Eigne Matrix Class Library
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MatrixBase< Derived > Class Template Reference
[Core module]
Base class for all dense matrices, vectors, and expressions. More...
#include <MatrixBase.h>
Inherits DenseBase< Derived >.
Inherited by ProductBase< Derived, Lhs, Rhs >.
Public Types | |
typedef Matrix< Scalar, EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime, ColsAtCompileTime)> | SquareMatrixType |
type of the equivalent square matrix | |
typedef Matrix< typename internal::traits< Derived > ::Scalar, internal::traits < Derived >::RowsAtCompileTime, internal::traits< Derived > ::ColsAtCompileTime, AutoAlign|(internal::traits < Derived >::Flags &RowMajorBit?RowMajor:ColMajor), internal::traits< Derived > ::MaxRowsAtCompileTime, internal::traits< Derived > ::MaxColsAtCompileTime > | PlainObject |
The plain matrix type corresponding to this expression. | |
Public Member Functions | |
Index | diagonalSize () const |
Derived & | operator= (const MatrixBase &other) |
Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1) | |
template<typename OtherDerived > | |
Derived & | operator+= (const MatrixBase< OtherDerived > &other) |
replaces *this by *this + other. | |
template<typename OtherDerived > | |
Derived & | operator-= (const MatrixBase< OtherDerived > &other) |
replaces *this by *this - other. | |
template<typename OtherDerived > | |
const ProductReturnType < Derived, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
const LazyProductReturnType < Derived, OtherDerived > ::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
Derived & | operator*= (const EigenBase< OtherDerived > &other) |
replaces *this by *this * other. | |
template<typename OtherDerived > | |
void | applyOnTheLeft (const EigenBase< OtherDerived > &other) |
replaces *this by other * *this . | |
template<typename OtherDerived > | |
void | applyOnTheRight (const EigenBase< OtherDerived > &other) |
replaces *this by *this * other. | |
template<typename DiagonalDerived > | |
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
template<typename OtherDerived > | |
internal::scalar_product_traits < typename internal::traits < Derived >::Scalar, typename internal::traits< OtherDerived > ::Scalar >::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
Scalar | eigen2_dot (const MatrixBase< OtherDerived > &other) const |
RealScalar | squaredNorm () const |
RealScalar | norm () const |
RealScalar | stableNorm () const |
RealScalar | blueNorm () const |
RealScalar | hypotNorm () const |
const PlainObject | normalized () const |
void | normalize () |
Normalizes the vector, i.e. | |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
This is the "in place" version of adjoint(): it replaces *this by its own transpose. | |
DiagonalReturnType | diagonal () |
ConstDiagonalReturnType | diagonal () const |
This is the const version of diagonal(). | |
DiagonalDynamicIndexReturnType | diagonal (Index index) |
ConstDiagonalDynamicIndexReturnType | diagonal (Index index) const |
This is the const version of diagonal(Index). | |
template<unsigned int Mode> | |
internal::eigen2_part_return_type < Derived, Mode >::type | part () |
template<unsigned int Mode> | |
const internal::eigen2_part_return_type < Derived, Mode >::type | part () const |
template<unsigned int Mode> | |
TriangularViewReturnType< Mode > ::Type | triangularView () |
template<unsigned int Mode> | |
ConstTriangularViewReturnType < Mode >::Type | triangularView () const |
This is the const version of MatrixBase::triangularView() | |
const DiagonalWrapper< const Derived > | asDiagonal () const |
Derived & | setIdentity () |
Writes the identity expression (not necessarily square) into *this. | |
Derived & | setIdentity (Index rows, Index cols) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
bool | isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
NoAlias< Derived, Eigen::MatrixBase > | noalias () |
const ForceAlignedAccess< Derived > | forceAlignedAccess () const |
ForceAlignedAccess< Derived > | forceAlignedAccess () |
template<bool Enable> | |
internal::add_const_on_value_type < typename internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type >::type | forceAlignedAccessIf () const |
template<bool Enable> | |
internal::conditional< Enable, ForceAlignedAccess< Derived > , Derived & >::type | forceAlignedAccessIf () |
Scalar | trace () const |
template<int p> | |
RealScalar | lpNorm () const |
ArrayWrapper< Derived > | array () |
const FullPivLU< PlainObject > | fullPivLu () const |
| |
const PartialPivLU< PlainObject > | partialPivLu () const |
| |
const LU< PlainObject > | lu () const |
| |
const internal::inverse_impl < Derived > | inverse () const |
| |
template<typename ResultType > | |
void | computeInverseAndDetWithCheck (ResultType &inverse, typename ResultType::Scalar &determinant, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
| |
template<typename ResultType > | |
void | computeInverseWithCheck (ResultType &inverse, bool &invertible, const RealScalar &absDeterminantThreshold=NumTraits< Scalar >::dummy_precision()) const |
| |
Scalar | determinant () const |
| |
const LLT< PlainObject > | llt () const |
| |
const LDLT< PlainObject > | ldlt () const |
| |
const HouseholderQR< PlainObject > | householderQr () const |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () const |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. | |
RealScalar | operatorNorm () const |
Computes the L2 operator norm. | |
JacobiSVD< PlainObject > | jacobiSvd (unsigned int computationOptions=0) const |
| |
template<typename OtherDerived > | |
cross_product_return_type < OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
| |
template<typename OtherDerived > | |
PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
| |
PlainObject | unitOrthogonal (void) const |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
| |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
Concatenates a linear transformation matrix and a uniform scaling. | |
HomogeneousReturnType | homogeneous () const |
| |
const HNormalizedReturnType | hnormalized () const |
| |
void | makeHouseholderInPlace (Scalar &tau, RealScalar &beta) |
Computes the elementary reflector H such that: where the transformation H is: and the vector v is: . | |
template<typename EssentialPart > | |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
Computes the elementary reflector H such that: where the transformation H is: and the vector v is: . | |
template<typename EssentialPart > | |
void | applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
Apply the elementary reflector H given by with from the left to a vector or matrix. | |
template<typename EssentialPart > | |
void | applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace) |
Apply the elementary reflector H given by with from the right to a vector or matrix. | |
template<typename OtherScalar > | |
void | applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
Applies the rotation in the plane j to the rows p and q of *this , i.e., it computes B = J * B, with . | |
template<typename OtherScalar > | |
void | applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j) |
Applies the rotation in the plane j to the columns p and q of *this , i.e., it computes B = B * J with . | |
template<typename OtherDerived > | |
Derived & | lazyAssign (const Flagged< OtherDerived, 0, EvalBeforeAssigningBit > &other) |
Static Public Member Functions | |
static const IdentityReturnType | Identity () |
static const IdentityReturnType | Identity (Index rows, Index cols) |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | Unit (Index i) |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
static const BasisReturnType | UnitW () |
Detailed Description
template<typename Derived>
class Eigen::MatrixBase< Derived >
Base class for all dense matrices, vectors, and expressions.
This class is the base that is inherited by all matrix, vector, and related expression types. Most of the Eigen API is contained in this class, and its base classes. Other important classes for the Eigen API are Matrix, and VectorwiseOp.
Note that some methods are defined in other modules such as the LU module LU module for all functions related to matrix inversions.
- Template Parameters:
-
Derived is the derived type, e.g. a matrix type, or an expression, etc.
When writing a function taking Eigen objects as argument, if you want your function to take as argument any matrix, vector, or expression, just let it take a MatrixBase argument. As an example, here is a function printFirstRow which, given a matrix, vector, or expression x, prints the first row of x.
template<typename Derived> void printFirstRow(const Eigen::MatrixBase<Derived>& x) { cout << x.row(0) << endl; }
This class can be extended with the help of the plugin mechanism described on the page TopicCustomizingEigen by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN
.
- See also:
- TopicClassHierarchy
Definition at line 48 of file MatrixBase.h.
Member Typedef Documentation
typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime, AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor), internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime > PlainObject |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
Definition at line 115 of file MatrixBase.h.
typedef Matrix<Scalar,EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime), EIGEN_SIZE_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType |
type of the equivalent square matrix
Definition at line 96 of file MatrixBase.h.
Member Function Documentation
const MatrixBase< Derived >::AdjointReturnType adjoint | ( | ) | const |
- Returns:
- an expression of the adjoint (i.e. conjugate transpose) of *this.
Example:
Output:
- Warning:
- If you want to replace a matrix by its own adjoint, do NOT do this: Instead, use the adjointInPlace() method:
m = m.adjoint(); // bug!!! caused by aliasing effect
which gives Eigen good opportunities for optimization, or alternatively you can also do:m.adjointInPlace();
m = m.adjoint().eval();
- See also:
- adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op
Definition at line 237 of file Transpose.h.
void adjointInPlace | ( | ) |
This is the "in place" version of adjoint(): it replaces *this
by its own transpose.
Thus, doing
m.adjointInPlace();
has the same effect on m as doing
m = m.adjoint().eval();
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own adjoint. If you just need the adjoint of a matrix, use adjoint().
- Note:
- if the matrix is not square, then
*this
must be a resizable matrix. This excludes (non-square) fixed-size matrices, block-expressions and maps.
- See also:
- transpose(), adjoint(), transposeInPlace()
Definition at line 323 of file Transpose.h.
void applyHouseholderOnTheLeft | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) |
Apply the elementary reflector H given by with from the left to a vector or matrix.
On input:
- Parameters:
-
essential the essential part of the vector v
tau the scaling factor of the Householder transformation workspace a pointer to working space with at least this->cols() * essential.size() entries
- See also:
- MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()
Definition at line 112 of file src/Householder/Householder.h.
void applyHouseholderOnTheRight | ( | const EssentialPart & | essential, |
const Scalar & | tau, | ||
Scalar * | workspace | ||
) |
Apply the elementary reflector H given by with from the right to a vector or matrix.
On input:
- Parameters:
-
essential the essential part of the vector v
tau the scaling factor of the Householder transformation workspace a pointer to working space with at least this->cols() * essential.size() entries
- See also:
- MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()
Definition at line 149 of file src/Householder/Householder.h.
void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other ) |
void applyOnTheLeft | ( | Index | p, |
Index | q, | ||
const JacobiRotation< OtherScalar > & | j | ||
) |
Applies the rotation in the plane j to the rows p and q of *this
, i.e., it computes B = J * B, with .
- See also:
- class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()
Definition at line 277 of file src/Jacobi/Jacobi.h.
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other ) |
replaces *this
by *this
* other.
It is equivalent to MatrixBase::operator*=().
Example:
Output:
Definition at line 544 of file MatrixBase.h.
ArrayWrapper<Derived> array | ( | ) |
- Returns:
- an Array expression of this matrix
- See also:
- ArrayBase::matrix()
Definition at line 316 of file MatrixBase.h.
const DiagonalWrapper< const Derived > asDiagonal | ( | ) | const |
- Returns:
- a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients
Example:
Output:
- See also:
- class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
Definition at line 278 of file DiagonalMatrix.h.
NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm | ( | ) | const |
- Returns:
- the l2 norm of
*this
using the Blue's algorithm. A Portable Fortran Program to Find the Euclidean Norm of a Vector, ACM TOMS, Vol 4, Issue 1, 1978.
For architecture/scalar types without vectorization, this version is much faster than stableNorm(). Otherwise the stableNorm() is faster.
- See also:
- norm(), stableNorm(), hypotNorm()
Definition at line 184 of file StableNorm.h.
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > colPivHouseholderQr | ( | ) | const |
- Returns:
- the column-pivoting Householder QR decomposition of
*this
.
- See also:
- class ColPivHouseholderQR
Definition at line 573 of file ColPivHouseholderQR.h.
void computeInverseAndDetWithCheck | ( | ResultType & | inverse, |
typename ResultType::Scalar & | determinant, | ||
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const |
Computation of matrix inverse and determinant, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
- Parameters:
-
inverse Reference to the matrix in which to store the inverse. determinant Reference to the variable in which to store the determinant. invertible Reference to the bool variable in which to store whether the matrix is invertible. absDeterminantThreshold Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.
Example:
Output:
- See also:
- inverse(), computeInverseWithCheck()
void computeInverseWithCheck | ( | ResultType & | inverse, |
bool & | invertible, | ||
const RealScalar & | absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() |
||
) | const |
Computation of matrix inverse, with invertibility check.
This is only for fixed-size square matrices of size up to 4x4.
- Parameters:
-
inverse Reference to the matrix in which to store the inverse. invertible Reference to the bool variable in which to store whether the matrix is invertible. absDeterminantThreshold Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold.
Example:
Output:
- See also:
- inverse(), computeInverseAndDetWithCheck()
MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- the cross product of
*this
and other
Here is a very good explanation of cross-product: http://xkcd.com/199/
- See also:
- MatrixBase::cross3()
Definition at line 26 of file OrthoMethods.h.
MatrixBase< Derived >::PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- the cross product of
*this
and other using only the x, y, and z coefficients
The size of *this
and other must be four. This function is especially useful when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
- See also:
- MatrixBase::cross()
Definition at line 74 of file OrthoMethods.h.
internal::traits< Derived >::Scalar determinant | ( | ) | const |
- Returns:
- the determinant of this matrix
Definition at line 92 of file Determinant.h.
MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType diagonal | ( | Index | index ) | const |
This is the const version of diagonal(Index).
Definition at line 202 of file Diagonal.h.
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal | ( | ) |
- Returns:
- an expression of the main diagonal of the matrix
*this
*this
is not required to be square.
Example:
Output:
- See also:
- class Diagonal
- Returns:
- an expression of the DiagIndex-th sub or super diagonal of the matrix
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
- See also:
- MatrixBase::diagonal(), class Diagonal
Definition at line 168 of file Diagonal.h.
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type diagonal | ( | ) | const |
This is the const version of diagonal().
This is the const version of diagonal<int>().
Definition at line 176 of file Diagonal.h.
MatrixBase< Derived >::DiagonalDynamicIndexReturnType diagonal | ( | Index | index ) |
- Returns:
- an expression of the DiagIndex-th sub or super diagonal of the matrix
*this
*this
is not required to be square.
The template parameter DiagIndex represent a super diagonal if DiagIndex > 0 and a sub diagonal otherwise. DiagIndex == 0 is equivalent to the main diagonal.
Example:
Output:
- See also:
- MatrixBase::diagonal(), class Diagonal
Definition at line 194 of file Diagonal.h.
Index diagonalSize | ( | ) | const |
- Returns:
- the size of the main diagonal, which is min(rows(),cols()).
- See also:
- rows(), cols(), SizeAtCompileTime.
Definition at line 101 of file MatrixBase.h.
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- the dot product of *this with other.
- Note:
- If the scalar type is complex numbers, then this function returns the hermitian (sesquilinear) dot product, conjugate-linear in the first variable and linear in the second variable.
- See also:
- squaredNorm(), norm()
internal::traits< Derived >::Scalar eigen2_dot | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable (conjugating the second variable). Of course this only makes a difference in the complex case.
This method is only available in EIGEN2_SUPPORT mode.
- See also:
- dot()
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues | ( | ) | const |
Computes the eigenvalues of a matrix.
- Returns:
- Column vector containing the eigenvalues.
This function computes the eigenvalues with the help of the EigenSolver class (for real matrices) or the ComplexEigenSolver class (for complex matrices).
The eigenvalues are repeated according to their algebraic multiplicity, so there are as many eigenvalues as rows in the matrix.
The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
Output:
- See also:
- EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()
Definition at line 67 of file MatrixBaseEigenvalues.h.
const ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | const |
- Returns:
- an expression of *this with forced aligned access
- See also:
- forceAlignedAccessIf(),class ForceAlignedAccess
Definition at line 107 of file ForceAlignedAccess.h.
ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) |
- Returns:
- an expression of *this with forced aligned access
- See also:
- forceAlignedAccessIf(), class ForceAlignedAccess
Definition at line 117 of file ForceAlignedAccess.h.
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf | ( | ) | const |
- Returns:
- an expression of *this with forced aligned access if Enable is true.
- See also:
- forceAlignedAccess(), class ForceAlignedAccess
Definition at line 128 of file ForceAlignedAccess.h.
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf | ( | ) |
- Returns:
- an expression of *this with forced aligned access if Enable is true.
- See also:
- forceAlignedAccess(), class ForceAlignedAccess
Definition at line 139 of file ForceAlignedAccess.h.
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr | ( | ) | const |
- Returns:
- the full-pivoting Householder QR decomposition of
*this
.
- See also:
- class FullPivHouseholderQR
Definition at line 615 of file FullPivHouseholderQR.h.
const FullPivLU< typename MatrixBase< Derived >::PlainObject > fullPivLu | ( | ) | const |
- Returns:
- the full-pivoting LU decomposition of
*this
.
- See also:
- class FullPivLU
Definition at line 744 of file FullPivLU.h.
const MatrixBase< Derived >::HNormalizedReturnType hnormalized | ( | ) | const |
- Returns:
- an expression of the homogeneous normalized vector of
*this
Example:
Output:
- See also:
- VectorwiseOp::hnormalized()
Definition at line 158 of file Homogeneous.h.
MatrixBase< Derived >::HomogeneousReturnType homogeneous | ( | ) | const |
- Returns:
- an expression of the equivalent homogeneous vector
Example:
Output:
- See also:
- class Homogeneous
Definition at line 127 of file Homogeneous.h.
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > householderQr | ( | ) | const |
- Returns:
- the Householder QR decomposition of
*this
.
- See also:
- class HouseholderQR
Definition at line 381 of file HouseholderQR.h.
NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm | ( | ) | const |
- Returns:
- the l2 norm of
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.
- See also:
- norm(), stableNorm()
Definition at line 196 of file StableNorm.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Identity | ( | ) | [static] |
- Returns:
- an expression of the identity matrix (not necessarily square).
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variant taking size arguments.
Example:
Output:
- See also:
- Identity(Index,Index), setIdentity(), isIdentity()
Definition at line 700 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType Identity | ( | Index | nbRows, |
Index | nbCols | ||
) | [static] |
- Returns:
- an expression of the identity matrix (not necessarily square).
The parameters nbRows and nbCols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Identity() should be used instead.
Example:
Output:
- See also:
- Identity(), setIdentity(), isIdentity()
Definition at line 683 of file CwiseNullaryOp.h.
const internal::inverse_impl< Derived > inverse | ( | ) | const |
- Returns:
- the matrix inverse of this matrix.
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
- Note:
- This matrix must be invertible, otherwise the result is undefined. If you need an invertibility check, do the following:
- for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
- for the general case, use class FullPivLU.
Output:
- See also:
- computeInverseAndDetWithCheck()
bool isDiagonal | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() ) |
const |
- Returns:
- true if *this is approximately equal to a diagonal matrix, within the precision given by prec.
Example:
Output:
- See also:
- asDiagonal()
Definition at line 292 of file DiagonalMatrix.h.
bool isIdentity | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() ) |
const |
- Returns:
- true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.
Example:
Output:
- See also:
- class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
Definition at line 717 of file CwiseNullaryOp.h.
bool isLowerTriangular | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() ) |
const |
- Returns:
- true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
- See also:
- isUpperTriangular()
Definition at line 817 of file TriangularMatrix.h.
bool isOrthogonal | ( | const MatrixBase< OtherDerived > & | other, |
const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() |
||
) | const |
bool isUnitary | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() ) |
const |
- Returns:
- true if *this is approximately an unitary matrix, within the precision given by prec. In the case where the Scalar type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
- Note:
- This can be used to check whether a family of vectors forms an orthonormal basis. Indeed,
m.isUnitary()
returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.
Example:
Output:
bool isUpperTriangular | ( | const RealScalar & | prec = NumTraits<Scalar>::dummy_precision() ) |
const |
- Returns:
- true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
- See also:
- isLowerTriangular()
Definition at line 791 of file TriangularMatrix.h.
JacobiSVD< typename MatrixBase< Derived >::PlainObject > jacobiSvd | ( | unsigned int | computationOptions = 0 ) |
const |
- Returns:
- the singular value decomposition of
*this
computed by two-sided Jacobi transformations.
- See also:
- class JacobiSVD
Definition at line 969 of file JacobiSVD.h.
Derived& lazyAssign | ( | const Flagged< OtherDerived, 0, EvalBeforeAssigningBit > & | other ) |
Definition at line 477 of file MatrixBase.h.
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- an expression of the matrix product of
*this
and other without implicit evaluation.
The returned product will behave like any other expressions: the coefficients of the product will be computed once at a time as requested. This might be useful in some extremely rare cases when only a small and no coherent fraction of the result's coefficients have to be computed.
- Warning:
- This version of the matrix product can be much much slower. So use it only if you know what you are doing and that you measured a true speed improvement.
- See also:
- operator*(const MatrixBase&)
Definition at line 615 of file GeneralProduct.h.
const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt | ( | ) | const |
const LLT< typename MatrixBase< Derived >::PlainObject > llt | ( | ) | const |
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm | ( | ) | const |
- Returns:
- the norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values of the coefficients of *this. If p is the special value Eigen::Infinity, this function returns the norm, that is the maximum of the absolute values of the coefficients of *this.
- See also:
- norm()
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu | ( | ) | const |
Synonym of partialPivLu().
- Returns:
- the partial-pivoting LU decomposition of
*this
.
- See also:
- class PartialPivLU
Definition at line 501 of file PartialPivLU.h.
void makeHouseholder | ( | EssentialPart & | essential, |
Scalar & | tau, | ||
RealScalar & | beta | ||
) | const |
Computes the elementary reflector H such that: where the transformation H is: and the vector v is: .
On output:
- Parameters:
-
essential the essential part of the vector v
tau the scaling factor of the Householder transformation beta the result of H * *this
- See also:
- MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()
Definition at line 65 of file src/Householder/Householder.h.
void makeHouseholderInPlace | ( | Scalar & | tau, |
RealScalar & | beta | ||
) |
Computes the elementary reflector H such that: where the transformation H is: and the vector v is: .
The essential part of the vector v
is stored in *this.
On output:
- Parameters:
-
tau the scaling factor of the Householder transformation beta the result of H * *this
- See also:
- MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()
Definition at line 42 of file src/Householder/Householder.h.
NoAlias< Derived, MatrixBase > noalias | ( | ) |
- Returns:
- a pseudo expression of
*this
with an operator= assuming no aliasing between*this
and the source expression.
More precisely, noalias() allows to bypass the EvalBeforeAssignBit flag. Currently, even though several expressions may alias, only product expressions have this flag. Therefore, noalias() is only usefull when the source expression contains a matrix product.
Here are some examples where noalias is usefull:
D.noalias() = A * B; D.noalias() += A.transpose() * B; D.noalias() -= 2 * A * B.adjoint();
On the other hand the following example will lead to a wrong result:
A.noalias() = A * B;
because the result matrix A is also an operand of the matrix product. Therefore, there is no alternative than evaluating A * B in a temporary, that is the default behavior when you write:
A = A * B;
- See also:
- class NoAlias
NumTraits< typename internal::traits< Derived >::Scalar >::Real norm | ( | ) | const |
- Returns:
- , for vectors, the l2 norm of
*this
, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of*this
with itself.
- See also:
- dot(), squaredNorm()
void normalize | ( | ) |
const MatrixBase< Derived >::PlainObject normalized | ( | ) | const |
- Returns:
- an expression of the quotient of *this by its own norm.
- See also:
- norm(), normalize()
bool operator!= | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- true if at least one pair of coefficients of
*this
and other are not exactly equal to each other.
- Warning:
- When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
- See also:
- isApprox(), operator==
Definition at line 295 of file MatrixBase.h.
MatrixBase< Derived >::ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s ) | const |
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* | ( | const DiagonalBase< DiagonalDerived > & | a_diagonal ) | const |
- Returns:
- the diagonal matrix product of
*this
by the diagonal matrix diagonal.
Definition at line 124 of file DiagonalProduct.h.
const ProductReturnType< Derived, OtherDerived >::Type operator* | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- the matrix product of
*this
and other.
- Note:
- If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
- See also:
- lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
Definition at line 574 of file GeneralProduct.h.
Derived & operator*= | ( | const EigenBase< OtherDerived > & | other ) |
replaces *this
by *this
* other.
- Returns:
- a reference to
*this
Example:
Output:
Definition at line 531 of file MatrixBase.h.
EIGEN_STRONG_INLINE Derived & operator+= | ( | const MatrixBase< OtherDerived > & | other ) |
replaces *this
by *this
+ other.
- Returns:
- a reference to
*this
Definition at line 221 of file CwiseBinaryOp.h.
EIGEN_STRONG_INLINE Derived & operator-= | ( | const MatrixBase< OtherDerived > & | other ) |
replaces *this
by *this
- other.
- Returns:
- a reference to
*this
Definition at line 207 of file CwiseBinaryOp.h.
EIGEN_STRONG_INLINE Derived & operator= | ( | const MatrixBase< Derived > & | other ) |
bool operator== | ( | const MatrixBase< OtherDerived > & | other ) | const |
- Returns:
- true if each coefficients of
*this
and other are all exactly equal.
- Warning:
- When using floating point scalar values you probably should rather use a fuzzy comparison such as isApprox()
- See also:
- isApprox(), operator!=
Definition at line 287 of file MatrixBase.h.
MatrixBase< Derived >::RealScalar operatorNorm | ( | ) | const |
Computes the L2 operator norm.
- Returns:
- Operator norm of the matrix.
This function computes the L2 operator norm of a matrix, which is also known as the spectral norm. The norm of a matrix is defined to be
where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix .
The current implementation uses the eigenvalues of , as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
Output:
Definition at line 122 of file MatrixBaseEigenvalues.h.
const internal::eigen2_part_return_type< Derived, Mode >::type part | ( | ) | const |
Definition at line 743 of file TriangularMatrix.h.
internal::eigen2_part_return_type< Derived, Mode >::type part | ( | ) |
Definition at line 751 of file TriangularMatrix.h.
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > partialPivLu | ( | ) | const |
- Returns:
- the partial-pivoting LU decomposition of
*this
.
- See also:
- class PartialPivLU
Definition at line 485 of file PartialPivLU.h.
EIGEN_STRONG_INLINE Derived & setIdentity | ( | Index | nbRows, |
Index | nbCols | ||
) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
- Parameters:
-
nbRows the new number of rows nbCols the new number of columns
Example:
Output:
- See also:
- MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
Definition at line 788 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE Derived & setIdentity | ( | ) |
Writes the identity expression (not necessarily square) into *this.
Example:
Output:
- See also:
- class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
Definition at line 772 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm | ( | ) | const |
- Returns:
- , for vectors, the squared l2 norm of
*this
, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of*this
with itself.
NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm | ( | ) | const |
- Returns:
- the l2 norm of
*this
avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficients
2 - compute in a standard way
For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.
- See also:
- norm(), blueNorm(), hypotNorm()
Definition at line 153 of file StableNorm.h.
EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar trace | ( | ) | const |
- Returns:
- the trace of
*this
, i.e. the sum of the coefficients on the main diagonal.
*this
can be any matrix, not necessarily square.
- See also:
- diagonal(), sum()
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView | ( | ) | const |
This is the const version of MatrixBase::triangularView()
Definition at line 780 of file TriangularMatrix.h.
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView | ( | ) |
- Returns:
- an expression of a triangular view extracted from the current matrix
The parameter Mode can have the following values: Upper
, StrictlyUpper
, UnitUpper
, Lower
, StrictlyLower
, UnitLower
.
Example:
Output:
- See also:
- class TriangularView
Definition at line 771 of file TriangularMatrix.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | newSize, |
Index | i | ||
) | [static] |
- Returns:
- an expression of the i-th unit (basis) vector.
- See also:
- MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 801 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | i ) | [static] |
- Returns:
- an expression of the i-th unit (basis) vector.
This variant is for fixed-size vector only.
- See also:
- MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 816 of file CwiseNullaryOp.h.
MatrixBase< Derived >::PlainObject unitOrthogonal | ( | void | ) | const |
- Returns:
- a unit vector which is orthogonal to
*this
The size of *this
must be at least 2. If the size is exactly 2, then the returned vector is a counter clock wise rotation of *this
, i.e., (-y,x).normalized().
- See also:
- cross()
Definition at line 210 of file OrthoMethods.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType UnitW | ( | ) | [static] |
- Returns:
- an expression of the W axis unit vector (0,0,0,1)
- See also:
- MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 859 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType UnitX | ( | ) | [static] |
- Returns:
- an expression of the X axis unit vector (1{,0}^*)
- See also:
- MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 829 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType UnitY | ( | ) | [static] |
- Returns:
- an expression of the Y axis unit vector (0,1{,0}^*)
- See also:
- MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 839 of file CwiseNullaryOp.h.
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType UnitZ | ( | ) | [static] |
- Returns:
- an expression of the Z axis unit vector (0,0,1{,0}^*)
- See also:
- MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
Definition at line 849 of file CwiseNullaryOp.h.
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