constructor with memory preallocation. | |
JacobiSVD (const MatrixType &matrix, unsigned int computationOptions=0) | |
Constructor performing the decomposition of given matrix. | |
JacobiSVD & | compute (const MatrixType &matrix, unsigned int computationOptions=0) |
Method performing the decomposition of given matrix. | |
const MatrixUType & | matrixU () const |
const MatrixVType & | matrixV () const |
const SingularValuesType & | singularValues () const |
bool | computeU () const |
bool | computeV () const |
template<typename Rhs > | |
const internal::solve_retval < JacobiSVD, Rhs > | solve (const MatrixBase< Rhs > &b) const |
Index | nonzeroSingularValues () const |
Index | rows () const |
Index | cols () const |
Protected Attributes | |
MatrixUType | m_matrixU |
MatrixVType | m_matrixV |
SingularValuesType | m_singularValues |
WorkMatrixType | m_workMatrix |
bool | m_isInitialized |
bool | m_computeFullU |
bool | m_computeThinU |
bool | m_computeFullV |
bool | m_computeThinV |
Index | m_nonzeroSingularValues |
Index | m_rows |
Index | m_cols |
Index | m_diagSize |
Private Member Functions | |
void | allocate (Index rows, Index cols, unsigned int computationOptions=0) |
Friends | |
struct | internal::svd_precondition_2x2_block_to_be_real |
struct | internal::qr_preconditioner_impl |
typedef internal::plain_col_type<MatrixType>::type JacobiSVD< _MatrixType, QRPreconditioner >::ColType |
Definition at line 369 of file JacobiSVD.h.
typedef MatrixType::Index JacobiSVD< _MatrixType, QRPreconditioner >::Index |
Definition at line 350 of file JacobiSVD.h.
typedef _MatrixType JacobiSVD< _MatrixType, QRPreconditioner >::MatrixType |
Definition at line 347 of file JacobiSVD.h.
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> JacobiSVD< _MatrixType, QRPreconditioner >::MatrixUType |
Definition at line 363 of file JacobiSVD.h.
typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> JacobiSVD< _MatrixType, QRPreconditioner >::MatrixVType |
Definition at line 366 of file JacobiSVD.h.
typedef NumTraits<typename MatrixType::Scalar>::Real JacobiSVD< _MatrixType, QRPreconditioner >::RealScalar |
Definition at line 349 of file JacobiSVD.h.
typedef internal::plain_row_type<MatrixType>::type JacobiSVD< _MatrixType, QRPreconditioner >::RowType |
Definition at line 368 of file JacobiSVD.h.
typedef MatrixType::Scalar JacobiSVD< _MatrixType, QRPreconditioner >::Scalar |
Definition at line 348 of file JacobiSVD.h.
typedef internal::plain_diag_type<MatrixType, RealScalar>::type JacobiSVD< _MatrixType, QRPreconditioner >::SingularValuesType |
Definition at line 367 of file JacobiSVD.h.
typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> JacobiSVD< _MatrixType, QRPreconditioner >::WorkMatrixType |
Definition at line 372 of file JacobiSVD.h.
anonymous enum |
RowsAtCompileTime | |
ColsAtCompileTime | |
DiagSizeAtCompileTime | |
MaxRowsAtCompileTime | |
MaxColsAtCompileTime | |
MaxDiagSizeAtCompileTime | |
MatrixOptions |
Definition at line 351 of file JacobiSVD.h.
JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD | ( | ) | [inline] |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via JacobiSVD::compute(const MatrixType&).
Definition at line 379 of file JacobiSVD.h.
JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD | ( | Index | rows, | |
Index | cols, | |||
unsigned int | computationOptions = 0 | |||
) | [inline] |
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
Definition at line 388 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::allocate().
JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD | ( | const MatrixType & | matrix, | |
unsigned int | computationOptions = 0 | |||
) | [inline] |
Constructor performing the decomposition of given matrix.
matrix | the matrix to decompose | |
computationOptions | optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit-field, the possible bits are ComputeFullU, ComputeThinU, ComputeFullV, ComputeThinV. |
Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non-default) FullPivHouseholderQR preconditioner.
Definition at line 403 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::compute().
void JacobiSVD< MatrixType, QRPreconditioner >::allocate | ( | Index | rows, | |
Index | cols, | |||
unsigned int | computationOptions = 0 | |||
) | [private] |
Definition at line 516 of file JacobiSVD.h.
References Dynamic, eigen_assert, EIGEN_IMPLIES, FullPivHouseholderQRPreconditioner, JacobiSVD< _MatrixType, QRPreconditioner >::m_cols, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullU, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullV, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinU, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinV, JacobiSVD< _MatrixType, QRPreconditioner >::m_diagSize, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixU, JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixV, JacobiSVD< _MatrixType, QRPreconditioner >::m_rows, JacobiSVD< _MatrixType, QRPreconditioner >::m_singularValues, JacobiSVD< _MatrixType, QRPreconditioner >::m_workMatrix, and PlainObjectBase< Derived >::resize().
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::compute(), and JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD().
Index JacobiSVD< _MatrixType, QRPreconditioner >::cols | ( | void | ) | const [inline] |
Definition at line 494 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::m_cols.
JacobiSVD< MatrixType, QRPreconditioner > & JacobiSVD< MatrixType, QRPreconditioner >::compute | ( | const MatrixType & | matrix, | |
unsigned int | computationOptions = 0 | |||
) |
Method performing the decomposition of given matrix.
matrix | the matrix to decompose | |
computationOptions | optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit-field, the possible bits are ComputeFullU, ComputeThinU, ComputeFullV, ComputeThinV. |
Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non-default) FullPivHouseholderQR preconditioner.
Definition at line 548 of file JacobiSVD.h.
References abs(), JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), PlainObjectBase< Derived >::coeff(), JacobiSVD< _MatrixType, QRPreconditioner >::computeU(), JacobiSVD< _MatrixType, QRPreconditioner >::computeV(), JacobiSVD< _MatrixType, QRPreconditioner >::m_cols, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullU, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullV, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinU, JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinV, JacobiSVD< _MatrixType, QRPreconditioner >::m_diagSize, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixU, JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixV, JacobiSVD< _MatrixType, QRPreconditioner >::m_nonzeroSingularValues, JacobiSVD< _MatrixType, QRPreconditioner >::m_rows, JacobiSVD< _MatrixType, QRPreconditioner >::m_singularValues, JacobiSVD< _MatrixType, QRPreconditioner >::m_workMatrix, internal::real_2x2_jacobi_svd(), Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >::swap(), and JacobiRotation< Scalar >::transpose().
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::JacobiSVD().
bool JacobiSVD< _MatrixType, QRPreconditioner >::computeU | ( | ) | const [inline] |
Definition at line 464 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullU, and JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinU.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixU(), internal::svd_precondition_2x2_block_to_be_real< MatrixType, QRPreconditioner, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and JacobiSVD< _MatrixType, QRPreconditioner >::solve().
bool JacobiSVD< _MatrixType, QRPreconditioner >::computeV | ( | ) | const [inline] |
Definition at line 466 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullV, and JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinV.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixV(), internal::svd_precondition_2x2_block_to_be_real< MatrixType, QRPreconditioner, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), and JacobiSVD< _MatrixType, QRPreconditioner >::solve().
const MatrixUType& JacobiSVD< _MatrixType, QRPreconditioner >::matrixU | ( | ) | const [inline] |
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the U matrix is n-by-n if you asked for ComputeFullU, and is n-by-m if you asked for ComputeThinU.
The m first columns of U are the left singular vectors of the matrix being decomposed.
This method asserts that you asked for U to be computed.
Definition at line 429 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::computeU(), eigen_assert, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, and JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixU.
Referenced by Transform< _Scalar, _Dim, _Mode >::computeRotationScaling(), Transform< _Scalar, _Dim, _Mode >::computeScalingRotation(), and umeyama().
const MatrixVType& JacobiSVD< _MatrixType, QRPreconditioner >::matrixV | ( | ) | const [inline] |
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the V matrix is p-by-p if you asked for ComputeFullV, and is p-by-m if you asked for ComputeThinV.
The m first columns of V are the right singular vectors of the matrix being decomposed.
This method asserts that you asked for V to be computed.
Definition at line 445 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::computeV(), eigen_assert, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, and JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixV.
Referenced by Transform< _Scalar, _Dim, _Mode >::computeRotationScaling(), Transform< _Scalar, _Dim, _Mode >::computeScalingRotation(), QuaternionBase< Derived >::setFromTwoVectors(), and umeyama().
Index JacobiSVD< _MatrixType, QRPreconditioner >::nonzeroSingularValues | ( | ) | const [inline] |
Definition at line 487 of file JacobiSVD.h.
References eigen_assert, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, and JacobiSVD< _MatrixType, QRPreconditioner >::m_nonzeroSingularValues.
Index JacobiSVD< _MatrixType, QRPreconditioner >::rows | ( | void | ) | const [inline] |
Definition at line 493 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::m_rows.
const SingularValuesType& JacobiSVD< _MatrixType, QRPreconditioner >::singularValues | ( | ) | const [inline] |
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the returned vector has size m.
Definition at line 457 of file JacobiSVD.h.
References eigen_assert, JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized, and JacobiSVD< _MatrixType, QRPreconditioner >::m_singularValues.
Referenced by Transform< _Scalar, _Dim, _Mode >::computeRotationScaling(), Transform< _Scalar, _Dim, _Mode >::computeScalingRotation(), and umeyama().
const internal::solve_retval<JacobiSVD, Rhs> JacobiSVD< _MatrixType, QRPreconditioner >::solve | ( | const MatrixBase< Rhs > & | b | ) | const [inline] |
b | the right-hand-side of the equation to solve. |
Definition at line 479 of file JacobiSVD.h.
References JacobiSVD< _MatrixType, QRPreconditioner >::computeU(), JacobiSVD< _MatrixType, QRPreconditioner >::computeV(), eigen_assert, and JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized.
friend struct internal::qr_preconditioner_impl [friend] |
Definition at line 512 of file JacobiSVD.h.
friend struct internal::svd_precondition_2x2_block_to_be_real [friend] |
Definition at line 510 of file JacobiSVD.h.
Index JacobiSVD< _MatrixType, QRPreconditioner >::m_cols [protected] |
Definition at line 507 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::cols(), and JacobiSVD< _MatrixType, QRPreconditioner >::compute().
bool JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullU [protected] |
Definition at line 505 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::computeU(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), and internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run().
bool JacobiSVD< _MatrixType, QRPreconditioner >::m_computeFullV [protected] |
Definition at line 506 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::computeV(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run().
bool JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinU [protected] |
Definition at line 505 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::computeU(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), and internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run().
bool JacobiSVD< _MatrixType, QRPreconditioner >::m_computeThinV [protected] |
Definition at line 506 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::computeV(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run().
Index JacobiSVD< _MatrixType, QRPreconditioner >::m_diagSize [protected] |
Definition at line 507 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), and JacobiSVD< _MatrixType, QRPreconditioner >::compute().
bool JacobiSVD< _MatrixType, QRPreconditioner >::m_isInitialized [protected] |
Definition at line 504 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixU(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixV(), JacobiSVD< _MatrixType, QRPreconditioner >::nonzeroSingularValues(), JacobiSVD< _MatrixType, QRPreconditioner >::singularValues(), and JacobiSVD< _MatrixType, QRPreconditioner >::solve().
MatrixUType JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixU [protected] |
Definition at line 500 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixU(), internal::svd_precondition_2x2_block_to_be_real< MatrixType, QRPreconditioner, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run().
MatrixVType JacobiSVD< _MatrixType, QRPreconditioner >::m_matrixV [protected] |
Definition at line 501 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixV(), internal::svd_precondition_2x2_block_to_be_real< MatrixType, QRPreconditioner, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run().
Index JacobiSVD< _MatrixType, QRPreconditioner >::m_nonzeroSingularValues [protected] |
Definition at line 507 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::compute(), and JacobiSVD< _MatrixType, QRPreconditioner >::nonzeroSingularValues().
Index JacobiSVD< _MatrixType, QRPreconditioner >::m_rows [protected] |
Definition at line 507 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), and JacobiSVD< _MatrixType, QRPreconditioner >::rows().
SingularValuesType JacobiSVD< _MatrixType, QRPreconditioner >::m_singularValues [protected] |
Definition at line 502 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), and JacobiSVD< _MatrixType, QRPreconditioner >::singularValues().
WorkMatrixType JacobiSVD< _MatrixType, QRPreconditioner >::m_workMatrix [protected] |
Definition at line 503 of file JacobiSVD.h.
Referenced by JacobiSVD< _MatrixType, QRPreconditioner >::allocate(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, HouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), internal::qr_preconditioner_impl< MatrixType, ColPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run(), internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreColsThanRows, true >::run(), and internal::qr_preconditioner_impl< MatrixType, FullPivHouseholderQRPreconditioner, PreconditionIfMoreRowsThanCols, true >::run().
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