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MatrixBase< Derived > Class Template Reference


Detailed Description

template<typename Derived>
class 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.

Parameters:
Derivedis 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;
    }
See also:
TopicClassHierarchy

Definition at line 58 of file MatrixBase.h.

#include <src/Core/MatrixBase.h>

Inheritance diagram for MatrixBase< Derived >:
Inheritance graph
[legend]

List of all members.

Classes

struct  ConstDiagonalIndexReturnType
struct  ConstSelfAdjointViewReturnType
struct  ConstTriangularViewReturnType
struct  DiagonalIndexReturnType
struct  SelfAdjointViewReturnType
struct  TriangularViewReturnType

Public Types

enum  { SizeMinusOne = SizeAtCompileTime==Dynamic ? Dynamic : SizeAtCompileTime-1 }
enum  { HomogeneousReturnTypeDirection = ColsAtCompileTime==1?Vertical:Horizontal }
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.
typedef Diagonal< Derived > DiagonalReturnType
typedef const Diagonal< const
Derived > 
ConstDiagonalReturnType
typedef Block< const Derived,
internal::traits< Derived >
::ColsAtCompileTime==1?SizeMinusOne:1,
internal::traits< Derived >
::ColsAtCompileTime==1?1:SizeMinusOne > 
ConstStartMinusOne
typedef CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Derived >::Scalar >
, ConstStartMinusOne
HNormalizedReturnType
typedef Homogeneous< Derived,
HomogeneousReturnTypeDirection > 
HomogeneousReturnType
typedef
internal::stem_function
< Scalar >::type 
StemFunction
MRPT plugin: Types
enum  { static_size = RowsAtCompileTime*ColsAtCompileTime }
typedef Scalar value_type
 Type of the elements.

Public Member Functions

Index diagonalSize () const
const CwiseUnaryOp
< internal::scalar_opposite_op
< typename internal::traits
< Derived >::Scalar >, Derived > 
operator- () const
const ScalarMultipleReturnType operator* (const Scalar &scalar) const
const ScalarMultipleReturnType operator* (const RealScalar &scalar) const
const CwiseUnaryOp
< internal::scalar_quotient1_op
< typename internal::traits
< Derived >::Scalar >, Derived > 
operator/ (const Scalar &scalar) const
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, Derived > 
operator* (const std::complex< Scalar > &scalar) const
 Overloaded for efficient real matrix times complex scalar value.
template<typename NewType >
internal::cast_return_type
< Derived, const CwiseUnaryOp
< internal::scalar_cast_op
< typename internal::traits
< Derived >::Scalar, NewType >
, Derived > >::type 
cast () const
ConjugateReturnType conjugate () const
RealReturnType real () const
const ImagReturnType imag () const
template<typename CustomUnaryOp >
const CwiseUnaryOp
< CustomUnaryOp, Derived > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
template<typename CustomViewOp >
const CwiseUnaryView
< CustomViewOp, Derived > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
NonConstRealReturnType real ()
NonConstImagReturnType imag ()
template<typename CustomBinaryOp , typename OtherDerived >
EIGEN_STRONG_INLINE const
CwiseBinaryOp< CustomBinaryOp,
Derived, OtherDerived > 
binaryExpr (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
EIGEN_STRONG_INLINE const
CwiseUnaryOp
< internal::scalar_abs_op
< Scalar >, Derived > 
cwiseAbs () const
EIGEN_STRONG_INLINE const
CwiseUnaryOp
< internal::scalar_abs2_op
< Scalar >, Derived > 
cwiseAbs2 () const
const CwiseUnaryOp
< internal::scalar_sqrt_op
< Scalar >, Derived > 
cwiseSqrt () const
const CwiseUnaryOp
< internal::scalar_inverse_op
< Scalar >, Derived > 
cwiseInverse () const
const CwiseUnaryOp
< std::binder1st
< std::equal_to< Scalar >
>, Derived > 
cwiseEqual (const Scalar &s) const
template<typename OtherDerived >
EIGEN_STRONG_INLINE const EIGEN_CWISE_PRODUCT_RETURN_TYPE (Derived, OtherDerived) cwiseProduct(const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::equal_to< Scalar >
, Derived, OtherDerived > 
cwiseEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, Derived, OtherDerived > 
cwiseNotEqual (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_STRONG_INLINE const
CwiseBinaryOp
< internal::scalar_min_op
< Scalar >, Derived,
OtherDerived > 
cwiseMin (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_STRONG_INLINE const
CwiseBinaryOp
< internal::scalar_max_op
< Scalar >, Derived,
OtherDerived > 
cwiseMax (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<typename OtherDerived >
EIGEN_STRONG_INLINE const
CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, Derived,
OtherDerived > 
cwiseQuotient (const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &other) const
template<class OtherDerived >
EIGEN_STRONG_INLINE void extractRow (size_t nRow, Eigen::EigenBase< OtherDerived > &v, size_t startingCol=0) const
 Extract one row from the matrix into a row vector.
template<typename T >
void extractRow (size_t nRow, std::vector< T > &v, size_t startingCol=0) const
template<class VECTOR >
EIGEN_STRONG_INLINE void extractRowAsCol (size_t nRow, VECTOR &v, size_t startingCol=0) const
 Extract one row from the matrix into a column vector.
template<class VECTOR >
EIGEN_STRONG_INLINE void extractCol (size_t nCol, VECTOR &v, size_t startingRow=0) const
 Extract one column from the matrix into a column vector.
template<typename T >
void extractCol (size_t nCol, std::vector< T > &v, size_t startingRow=0) const
template<class MATRIX >
EIGEN_STRONG_INLINE void extractMatrix (const size_t firstRow, const size_t firstCol, MATRIX &m) const
template<class MATRIX >
EIGEN_STRONG_INLINE void extractMatrix (const size_t firstRow, const size_t firstCol, const size_t nRows, const size_t nCols, MATRIX &m) const
template<class MATRIX >
EIGEN_STRONG_INLINE void extractSubmatrix (const size_t row_first, const size_t row_last, const size_t col_first, const size_t col_last, MATRIX &out) const
 Get a submatrix, given its bounds: first & last column and row (inclusive).
template<class MATRIX >
void extractSubmatrixSymmetricalBlocks (const size_t block_size, const std::vector< size_t > &block_indices, MATRIX &out) const
 Get a submatrix from a square matrix, by collecting the elements M(idxs,idxs), where idxs is a sequence {block_indices(i):block_indices(i)+block_size-1} for all "i" up to the size of block_indices.
template<class MATRIX >
void extractSubmatrixSymmetrical (const std::vector< size_t > &indices, MATRIX &out) const
 Get a submatrix from a square matrix, by collecting the elements M(idxs,idxs), where idxs is the sequence of indices passed as argument.
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 DenseBase< OtherDerived > &other)
 Copies other into *this.
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
template<typename OtherDerived >
Derived & operator= (const ReturnByValue< OtherDerived > &other)
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 *this * other.
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 >
Scalar 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().
template<int Index>
DiagonalIndexReturnType< Index >
::Type 
diagonal ()
template<int Index>
ConstDiagonalIndexReturnType
< Index >::Type 
diagonal () const
MatrixBase::template
DiagonalIndexReturnType
< Dynamic >::Type 
diagonal (Index index)
MatrixBase::template
ConstDiagonalIndexReturnType
< Dynamic >::Type 
diagonal (Index index) const
 This is the const version of diagonal(Index).
template<unsigned int Mode>
TriangularView< Derived, Mode > part ()
template<unsigned int Mode>
const TriangularView< Derived,
Mode > 
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()
template<unsigned int UpLo>
SelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView ()
template<unsigned int UpLo>
ConstSelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView () const
const SparseView< Derived > sparseView (const Scalar &m_reference=Scalar(0), typename NumTraits< Scalar >::Real m_epsilon=NumTraits< Scalar >::dummy_precision()) const
const DiagonalWrapper< 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 (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isLowerTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool isOrthogonal (const MatrixBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
bool isUnitary (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
MatrixBase< Derived > & matrix ()
const MatrixBase< Derived > & matrix () const
ArrayWrapper< Derived > array ()
const ArrayWrapper< Derived > array () const
const FullPivLU< PlainObjectfullPivLu () const
 
const PartialPivLU< PlainObjectpartialPivLu () const
 
const PartialPivLU< PlainObjectlu () 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< PlainObjectllt () const
 
const LDLT< PlainObjectldlt () const
 
const HouseholderQR< PlainObjecthouseholderQr () 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< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
template<typename OtherDerived >
PlainObject 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.
const HNormalizedReturnType hnormalized () const
 
HomogeneousReturnType homogeneous () const
 
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
 Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $.
template<typename EssentialPart >
void applyHouseholderOnTheLeft (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
template<typename EssentialPart >
void applyHouseholderOnTheRight (const EssentialPart &essential, const Scalar &tau, Scalar *workspace)
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 $ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) $.
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 $ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) $.
const
MatrixExponentialReturnValue
< Derived > 
exp () const
const
MatrixFunctionReturnValue
< Derived > 
matrixFunction (StemFunction f) const
const
MatrixFunctionReturnValue
< Derived > 
cosh () const
const
MatrixFunctionReturnValue
< Derived > 
sinh () const
const
MatrixFunctionReturnValue
< Derived > 
cos () const
const
MatrixFunctionReturnValue
< Derived > 
sin () const
MRPT plugin: Set/get/load/save and other miscelaneous methods
EIGEN_STRONG_INLINE void fill (const Scalar v)
EIGEN_STRONG_INLINE void assign (const Scalar v)
EIGEN_STRONG_INLINE void assign (size_t N, const Scalar v)
EIGEN_STRONG_INLINE size_t getRowCount () const
 Get number of rows.
EIGEN_STRONG_INLINE size_t getColCount () const
 Get number of columns.
EIGEN_STRONG_INLINE void unit (const size_t nRows, const Scalar diag_vals)
 Make the matrix an identity matrix (the diagonal values can be 1.0 or any other value)
EIGEN_STRONG_INLINE void unit ()
 Make the matrix an identity matrix.
EIGEN_STRONG_INLINE void eye ()
 Make the matrix an identity matrix.
EIGEN_STRONG_INLINE void zeros ()
 Set all elements to zero.
EIGEN_STRONG_INLINE void zeros (const size_t row, const size_t col)
 Resize and set all elements to zero.
EIGEN_STRONG_INLINE void ones (const size_t row, const size_t col)
 Resize matrix and set all elements to one.
EIGEN_STRONG_INLINE void ones ()
 Set all elements to one.
EIGEN_STRONG_INLINE Scalarget_unsafe_row (size_t row)
 Fast but unsafe method to obtain a pointer to a given row of the matrix (Use only in time critical applications) VERY IMPORTANT WARNING: You must be aware of the memory layout, either Column or Row-major ordering.
EIGEN_STRONG_INLINE const Scalarget_unsafe_row (size_t row) const
EIGEN_STRONG_INLINE Scalar get_unsafe (const size_t row, const size_t col) const
 Read-only access to one element (Use with caution, bounds are not checked!)
EIGEN_STRONG_INLINE Scalarget_unsafe (const size_t row, const size_t col)
 Reference access to one element (Use with caution, bounds are not checked!)
EIGEN_STRONG_INLINE void set_unsafe (const size_t row, const size_t col, const Scalar val)
 Sets an element (Use with caution, bounds are not checked!)
EIGEN_STRONG_INLINE void push_back (Scalar val)
 Insert an element at the end of the container (for 1D vectors/arrays)
EIGEN_STRONG_INLINE bool isSquare () const
EIGEN_STRONG_INLINE bool isSingular (const Scalar absThreshold=0) const
bool fromMatlabStringFormat (const std::string &s, bool dumpErrorMsgToStdErr=true)
 Read a matrix from a string in Matlab-like format, for example "[1 0 2; 0 4 -1]" The string must start with '[' and end with ']'.
std::string inMatlabFormat (const size_t decimal_digits=6) const
 Dump matrix in matlab format.
void saveToTextFile (const std::string &file, mrpt::math::TMatrixTextFileFormat fileFormat=mrpt::math::MATRIX_FORMAT_ENG, bool appendMRPTHeader=false, const std::string &userHeader=std::string()) const
 Save matrix to a text file, compatible with MATLAB text format (see also the methods of matrix classes themselves).
void loadFromTextFile (const std::string &file)
 Load matrix from a text file, compatible with MATLAB text format.
void loadFromTextFile (std::istream &_input_text_stream)
EIGEN_STRONG_INLINE void multiplyColumnByScalar (size_t c, Scalar s)
EIGEN_STRONG_INLINE void multiplyRowByScalar (size_t r, Scalar s)
EIGEN_STRONG_INLINE void swapCols (size_t i1, size_t i2)
EIGEN_STRONG_INLINE void swapRows (size_t i1, size_t i2)
EIGEN_STRONG_INLINE size_t countNonZero () const
EIGEN_STRONG_INLINE Scalar maximum () const
 [VECTORS OR MATRICES] Finds the maximum value

Exceptions:
std::exceptionOn an empty input container

EIGEN_STRONG_INLINE Scalar minimum () const
 [VECTORS OR MATRICES] Finds the minimum value
EIGEN_STRONG_INLINE void minimum_maximum (Scalar &out_min, Scalar &out_max) const
 [VECTORS OR MATRICES] Compute the minimum and maximum of a container at once
EIGEN_STRONG_INLINE Scalar maximum (size_t *maxIndex) const
 [VECTORS ONLY] Finds the maximum value (and the corresponding zero-based index) from a given container.
void find_index_max_value (size_t &u, size_t &v, Scalar &valMax) const
 [VECTORS OR MATRICES] Finds the maximum value (and the corresponding zero-based index) from a given container.
EIGEN_STRONG_INLINE Scalar minimum (size_t *minIndex) const
 [VECTORS ONLY] Finds the minimum value (and the corresponding zero-based index) from a given container.
EIGEN_STRONG_INLINE void minimum_maximum (Scalar &out_min, Scalar &out_max, size_t *minIndex, size_t *maxIndex) const
 [VECTORS ONLY] Compute the minimum and maximum of a container at once
EIGEN_STRONG_INLINE Scalar norm_inf () const
 Compute the norm-infinite of a vector ($f[ ||{v}||_ $f]), ie the maximum absolute value of the elements.
EIGEN_STRONG_INLINE Scalar squareNorm () const
 Compute the square norm of a vector/array/matrix (the Euclidean distance to the origin, taking all the elements as a single vector).
EIGEN_STRONG_INLINE Scalar sumAll () const
template<typename OtherDerived >
EIGEN_STRONG_INLINE void laplacian (Eigen::MatrixBase< OtherDerived > &ret) const
 Computes the laplacian of this square graph weight matrix.
EIGEN_STRONG_INLINE void setSize (size_t row, size_t col)
 Changes the size of matrix, maintaining its previous content as possible and padding with zeros where applicable.
template<class OUTVECT >
void largestEigenvector (OUTVECT &x, Scalar resolution=Scalar(0.01), size_t maxIterations=6, int *out_Iterations=NULL, float *out_estimatedResolution=NULL) const
 Efficiently computes only the biggest eigenvector of the matrix using the Power Method, and returns it in the passed vector "x".
MatrixBase< Derived > & operator^= (const unsigned int pow)
 Combined matrix power and assignment operator.
EIGEN_STRONG_INLINE void scalarPow (const Scalar s)
 Scalar power of all elements to a given power, this is diferent of ^ operator.
EIGEN_STRONG_INLINE bool isDiagonal () const
 Checks for matrix type.
EIGEN_STRONG_INLINE Scalar maximumDiagonal () const
 Finds the maximum value in the diagonal of the matrix.
EIGEN_STRONG_INLINE double mean () const
 Computes the mean of the entire matrix.
template<class VEC >
void meanAndStd (VEC &outMeanVector, VEC &outStdVector, const bool unbiased_variance=true) const
 Computes a row with the mean values of each column in the matrix and the associated vector with the standard deviation of each column.
void meanAndStdAll (double &outMean, double &outStd, const bool unbiased_variance=true) const
 Computes the mean and standard deviation of all the elements in the matrix as a whole.
template<typename MAT >
EIGEN_STRONG_INLINE void insertMatrix (size_t r, size_t c, const MAT &m)
 Insert matrix "m" into this matrix at indices (r,c), that is, (*this)(r,c)=m(0,0) and so on.
template<typename MAT >
EIGEN_STRONG_INLINE void insertMatrixTranspose (size_t r, size_t c, const MAT &m)
template<typename MAT >
EIGEN_STRONG_INLINE void insertRow (size_t nRow, const MAT &aRow)
template<typename MAT >
EIGEN_STRONG_INLINE void insertCol (size_t nCol, const MAT &aCol)
EIGEN_STRONG_INLINE void removeColumns (const std::vector< size_t > &idxsToRemove)
 Remove columns of the matrix.
EIGEN_STRONG_INLINE void unsafeRemoveColumns (const std::vector< size_t > &idxs)
 Remove columns of the matrix.
EIGEN_STRONG_INLINE void removeRows (const std::vector< size_t > &idxsToRemove)
 Remove rows of the matrix.
EIGEN_STRONG_INLINE void unsafeRemoveRows (const std::vector< size_t > &idxs)
 Remove rows of the matrix.
EIGEN_STRONG_INLINE const
AdjointReturnType 
t () const
 Transpose.
EIGEN_STRONG_INLINE PlainObject inv () const
template<class MATRIX >
EIGEN_STRONG_INLINE void inv (MATRIX &outMat) const
template<class MATRIX >
EIGEN_STRONG_INLINE void inv_fast (MATRIX &outMat) const
EIGEN_STRONG_INLINE Scalar det () const
Multiply and extra addition functions
EIGEN_STRONG_INLINE bool empty () const
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void add_Ac (const OTHERMATRIX &m, const Scalar c)
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void substract_Ac (const OTHERMATRIX &m, const Scalar c)
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void substract_At (const OTHERMATRIX &m)
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void substract_An (const OTHERMATRIX &m, const size_t n)
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void add_AAt (const OTHERMATRIX &A)
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void substract_AAt (const OTHERMATRIX &A)
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void multiply (const MATRIX1 &A, const MATRIX2 &B)
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void multiply_AB (const MATRIX1 &A, const MATRIX2 &B)
template<typename MATRIX1 , typename MATRIX2 >
EIGEN_STRONG_INLINE void multiply_AtB (const MATRIX1 &A, const MATRIX2 &B)
template<typename OTHERVECTOR1 , typename OTHERVECTOR2 >
EIGEN_STRONG_INLINE void multiply_Ab (const OTHERVECTOR1 &vIn, OTHERVECTOR2 &vOut, bool accumToOutput=false) const
template<typename OTHERVECTOR1 , typename OTHERVECTOR2 >
EIGEN_STRONG_INLINE void multiply_Atb (const OTHERVECTOR1 &vIn, OTHERVECTOR2 &vOut, bool accumToOutput=false) const
template<typename MAT_C , typename MAT_R >
EIGEN_STRONG_INLINE void multiply_HCHt (const MAT_C &C, MAT_R &R, bool accumResultInOutput=false) const
template<typename MAT_C , typename MAT_R >
EIGEN_STRONG_INLINE void multiply_HtCH (const MAT_C &C, MAT_R &R, bool accumResultInOutput=false) const
template<typename MAT_C >
EIGEN_STRONG_INLINE Scalar multiply_HCHt_scalar (const MAT_C &C) const
template<typename MAT_C >
EIGEN_STRONG_INLINE Scalar multiply_HtCH_scalar (const MAT_C &C) const
template<typename MAT_A >
EIGEN_STRONG_INLINE void multiply_AAt_scalar (const MAT_A &A, typename MAT_A::value_type f)
template<typename MAT_A >
EIGEN_STRONG_INLINE void multiply_AtA_scalar (const MAT_A &A, typename MAT_A::value_type f)
template<class MAT_A , class SKEW_3VECTOR >
void multiply_A_skew3 (const MAT_A &A, const SKEW_3VECTOR &v)
template<class SKEW_3VECTOR , class MAT_A >
void multiply_skew3_A (const SKEW_3VECTOR &v, const MAT_A &A)
template<class MAT_A , class MAT_OUT >
EIGEN_STRONG_INLINE void multiply_subMatrix (const MAT_A &A, MAT_OUT &outResult, const size_t A_cols_offset, const size_t A_rows_offset, const size_t A_col_count) const
 outResult = this * A
template<class MAT_A , class MAT_B , class MAT_C >
void multiply_ABC (const MAT_A &A, const MAT_B &B, const MAT_C &C)
template<class MAT_A , class MAT_B , class MAT_C >
void multiply_ABCt (const MAT_A &A, const MAT_B &B, const MAT_C &C)
template<class MAT_A , class MAT_B , class MAT_C >
void multiply_AtBC (const MAT_A &A, const MAT_B &B, const MAT_C &C)
template<class MAT_A , class MAT_B >
EIGEN_STRONG_INLINE void multiply_ABt (const MAT_A &A, const MAT_B &B)
template<class MAT_A >
EIGEN_STRONG_INLINE void multiply_AAt (const MAT_A &A)
template<class MAT_A >
EIGEN_STRONG_INLINE void multiply_AtA (const MAT_A &A)
template<class MAT_A , class MAT_B >
EIGEN_STRONG_INLINE void multiply_result_is_symmetric (const MAT_A &A, const MAT_B &B)
template<class MAT2 , class MAT3 >
EIGEN_STRONG_INLINE void leftDivideSquare (const MAT2 &A, MAT3 &RES) const
 Matrix left divide: RES = A-1 * this , with A being squared (using the Eigen::ColPivHouseholderQR method)
template<class MAT2 , class MAT3 >
EIGEN_STRONG_INLINE void rightDivideSquare (const MAT2 &B, MAT3 &RES) const
 Matrix right divide: RES = this * B-1, with B being squared (using the Eigen::ColPivHouseholderQR method)
Eigenvalue / Eigenvectors
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void eigenVectors (MATRIX1 &eVecs, MATRIX2 &eVals) const
 [For square matrices only] Compute the eigenvectors and eigenvalues (sorted), both returned as matrices: eigenvectors are the columns in "eVecs", and eigenvalues in ascending order as the diagonal of "eVals".
template<class MATRIX1 , class VECTOR1 >
EIGEN_STRONG_INLINE void eigenVectorsVec (MATRIX1 &eVecs, VECTOR1 &eVals) const
 [For square matrices only] Compute the eigenvectors and eigenvalues (sorted), eigenvectors are the columns in "eVecs", and eigenvalues are returned in in ascending order in the vector "eVals".
template<class VECTOR >
EIGEN_STRONG_INLINE void eigenValues (VECTOR &eVals) const
 [For square matrices only] Compute the eigenvectors and eigenvalues (sorted), and return only the eigenvalues in the vector "eVals".
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void eigenVectorsSymmetric (MATRIX1 &eVecs, MATRIX2 &eVals) const
 [For symmetric matrices only] Compute the eigenvectors and eigenvalues (in no particular order), both returned as matrices: eigenvectors are the columns, and eigenvalues
template<class MATRIX1 , class VECTOR1 >
EIGEN_STRONG_INLINE void eigenVectorsSymmetricVec (MATRIX1 &eVecs, VECTOR1 &eVals) const
 [For symmetric matrices only] Compute the eigenvectors and eigenvalues (in no particular order), both returned as matrices: eigenvectors are the columns, and eigenvalues
Linear algebra & decomposition-based methods
template<class MATRIX >
EIGEN_STRONG_INLINE bool chol (MATRIX &U) const
 Cholesky M=UT * U decomposition for simetric matrix (upper-half of the matrix will be actually ignored)
EIGEN_STRONG_INLINE size_t rank (double threshold=0) const
 Gets the rank of the matrix via the Eigen::ColPivHouseholderQR method.
Scalar and element-wise extra operators
EIGEN_STRONG_INLINE MatrixBase
< Derived > & 
Sqrt ()
EIGEN_STRONG_INLINE PlainObject Sqrt () const
EIGEN_STRONG_INLINE MatrixBase
< Derived > & 
Abs ()
EIGEN_STRONG_INLINE PlainObject Abs () const
EIGEN_STRONG_INLINE MatrixBase
< Derived > & 
Log ()
EIGEN_STRONG_INLINE PlainObject Log () const
EIGEN_STRONG_INLINE MatrixBase
< Derived > & 
Exp ()
EIGEN_STRONG_INLINE PlainObject Exp () const
EIGEN_STRONG_INLINE MatrixBase
< Derived > & 
Square ()
EIGEN_STRONG_INLINE PlainObject Square () const
void normalize (Scalar valMin, Scalar valMax)
 Scales all elements such as the minimum & maximum values are shifted to the given values.
void adjustRange (Scalar valMin, Scalar valMax)

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 ()

Protected Member Functions

 MatrixBase ()
template<typename OtherDerived >
Derived & operator+= (const ArrayBase< OtherDerived > &array)
template<typename OtherDerived >
Derived & operator-= (const ArrayBase< OtherDerived > &array)

Private Member Functions

 MatrixBase (int)
 MatrixBase (int, int)
template<typename OtherDerived >
 MatrixBase (const MatrixBase< OtherDerived > &)

Friends

const ScalarMultipleReturnType operator* (const Scalar &scalar, const StorageBaseType &matrix)
const CwiseUnaryOp
< internal::scalar_multiple2_op
< Scalar, std::complex< Scalar >
>, Derived > 
operator* (const std::complex< Scalar > &scalar, const StorageBaseType &matrix)

MRPT plugin: Basic iterators. These iterators are intended for 1D matrices only, i.e. column or row vectors.

typedef Scalariterator
typedef const Scalarconst_iterator
EIGEN_STRONG_INLINE iterator begin ()
EIGEN_STRONG_INLINE iterator end ()
EIGEN_STRONG_INLINE const_iterator begin () const
EIGEN_STRONG_INLINE const_iterator end () const

Member Typedef Documentation

template<typename Derived>
typedef const Scalar* MatrixBase< Derived >::const_iterator

Definition at line 45 of file MatrixBase.h.

template<typename Derived>
typedef const Diagonal<const Derived> MatrixBase< Derived >::ConstDiagonalReturnType

Definition at line 218 of file MatrixBase.h.

template<typename Derived>
typedef Block<const Derived, internal::traits<Derived>::ColsAtCompileTime==1 ? SizeMinusOne : 1, internal::traits<Derived>::ColsAtCompileTime==1 ? 1 : SizeMinusOne> MatrixBase< Derived >::ConstStartMinusOne

Definition at line 363 of file MatrixBase.h.

template<typename Derived>
typedef Diagonal<Derived> MatrixBase< Derived >::DiagonalReturnType

Definition at line 216 of file MatrixBase.h.

template<typename Derived>
typedef CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, ConstStartMinusOne > MatrixBase< Derived >::HNormalizedReturnType

Definition at line 365 of file MatrixBase.h.

template<typename Derived>
typedef Homogeneous<Derived, HomogeneousReturnTypeDirection> MatrixBase< Derived >::HomogeneousReturnType

Definition at line 371 of file MatrixBase.h.

template<typename Derived>
typedef Scalar* MatrixBase< Derived >::iterator

Definition at line 44 of file MatrixBase.h.

template<typename Derived>
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 > MatrixBase< Derived >::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&.

Reimplemented in ProductBase< Derived, Lhs, Rhs >, ScaledProduct< NestedProduct >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.

Definition at line 125 of file MatrixBase.h.

template<typename Derived>
typedef internal::stem_function<Scalar>::type MatrixBase< Derived >::StemFunction

Definition at line 399 of file MatrixBase.h.

template<typename Derived>
typedef Scalar MatrixBase< Derived >::value_type

Type of the elements.

Definition at line 36 of file MatrixBase.h.


Member Enumeration Documentation

template<typename Derived>
anonymous enum
Enumerator:
static_size 

Definition at line 38 of file MatrixBase.h.

template<typename Derived>
anonymous enum
Enumerator:
SizeMinusOne 

Definition at line 358 of file MatrixBase.h.

template<typename Derived>
anonymous enum
Enumerator:
HomogeneousReturnTypeDirection 

Definition at line 370 of file MatrixBase.h.


Constructor & Destructor Documentation

template<typename Derived>
MatrixBase< Derived >::MatrixBase (  ) [inline, protected]

Definition at line 443 of file MatrixBase.h.

template<typename Derived>
MatrixBase< Derived >::MatrixBase ( int   ) [explicit, private]
template<typename Derived>
MatrixBase< Derived >::MatrixBase ( int  ,
int   
) [private]
template<typename Derived>
template<typename OtherDerived >
MatrixBase< Derived >::MatrixBase ( const MatrixBase< OtherDerived > &   ) [explicit, private]

Member Function Documentation

template<typename Derived>
EIGEN_STRONG_INLINE MatrixBase<Derived>& MatrixBase< Derived >::Abs (  ) [inline]

Definition at line 727 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::Abs (  ) const [inline]

Definition at line 728 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::add_AAt ( const OTHERMATRIX &  A ) [inline]

this += A + AT

Definition at line 505 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::add_Ac ( const OTHERMATRIX &  m,
const Scalar  c 
) [inline]

Add c (scalar) times A to this matrix: this += A * c

Definition at line 494 of file MatrixBase.h.

template<typename Derived >
const MatrixBase< Derived >::AdjointReturnType MatrixBase< Derived >::adjoint (  ) const [inline]
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:
 m = m.adjoint(); // bug!!! caused by aliasing effect
Instead, use the adjointInPlace() method:
 m.adjointInPlace();
which gives Eigen good opportunities for optimization, or alternatively you can also do:
 m = m.adjoint().eval();
See also:
adjointInPlace(), transpose(), conjugate(), class Transpose, class internal::scalar_conjugate_op

Definition at line 249 of file Transpose.h.

template<typename Derived >
void MatrixBase< Derived >::adjointInPlace (  ) [inline]

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.
See also:
transpose(), adjoint(), transposeInPlace()

Definition at line 331 of file Transpose.h.

References DenseBase< Derived >::eval().

template<typename Derived>
void MatrixBase< Derived >::adjustRange ( Scalar  valMin,
Scalar  valMax 
) [inline]

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 751 of file MatrixBase.h.

template<typename Derived >
template<typename EssentialPart >
void MatrixBase< Derived >::applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

Definition at line 90 of file Householder.h.

References row().

template<typename Derived >
template<typename EssentialPart >
void MatrixBase< Derived >::applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

Definition at line 112 of file Householder.h.

References col().

template<typename Derived >
template<typename OtherDerived >
void MatrixBase< Derived >::applyOnTheLeft ( const EigenBase< OtherDerived > &  other ) [inline]

replaces *this by *this * other.

Definition at line 167 of file EigenBase.h.

References EigenBase< Derived >::derived().

template<typename Derived >
template<typename OtherScalar >
void MatrixBase< Derived >::applyOnTheLeft ( Index  p,
Index  q,
const JacobiRotation< OtherScalar > &  j 
) [inline]

Applies the rotation in the plane j to the rows p and q of *this, i.e., it computes B = J * B, with $ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) $.

See also:
class JacobiRotation, MatrixBase::applyOnTheRight(), internal::apply_rotation_in_the_plane()

Definition at line 282 of file Jacobi.h.

References internal::apply_rotation_in_the_plane(), row(), and internal::y.

template<typename Derived >
template<typename OtherDerived >
void MatrixBase< Derived >::applyOnTheRight ( const EigenBase< OtherDerived > &  other ) [inline]

replaces *this by *this * other.

It is equivalent to MatrixBase::operator*=()

Definition at line 159 of file EigenBase.h.

References EigenBase< Derived >::derived().

template<typename Derived >
template<typename OtherScalar >
void MatrixBase< Derived >::applyOnTheRight ( Index  p,
Index  q,
const JacobiRotation< OtherScalar > &  j 
) [inline]

Applies the rotation in the plane j to the columns p and q of *this, i.e., it computes B = B * J with $ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) $.

See also:
class JacobiRotation, MatrixBase::applyOnTheLeft(), internal::apply_rotation_in_the_plane()

Definition at line 297 of file Jacobi.h.

References internal::apply_rotation_in_the_plane(), col(), JacobiRotation< Scalar >::transpose(), and internal::y.

template<typename Derived>
ArrayWrapper<Derived> MatrixBase< Derived >::array (  ) [inline]
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()

Definition at line 307 of file MatrixBase.h.

template<typename Derived>
const ArrayWrapper<Derived> MatrixBase< Derived >::array (  ) const [inline]

Definition at line 308 of file MatrixBase.h.

template<typename Derived >
const DiagonalWrapper< Derived > MatrixBase< Derived >::asDiagonal (  ) const [inline]
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 260 of file DiagonalMatrix.h.

Referenced by Transform< _Scalar, _Dim, _Mode >::fromPositionOrientationScale(), Transform< _Scalar, _Dim, _Mode >::prescale(), Transform< _Scalar, _Dim, _Mode >::scale(), and Scaling().

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::assign ( const Scalar  v ) [inline]

Fill all the elements with a given value

Definition at line 62 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::assign ( size_t  N,
const Scalar  v 
) [inline]

Resize to N and set all the elements to a given value

Definition at line 64 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE iterator MatrixBase< Derived >::begin (  ) [inline]

Definition at line 47 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const_iterator MatrixBase< Derived >::begin (  ) const [inline]

Definition at line 49 of file MatrixBase.h.

template<typename Derived>
template<typename CustomBinaryOp , typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived> MatrixBase< Derived >::binaryExpr ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const [inline]
Returns:
an expression of the difference of *this and other
Note:
If you want to substract a given scalar from all coefficients, see Cwise::operator-().
See also:
class CwiseBinaryOp, operator-=()
Returns:
an expression of the sum of *this and other
Note:
If you want to add a given scalar to all coefficients, see Cwise::operator+().
See also:
class CwiseBinaryOp, operator+=()
Returns:
an expression of a custom coefficient-wise operator func of *this and other

The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)

Here is an example illustrating the use of custom functors:

Output:

See also:
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()

Definition at line 58 of file MatrixBase.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::blueNorm (  ) const [inline]
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 86 of file StableNorm.h.

References abs(), abs2(), eigen_assert, std::pow(), mrpt::math::size(), and internal::sqrt().

template<typename Derived>
template<typename NewType >
internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, Derived> >::type MatrixBase< Derived >::cast (  ) const [inline]
Returns:
an expression of *this with the Scalar type casted to NewScalar.

The template parameter NewScalar is the type we are casting the scalars to.

See also:
class CwiseUnaryOp

Definition at line 108 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE bool MatrixBase< Derived >::chol ( MATRIX &  U ) const [inline]

Cholesky M=UT * U decomposition for simetric matrix (upper-half of the matrix will be actually ignored)

Definition at line 698 of file MatrixBase.h.

template<typename Derived >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::colPivHouseholderQr (  ) const
Returns:
the column-pivoting Householder QR decomposition of *this.
See also:
class ColPivHouseholderQR

Definition at line 526 of file ColPivHouseholderQR.h.

template<typename Derived >
template<typename ResultType >
void MatrixBase< Derived >::computeInverseAndDetWithCheck ( ResultType &  inverse,
typename ResultType::Scalar &  determinant,
bool &  invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

Computation of matrix inverse and determinant, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Parameters:
inverseReference to the matrix in which to store the inverse.
determinantReference to the variable in which to store the inverse.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional 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()

Definition at line 356 of file Inverse.h.

References eigen_assert.

template<typename Derived >
template<typename ResultType >
void MatrixBase< Derived >::computeInverseWithCheck ( ResultType &  inverse,
bool &  invertible,
const RealScalar absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

Computation of matrix inverse, with invertibility check.

This is only for fixed-size square matrices of size up to 4x4.

Parameters:
inverseReference to the matrix in which to store the inverse.
invertibleReference to the bool variable in which to store whether the matrix is invertible.
absDeterminantThresholdOptional 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()

Definition at line 395 of file Inverse.h.

References eigen_assert.

template<typename Derived>
ConjugateReturnType MatrixBase< Derived >::conjugate (  ) const [inline]
Returns:
an expression of the complex conjugate of *this.
See also:
adjoint()

Definition at line 117 of file MatrixBase.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase< Derived >::cos (  ) const
template<typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase< Derived >::cosh (  ) const
template<typename Derived>
EIGEN_STRONG_INLINE size_t MatrixBase< Derived >::countNonZero (  ) const [inline]

Definition at line 190 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
MatrixBase< Derived >::PlainObject MatrixBase< Derived >::cross ( const MatrixBase< OtherDerived > &  other ) const [inline]

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 39 of file OrthoMethods.h.

References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE.

template<typename Derived >
template<typename OtherDerived >
MatrixBase< Derived >::PlainObject MatrixBase< Derived >::cross3 ( const MatrixBase< OtherDerived > &  other ) const [inline]

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 87 of file OrthoMethods.h.

References EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE, and Architecture::Target.

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs_op<Scalar>,Derived> MatrixBase< Derived >::cwiseAbs (  ) const [inline]
Returns:
an expression of the coefficient-wise absolute value of *this

Example:

Output:

See also:
cwiseAbs2()

Definition at line 37 of file MatrixBase.h.

Referenced by internal::lpNorm_selector< Derived, Infinity >::run(), internal::lpNorm_selector< Derived, 1 >::run(), and internal::lpNorm_selector< Derived, p >::run().

template<typename Derived>
EIGEN_STRONG_INLINE const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>,Derived> MatrixBase< Derived >::cwiseAbs2 (  ) const [inline]
Returns:
an expression of the coefficient-wise squared absolute value of *this

Example:

Output:

See also:
cwiseAbs()

Definition at line 47 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >,Derived> MatrixBase< Derived >::cwiseEqual ( const Scalar s ) const [inline]
Returns:
an expression of the coefficient-wise == operator of *this and a scalar s
Warning:
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().
See also:
cwiseEqual(const MatrixBase<OtherDerived> &) const

Definition at line 79 of file MatrixBase.h.

Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::sumAll().

template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::equal_to<Scalar>, Derived, OtherDerived> MatrixBase< Derived >::cwiseEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other ) const [inline]
Returns:
an expression of the coefficient-wise == operator of *this and other
Warning:
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

See also:
cwiseNotEqual(), isApprox(), isMuchSmallerThan()

Definition at line 57 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>,Derived> MatrixBase< Derived >::cwiseInverse (  ) const [inline]
Returns:
an expression of the coefficient-wise inverse of *this.

Example:

Output:

See also:
cwiseProduct()

Definition at line 67 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, Derived, OtherDerived> MatrixBase< Derived >::cwiseMax ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other ) const [inline]
Returns:
an expression of the coefficient-wise max of *this and other

Example:

Output:

See also:
class CwiseBinaryOp, min()

Definition at line 104 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, Derived, OtherDerived> MatrixBase< Derived >::cwiseMin ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other ) const [inline]
Returns:
an expression of the coefficient-wise min of *this and other

Example:

Output:

See also:
class CwiseBinaryOp, max()

Definition at line 90 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::not_equal_to<Scalar>, Derived, OtherDerived> MatrixBase< Derived >::cwiseNotEqual ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other ) const [inline]
Returns:
an expression of the coefficient-wise != operator of *this and other
Warning:
this performs an exact comparison, which is generally a bad idea with floating-point types. In order to check for equality between two vectors or matrices with floating-point coefficients, it is generally a far better idea to use a fuzzy comparison as provided by isApprox() and isMuchSmallerThan().

Example:

Output:

See also:
cwiseEqual(), isApprox(), isMuchSmallerThan()

Definition at line 76 of file MatrixBase.h.

Referenced by MatrixBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true > >::operator!=().

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, Derived, OtherDerived> MatrixBase< Derived >::cwiseQuotient ( const EIGEN_CURRENT_STORAGE_BASE_CLASS< OtherDerived > &  other ) const [inline]
Returns:
an expression of the coefficient-wise quotient of *this and other

Example:

Output:

See also:
class CwiseBinaryOp, cwiseProduct(), cwiseInverse()

Definition at line 118 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>,Derived> MatrixBase< Derived >::cwiseSqrt (  ) const [inline]
Returns:
an expression of the coefficient-wise square root of *this.

Example:

Output:

See also:
cwisePow(), cwiseSquare()

Definition at line 57 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::det (  ) const [inline]

Definition at line 483 of file MatrixBase.h.

template<typename Derived >
internal::traits< Derived >::Scalar MatrixBase< Derived >::determinant (  ) const [inline]

Returns:
the determinant of this matrix

Definition at line 105 of file Determinant.h.

template<typename Derived >
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type MatrixBase< Derived >::diagonal (  ) [inline]
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 158 of file Diagonal.h.

Referenced by MatrixBase< Derived >::trace().

template<typename Derived >
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type MatrixBase< Derived >::diagonal (  ) const [inline]

This is the const version of diagonal().

This is the const version of diagonal<int>().

Reimplemented in ProductBase< Derived, Lhs, Rhs >, ProductBase< Derived, Lhs, Rhs >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.

Definition at line 166 of file Diagonal.h.

template<typename Derived>
template<int Index>
DiagonalIndexReturnType<Index>::Type MatrixBase< Derived >::diagonal (  )
template<typename Derived>
template<int Index>
ConstDiagonalIndexReturnType<Index>::Type MatrixBase< Derived >::diagonal (  ) const

Reimplemented in ProductBase< Derived, Lhs, Rhs >, ProductBase< Derived, Lhs, Rhs >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, CoeffBasedProduct< LhsNested, RhsNested, NestingFlags >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemmProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, 0, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, true, Lhs, false, Rhs, true >, Lhs, Rhs >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< ScaledProduct< NestedProduct >, NestedProduct::_LhsNested, NestedProduct::_RhsNested >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, LhsIsTriangular, Lhs, false, Rhs, false >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, OuterProduct >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< DenseTimeSparseSelfAdjointProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< GeneralProduct< Lhs, Rhs, GemvProduct >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, 0, true, Rhs, RhsMode, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< TriangularProduct< Mode, false, Lhs, true, Rhs, false >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< DenseTimeSparseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseSelfAdjointTimeDenseProduct< Lhs, Rhs, UpLo >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SparseTimeDenseProduct< Lhs, Rhs >, Lhs, Rhs >, ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >, and ProductBase< SelfadjointProductMatrix< Lhs, LhsMode, false, Rhs, RhsMode, false >, Lhs, Rhs >.

template<typename Derived >
MatrixBase< Derived >::template DiagonalIndexReturnType< Dynamic >::Type MatrixBase< Derived >::diagonal ( Index  index ) [inline]
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 184 of file Diagonal.h.

template<typename Derived >
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Dynamic >::Type MatrixBase< Derived >::diagonal ( Index  index ) const [inline]
template<typename Derived>
Index MatrixBase< Derived >::diagonalSize (  ) const [inline]
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.

Definition at line 111 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
internal::traits< Derived >::Scalar MatrixBase< Derived >::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()

Definition at line 74 of file Dot.h.

References eigen_assert, EIGEN_STATIC_ASSERT, EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE, EIGEN_STATIC_ASSERT_VECTOR_ONLY, internal::dot_nocheck< T, U, NeedToTranspose >::run(), and mrpt::math::size().

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::EIGEN_CWISE_PRODUCT_RETURN_TYPE ( Derived  ,
OtherDerived   
) const [inline]
Returns:
an expression of the Schur product (coefficient wise product) of *this and other

Example:

Output:

See also:
class CwiseBinaryOp, cwiseAbs2

Definition at line 37 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::EigenvaluesReturnType MatrixBase< Derived >::eigenvalues (  ) const [inline]

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 80 of file MatrixBaseEigenvalues.h.

template<typename Derived>
template<class VECTOR >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eigenValues ( VECTOR &  eVals ) const [inline]

[For square matrices only] Compute the eigenvectors and eigenvalues (sorted), and return only the eigenvalues in the vector "eVals".

Note:
Warning: Only the real part of complex eigenvectors and eigenvalues are returned.
See also:
eigenVectorsSymmetric, eigenVectorsVec

Definition at line 670 of file MatrixBase.h.

template<class Derived >
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eigenVectors ( MATRIX1 &  eVecs,
MATRIX2 &  eVals 
) const

[For square matrices only] Compute the eigenvectors and eigenvalues (sorted), both returned as matrices: eigenvectors are the columns in "eVecs", and eigenvalues in ascending order as the diagonal of "eVals".

Compute the eigenvectors and eigenvalues, both returned as matrices: eigenvectors are the columns, and eigenvalues.

Note:
Warning: Only the real part of complex eigenvectors and eigenvalues are returned.
See also:
eigenVectorsSymmetric, eigenVectorsVec

Definition at line 88 of file eigen_plugins_impl.h.

References eigenVectorsVec().

template<class Derived >
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eigenVectorsSymmetric ( MATRIX1 &  eVecs,
MATRIX2 &  eVals 
) const

[For symmetric matrices only] Compute the eigenvectors and eigenvalues (in no particular order), both returned as matrices: eigenvectors are the columns, and eigenvalues

Compute the eigenvectors and eigenvalues, both returned as matrices: eigenvectors are the columns, and eigenvalues.

See also:
eigenVectors

Definition at line 127 of file eigen_plugins_impl.h.

References eigenVectorsSymmetricVec().

template<class Derived >
template<class MATRIX1 , class VECTOR1 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eigenVectorsSymmetricVec ( MATRIX1 &  eVecs,
VECTOR1 &  eVals 
) const

[For symmetric matrices only] Compute the eigenvectors and eigenvalues (in no particular order), both returned as matrices: eigenvectors are the columns, and eigenvalues

Compute the eigenvectors and eigenvalues, both returned as matrices: eigenvectors are the columns, and eigenvalues.

See also:
eigenVectorsVec

Definition at line 140 of file eigen_plugins_impl.h.

References Eigen::SelfAdjointEigenSolver< _MatrixType >::eigenvalues(), and Eigen::SelfAdjointEigenSolver< _MatrixType >::eigenvectors().

template<class Derived >
template<class MATRIX1 , class VECTOR1 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eigenVectorsVec ( MATRIX1 &  eVecs,
VECTOR1 &  eVals 
) const

[For square matrices only] Compute the eigenvectors and eigenvalues (sorted), eigenvectors are the columns in "eVecs", and eigenvalues are returned in in ascending order in the vector "eVals".

Compute the eigenvectors and eigenvalues, both returned as matrices: eigenvectors are the columns, and eigenvalues.

Note:
Warning: Only the real part of complex eigenvectors and eigenvalues are returned.
See also:
eigenVectorsSymmetric, eigenVectorsVec

Definition at line 101 of file eigen_plugins_impl.h.

References Eigen::EigenSolver< _MatrixType >::eigenvalues(), and Eigen::EigenSolver< _MatrixType >::eigenvectors().

template<typename Derived>
EIGEN_STRONG_INLINE bool MatrixBase< Derived >::empty (  ) const [inline]

Definition at line 491 of file MatrixBase.h.

template<typename Derived>
VectorBlock< Derived, Size > MatrixBase< Derived >::end (  ) [inline]
Deprecated:
use DenseMase::tail()

Definition at line 48 of file MatrixBase.h.

template<typename Derived>
const VectorBlock< Derived, Size > MatrixBase< Derived >::end (  ) const [inline]
Deprecated:
use DenseMase::tail()

Definition at line 50 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::Exp (  ) const [inline]

Definition at line 734 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE MatrixBase<Derived>& MatrixBase< Derived >::Exp (  ) [inline]

Definition at line 733 of file MatrixBase.h.

template<typename Derived>
const MatrixExponentialReturnValue<Derived> MatrixBase< Derived >::exp (  ) const
template<typename Derived>
template<class VECTOR >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractCol ( size_t  nCol,
VECTOR &  v,
size_t  startingRow = 0 
) const [inline]

Extract one column from the matrix into a column vector.

Definition at line 774 of file MatrixBase.h.

template<typename Derived>
template<typename T >
void MatrixBase< Derived >::extractCol ( size_t  nCol,
std::vector< T > &  v,
size_t  startingRow = 0 
) const [inline]

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 778 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractMatrix ( const size_t  firstRow,
const size_t  firstCol,
MATRIX &  m 
) const [inline]

Definition at line 784 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractMatrix ( const size_t  firstRow,
const size_t  firstCol,
const size_t  nRows,
const size_t  nCols,
MATRIX &  m 
) const [inline]

Definition at line 788 of file MatrixBase.h.

template<typename Derived>
template<class OtherDerived >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractRow ( size_t  nRow,
Eigen::EigenBase< OtherDerived > &  v,
size_t  startingCol = 0 
) const [inline]

Extract one row from the matrix into a row vector.

Definition at line 757 of file MatrixBase.h.

template<typename Derived>
template<typename T >
void MatrixBase< Derived >::extractRow ( size_t  nRow,
std::vector< T > &  v,
size_t  startingCol = 0 
) const [inline]

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 761 of file MatrixBase.h.

template<typename Derived>
template<class VECTOR >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractRowAsCol ( size_t  nRow,
VECTOR &  v,
size_t  startingCol = 0 
) const [inline]

Extract one row from the matrix into a column vector.

Definition at line 767 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::extractSubmatrix ( const size_t  row_first,
const size_t  row_last,
const size_t  col_first,
const size_t  col_last,
MATRIX &  out 
) const [inline]

Get a submatrix, given its bounds: first & last column and row (inclusive).

Definition at line 796 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
void MatrixBase< Derived >::extractSubmatrixSymmetrical ( const std::vector< size_t > &  indices,
MATRIX &  out 
) const [inline]

Get a submatrix from a square matrix, by collecting the elements M(idxs,idxs), where idxs is the sequence of indices passed as argument.

A perfect application of this method is in extracting covariance matrices of a subset of variables from the full covariance matrix.

See also:
extractSubmatrix, extractSubmatrixSymmetricalBlocks

Definition at line 839 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
void MatrixBase< Derived >::extractSubmatrixSymmetricalBlocks ( const size_t  block_size,
const std::vector< size_t > &  block_indices,
MATRIX &  out 
) const [inline]

Get a submatrix from a square matrix, by collecting the elements M(idxs,idxs), where idxs is a sequence {block_indices(i):block_indices(i)+block_size-1} for all "i" up to the size of block_indices.

A perfect application of this method is in extracting covariance matrices of a subset of variables from the full covariance matrix.

See also:
extractSubmatrix, extractSubmatrixSymmetrical

Definition at line 807 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::eye (  ) [inline]

Make the matrix an identity matrix.

Definition at line 84 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::fill ( const Scalar  v ) [inline]

Fill all the elements with a given value

Definition at line 59 of file MatrixBase.h.

template<typename Derived>
void MatrixBase< Derived >::find_index_max_value ( size_t &  u,
size_t &  v,
Scalar valMax 
) const [inline]

[VECTORS OR MATRICES] Finds the maximum value (and the corresponding zero-based index) from a given container.

Exceptions:
std::exceptionOn an empty input vector

Definition at line 237 of file MatrixBase.h.

template<typename Derived >
const ForceAlignedAccess< Derived > MatrixBase< Derived >::forceAlignedAccess (  ) const [inline]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(),class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

Definition at line 120 of file ForceAlignedAccess.h.

template<typename Derived >
ForceAlignedAccess< Derived > MatrixBase< Derived >::forceAlignedAccess (  ) [inline]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

Definition at line 130 of file ForceAlignedAccess.h.

template<typename Derived >
template<bool Enable>
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type MatrixBase< Derived >::forceAlignedAccessIf (  ) const [inline]
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

Definition at line 141 of file ForceAlignedAccess.h.

template<typename Derived >
template<bool Enable>
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type MatrixBase< Derived >::forceAlignedAccessIf (  ) [inline]
Returns:
an expression of *this with forced aligned access if Enable is true.
See also:
forceAlignedAccess(), class ForceAlignedAccess

Reimplemented from DenseBase< Derived >.

Definition at line 152 of file ForceAlignedAccess.h.

template<class Derived >
bool MatrixBase< Derived >::fromMatlabStringFormat ( const std::string &  s,
bool  dumpErrorMsgToStdErr = true 
)

Read a matrix from a string in Matlab-like format, for example "[1 0 2; 0 4 -1]" The string must start with '[' and end with ']'.

Rows are separated by semicolons ';' and columns in each row by one or more whitespaces ' ', commas ',' or tabs ''.

This format is also used for CConfigFile::read_matrix.

This template method can be instantiated for matrices of the types: int, long, unsinged int, unsigned long, float, double, long double

Returns:
true on success. false if the string is malformed, and then the matrix will be resized to 0x0.
See also:
inMatlabFormat, CConfigFile::read_matrix

Definition at line 150 of file eigen_plugins_impl.h.

References internal_mrpt::MatOrVecResizer< R, C >::doit(), Dynamic, and end().

template<typename Derived >
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::fullPivHouseholderQr (  ) const
Returns:
the full-pivoting Householder QR decomposition of *this.
See also:
class FullPivHouseholderQR

Definition at line 454 of file FullPivHouseholderQR.h.

template<typename Derived >
const FullPivLU< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::fullPivLu (  ) const [inline]

Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU

Definition at line 749 of file FullPivLU.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::get_unsafe ( const size_t  row,
const size_t  col 
) const [inline]

Read-only access to one element (Use with caution, bounds are not checked!)

Definition at line 103 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar& MatrixBase< Derived >::get_unsafe ( const size_t  row,
const size_t  col 
) [inline]

Reference access to one element (Use with caution, bounds are not checked!)

Definition at line 111 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar* MatrixBase< Derived >::get_unsafe_row ( size_t  row ) [inline]

Fast but unsafe method to obtain a pointer to a given row of the matrix (Use only in time critical applications) VERY IMPORTANT WARNING: You must be aware of the memory layout, either Column or Row-major ordering.

Definition at line 99 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const Scalar* MatrixBase< Derived >::get_unsafe_row ( size_t  row ) const [inline]

Definition at line 100 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE size_t MatrixBase< Derived >::getColCount (  ) const [inline]

Get number of columns.

Definition at line 69 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE size_t MatrixBase< Derived >::getRowCount (  ) const [inline]

Get number of rows.

Definition at line 67 of file MatrixBase.h.

template<typename Derived >
const MatrixBase< Derived >::HNormalizedReturnType MatrixBase< Derived >::hnormalized (  ) const [inline]

Returns:
an expression of the homogeneous normalized vector of *this

Example:

Output:

See also:
VectorwiseOp::hnormalized()

Definition at line 171 of file Homogeneous.h.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY, and mrpt::math::size().

template<typename Derived >
MatrixBase< Derived >::HomogeneousReturnType MatrixBase< Derived >::homogeneous (  ) const [inline]

Returns:
an expression of the equivalent homogeneous vector

Example:

Output:

See also:
class Homogeneous

Definition at line 140 of file Homogeneous.h.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

template<typename Derived >
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::householderQr (  ) const
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR

Definition at line 349 of file HouseholderQR.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::hypotNorm (  ) const [inline]
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 181 of file StableNorm.h.

References cwiseAbs().

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType MatrixBase< Derived >::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 689 of file CwiseNullaryOp.h.

References EIGEN_STATIC_ASSERT_FIXED_SIZE.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::IdentityReturnType MatrixBase< Derived >::Identity ( Index  rows,
Index  cols 
) [static]
Returns:
an expression of the identity matrix (not necessarily square).

The parameters rows and cols 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 672 of file CwiseNullaryOp.h.

template<typename Derived>
const ImagReturnType MatrixBase< Derived >::imag (  ) const [inline]
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()

Definition at line 132 of file MatrixBase.h.

template<typename Derived>
NonConstImagReturnType MatrixBase< Derived >::imag (  ) [inline]
Returns:
a non const expression of the imaginary part of *this.
See also:
real()

Definition at line 188 of file MatrixBase.h.

template<class Derived >
std::string MatrixBase< Derived >::inMatlabFormat ( const size_t  decimal_digits = 6 ) const

Dump matrix in matlab format.

This template method can be instantiated for matrices of the types: int, long, unsinged int, unsigned long, float, double, long double

See also:
fromMatlabStringFormat

Definition at line 245 of file eigen_plugins_impl.h.

template<typename Derived>
template<typename MAT >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::insertCol ( size_t  nCol,
const MAT &  aCol 
) [inline]

Definition at line 427 of file MatrixBase.h.

template<typename Derived>
template<typename MAT >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::insertMatrix ( size_t  r,
size_t  c,
const MAT &  m 
) [inline]

Insert matrix "m" into this matrix at indices (r,c), that is, (*this)(r,c)=m(0,0) and so on.

Definition at line 421 of file MatrixBase.h.

template<typename Derived>
template<typename MAT >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::insertMatrixTranspose ( size_t  r,
size_t  c,
const MAT &  m 
) [inline]

Definition at line 424 of file MatrixBase.h.

template<typename Derived>
template<typename MAT >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::insertRow ( size_t  nRow,
const MAT &  aRow 
) [inline]

Definition at line 426 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::inv (  ) const [inline]

Definition at line 480 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::inv ( MATRIX &  outMat ) const [inline]

Definition at line 481 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::inv_fast ( MATRIX &  outMat ) const [inline]

Definition at line 482 of file MatrixBase.h.

template<typename Derived >
const internal::inverse_impl< Derived > MatrixBase< Derived >::inverse (  ) const [inline]

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: Example:
Output:
See also:
computeInverseAndDetWithCheck()

Definition at line 329 of file Inverse.h.

References eigen_assert, and EIGEN_STATIC_ASSERT.

Referenced by Hyperplane< _Scalar, _AmbientDim >::transform().

template<typename Derived>
EIGEN_STRONG_INLINE bool MatrixBase< Derived >::isDiagonal (  ) const [inline]

Checks for matrix type.

Definition at line 360 of file MatrixBase.h.

template<typename Derived >
bool MatrixBase< Derived >::isDiagonal ( 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 274 of file DiagonalMatrix.h.

References abs(), and internal::isMuchSmallerThan().

template<typename Derived >
bool MatrixBase< Derived >::isIdentity ( 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 706 of file CwiseNullaryOp.h.

References internal::isApprox(), and internal::isMuchSmallerThan().

template<typename Derived >
bool MatrixBase< Derived >::isLowerTriangular ( 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(), extract(), part(), marked()

Definition at line 754 of file TriangularMatrix.h.

References abs().

template<typename Derived >
template<typename OtherDerived >
bool MatrixBase< Derived >::isOrthogonal ( const MatrixBase< OtherDerived > &  other,
RealScalar  prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns:
true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

Output:

Definition at line 205 of file Dot.h.

References abs2().

template<typename Derived>
EIGEN_STRONG_INLINE bool MatrixBase< Derived >::isSingular ( const Scalar  absThreshold = 0 ) const [inline]

Definition at line 134 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE bool MatrixBase< Derived >::isSquare (  ) const [inline]

Definition at line 133 of file MatrixBase.h.

template<typename Derived >
bool MatrixBase< Derived >::isUnitary ( 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:

Definition at line 224 of file Dot.h.

References internal::isApprox(), and internal::isMuchSmallerThan().

template<typename Derived >
bool MatrixBase< Derived >::isUpperTriangular ( 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(), extract(), part(), marked()

Definition at line 729 of file TriangularMatrix.h.

References abs().

template<typename Derived >
JacobiSVD< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::jacobiSvd ( unsigned int  computationOptions = 0 ) const

Definition at line 671 of file JacobiSVD.h.

template<typename Derived>
template<typename OtherDerived >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::laplacian ( Eigen::MatrixBase< OtherDerived > &  ret ) const [inline]

Computes the laplacian of this square graph weight matrix.

The laplacian matrix is L = D - W, with D a diagonal matrix with the degree of each node, W the

Definition at line 284 of file MatrixBase.h.

template<typename Derived>
template<class OUTVECT >
void MatrixBase< Derived >::largestEigenvector ( OUTVECT &  x,
Scalar  resolution = Scalar(0.01),
size_t  maxIterations = 6,
int *  out_Iterations = NULL,
float *  out_estimatedResolution = NULL 
) const [inline]

Efficiently computes only the biggest eigenvector of the matrix using the Power Method, and returns it in the passed vector "x".

Definition at line 320 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
const LazyProductReturnType< Derived, OtherDerived >::Type MatrixBase< Derived >::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 561 of file Product.h.

References Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

template<typename Derived >
const LDLT< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::ldlt (  ) const [inline]

Returns:
the Cholesky decomposition with full pivoting without square root of *this

Definition at line 440 of file LDLT.h.

template<typename Derived>
template<class MAT2 , class MAT3 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::leftDivideSquare ( const MAT2 &  A,
MAT3 &  RES 
) const [inline]

Matrix left divide: RES = A-1 * this , with A being squared (using the Eigen::ColPivHouseholderQR method)

Definition at line 627 of file MatrixBase.h.

template<typename Derived >
const LLT< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::llt (  ) const [inline]

Returns:
the LLT decomposition of *this

Definition at line 358 of file LLT.h.

template<class Derived >
void MatrixBase< Derived >::loadFromTextFile ( const std::string &  file )

Load matrix from a text file, compatible with MATLAB text format.

Lines starting with '' or '#' are interpreted as comments and ignored.

See also:
saveToTextFile, fromMatlabStringFormat

Definition at line 308 of file eigen_plugins_impl.h.

References loadFromTextFile().

template<class Derived >
void MatrixBase< Derived >::loadFromTextFile ( std::istream &  _input_text_stream )

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 316 of file eigen_plugins_impl.h.

References internal_mrpt::MatOrVecResizer< R, C >::doit(), and Dynamic.

template<typename Derived>
EIGEN_STRONG_INLINE MatrixBase<Derived>& MatrixBase< Derived >::Log (  ) [inline]

Definition at line 730 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::Log (  ) const [inline]

Definition at line 731 of file MatrixBase.h.

template<typename Derived >
template<int p>
NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::lpNorm (  ) const [inline]
Returns:
the $ \ell^p $ 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 $ \ell^\infty $ norm, that is the maximum of the absolute values of the coefficients of *this.
See also:
norm()

Reimplemented from DenseBase< Derived >.

Definition at line 189 of file Dot.h.

References internal::lpNorm_selector< Derived, p >::run().

template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::lu (  ) const [inline]

Synonym of partialPivLu().

Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU

Definition at line 510 of file PartialPivLU.h.

template<typename Derived >
template<typename EssentialPart >
void MatrixBase< Derived >::makeHouseholder ( EssentialPart &  essential,
Scalar tau,
RealScalar beta 
) const

Computes the elementary reflector H such that: $ H *this = [ beta 0 ... 0]^T $ where the transformation H is: $ H = I - tau v v^*$ and the vector v is: $ v^T = [1 essential^T] $.

On output:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the householder transformation
betathe result of H * *this
See also:
MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()

Definition at line 62 of file Householder.h.

References abs2(), EIGEN_STATIC_ASSERT_VECTOR_ONLY, imag(), real(), mrpt::math::size(), and internal::sqrt().

template<typename Derived >
void MatrixBase< Derived >::makeHouseholderInPlace ( Scalar tau,
RealScalar beta 
)

Definition at line 39 of file Householder.h.

References mrpt::math::size().

template<typename Derived>
const MatrixBase<Derived>& MatrixBase< Derived >::matrix (  ) const [inline]

Definition at line 303 of file MatrixBase.h.

template<typename Derived>
MatrixBase<Derived>& MatrixBase< Derived >::matrix (  ) [inline]

Definition at line 302 of file MatrixBase.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase< Derived >::matrixFunction ( StemFunction  f ) const
template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::maximum ( size_t *  maxIndex ) const [inline]

[VECTORS ONLY] Finds the maximum value (and the corresponding zero-based index) from a given container.

Exceptions:
std::exceptionOn an empty input vector

Definition at line 225 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::maximum (  ) const [inline]

[VECTORS OR MATRICES] Finds the maximum value

Exceptions:
std::exceptionOn an empty input container

Definition at line 195 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::maximumDiagonal (  ) const [inline]

Finds the maximum value in the diagonal of the matrix.

Definition at line 370 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE double MatrixBase< Derived >::mean (  ) const [inline]

Computes the mean of the entire matrix.

See also:
meanAndStdAll

Reimplemented from DenseBase< Derived >.

Definition at line 374 of file MatrixBase.h.

template<typename Derived>
template<class VEC >
void MatrixBase< Derived >::meanAndStd ( VEC &  outMeanVector,
VEC &  outStdVector,
const bool  unbiased_variance = true 
) const [inline]

Computes a row with the mean values of each column in the matrix and the associated vector with the standard deviation of each column.

See also:
mean,meanAndStdAll
Exceptions:
std::exceptionIf the matrix/vector is empty.
Parameters:
unbiased_varianceStandard deviation is sum(vals-mean)/K, with K=N-1 or N for unbiased_variance=true or false, respectively.

Definition at line 385 of file MatrixBase.h.

template<typename Derived>
void MatrixBase< Derived >::meanAndStdAll ( double &  outMean,
double &  outStd,
const bool  unbiased_variance = true 
) const [inline]

Computes the mean and standard deviation of all the elements in the matrix as a whole.

See also:
mean,meanAndStd
Exceptions:
std::exceptionIf the matrix/vector is empty.
Parameters:
unbiased_varianceStandard deviation is sum(vals-mean)/K, with K=N-1 or N for unbiased_variance=true or false, respectively.

Definition at line 407 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::minimum ( size_t *  minIndex ) const [inline]

[VECTORS ONLY] Finds the minimum value (and the corresponding zero-based index) from a given container.

See also:
maximum, minimum_maximum
Exceptions:
std::exceptionOn an empty input vector

Definition at line 249 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::minimum (  ) const [inline]

[VECTORS OR MATRICES] Finds the minimum value

See also:
maximum, minimum_maximum
Exceptions:
std::exceptionOn an empty input container

Definition at line 204 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::minimum_maximum ( Scalar out_min,
Scalar out_max,
size_t *  minIndex,
size_t *  maxIndex 
) const [inline]

[VECTORS ONLY] Compute the minimum and maximum of a container at once

See also:
maximum, minimum
Exceptions:
std::exceptionOn an empty input vector

Definition at line 261 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::minimum_maximum ( Scalar out_min,
Scalar out_max 
) const [inline]

[VECTORS OR MATRICES] Compute the minimum and maximum of a container at once

See also:
maximum, minimum
Exceptions:
std::exceptionOn an empty input container

Definition at line 213 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply ( const MATRIX1 &  A,
const MATRIX2 &  B 
) [inline]
Parameters:
Bthis = A * B

Definition at line 511 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class SKEW_3VECTOR >
void MatrixBase< Derived >::multiply_A_skew3 ( const MAT_A &  A,
const SKEW_3VECTOR &  v 
) [inline]

this = A * skew(v), with v being a 3-vector (or 3-array) and skew(v) the skew symmetric matrix of v (see mrpt::math::skew_symmetric3)

Definition at line 575 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AAt ( const MAT_A &  A ) [inline]
Parameters:
Athis = A * AT

Definition at line 610 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_A >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AAt_scalar ( const MAT_A &  A,
typename MAT_A::value_type  f 
) [inline]

this = C * CT * f (with a matrix C and a scalar f).

Definition at line 565 of file MatrixBase.h.

template<typename Derived>
template<class MATRIX1 , class MATRIX2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AB ( const MATRIX1 &  A,
const MATRIX2 &  B 
) [inline]
Parameters:
Bthis = A * B

Definition at line 514 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERVECTOR1 , typename OTHERVECTOR2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_Ab ( const OTHERVECTOR1 &  vIn,
OTHERVECTOR2 &  vOut,
bool  accumToOutput = false 
) const [inline]

Computes the vector vOut = this * vIn, where "vIn" is a column vector of the appropriate length.

Definition at line 525 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_B , class MAT_C >
void MatrixBase< Derived >::multiply_ABC ( const MAT_A &  A,
const MAT_B &  B,
const MAT_C &  C 
) [inline]
Parameters:
Cthis = A*B*C

Definition at line 590 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_B , class MAT_C >
void MatrixBase< Derived >::multiply_ABCt ( const MAT_A &  A,
const MAT_B &  B,
const MAT_C &  C 
) [inline]
Parameters:
Cthis = A*B*(CT)

Definition at line 595 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_B >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_ABt ( const MAT_A &  A,
const MAT_B &  B 
) [inline]
Parameters:
Bthis = A * BT

Definition at line 605 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AtA ( const MAT_A &  A ) [inline]
Parameters:
Athis = AT * A

Definition at line 615 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_A >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AtA_scalar ( const MAT_A &  A,
typename MAT_A::value_type  f 
) [inline]

this = CT * C * f (with a matrix C and a scalar f).

Definition at line 570 of file MatrixBase.h.

template<typename Derived>
template<typename MATRIX1 , typename MATRIX2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_AtB ( const MATRIX1 &  A,
const MATRIX2 &  B 
) [inline]
Parameters:
Bthis=A^t * B

Definition at line 519 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERVECTOR1 , typename OTHERVECTOR2 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_Atb ( const OTHERVECTOR1 &  vIn,
OTHERVECTOR2 &  vOut,
bool  accumToOutput = false 
) const [inline]

Computes the vector vOut = thisT * vIn, where "vIn" is a column vector of the appropriate length.

Definition at line 532 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_B , class MAT_C >
void MatrixBase< Derived >::multiply_AtBC ( const MAT_A &  A,
const MAT_B &  B,
const MAT_C &  C 
) [inline]
Parameters:
Cthis = A(T)*B*C

Definition at line 600 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_C , typename MAT_R >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_HCHt ( const MAT_C &  C,
MAT_R &  R,
bool  accumResultInOutput = false 
) const [inline]

< R = this * C * thisT

Definition at line 538 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_C >
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::multiply_HCHt_scalar ( const MAT_C &  C ) const [inline]

R = H * C * HT (with a vector H and a symmetric matrix C) In fact when H is a vector, multiply_HCHt_scalar and multiply_HtCH_scalar are exactly equivalent

Definition at line 553 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_C , typename MAT_R >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_HtCH ( const MAT_C &  C,
MAT_R &  R,
bool  accumResultInOutput = false 
) const [inline]

< R = thisT * C * this

Definition at line 545 of file MatrixBase.h.

template<typename Derived>
template<typename MAT_C >
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::multiply_HtCH_scalar ( const MAT_C &  C ) const [inline]

R = HT * C * H (with a vector H and a symmetric matrix C) In fact when H is a vector, multiply_HCHt_scalar and multiply_HtCH_scalar are exactly equivalent

Definition at line 559 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_B >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_result_is_symmetric ( const MAT_A &  A,
const MAT_B &  B 
) [inline]
Parameters:
Bthis = A * B (result is symmetric)

Definition at line 620 of file MatrixBase.h.

template<typename Derived>
template<class SKEW_3VECTOR , class MAT_A >
void MatrixBase< Derived >::multiply_skew3_A ( const SKEW_3VECTOR &  v,
const MAT_A &  A 
) [inline]

this = skew(v)*A, with v being a 3-vector (or 3-array) and skew(v) the skew symmetric matrix of v (see mrpt::math::skew_symmetric3)

Definition at line 579 of file MatrixBase.h.

template<typename Derived>
template<class MAT_A , class MAT_OUT >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiply_subMatrix ( const MAT_A &  A,
MAT_OUT &  outResult,
const size_t  A_cols_offset,
const size_t  A_rows_offset,
const size_t  A_col_count 
) const [inline]

outResult = this * A

Definition at line 585 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiplyColumnByScalar ( size_t  c,
Scalar  s 
) [inline]

Definition at line 184 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::multiplyRowByScalar ( size_t  r,
Scalar  s 
) [inline]

Definition at line 185 of file MatrixBase.h.

template<typename Derived >
NoAlias< Derived, MatrixBase > MatrixBase< Derived >::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

Definition at line 131 of file NoAlias.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::norm (  ) const [inline]
Returns:
the l2 norm of *this, i.e., for vectors, the square root of the dot product of *this with itself.
See also:
dot(), squaredNorm()

Definition at line 104 of file Dot.h.

References internal::sqrt().

Referenced by internal::lpNorm_selector< Derived, 2 >::run().

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::norm_inf (  ) const [inline]

Compute the norm-infinite of a vector ($f[ ||{v}||_ $f]), ie the maximum absolute value of the elements.

Definition at line 272 of file MatrixBase.h.

template<typename Derived>
void MatrixBase< Derived >::normalize ( Scalar  valMin,
Scalar  valMax 
) [inline]

Scales all elements such as the minimum & maximum values are shifted to the given values.

Definition at line 740 of file MatrixBase.h.

template<typename Derived >
void MatrixBase< Derived >::normalize (  ) [inline]

Normalizes the vector, i.e.

divides it by its own norm.

See also:
norm(), normalized()

Definition at line 132 of file Dot.h.

References mrpt::math::norm().

template<typename Derived >
const MatrixBase< Derived >::PlainObject MatrixBase< Derived >::normalized (  ) const [inline]
Returns:
an expression of the quotient of *this by its own norm.
See also:
norm(), normalize()

Definition at line 117 of file Dot.h.

Referenced by QuaternionBase< Derived >::setFromTwoVectors().

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::ones ( const size_t  row,
const size_t  col 
) [inline]

Resize matrix and set all elements to one.

Definition at line 92 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::ones (  ) [inline]

Set all elements to one.

Definition at line 94 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
bool MatrixBase< Derived >::operator!= ( const MatrixBase< OtherDerived > &  other ) const [inline]
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 286 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::ScalarMultipleReturnType MatrixBase< Derived >::operator* ( const UniformScaling< Scalar > &  s ) const

Concatenates a linear transformation matrix and a uniform scaling.

Definition at line 119 of file Scaling.h.

References UniformScaling< _Scalar >::factor().

template<typename Derived>
const ScalarMultipleReturnType MatrixBase< Derived >::operator* ( const RealScalar scalar ) const
template<typename Derived >
template<typename DiagonalDerived >
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > MatrixBase< Derived >::operator* ( const DiagonalBase< DiagonalDerived > &  diagonal ) const [inline]
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.

Definition at line 119 of file DiagonalProduct.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, Derived> MatrixBase< Derived >::operator* ( const std::complex< Scalar > &  scalar ) const [inline]

Overloaded for efficient real matrix times complex scalar value.

Definition at line 85 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
const ProductReturnType< Derived, OtherDerived >::Type MatrixBase< Derived >::operator* ( const MatrixBase< OtherDerived > &  other ) const [inline]
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 520 of file Product.h.

References Dynamic, EIGEN_PREDICATE_SAME_MATRIX_SIZE, and EIGEN_STATIC_ASSERT.

template<typename Derived>
const ScalarMultipleReturnType MatrixBase< Derived >::operator* ( const Scalar scalar ) const [inline]
Returns:
an expression of *this scaled by the scalar factor scalar

Definition at line 65 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
Derived & MatrixBase< Derived >::operator*= ( const EigenBase< OtherDerived > &  other ) [inline]

replaces *this by *this * other.

Returns:
a reference to *this

Definition at line 150 of file EigenBase.h.

References EigenBase< Derived >::derived().

template<typename Derived >
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator+= ( const MatrixBase< OtherDerived > &  other )

replaces *this by *this + other.

Returns:
a reference to *this

Definition at line 233 of file CwiseBinaryOp.h.

template<typename Derived>
template<typename OtherDerived >
Derived& MatrixBase< Derived >::operator+= ( const ArrayBase< OtherDerived > &  array ) [inline, protected]

Definition at line 451 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>,Derived> MatrixBase< Derived >::operator- (  ) const [inline]
Returns:
an expression of the opposite of *this

Definition at line 60 of file MatrixBase.h.

template<typename Derived>
template<typename OtherDerived >
Derived& MatrixBase< Derived >::operator-= ( const ArrayBase< OtherDerived > &  array ) [inline, protected]

Definition at line 454 of file MatrixBase.h.

template<typename Derived >
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator-= ( const MatrixBase< OtherDerived > &  other )

replaces *this by *this - other.

Returns:
a reference to *this

Definition at line 219 of file CwiseBinaryOp.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, Derived> MatrixBase< Derived >::operator/ ( const Scalar scalar ) const [inline]
Returns:
an expression of *this divided by the scalar value scalar

Definition at line 77 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator= ( const MatrixBase< Derived > &  other )

Special case of the template operator=, in order to prevent the compiler from generating a default operator= (issue hit with g++ 4.1)

Definition at line 565 of file Assign.h.

template<typename Derived >
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator= ( const EigenBase< OtherDerived > &  other )

Copies the generic expression other into *this.

The expression must provide a (templated) evalTo(Derived& dst) const function which does the actual job. In practice, this allows any user to write its own special matrix without having to modify MatrixBase

Returns:
a reference to *this.

Reimplemented from DenseBase< Derived >.

Definition at line 579 of file Assign.h.

References EigenBase< Derived >::derived().

template<typename Derived >
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator= ( const DenseBase< OtherDerived > &  other )

Copies other into *this.

Returns:
a reference to *this.

Reimplemented from DenseBase< Derived >.

Definition at line 572 of file Assign.h.

template<typename Derived >
template<typename OtherDerived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::operator= ( const ReturnByValue< OtherDerived > &  other )

Reimplemented from DenseBase< Derived >.

Definition at line 587 of file Assign.h.

References ReturnByValue< Derived >::evalTo().

template<typename Derived>
template<typename OtherDerived >
bool MatrixBase< Derived >::operator== ( const MatrixBase< OtherDerived > &  other ) const [inline]
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 278 of file MatrixBase.h.

template<typename Derived>
MatrixBase<Derived>& MatrixBase< Derived >::operator^= ( const unsigned int  pow ) [inline]

Combined matrix power and assignment operator.

Definition at line 346 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::RealScalar MatrixBase< Derived >::operatorNorm (  ) const [inline]

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 $ A $ is defined to be

\[ \|A\|_2 = \max_x \frac{\|Ax\|_2}{\|x\|_2} \]

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 $ A^*A $.

The current implementation uses the eigenvalues of $ A^*A $, 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:

See also:
SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()

Definition at line 135 of file MatrixBaseEigenvalues.h.

References internal::sqrt().

template<typename Derived >
template<unsigned int Mode>
EIGEN_DEPRECATED TriangularView< Derived, Mode > MatrixBase< Derived >::part (  )
template<typename Derived >
template<unsigned int Mode>
EIGEN_DEPRECATED const TriangularView< Derived, Mode > MatrixBase< Derived >::part (  ) const
template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > MatrixBase< Derived >::partialPivLu (  ) const [inline]

Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU

Definition at line 495 of file PartialPivLU.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::push_back ( Scalar  val ) [inline]

Insert an element at the end of the container (for 1D vectors/arrays)

Definition at line 126 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE size_t MatrixBase< Derived >::rank ( double  threshold = 0 ) const [inline]

Gets the rank of the matrix via the Eigen::ColPivHouseholderQR method.

Parameters:
thresholdIf set to >0, it's used as threshold instead of Eigen's default one.

Definition at line 710 of file MatrixBase.h.

template<typename Derived>
RealReturnType MatrixBase< Derived >::real (  ) const [inline]
Returns:
a read-only expression of the real part of *this.
See also:
imag()

Definition at line 126 of file MatrixBase.h.

template<typename Derived>
NonConstRealReturnType MatrixBase< Derived >::real (  ) [inline]
Returns:
a non const expression of the real part of *this.
See also:
imag()

Definition at line 182 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::removeColumns ( const std::vector< size_t > &  idxsToRemove ) [inline]

Remove columns of the matrix.

Definition at line 430 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::removeRows ( const std::vector< size_t > &  idxsToRemove ) [inline]

Remove rows of the matrix.

Definition at line 454 of file MatrixBase.h.

template<typename Derived>
template<class MAT2 , class MAT3 >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::rightDivideSquare ( const MAT2 &  B,
MAT3 &  RES 
) const [inline]

Matrix right divide: RES = this * B-1, with B being squared (using the Eigen::ColPivHouseholderQR method)

Definition at line 636 of file MatrixBase.h.

template<class Derived >
void MatrixBase< Derived >::saveToTextFile ( const std::string &  file,
mrpt::math::TMatrixTextFileFormat  fileFormat = mrpt::math::MATRIX_FORMAT_ENG,
bool  appendMRPTHeader = false,
const std::string &  userHeader = std::string() 
) const

Save matrix to a text file, compatible with MATLAB text format (see also the methods of matrix classes themselves).

Parameters:
theMatrixIt can be a CMatrixTemplate or a CMatrixFixedNumeric.
fileThe target filename.
fileFormatSee TMatrixTextFileFormat. The format of the numbers in the text file.
appendMRPTHeaderInsert this header to the file "% File generated by MRPT. Load with MATLAB with: VAR=load(FILENAME);"
userHeaderAdditional text to be written at the head of the file. Typically MALAB comments "% This file blah blah". Final end-of-line is not needed.
See also:
loadFromTextFile, CMatrixTemplate::inMatlabFormat, SAVE_MATRIX

Definition at line 261 of file eigen_plugins_impl.h.

References mrpt::system::os::fclose(), mrpt::system::os::fopen(), mrpt::system::os::fprintf(), mrpt::math::MATRIX_FORMAT_ENG, mrpt::math::MATRIX_FORMAT_FIXED, mrpt::math::MATRIX_FORMAT_INT, and mrpt::system::MRPT_getVersion().

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::scalarPow ( const Scalar  s ) [inline]

Scalar power of all elements to a given power, this is diferent of ^ operator.

Definition at line 357 of file MatrixBase.h.

template<typename Derived >
template<unsigned int UpLo>
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type MatrixBase< Derived >::selfadjointView (  )

Definition at line 294 of file SelfAdjointView.h.

template<typename Derived >
template<unsigned int UpLo>
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type MatrixBase< Derived >::selfadjointView (  ) const

Definition at line 286 of file SelfAdjointView.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::set_unsafe ( const size_t  row,
const size_t  col,
const Scalar  val 
) [inline]

Sets an element (Use with caution, bounds are not checked!)

Definition at line 118 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE Derived & MatrixBase< 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 761 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE Derived & MatrixBase< Derived >::setIdentity ( Index  rows,
Index  cols 
)

Resizes to the given size, and writes the identity expression (not necessarily square) into *this.

Parameters:
rowsthe new number of rows
colsthe new number of columns

Example:

Output:

See also:
MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()

Definition at line 777 of file CwiseNullaryOp.h.

References DenseBase< Derived >::resize().

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::setSize ( size_t  row,
size_t  col 
) [inline]

Changes the size of matrix, maintaining its previous content as possible and padding with zeros where applicable.

**WARNING**: MRPT's add-on method setSize() pads with zeros, while Eigen's resize() does NOT (new elements are undefined).

Definition at line 301 of file MatrixBase.h.

template<typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase< Derived >::sin (  ) const
template<typename Derived>
const MatrixFunctionReturnValue<Derived> MatrixBase< Derived >::sinh (  ) const
template<typename Derived >
const SparseView< Derived > MatrixBase< Derived >::sparseView ( const Scalar m_reference = Scalar(0),
typename NumTraits< Scalar >::Real  m_epsilon = NumTraits<Scalar>::dummy_precision() 
) const

Definition at line 103 of file SparseView.h.

template<typename Derived>
EIGEN_STRONG_INLINE MatrixBase<Derived>& MatrixBase< Derived >::Sqrt (  ) [inline]

Definition at line 724 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::Sqrt (  ) const [inline]

Definition at line 725 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE MatrixBase<Derived>& MatrixBase< Derived >::Square (  ) [inline]

Definition at line 736 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE PlainObject MatrixBase< Derived >::Square (  ) const [inline]

Definition at line 737 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::squaredNorm (  ) const
Returns:
the squared l2 norm of *this, i.e., for vectors, the dot product of *this with itself.
See also:
dot(), norm()

Definition at line 94 of file Dot.h.

References real().

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::squareNorm (  ) const [inline]

Compute the square norm of a vector/array/matrix (the Euclidean distance to the origin, taking all the elements as a single vector).

See also:
norm

Definition at line 275 of file MatrixBase.h.

template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real MatrixBase< Derived >::stableNorm (  ) const [inline]
Returns:
the l2 norm of *this avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s 2 - compute $ s \Vert \frac{*this}{s} \Vert $ 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 57 of file StableNorm.h.

References AlignedBit, DirectAccessBit, internal::first_aligned(), mrpt::math::size(), internal::sqrt(), and internal::stable_norm_kernel().

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::substract_AAt ( const OTHERMATRIX &  A ) [inline]

this -= A + AT

Definition at line 508 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::substract_Ac ( const OTHERMATRIX &  m,
const Scalar  c 
) [inline]

Substract c (scalar) times A to this matrix: this -= A * c

Definition at line 496 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::substract_An ( const OTHERMATRIX &  m,
const size_t  n 
) [inline]

Substract n (integer) times A to this matrix: this -= A * n

Definition at line 502 of file MatrixBase.h.

template<typename Derived>
template<typename OTHERMATRIX >
EIGEN_STRONG_INLINE void MatrixBase< Derived >::substract_At ( const OTHERMATRIX &  m ) [inline]

Substract A transposed to this matrix: this -= A.adjoint()

Definition at line 499 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE Scalar MatrixBase< Derived >::sumAll (  ) const [inline]

Sum all the elements, returning a value of the same type than the container

Definition at line 278 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::swapCols ( size_t  i1,
size_t  i2 
) [inline]

Definition at line 187 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::swapRows ( size_t  i1,
size_t  i2 
) [inline]

Definition at line 188 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE const AdjointReturnType MatrixBase< Derived >::t (  ) const [inline]

Transpose.

Definition at line 478 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE internal::traits< Derived >::Scalar MatrixBase< Derived >::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()

Reimplemented from DenseBase< Derived >.

Definition at line 399 of file Redux.h.

References MatrixBase< Derived >::diagonal().

template<typename Derived >
template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type MatrixBase< Derived >::triangularView (  ) const

This is the const version of MatrixBase::triangularView()

Definition at line 718 of file TriangularMatrix.h.

template<typename Derived >
template<unsigned int Mode>
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type MatrixBase< Derived >::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 709 of file TriangularMatrix.h.

template<typename Derived>
template<typename CustomUnaryOp >
const CwiseUnaryOp<CustomUnaryOp, Derived> MatrixBase< Derived >::unaryExpr ( const CustomUnaryOp &  func = CustomUnaryOp() ) const [inline]

Apply a unary operator coefficient-wise.

Parameters:
[in]funcFunctor implementing the unary operator
Template Parameters:
CustomUnaryOpType of func
Returns:
An expression of a custom coefficient-wise unary operator func of *this

The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.

Example:

Output:

Genuine functors allow for more possibilities, for instance it may contain a state.

Example:

Output:

See also:
class CwiseUnaryOp, class CwiseBinaryOp

Definition at line 155 of file MatrixBase.h.

template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, Derived> MatrixBase< Derived >::unaryViewExpr ( const CustomViewOp &  func = CustomViewOp() ) const [inline]
Returns:
an expression of a custom coefficient-wise unary operator func of *this

The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.

Example:

Output:

See also:
class CwiseUnaryOp, class CwiseBinaryOp

Definition at line 173 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::unit (  ) [inline]

Make the matrix an identity matrix.

Definition at line 82 of file MatrixBase.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::Unit ( Index  size,
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 790 of file CwiseNullaryOp.h.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::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 805 of file CwiseNullaryOp.h.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::unit ( const size_t  nRows,
const Scalar  diag_vals 
) [inline]

Make the matrix an identity matrix (the diagonal values can be 1.0 or any other value)

Definition at line 72 of file MatrixBase.h.

template<typename Derived >
MatrixBase< Derived >::PlainObject MatrixBase< Derived >::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 223 of file OrthoMethods.h.

References EIGEN_STATIC_ASSERT_VECTOR_ONLY, and internal::unitOrthogonal_selector< Derived, Size >::run().

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::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 848 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::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 818 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::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 828 of file CwiseNullaryOp.h.

template<typename Derived >
EIGEN_STRONG_INLINE const MatrixBase< Derived >::BasisReturnType MatrixBase< Derived >::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 838 of file CwiseNullaryOp.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::unsafeRemoveColumns ( const std::vector< size_t > &  idxs ) [inline]

Remove columns of the matrix.

The unsafe version assumes that, the indices are sorted in ascending order.

Definition at line 441 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::unsafeRemoveRows ( const std::vector< size_t > &  idxs ) [inline]

Remove rows of the matrix.

The unsafe version assumes that, the indices are sorted in ascending order.

Definition at line 465 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::zeros ( const size_t  row,
const size_t  col 
) [inline]

Resize and set all elements to zero.

Definition at line 89 of file MatrixBase.h.

template<typename Derived>
EIGEN_STRONG_INLINE void MatrixBase< Derived >::zeros (  ) [inline]

Set all elements to zero.

Definition at line 87 of file MatrixBase.h.


Friends And Related Function Documentation

template<typename Derived>
const ScalarMultipleReturnType operator* ( const Scalar scalar,
const StorageBaseType &  matrix 
) [friend]

Definition at line 92 of file MatrixBase.h.

template<typename Derived>
const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, Derived> operator* ( const std::complex< Scalar > &  scalar,
const StorageBaseType &  matrix 
) [friend]

Definition at line 96 of file MatrixBase.h.




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