Eigen  3.3.3
Eigen::MatrixBase< Derived > Class Template Reference

Detailed Description

template<typename Derived>
class Eigen::MatrixBase< Derived >

Base class for all dense matrices, vectors, and expressions.

This class is the base that is inherited by all matrix, vector, and related expression types. Most of the Eigen API is contained in this class, and its base classes. Other important classes for the Eigen API are Matrix, and VectorwiseOp.

Note that some methods are defined in other modules such as the LU module LU module for all functions related to matrix inversions.

Template Parameters:
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;
    }

This class can be extended with the help of the plugin mechanism described on the page Extending MatrixBase (and other classes) by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN.

See also:
The class hierarchy
+ Inheritance diagram for Eigen::MatrixBase< Derived >:

List of all members.

Public Types

typedef Base::PlainObject PlainObject
 The plain matrix or array type corresponding to this expression.

Public Member Functions

const AdjointReturnType adjoint () const
void adjointInPlace ()
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 OtherDerived >
void applyOnTheLeft (const EigenBase< OtherDerived > &other)
template<typename OtherScalar >
void applyOnTheLeft (Index p, Index q, const JacobiRotation< OtherScalar > &j)
template<typename OtherDerived >
void applyOnTheRight (const EigenBase< OtherDerived > &other)
template<typename OtherScalar >
void applyOnTheRight (Index p, Index q, const JacobiRotation< OtherScalar > &j)
ArrayWrapper< Derived > array ()
const ArrayWrapper< const Derived > array () const
const DiagonalWrapper< const
Derived > 
asDiagonal () const
BDCSVD< PlainObjectbdcSvd (unsigned int computationOptions=0) const
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp
< CustomBinaryOp, const
Derived, const OtherDerived > 
binaryExpr (const Eigen::MatrixBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const
RealScalar blueNorm () const
template<typename NewType >
CastXpr< NewType >::Type cast () const
const ColPivHouseholderQR
< PlainObject
colPivHouseholderQr () const
const
CompleteOrthogonalDecomposition
< PlainObject
completeOrthogonalDecomposition () 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
ConjugateReturnType conjugate () const
template<typename OtherDerived >
PlainObject cross (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
PlainObject cross3 (const MatrixBase< OtherDerived > &other) const
const CwiseAbsReturnType cwiseAbs () const
const CwiseAbs2ReturnType cwiseAbs2 () const
template<typename OtherDerived >
const CwiseBinaryOp
< std::equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseScalarEqualReturnType cwiseEqual (const Scalar &s) const
const CwiseInverseReturnType cwiseInverse () const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar, Scalar >, const
Derived, const OtherDerived > 
cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_max_op
< Scalar, Scalar >, const
Derived, const
ConstantReturnType > 
cwiseMax (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, Scalar >, const
Derived, const OtherDerived > 
cwiseMin (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseBinaryOp
< internal::scalar_min_op
< Scalar, Scalar >, const
Derived, const
ConstantReturnType > 
cwiseMin (const Scalar &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< std::not_equal_to< Scalar >
, const Derived, const
OtherDerived > 
cwiseNotEqual (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_product_op
< Derived::Scalar,
OtherDerived::Scalar >, const
Derived, const OtherDerived > 
cwiseProduct (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar >, const Derived,
const OtherDerived > 
cwiseQuotient (const Eigen::MatrixBase< OtherDerived > &other) const
const CwiseSignReturnType cwiseSign () const
const CwiseSqrtReturnType cwiseSqrt () const
Scalar determinant () const
DiagonalReturnType diagonal ()
ConstDiagonalReturnType diagonal () const
DiagonalDynamicIndexReturnType diagonal (Index index)
ConstDiagonalDynamicIndexReturnType diagonal (Index index) const
Index diagonalSize () const
template<typename OtherDerived >
ScalarBinaryOpTraits< typename
internal::traits< Derived >
::Scalar, typename
internal::traits< OtherDerived >
::Scalar >::ReturnType 
dot (const MatrixBase< OtherDerived > &other) const
EigenvaluesReturnType eigenvalues () const
 Computes the eigenvalues of a matrix.
Matrix< Scalar, 3, 1 > eulerAngles (Index a0, Index a1, Index a2) const
const Derived & forceAlignedAccess () const
Derived & forceAlignedAccess ()
template<bool Enable>
const Derived & forceAlignedAccessIf () const
template<bool Enable>
Derived & forceAlignedAccessIf ()
const FullPivHouseholderQR
< PlainObject
fullPivHouseholderQr () const
const FullPivLU< PlainObjectfullPivLu () const
const HNormalizedReturnType hnormalized () const
 homogeneous normalization
HomogeneousReturnType homogeneous () const
const HouseholderQR< PlainObjecthouseholderQr () const
RealScalar hypotNorm () const
const ImagReturnType imag () const
NonConstImagReturnType imag ()
const Inverse< Derived > inverse () const
bool isDiagonal (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isIdentity (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isLowerTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
template<typename OtherDerived >
bool isOrthogonal (const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isUnitary (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
bool isUpperTriangular (const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
JacobiSVD< PlainObjectjacobiSvd (unsigned int computationOptions=0) const
template<typename OtherDerived >
const Product< Derived,
OtherDerived, LazyProduct > 
lazyProduct (const MatrixBase< OtherDerived > &other) const
const LDLT< PlainObjectldlt () const
const LLT< PlainObjectllt () const
template<int p>
RealScalar lpNorm () const
const PartialPivLU< PlainObjectlu () const
template<typename EssentialPart >
void makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const
void makeHouseholderInPlace (Scalar &tau, RealScalar &beta)
NoAlias< Derived,
Eigen::MatrixBase
noalias ()
RealScalar norm () const
void normalize ()
const PlainObject normalized () const
template<typename OtherDerived >
bool operator!= (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_and_op,
const Derived, const
OtherDerived > 
operator&& (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< Scalar, T >, Derived,
Constant< T > > 
operator* (const T &scalar) const
template<typename OtherDerived >
const Product< Derived,
OtherDerived > 
operator* (const MatrixBase< OtherDerived > &other) const
template<typename DiagonalDerived >
const Product< Derived,
DiagonalDerived, LazyProduct > 
operator* (const DiagonalBase< DiagonalDerived > &diagonal) const
template<typename OtherDerived >
Derived & operator*= (const EigenBase< OtherDerived > &other)
template<typename OtherDerived >
const CwiseBinaryOp< sum
< Scalar >, const Derived,
const OtherDerived > 
operator+ (const Eigen::MatrixBase< OtherDerived > &other) const
template<typename OtherDerived >
Derived & operator+= (const MatrixBase< OtherDerived > &other)
template<typename OtherDerived >
const CwiseBinaryOp
< difference< Scalar >, const
Derived, const OtherDerived > 
operator- (const Eigen::MatrixBase< OtherDerived > &other) const
const NegativeReturnType operator- () const
template<typename OtherDerived >
Derived & operator-= (const MatrixBase< OtherDerived > &other)
template<typename T >
const CwiseBinaryOp
< internal::scalar_quotient_op
< Scalar, T >, Derived,
Constant< T > > 
operator/ (const T &scalar) const
Derived & operator= (const MatrixBase &other)
template<typename OtherDerived >
Derived & operator= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived >
Derived & operator= (const EigenBase< OtherDerived > &other)
 Copies the generic expression other into *this.
template<typename OtherDerived >
bool operator== (const MatrixBase< OtherDerived > &other) const
RealScalar operatorNorm () const
 Computes the L2 operator norm.
template<typename OtherDerived >
const CwiseBinaryOp
< internal::scalar_boolean_or_op,
const Derived, const
OtherDerived > 
operator|| (const Eigen::MatrixBase< OtherDerived > &other) const
const PartialPivLU< PlainObjectpartialPivLu () const
RealReturnType real () const
NonConstRealReturnType real ()
template<unsigned int UpLo>
SelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView ()
template<unsigned int UpLo>
ConstSelfAdjointViewReturnType
< UpLo >::Type 
selfadjointView () const
Derived & setIdentity ()
Derived & setIdentity (Index rows, Index cols)
 Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
const SparseView< Derived > sparseView (const Scalar &m_reference=Scalar(0), const typename NumTraits< Scalar >::Real &m_epsilon=NumTraits< Scalar >::dummy_precision()) const
RealScalar squaredNorm () const
RealScalar stableNorm () const
void stableNormalize ()
const PlainObject stableNormalized () const
Scalar trace () const
template<unsigned int Mode>
TriangularViewReturnType< Mode >
::Type 
triangularView ()
template<unsigned int Mode>
ConstTriangularViewReturnType
< Mode >::Type 
triangularView () const
template<typename CustomUnaryOp >
const CwiseUnaryOp
< CustomUnaryOp, const Derived > 
unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const
 Apply a unary operator coefficient-wise.
template<typename CustomViewOp >
const CwiseUnaryView
< CustomViewOp, const Derived > 
unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const
PlainObject unitOrthogonal (void) const

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 UnitW ()
static const BasisReturnType UnitX ()
static const BasisReturnType UnitY ()
static const BasisReturnType UnitZ ()

Friends

template<typename T >
const CwiseBinaryOp
< internal::scalar_product_op
< T, Scalar >, Constant< T >
, Derived > 
operator* (const T &scalar, const StorageBaseType &expr)

Member Typedef Documentation

template<typename Derived>
typedef Base::PlainObject Eigen::MatrixBase< Derived >::PlainObject

The plain matrix or array 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 from Eigen::DenseBase< Derived >.

Reimplemented in Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.


Member Function Documentation

template<typename Derived >
const MatrixBase< Derived >::AdjointReturnType Eigen::MatrixBase< Derived >::adjoint ( ) const [inline]
Returns:
an expression of the adjoint (i.e. conjugate transpose) of *this.

Example:

Matrix2cf m = Matrix2cf::Random();
cout << "Here is the 2x2 complex matrix m:" << endl << m << endl;
cout << "Here is the adjoint of m:" << endl << m.adjoint() << endl;

Output:

Here is the 2x2 complex matrix m:
 (-0.211,0.68) (-0.605,0.823)
 (0.597,0.566)  (0.536,-0.33)
Here is the adjoint of m:
 (-0.211,-0.68)  (0.597,-0.566)
(-0.605,-0.823)    (0.536,0.33)
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
template<typename Derived >
void Eigen::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. This excludes (non-square) fixed-size matrices, block-expressions and maps.
See also:
transpose(), adjoint(), transposeInPlace()
template<typename Derived >
template<typename EssentialPart >
void Eigen::MatrixBase< Derived >::applyHouseholderOnTheLeft ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

Apply the elementary reflector H given by $ H = I - tau v v^*$ with $ v^T = [1 essential^T] $ from the left to a vector or matrix.

On input:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheRight()
template<typename Derived >
template<typename EssentialPart >
void Eigen::MatrixBase< Derived >::applyHouseholderOnTheRight ( const EssentialPart &  essential,
const Scalar tau,
Scalar workspace 
)

Apply the elementary reflector H given by $ H = I - tau v v^*$ with $ v^T = [1 essential^T] $ from the right to a vector or matrix.

On input:

Parameters:
essentialthe essential part of the vector v
tauthe scaling factor of the Householder transformation
workspacea pointer to working space with at least this->cols() * essential.size() entries
See also:
MatrixBase::makeHouseholder(), MatrixBase::makeHouseholderInPlace(), MatrixBase::applyHouseholderOnTheLeft()
template<typename Derived >
template<typename OtherDerived >
void Eigen::MatrixBase< Derived >::applyOnTheLeft ( const EigenBase< OtherDerived > &  other) [inline]

replaces *this by other * *this.

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A.applyOnTheLeft(B); 
cout << "After applyOnTheLeft, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After applyOnTheLeft, A = 
-0.211  0.823  0.536
 0.566 -0.605 -0.444
  0.68  0.597  -0.33
template<typename Derived >
template<typename OtherScalar >
void Eigen::MatrixBase< Derived >::applyOnTheLeft ( Index  p,
Index  q,
const JacobiRotation< OtherScalar > &  j 
) [inline]

This is defined in the Jacobi module.

 #include <Eigen/Jacobi> 

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

replaces *this by *this * other. It is equivalent to MatrixBase::operator*=().

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566
template<typename Derived>
ArrayWrapper<Derived> Eigen::MatrixBase< Derived >::array ( ) [inline]
Returns:
an Array expression of this matrix
See also:
ArrayBase::matrix()
template<typename Derived>
const ArrayWrapper<const Derived> Eigen::MatrixBase< Derived >::array ( ) const [inline]
Returns:
a const Array expression of this matrix
See also:
ArrayBase::matrix()
template<typename Derived >
const DiagonalWrapper< const Derived > Eigen::MatrixBase< Derived >::asDiagonal ( ) const [inline]
Returns:
a pseudo-expression of a diagonal matrix with *this as vector of diagonal coefficients

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Example:

cout << Matrix3i(Vector3i(2,5,6).asDiagonal()) << endl;

Output:

2 0 0
0 5 0
0 0 6
See also:
class DiagonalWrapper, class DiagonalMatrix, diagonal(), isDiagonal()
template<typename Derived >
BDCSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::bdcSvd ( unsigned int  computationOptions = 0) const [inline]

This is defined in the SVD module.

 #include <Eigen/SVD> 
Returns:
the singular value decomposition of *this computed by Divide & Conquer algorithm
See also:
class BDCSVD
template<typename Derived>
template<typename CustomBinaryOp , typename OtherDerived >
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::binaryExpr ( const Eigen::MatrixBase< OtherDerived > &  other,
const CustomBinaryOp &  func = CustomBinaryOp() 
) const [inline]
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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template binary functor
template<typename Scalar> struct MakeComplexOp {
  EIGEN_EMPTY_STRUCT_CTOR(MakeComplexOp)
  typedef complex<Scalar> result_type;
  complex<Scalar> operator()(const Scalar& a, const Scalar& b) const { return complex<Scalar>(a,b); }
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random(), m2 = Matrix4d::Random();
  cout << m1.binaryExpr(m2, MakeComplexOp<double>()) << endl;
  return 0;
}

Output:

   (0.68,0.271)  (0.823,-0.967) (-0.444,-0.687)   (-0.27,0.998)
 (-0.211,0.435) (-0.605,-0.514)  (0.108,-0.198) (0.0268,-0.563)
 (0.566,-0.717)  (-0.33,-0.726) (-0.0452,-0.74)  (0.904,0.0259)
  (0.597,0.214)   (0.536,0.608)  (0.258,-0.782)   (0.832,0.678)
See also:
class CwiseBinaryOp, operator+(), operator-(), cwiseProduct()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::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()
template<typename Derived>
template<typename NewType >
CastXpr<NewType>::Type Eigen::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
template<typename Derived >
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::colPivHouseholderQr ( ) const [inline]
Returns:
the column-pivoting Householder QR decomposition of *this.
See also:
class ColPivHouseholderQR
template<typename Derived >
const CompleteOrthogonalDecomposition< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::completeOrthogonalDecomposition ( ) const [inline]
Returns:
the complete orthogonal decomposition of *this.
See also:
class CompleteOrthogonalDecomposition
template<typename Derived >
template<typename ResultType >
void Eigen::MatrixBase< Derived >::computeInverseAndDetWithCheck ( ResultType &  inverse,
typename ResultType::Scalar &  determinant,
bool &  invertible,
const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 

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 determinant.
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:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
double determinant;
m.computeInverseAndDetWithCheck(inverse,determinant,invertible);
cout << "Its determinant is " << determinant << endl;
if(invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
}
else {
  cout << "It is not invertible." << endl;
}

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its determinant is 0.209
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
inverse(), computeInverseWithCheck()
template<typename Derived >
template<typename ResultType >
void Eigen::MatrixBase< Derived >::computeInverseWithCheck ( ResultType &  inverse,
bool &  invertible,
const RealScalar &  absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() 
) const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 

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:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix3d inverse;
bool invertible;
m.computeInverseWithCheck(inverse,invertible);
if(invertible) {
  cout << "It is invertible, and its inverse is:" << endl << inverse << endl;
}
else {
  cout << "It is not invertible." << endl;
}

Output:

Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
It is invertible, and its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
inverse(), computeInverseAndDetWithCheck()
template<typename Derived>
ConjugateReturnType Eigen::MatrixBase< Derived >::conjugate ( ) const [inline]
Returns:
an expression of the complex conjugate of *this.
See also:
Math functions, MatrixBase::adjoint()
template<typename Derived>
const CwiseAbsReturnType Eigen::MatrixBase< Derived >::cwiseAbs ( ) const [inline]
Returns:
an expression of the coefficient-wise absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,   
     -5, 1, 0;
cout << m.cwiseAbs() << endl;

Output:

2 4 6
5 1 0
See also:
cwiseAbs2()
template<typename Derived>
const CwiseAbs2ReturnType Eigen::MatrixBase< Derived >::cwiseAbs2 ( ) const [inline]
Returns:
an expression of the coefficient-wise squared absolute value of *this

Example:

MatrixXd m(2,3);
m << 2, -4, 6,   
     -5, 1, 0;
cout << m.cwiseAbs2() << endl;

Output:

 4 16 36
25  1  0
See also:
cwiseAbs()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseEqual ( const Eigen::MatrixBase< 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:

MatrixXi m(2,2);
m << 1, 0,
     1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are equal: " << count << endl;

Output:

Comparing m with identity matrix:
1 1
0 1
Number of coefficients that are equal: 3
See also:
cwiseNotEqual(), isApprox(), isMuchSmallerThan()
template<typename Derived>
const CwiseScalarEqualReturnType Eigen::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
template<typename Derived>
const CwiseInverseReturnType Eigen::MatrixBase< Derived >::cwiseInverse ( ) const [inline]
Returns:
an expression of the coefficient-wise inverse of *this.

Example:

MatrixXd m(2,3);
m << 2, 0.5, 1,   
     3, 0.25, 1;
cout << m.cwiseInverse() << endl;

Output:

  0.5     2     1
0.333     4     1
See also:
cwiseProduct()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMax ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the coefficient-wise max of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMax(w) << endl;

Output:

4
3
4
See also:
class CwiseBinaryOp, min()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_max_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMax ( const Scalar other) const [inline]
Returns:
an expression of the coefficient-wise max of *this and scalar other
See also:
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseMin ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the coefficient-wise min of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseMin(w) << endl;

Output:

2
2
3
See also:
class CwiseBinaryOp, max()
template<typename Derived>
const CwiseBinaryOp<internal::scalar_min_op<Scalar,Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase< Derived >::cwiseMin ( const Scalar other) const [inline]
Returns:
an expression of the coefficient-wise min of *this and scalar other
See also:
class CwiseBinaryOp, min()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseNotEqual ( const Eigen::MatrixBase< 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:

MatrixXi m(2,2);
m << 1, 0,
     1, 1;
cout << "Comparing m with identity matrix:" << endl;
cout << m.cwiseNotEqual(MatrixXi::Identity(2,2)) << endl;
int count = m.cwiseNotEqual(MatrixXi::Identity(2,2)).count();
cout << "Number of coefficients that are not equal: " << count << endl;

Output:

Comparing m with identity matrix:
0 0
1 0
Number of coefficients that are not equal: 1
See also:
cwiseEqual(), isApprox(), isMuchSmallerThan()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< internal::scalar_product_op < Derived ::Scalar, OtherDerived ::Scalar>, const Derived , const OtherDerived > Eigen::MatrixBase< Derived >::cwiseProduct ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the Schur product (coefficient wise product) of *this and other

Example:

Matrix3i a = Matrix3i::Random(), b = Matrix3i::Random();
Matrix3i c = a.cwiseProduct(b);
cout << "a:\n" << a << "\nb:\n" << b << "\nc:\n" << c << endl;

Output:

a:
 7  6 -3
-2  9  6
 6 -6 -5
b:
 1 -3  9
 0  0  3
 3  9  5
c:
  7 -18 -27
  0   0  18
 18 -54 -25
See also:
class CwiseBinaryOp, cwiseAbs2
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::cwiseQuotient ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the coefficient-wise quotient of *this and other

Example:

Vector3d v(2,3,4), w(4,2,3);
cout << v.cwiseQuotient(w) << endl;

Output:

 0.5
 1.5
1.33
See also:
class CwiseBinaryOp, cwiseProduct(), cwiseInverse()
template<typename Derived>
const CwiseSignReturnType Eigen::MatrixBase< Derived >::cwiseSign ( ) const [inline]
Returns:
an expression of the coefficient-wise signum of *this.

Example:

MatrixXd m(2,3);
m <<  2, -4, 6,
     -5,  1, 0;
cout << m.cwiseSign() << endl;

Output:

 1 -1  1
-1  1  0
template<typename Derived>
const CwiseSqrtReturnType Eigen::MatrixBase< Derived >::cwiseSqrt ( ) const [inline]
Returns:
an expression of the coefficient-wise square root of *this.

Example:

Vector3d v(1,2,4);
cout << v.cwiseSqrt() << endl;

Output:

   1
1.41
   2
See also:
cwisePow(), cwiseSquare()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::determinant ( ) const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the determinant of this matrix
template<typename Derived >
MatrixBase< Derived >::template DiagonalIndexReturnType< Index_ >::Type Eigen::MatrixBase< Derived >::diagonal ( ) [inline]
Returns:
an expression of the main diagonal of the matrix *this

*this is not required to be square.

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the main diagonal of m:" << endl
     << m.diagonal() << endl;

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here are the coefficients on the main diagonal of m:
 7
 9
-5
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:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal<1>().transpose() << endl
     << m.diagonal<-2>().transpose() << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also:
MatrixBase::diagonal(), class Diagonal
template<typename Derived >
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index_ >::Type Eigen::MatrixBase< Derived >::diagonal ( ) const [inline]

This is the const version of diagonal().

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

template<typename Derived >
MatrixBase< Derived >::DiagonalDynamicIndexReturnType Eigen::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:

Matrix4i m = Matrix4i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:" << endl
     << m.diagonal(1).transpose() << endl
     << m.diagonal(-2).transpose() << endl;

Output:

Here is the matrix m:
 7  9 -5 -3
-2 -6  1  0
 6 -3  0  9
 6  6  3  9
Here are the coefficients on the 1st super-diagonal and 2nd sub-diagonal of m:
9 1 9
6 6
See also:
MatrixBase::diagonal(), class Diagonal
template<typename Derived >
MatrixBase< Derived >::ConstDiagonalDynamicIndexReturnType Eigen::MatrixBase< Derived >::diagonal ( Index  index) const [inline]

This is the const version of diagonal(Index).

template<typename Derived>
Index Eigen::MatrixBase< Derived >::diagonalSize ( ) const [inline]
Returns:
the size of the main diagonal, which is min(rows(),cols()).
See also:
rows(), cols(), SizeAtCompileTime.
template<typename Derived >
template<typename OtherDerived >
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType Eigen::MatrixBase< Derived >::dot ( const MatrixBase< OtherDerived > &  other) const
Returns:
the dot product of *this with other.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

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

Computes the eigenvalues of a matrix.

Returns:
Column vector containing the eigenvalues.

This is defined in the Eigenvalues module.

 #include <Eigen/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:

MatrixXd ones = MatrixXd::Ones(3,3);
VectorXcd eivals = ones.eigenvalues();
cout << "The eigenvalues of the 3x3 matrix of ones are:" << endl << eivals << endl;

Output:

The eigenvalues of the 3x3 matrix of ones are:
(-5.31e-17,0)
        (3,0)
        (0,0)
See also:
EigenSolver::eigenvalues(), ComplexEigenSolver::eigenvalues(), SelfAdjointView::eigenvalues()
template<typename Derived >
const ForceAlignedAccess< Derived > Eigen::MatrixBase< Derived >::forceAlignedAccess ( ) const [inline]
Returns:
an expression of *this with forced aligned access
See also:
forceAlignedAccessIf(),class ForceAlignedAccess

Reimplemented from Eigen::DenseBase< Derived >.

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

Reimplemented from Eigen::DenseBase< Derived >.

template<typename Derived >
template<bool Enable>
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type Eigen::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 Eigen::DenseBase< Derived >.

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

Reimplemented from Eigen::DenseBase< Derived >.

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

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the full-pivoting LU decomposition of *this.
See also:
class FullPivLU
template<typename Derived >
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::householderQr ( ) const [inline]
Returns:
the Householder QR decomposition of *this.
See also:
class HouseholderQR
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::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()
template<typename Derived >
const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( ) [inline, 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:

cout << Matrix<double, 3, 4>::Identity() << endl;

Output:

1 0 0 0
0 1 0 0
0 0 1 0
See also:
Identity(Index,Index), setIdentity(), isIdentity()
template<typename Derived >
const MatrixBase< Derived >::IdentityReturnType Eigen::MatrixBase< Derived >::Identity ( Index  rows,
Index  cols 
) [inline, 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:

cout << MatrixXd::Identity(4, 3) << endl;

Output:

1 0 0
0 1 0
0 0 1
0 0 0
See also:
Identity(), setIdentity(), isIdentity()
template<typename Derived>
const ImagReturnType Eigen::MatrixBase< Derived >::imag ( ) const [inline]
Returns:
an read-only expression of the imaginary part of *this.
See also:
real()
template<typename Derived>
NonConstImagReturnType Eigen::MatrixBase< Derived >::imag ( ) [inline]
Returns:
a non const expression of the imaginary part of *this.
See also:
real()
template<typename Derived >
const Inverse< Derived > Eigen::MatrixBase< Derived >::inverse ( ) const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
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:
Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Its inverse is:" << endl << m.inverse() << endl;
Output:
Here is the matrix m:
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
Its inverse is:
-0.199   2.23   2.84
  1.01 -0.555  -1.42
 -1.62   3.59   3.29
See also:
computeInverseAndDetWithCheck()
template<typename Derived >
bool Eigen::MatrixBase< Derived >::isDiagonal ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
Returns:
true if *this is approximately equal to a diagonal matrix, within the precision given by prec.

Example:

Matrix3d m = 10000 * Matrix3d::Identity();
m(0,2) = 1;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isDiagonal() returns: " << m.isDiagonal() << endl;
cout << "m.isDiagonal(1e-3) returns: " << m.isDiagonal(1e-3) << endl;

Output:

Here's the matrix m:
1e+04     0     1
    0 1e+04     0
    0     0 1e+04
m.isDiagonal() returns: 0
m.isDiagonal(1e-3) returns: 1
See also:
asDiagonal()
template<typename Derived >
bool Eigen::MatrixBase< Derived >::isIdentity ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
Returns:
true if *this is approximately equal to the identity matrix (not necessarily square), within the precision given by prec.

Example:

Matrix3d m = Matrix3d::Identity();
m(0,2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isIdentity() returns: " << m.isIdentity() << endl;
cout << "m.isIdentity(1e-3) returns: " << m.isIdentity(1e-3) << endl;

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isIdentity() returns: 0
m.isIdentity(1e-3) returns: 1
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity()
template<typename Derived >
bool Eigen::MatrixBase< Derived >::isLowerTriangular ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
Returns:
true if *this is approximately equal to a lower triangular matrix, within the precision given by prec.
See also:
isUpperTriangular()
template<typename Derived >
template<typename OtherDerived >
bool Eigen::MatrixBase< Derived >::isOrthogonal ( const MatrixBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns:
true if *this is approximately orthogonal to other, within the precision given by prec.

Example:

Vector3d v(1,0,0);
Vector3d w(1e-4,0,1);
cout << "Here's the vector v:" << endl << v << endl;
cout << "Here's the vector w:" << endl << w << endl;
cout << "v.isOrthogonal(w) returns: " << v.isOrthogonal(w) << endl;
cout << "v.isOrthogonal(w,1e-3) returns: " << v.isOrthogonal(w,1e-3) << endl;

Output:

Here's the vector v:
1
0
0
Here's the vector w:
0.0001
     0
     1
v.isOrthogonal(w) returns: 0
v.isOrthogonal(w,1e-3) returns: 1
template<typename Derived >
bool Eigen::MatrixBase< Derived >::isUnitary ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
Returns:
true if *this is approximately an unitary matrix, within the precision given by prec. In the case where the Scalar type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
Note:
This can be used to check whether a family of vectors forms an orthonormal basis. Indeed, m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an orthonormal basis.

Example:

Matrix3d m = Matrix3d::Identity();
m(0,2) = 1e-4;
cout << "Here's the matrix m:" << endl << m << endl;
cout << "m.isUnitary() returns: " << m.isUnitary() << endl;
cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;

Output:

Here's the matrix m:
     1      0 0.0001
     0      1      0
     0      0      1
m.isUnitary() returns: 0
m.isUnitary(1e-3) returns: 1
template<typename Derived >
bool Eigen::MatrixBase< Derived >::isUpperTriangular ( const RealScalar &  prec = NumTraits<Scalar>::dummy_precision()) const
Returns:
true if *this is approximately equal to an upper triangular matrix, within the precision given by prec.
See also:
isLowerTriangular()
template<typename Derived >
JacobiSVD< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::jacobiSvd ( unsigned int  computationOptions = 0) const [inline]

This is defined in the SVD module.

 #include <Eigen/SVD> 
Returns:
the singular value decomposition of *this computed by two-sided Jacobi transformations.
See also:
class JacobiSVD
template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived, LazyProduct > Eigen::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&)
template<typename Derived >
const LDLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::ldlt ( ) const [inline]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky> 
Returns:
the Cholesky decomposition with full pivoting without square root of *this
See also:
SelfAdjointView::ldlt()
template<typename Derived >
const LLT< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::llt ( ) const [inline]

This is defined in the Cholesky module.

 #include <Eigen/Cholesky> 
Returns:
the LLT decomposition of *this
See also:
SelfAdjointView::llt()
template<typename Derived >
template<int p>
MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::lpNorm ( ) const
Returns:
the coefficient-wise $ \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.

In all cases, if *this is empty, then the value 0 is returned.

Note:
For matrices, this function does not compute the operator-norm. That is, if *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and $\infty$-norm matrix operator norms using partial reductions .
See also:
norm()

Reimplemented from Eigen::DenseBase< Derived >.

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

This is defined in the LU module.

 #include <Eigen/LU> 

Synonym of partialPivLu().

Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU
template<typename Derived >
template<typename EssentialPart >
void Eigen::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()
template<typename Derived >
void Eigen::MatrixBase< Derived >::makeHouseholderInPlace ( Scalar tau,
RealScalar &  beta 
)

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] $

The essential part of the vector v is stored in *this.

On output:

Parameters:
tauthe scaling factor of the Householder transformation
betathe result of H * *this
See also:
MatrixBase::makeHouseholder(), MatrixBase::applyHouseholderOnTheLeft(), MatrixBase::applyHouseholderOnTheRight()
template<typename Derived >
NoAlias< Derived, MatrixBase > Eigen::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
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::norm ( ) const [inline]
Returns:
, for vectors, the l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the square root of the sum of the square of all the matrix entries. For vectors, this is also equals to the square root of the dot product of *this with itself.
See also:
lpNorm(), dot(), squaredNorm()
template<typename Derived >
void Eigen::MatrixBase< Derived >::normalize ( ) [inline]

Normalizes the vector, i.e. divides it by its own norm.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

Warning:
If the input vector is too small (i.e., this->norm()==0), then *this is left unchanged.
See also:
norm(), normalized()
template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::normalized ( ) const [inline]
Returns:
an expression of the quotient of *this by its own norm.
Warning:
If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
norm(), normalize()
template<typename Derived>
template<typename OtherDerived >
bool Eigen::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==
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator&& ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the coefficient-wise boolean and operator of *this and other
Warning:
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) && (v<0)) << endl;

Output:

0
0
0
See also:
operator||(), select()
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<Scalar,T>,Derived,Constant<T> > Eigen::MatrixBase< Derived >::operator* ( const T &  scalar) const
Returns:
an expression of *this scaled by the scalar factor scalar
Template Parameters:
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
template<typename Derived >
template<typename OtherDerived >
const Product< Derived, OtherDerived > Eigen::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*()
template<typename Derived >
template<typename DiagonalDerived >
const Product< Derived, DiagonalDerived, LazyProduct > Eigen::MatrixBase< Derived >::operator* ( const DiagonalBase< DiagonalDerived > &  a_diagonal) const [inline]
Returns:
the diagonal matrix product of *this by the diagonal matrix diagonal.
template<typename Derived >
template<typename OtherDerived >
Derived & Eigen::MatrixBase< Derived >::operator*= ( const EigenBase< OtherDerived > &  other) [inline]

replaces *this by *this * other.

Returns:
a reference to *this

Example:

Matrix3f A = Matrix3f::Random(3,3), B;
B << 0,1,0,  
     0,0,1,  
     1,0,0;
cout << "At start, A = " << endl << A << endl;
A *= B;
cout << "After A *= B, A = " << endl << A << endl;
A.applyOnTheRight(B);  // equivalent to A *= B
cout << "After applyOnTheRight, A = " << endl << A << endl;

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< sum <Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator+ ( const Eigen::MatrixBase< OtherDerived > &  other) const
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+=()
template<typename Derived >
template<typename OtherDerived >
Derived & Eigen::MatrixBase< Derived >::operator+= ( const MatrixBase< OtherDerived > &  other) [inline]

replaces *this by *this + other.

Returns:
a reference to *this
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp< difference <Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator- ( const Eigen::MatrixBase< OtherDerived > &  other) const
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-=()
template<typename Derived>
const NegativeReturnType Eigen::MatrixBase< Derived >::operator- ( ) const [inline]
Returns:
an expression of the opposite of *this
template<typename Derived >
template<typename OtherDerived >
Derived & Eigen::MatrixBase< Derived >::operator-= ( const MatrixBase< OtherDerived > &  other) [inline]

replaces *this by *this - other.

Returns:
a reference to *this
template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar,T>,Derived,Constant<T> > Eigen::MatrixBase< Derived >::operator/ ( const T &  scalar) const
Returns:
an expression of *this divided by the scalar value scalar
Template Parameters:
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.
template<typename Derived >
Derived & Eigen::MatrixBase< Derived >::operator= ( const MatrixBase< Derived > &  other) [inline]

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

Copies other into *this.

Returns:
a reference to *this.

Reimplemented from Eigen::DenseBase< Derived >.

Reimplemented in Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.

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

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 Eigen::DenseBase< Derived >.

Reimplemented in Eigen::PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >, and Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >.

template<typename Derived>
template<typename OtherDerived >
bool Eigen::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!=
template<typename Derived >
MatrixBase< Derived >::RealScalar Eigen::MatrixBase< Derived >::operatorNorm ( ) const [inline]

Computes the L2 operator norm.

Returns:
Operator norm of the matrix.

This is defined in the Eigenvalues module.

 #include <Eigen/Eigenvalues> 

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:

MatrixXd ones = MatrixXd::Ones(3,3);
cout << "The operator norm of the 3x3 matrix of ones is "
     << ones.operatorNorm() << endl;

Output:

The operator norm of the 3x3 matrix of ones is 3
See also:
SelfAdjointView::eigenvalues(), SelfAdjointView::operatorNorm()
template<typename Derived>
template<typename OtherDerived >
const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived> Eigen::MatrixBase< Derived >::operator|| ( const Eigen::MatrixBase< OtherDerived > &  other) const [inline]
Returns:
an expression of the coefficient-wise boolean or operator of *this and other
Warning:
this operator is for expression of bool only.

Example:

Array3d v(-1,2,1), w(-3,2,3);
cout << ((v<w) || (v<0)) << endl;

Output:

1
0
1
See also:
operator&&(), select()
template<typename Derived >
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > Eigen::MatrixBase< Derived >::partialPivLu ( ) const [inline]

This is defined in the LU module.

 #include <Eigen/LU> 
Returns:
the partial-pivoting LU decomposition of *this.
See also:
class PartialPivLU
template<typename Derived>
RealReturnType Eigen::MatrixBase< Derived >::real ( ) const [inline]
Returns:
a read-only expression of the real part of *this.
See also:
imag()
template<typename Derived>
NonConstRealReturnType Eigen::MatrixBase< Derived >::real ( ) [inline]
Returns:
a non const expression of the real part of *this.
See also:
imag()
template<typename Derived >
template<unsigned int UpLo>
MatrixBase< Derived >::template SelfAdjointViewReturnType< UpLo >::Type Eigen::MatrixBase< Derived >::selfadjointView ( )
Returns:
an expression of a symmetric/self-adjoint view extracted from the upper or lower triangular part of the current matrix

The parameter UpLo can be either #Upper or #Lower

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the symmetric matrix extracted from the upper part of m:" << endl
     << Matrix3i(m.selfadjointView<Upper>()) << endl;
cout << "Here is the symmetric matrix extracted from the lower part of m:" << endl
     << Matrix3i(m.selfadjointView<Lower>()) << endl;

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the symmetric matrix extracted from the upper part of m:
 7  6 -3
 6  9  6
-3  6 -5
Here is the symmetric matrix extracted from the lower part of m:
 7 -2  6
-2  9 -6
 6 -6 -5
See also:
class SelfAdjointView
template<typename Derived >
template<unsigned int UpLo>
MatrixBase< Derived >::template ConstSelfAdjointViewReturnType< UpLo >::Type Eigen::MatrixBase< Derived >::selfadjointView ( ) const

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

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

Writes the identity expression (not necessarily square) into *this.

Example:

Matrix4i m = Matrix4i::Zero();
m.block<3,3>(1,0).setIdentity();
cout << m << endl;

Output:

0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
See also:
class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity()
template<typename Derived >
Derived & Eigen::MatrixBase< Derived >::setIdentity ( Index  rows,
Index  cols 
) [inline]

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:

MatrixXf m;
m.setIdentity(3, 3);
cout << m << endl;

Output:

1 0 0
0 1 0
0 0 1
See also:
MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::MatrixBase< Derived >::squaredNorm ( ) const [inline]
Returns:
, for vectors, the squared l2 norm of *this, and for matrices the Frobenius norm. In both cases, it consists in the sum of the square of all the matrix entries. For vectors, this is also equals to the dot product of *this with itself.
See also:
dot(), norm(), lpNorm()
template<typename Derived >
NumTraits< typename internal::traits< Derived >::Scalar >::Real Eigen::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()
template<typename Derived >
void Eigen::MatrixBase< Derived >::stableNormalize ( ) [inline]

Normalizes the vector while avoid underflow and overflow

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

This method is analogue to the normalize() method, but it reduces the risk of underflow and overflow when computing the norm.

Warning:
If the input vector is too small (i.e., this->norm()==0), then *this is left unchanged.
See also:
stableNorm(), stableNormalized(), normalize()
template<typename Derived >
const MatrixBase< Derived >::PlainObject Eigen::MatrixBase< Derived >::stableNormalized ( ) const [inline]
Returns:
an expression of the quotient of *this by its own norm while avoiding underflow and overflow.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

This method is analogue to the normalized() method, but it reduces the risk of underflow and overflow when computing the norm.

Warning:
If the input vector is too small (i.e., this->norm()==0), then this function returns a copy of the input.
See also:
stableNorm(), stableNormalize(), normalized()
template<typename Derived >
internal::traits< Derived >::Scalar Eigen::MatrixBase< Derived >::trace ( ) const [inline]
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 Eigen::DenseBase< Derived >.

template<typename Derived >
template<unsigned int Mode>
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type Eigen::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:

Matrix3i m = Matrix3i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the upper-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::Upper>()) << endl;
cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::StrictlyUpper>()) << endl;
cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl
     << Matrix3i(m.triangularView<Eigen::UnitLower>()) << endl;
// FIXME need to implement output for triangularViews (Bug 885)

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the upper-triangular matrix extracted from m:
 7  6 -3
 0  9  6
 0  0 -5
Here is the strictly-upper-triangular matrix extracted from m:
 0  6 -3
 0  0  6
 0  0  0
Here is the unit-lower-triangular matrix extracted from m:
 1  0  0
-2  1  0
 6 -6  1
See also:
class TriangularView
template<typename Derived >
template<unsigned int Mode>
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type Eigen::MatrixBase< Derived >::triangularView ( ) const

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

template<typename Derived>
template<typename CustomUnaryOp >
const CwiseUnaryOp<CustomUnaryOp, const Derived> Eigen::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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define function to be applied coefficient-wise
double ramp(double x)
{
  if (x > 0)
    return x;
  else 
    return 0;
}

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random();
  cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(ptr_fun(ramp)) << endl;
  return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
  0.68  0.823      0      0
     0      0  0.108 0.0268
 0.566      0      0  0.904
 0.597  0.536  0.258  0.832

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

Example:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
  CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
  const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
  Scalar m_inf, m_sup;
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random();
  cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
  return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also:
unaryViewExpr, binaryExpr, class CwiseUnaryOp
template<typename Derived>
template<typename CustomViewOp >
const CwiseUnaryView<CustomViewOp, const Derived> Eigen::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:

#include <Eigen/Core>
#include <iostream>
using namespace Eigen;
using namespace std;

// define a custom template unary functor
template<typename Scalar>
struct CwiseClampOp {
  CwiseClampOp(const Scalar& inf, const Scalar& sup) : m_inf(inf), m_sup(sup) {}
  const Scalar operator()(const Scalar& x) const { return x<m_inf ? m_inf : (x>m_sup ? m_sup : x); }
  Scalar m_inf, m_sup;
};

int main(int, char**)
{
  Matrix4d m1 = Matrix4d::Random();
  cout << m1 << endl << "becomes: " << endl << m1.unaryExpr(CwiseClampOp<double>(-0.5,0.5)) << endl;
  return 0;
}

Output:

   0.68   0.823  -0.444   -0.27
 -0.211  -0.605   0.108  0.0268
  0.566   -0.33 -0.0452   0.904
  0.597   0.536   0.258   0.832
becomes: 
    0.5     0.5  -0.444   -0.27
 -0.211    -0.5   0.108  0.0268
    0.5   -0.33 -0.0452     0.5
    0.5     0.5   0.258     0.5
See also:
unaryExpr, binaryExpr class CwiseUnaryOp
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  newSize,
Index  i 
) [inline, static]
Returns:
an expression of the i-th unit (basis) vector.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::Unit ( Index  i) [inline, static]
Returns:
an expression of the i-th unit (basis) vector.

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

This variant is for fixed-size vector only.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitW ( ) [inline, static]
Returns:
an expression of the W axis unit vector (0,0,0,1)

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitX ( ) [inline, static]
Returns:
an expression of the X axis unit vector (1{,0}^*)

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitY ( ) [inline, static]
Returns:
an expression of the Y axis unit vector (0,1{,0}^*)

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()
template<typename Derived >
const MatrixBase< Derived >::BasisReturnType Eigen::MatrixBase< Derived >::UnitZ ( ) [inline, static]
Returns:
an expression of the Z axis unit vector (0,0,1{,0}^*)

This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.

See also:
MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW()

Friends And Related Function Documentation

template<typename Derived>
template<typename T >
const CwiseBinaryOp<internal::scalar_product_op<T,Scalar>,Constant<T>,Derived> operator* ( const T &  scalar,
const StorageBaseType &  expr 
) [friend]
Returns:
an expression of expr scaled by the scalar factor scalar
Template Parameters:
Tis the scalar type of scalar. It must be compatible with the scalar type of the given expression.

The documentation for this class was generated from the following files:
 All Classes Functions Variables Typedefs Enumerations Enumerator Friends