Base class for all dense matrices, vectors, and expressions. More...
Public Types | |
typedef Matrix< typename internal::traits< Derived > ::Scalar, internal::traits < Derived >::RowsAtCompileTime, internal::traits< Derived > ::ColsAtCompileTime, AutoAlign|(internal::traits < Derived >::Flags &RowMajorBit?RowMajor:ColMajor), internal::traits< Derived > ::MaxRowsAtCompileTime, internal::traits< Derived > ::MaxColsAtCompileTime > | PlainObject |
The plain matrix type corresponding to this expression. | |
Public Member Functions | |
const AdjointReturnType | adjoint () const |
void | adjointInPlace () |
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 DiagonalWrapper< const Derived > | asDiagonal () 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 > | |
internal::cast_return_type < Derived, const CwiseUnaryOp < internal::scalar_cast_op < typename internal::traits < Derived >::Scalar, NewType > , const Derived > >::type | cast () const |
const ColPivHouseholderQR < PlainObject > | colPivHouseholderQr () 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 > | |
cross_product_return_type < OtherDerived >::type | cross (const MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
PlainObject | cross3 (const MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_abs_op < Scalar >, const Derived > | cwiseAbs () const |
const CwiseUnaryOp < internal::scalar_abs2_op < Scalar >, const Derived > | cwiseAbs2 () const |
const CwiseUnaryOp < std::binder1st < std::equal_to< Scalar > >, const Derived > | cwiseEqual (const Scalar &s) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < std::equal_to< Scalar > , const Derived, const OtherDerived > | cwiseEqual (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_inverse_op < Scalar >, const Derived > | cwiseInverse () const |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_max_op < Scalar >, const Derived, const OtherDerived > | cwiseMax (const Eigen::MatrixBase< OtherDerived > &other) const |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_min_op < Scalar >, const Derived, const OtherDerived > | cwiseMin (const Eigen::MatrixBase< OtherDerived > &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 < typename internal::traits < Derived >::Scalar, typename internal::traits< 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 CwiseUnaryOp < internal::scalar_sqrt_op < Scalar >, const Derived > | cwiseSqrt () const |
Scalar | determinant () const |
DiagonalReturnType | diagonal () |
const ConstDiagonalReturnType | diagonal () const |
DiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) |
ConstDiagonalIndexReturnType < Dynamic >::Type | diagonal (Index index) const |
Index | diagonalSize () const |
template<typename OtherDerived > | |
internal::scalar_product_traits < typename internal::traits < Derived >::Scalar, typename internal::traits< OtherDerived > ::Scalar >::ReturnType | dot (const MatrixBase< OtherDerived > &other) const |
EigenvaluesReturnType | eigenvalues () const |
Computes the eigenvalues of a matrix. | |
Matrix< Scalar, 3, 1 > | eulerAngles (Index a0, Index a1, Index a2) const |
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 () |
const FullPivHouseholderQR < PlainObject > | fullPivHouseholderQr () const |
const FullPivLU< PlainObject > | fullPivLu () const |
const HNormalizedReturnType | hnormalized () const |
HomogeneousReturnType | homogeneous () const |
const HouseholderQR< PlainObject > | householderQr () const |
RealScalar | hypotNorm () const |
NonConstImagReturnType | imag () |
const ImagReturnType | imag () const |
const internal::inverse_impl < Derived > | inverse () const |
bool | isDiagonal (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
bool | isIdentity (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 |
bool | isUpperTriangular (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
template<typename OtherDerived > | |
const LazyProductReturnType < Derived, OtherDerived > ::Type | lazyProduct (const MatrixBase< OtherDerived > &other) const |
const LDLT< PlainObject > | ldlt () const |
const LLT< PlainObject > | llt () const |
template<int p> | |
RealScalar | lpNorm () const |
const PartialPivLU< PlainObject > | lu () const |
template<typename EssentialPart > | |
void | makeHouseholder (EssentialPart &essential, Scalar &tau, RealScalar &beta) const |
NoAlias< Derived, Eigen::MatrixBase > | noalias () |
RealScalar | norm () const |
void | normalize () |
const PlainObject | normalized () const |
template<typename OtherDerived > | |
bool | operator!= (const MatrixBase< OtherDerived > &other) const |
ScalarMultipleReturnType | operator* (const UniformScaling< Scalar > &s) const |
template<typename OtherDerived > | |
const ProductReturnType < Derived, OtherDerived > ::Type | operator* (const MatrixBase< OtherDerived > &other) const |
template<typename DiagonalDerived > | |
const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > | operator* (const DiagonalBase< DiagonalDerived > &diagonal) const |
const CwiseUnaryOp < internal::scalar_multiple2_op < Scalar, std::complex< Scalar > >, const Derived > | operator* (const std::complex< Scalar > &scalar) const |
const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
template<typename OtherDerived > | |
Derived & | operator*= (const EigenBase< OtherDerived > &other) |
template<typename OtherDerived > | |
const CwiseBinaryOp < internal::scalar_sum_op < 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 < internal::scalar_difference_op < Scalar >, const Derived, const OtherDerived > | operator- (const Eigen::MatrixBase< OtherDerived > &other) const |
const CwiseUnaryOp < internal::scalar_opposite_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator- () const |
template<typename OtherDerived > | |
Derived & | operator-= (const MatrixBase< OtherDerived > &other) |
const CwiseUnaryOp < internal::scalar_quotient1_op < typename internal::traits < Derived >::Scalar >, const Derived > | operator/ (const Scalar &scalar) const |
template<typename OtherDerived > | |
Derived & | operator= (const EigenBase< OtherDerived > &other) |
Copies the generic expression other into *this. | |
Derived & | operator= (const MatrixBase &other) |
template<typename OtherDerived > | |
Derived & | operator= (const DenseBase< OtherDerived > &other) |
template<typename OtherDerived > | |
bool | operator== (const MatrixBase< OtherDerived > &other) const |
RealScalar | operatorNorm () const |
Computes the L2 operator norm. | |
const PartialPivLU< PlainObject > | partialPivLu () const |
RealReturnType | real () const |
NonConstRealReturnType | real () |
Derived & | setIdentity (Index rows, Index cols) |
Resizes to the given size, and writes the identity expression (not necessarily square) into *this. | |
Derived & | setIdentity () |
RealScalar | squaredNorm () const |
RealScalar | stableNorm () 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 i) |
static const BasisReturnType | Unit (Index size, Index i) |
static const BasisReturnType | UnitW () |
static const BasisReturnType | UnitX () |
static const BasisReturnType | UnitY () |
static const BasisReturnType | UnitZ () |
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.
Derived | is the derived type, e.g. a matrix type, or an expression, etc. |
When writing a function taking Eigen objects as argument, if you want your function to take as argument any matrix, vector, or expression, just let it take a MatrixBase argument. As an example, here is a function printFirstRow which, given a matrix, vector, or expression x, prints the first row of x.
template<typename Derived> void printFirstRow(const Eigen::MatrixBase<Derived>& x) { cout << x.row(0) << endl; }
This class can be extended with the help of the plugin mechanism described on the page Customizing/Extending Eigen by defining the preprocessor symbol EIGEN_MATRIXBASE_PLUGIN
.
typedef Matrix<typename internal::traits<Derived>::Scalar, internal::traits<Derived>::RowsAtCompileTime, internal::traits<Derived>::ColsAtCompileTime, AutoAlign | (internal::traits<Derived>::Flags&RowMajorBit ? RowMajor : ColMajor), internal::traits<Derived>::MaxRowsAtCompileTime, internal::traits<Derived>::MaxColsAtCompileTime > PlainObject |
The plain matrix type corresponding to this expression.
This is not necessarily exactly the return type of eval(). In the case of plain matrices, the return type of eval() is a const reference to a matrix, not a matrix! It is however guaranteed that the return type of eval() is either PlainObject or const PlainObject&.
const MatrixBase< Derived >::AdjointReturnType adjoint | ( | ) | const [inline] |
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)
m = m.adjoint(); // bug!!! caused by aliasing effect
m.adjointInPlace();
m = m.adjoint().eval();
void 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().
*this
must be a resizable matrix.void applyOnTheLeft | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
* other.
void 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 .
void applyOnTheRight | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
* other. It is equivalent to MatrixBase::operator*=()
ArrayWrapper<Derived> array | ( | ) | [inline] |
const DiagonalWrapper< const Derived > asDiagonal | ( | ) | const [inline] |
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
const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> binaryExpr | ( | const Eigen::MatrixBase< OtherDerived > & | other, | |
const CustomBinaryOp & | func = CustomBinaryOp() | |||
) | const [inline] |
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)
NumTraits< typename internal::traits< Derived >::Scalar >::Real blueNorm | ( | ) | const [inline] |
*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.
internal::cast_return_type<Derived,const CwiseUnaryOp<internal::scalar_cast_op<typename internal::traits<Derived>::Scalar, NewType>, const Derived> >::type cast | ( | ) | const [inline] |
The template parameter NewScalar is the type we are casting the scalars to.
const ColPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > colPivHouseholderQr | ( | ) | const |
*this
.void 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.
inverse | Reference to the matrix in which to store the inverse. | |
determinant | Reference to the variable in which to store the inverse. | |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. | |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
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
void 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.
inverse | Reference to the matrix in which to store the inverse. | |
invertible | Reference to the bool variable in which to store whether the matrix is invertible. | |
absDeterminantThreshold | Optional parameter controlling the invertibility check. The matrix will be declared invertible if the absolute value of its determinant is greater than this threshold. |
Example:
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
ConjugateReturnType conjugate | ( | ) | const [inline] |
*this
.MatrixBase< Derived >::template cross_product_return_type< OtherDerived >::type cross | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other Here is a very good explanation of cross-product: http://xkcd.com/199/
MatrixBase< Derived >::PlainObject cross3 | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
and other using only the x, y, and z coefficientsThe 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.
const CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> cwiseAbs | ( | ) | const [inline] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs() << endl;
Output:
2 4 6 5 1 0
const CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> cwiseAbs2 | ( | ) | const [inline] |
*this
Example:
MatrixXd m(2,3); m << 2, -4, 6, -5, 1, 0; cout << m.cwiseAbs2() << endl;
Output:
4 16 36 25 1 0
const CwiseUnaryOp<std::binder1st<std::equal_to<Scalar> >, const Derived> cwiseEqual | ( | const Scalar & | s | ) | const [inline] |
*this
and a scalar s const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> cwiseEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
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
const CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> cwiseInverse | ( | ) | const [inline] |
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
const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived, const OtherDerived> cwiseMax | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMax(w) << endl;
Output:
4 3 4
const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const OtherDerived> cwiseMin | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseMin(w) << endl;
Output:
2 2 3
const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> cwiseNotEqual | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
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
const CwiseBinaryOp< internal::scalar_product_op< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >, const Derived , const OtherDerived > cwiseProduct | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
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
const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> cwiseQuotient | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
Example:
Vector3d v(2,3,4), w(4,2,3); cout << v.cwiseQuotient(w) << endl;
Output:
0.5 1.5 1.33
const CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> cwiseSqrt | ( | ) | const [inline] |
Example:
Vector3d v(1,2,4); cout << v.cwiseSqrt() << endl;
Output:
1 1.41 2
internal::traits< Derived >::Scalar determinant | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
MatrixBase< Derived >::template DiagonalIndexReturnType< Index >::Type diagonal | ( | ) | [inline] |
*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
*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
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Index >::Type diagonal | ( | ) | const [inline] |
This is the const version of diagonal().
This is the const version of diagonal<int>().
MatrixBase< Derived >::template DiagonalIndexReturnType< Dynamic >::Type diagonal | ( | Index | index | ) | [inline] |
*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
MatrixBase< Derived >::template ConstDiagonalIndexReturnType< Dynamic >::Type diagonal | ( | Index | index | ) | const [inline] |
This is the const version of diagonal(Index).
Index diagonalSize | ( | ) | const [inline] |
internal::scalar_product_traits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot | ( | const MatrixBase< OtherDerived > & | other | ) | const |
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.
MatrixBase< Derived >::EigenvaluesReturnType eigenvalues | ( | ) | const [inline] |
Computes the eigenvalues of a matrix.
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)
const ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
ForceAlignedAccess< Derived > forceAlignedAccess | ( | ) | [inline] |
Reimplemented from DenseBase< Derived >.
internal::add_const_on_value_type< typename internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type >::type forceAlignedAccessIf | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
internal::conditional< Enable, ForceAlignedAccess< Derived >, Derived & >::type forceAlignedAccessIf | ( | ) | [inline] |
Reimplemented from DenseBase< Derived >.
const FullPivHouseholderQR< typename MatrixBase< Derived >::PlainObject > fullPivHouseholderQr | ( | ) | const |
*this
.const FullPivLU< typename MatrixBase< Derived >::PlainObject > fullPivLu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.const MatrixBase< Derived >::HNormalizedReturnType hnormalized | ( | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
*this
Example:
Output:
MatrixBase< Derived >::HomogeneousReturnType homogeneous | ( | ) | const [inline] |
This is defined in the Geometry module.
#include <Eigen/Geometry>
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:
Output:
const HouseholderQR< typename MatrixBase< Derived >::PlainObject > householderQr | ( | ) | const |
*this
.NumTraits< typename internal::traits< Derived >::Scalar >::Real hypotNorm | ( | ) | const [inline] |
*this
avoiding undeflow and overflow. This version use a concatenation of hypot() calls, and it is very slow.const MatrixBase< Derived >::IdentityReturnType Identity | ( | ) | [inline, static] |
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
const MatrixBase< Derived >::IdentityReturnType Identity | ( | Index | rows, | |
Index | cols | |||
) | [inline, static] |
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
const ImagReturnType imag | ( | ) | const [inline] |
*this
.NonConstImagReturnType imag | ( | ) | [inline] |
*this
.const internal::inverse_impl< Derived > inverse | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
For small fixed sizes up to 4x4, this method uses cofactors. In the general case, this method uses class PartialPivLU.
Matrix3d m = Matrix3d::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Its inverse is:" << endl << m.inverse() << endl;
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
bool isDiagonal | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
) | const |
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
bool isIdentity | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
) | const |
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
bool isLowerTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
) | const |
bool isOrthogonal | ( | const MatrixBase< OtherDerived > & | other, | |
RealScalar | prec = NumTraits<Scalar>::dummy_precision() | |||
) | const |
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
bool isUnitary | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
) | const |
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
bool isUpperTriangular | ( | RealScalar | prec = NumTraits<Scalar>::dummy_precision() |
) | const |
const LazyProductReturnType< Derived, OtherDerived >::Type lazyProduct | ( | const MatrixBase< OtherDerived > & | other | ) | const |
*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.
const LDLT< typename MatrixBase< Derived >::PlainObject > ldlt | ( | ) | const [inline] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
const LLT< typename MatrixBase< Derived >::PlainObject > llt | ( | ) | const [inline] |
This is defined in the Cholesky module.
#include <Eigen/Cholesky>
*this
NumTraits< typename internal::traits< Derived >::Scalar >::Real lpNorm | ( | ) | const [inline] |
Reimplemented from DenseBase< Derived >.
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > lu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
Synonym of partialPivLu().
*this
.void makeHouseholder | ( | EssentialPart & | essential, | |
Scalar & | tau, | |||
RealScalar & | beta | |||
) | const |
Computes the elementary reflector H such that: where the transformation H is:
and the vector v is:
On output:
essential | the essential part of the vector v | |
tau | the scaling factor of the householder transformation | |
beta | the result of H * *this |
NoAlias< Derived, MatrixBase > noalias | ( | ) |
*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;
NumTraits< typename internal::traits< Derived >::Scalar >::Real norm | ( | ) | const [inline] |
void 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.
const MatrixBase< Derived >::PlainObject normalized | ( | ) | const [inline] |
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.
bool operator!= | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other are not exactly equal to each other. const ProductReturnType< Derived, OtherDerived >::Type operator* | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other.const DiagonalProduct< Derived, DiagonalDerived, OnTheRight > operator* | ( | const DiagonalBase< DiagonalDerived > & | diagonal | ) | const [inline] |
*this
by the diagonal matrix diagonal. const ScalarMultipleReturnType operator* | ( | const Scalar & | scalar | ) | const [inline] |
*this
scaled by the scalar factor scalar const CwiseUnaryOp<internal::scalar_multiple2_op<Scalar,std::complex<Scalar> >, const Derived> operator* | ( | const std::complex< Scalar > & | scalar | ) | const [inline] |
Overloaded for efficient real matrix times complex scalar value
MatrixBase< Derived >::ScalarMultipleReturnType operator* | ( | const UniformScaling< Scalar > & | s | ) | const |
Concatenates a linear transformation matrix and a uniform scaling
Derived & operator*= | ( | const EigenBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
* other.
*this
const CwiseBinaryOp< internal::scalar_sum_op <Scalar>, const Derived, const OtherDerived> operator+ | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other Derived & operator+= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
+ other.
*this
const CwiseUnaryOp<internal::scalar_opposite_op<typename internal::traits<Derived>::Scalar>, const Derived> operator- | ( | ) | const [inline] |
*this
const CwiseBinaryOp< internal::scalar_difference_op <Scalar>, const Derived, const OtherDerived> operator- | ( | const Eigen::MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other Derived & operator-= | ( | const MatrixBase< OtherDerived > & | other | ) | [inline] |
replaces *this
by *this
- other.
*this
const CwiseUnaryOp<internal::scalar_quotient1_op<typename internal::traits<Derived>::Scalar>, const Derived> operator/ | ( | const Scalar & | scalar | ) | const [inline] |
*this
divided by the scalar value scalar Derived& operator= | ( | const DenseBase< OtherDerived > & | other | ) |
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
Reimplemented from DenseBase< Derived >.
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)
bool operator== | ( | const MatrixBase< OtherDerived > & | other | ) | const [inline] |
*this
and other are all exactly equal. MatrixBase< Derived >::RealScalar operatorNorm | ( | ) | const [inline] |
Computes the L2 operator norm.
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 is defined to be
where the maximum is over all vectors and the norm on the right is the Euclidean vector norm. The norm equals the largest singular value, which is the square root of the largest eigenvalue of the positive semi-definite matrix .
The current implementation uses the eigenvalues of , as computed by SelfAdjointView::eigenvalues(), to compute the operator norm of a matrix. The SelfAdjointView class provides a better algorithm for selfadjoint matrices.
Example:
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
const PartialPivLU< typename MatrixBase< Derived >::PlainObject > partialPivLu | ( | ) | const [inline] |
This is defined in the LU module.
#include <Eigen/LU>
*this
.RealReturnType real | ( | ) | const [inline] |
*this
.NonConstRealReturnType real | ( | ) | [inline] |
*this
.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
Resizes to the given size, and writes the identity expression (not necessarily square) into *this.
rows | the new number of rows | |
cols | the new number of columns |
Example:
MatrixXf m; m.setIdentity(3, 3); cout << m << endl;
Output:
1 0 0 0 1 0 0 0 1
NumTraits< typename internal::traits< Derived >::Scalar >::Real squaredNorm | ( | ) | const [inline] |
NumTraits< typename internal::traits< Derived >::Scalar >::Real stableNorm | ( | ) | const [inline] |
*this
avoiding underflow and overflow. This version use a blockwise two passes algorithm: 1 - find the absolute largest coefficient s
2 - compute For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.
internal::traits< Derived >::Scalar trace | ( | ) | const [inline] |
*this
, i.e. the sum of the coefficients on the main diagonal.*this
can be any matrix, not necessarily square.
Reimplemented from DenseBase< Derived >.
MatrixBase< Derived >::template ConstTriangularViewReturnType< Mode >::Type triangularView | ( | ) | const |
This is the const version of MatrixBase::triangularView()
MatrixBase< Derived >::template TriangularViewReturnType< Mode >::Type triangularView | ( | ) |
The parameter Mode can have the following values: Upper
, StrictlyUpper
, UnitUpper
, Lower
, StrictlyLower
, UnitLower
.
Example:
#ifndef _MSC_VER #warning deprecated #endif /* deprecated Matrix3i m = Matrix3i::Random(); cout << "Here is the matrix m:" << endl << m << endl; cout << "Here is the upper-triangular matrix extracted from m:" << endl << m.part<Eigen::UpperTriangular>() << endl; cout << "Here is the strictly-upper-triangular matrix extracted from m:" << endl << m.part<Eigen::StrictlyUpperTriangular>() << endl; cout << "Here is the unit-lower-triangular matrix extracted from m:" << endl << m.part<Eigen::UnitLowerTriangular>() << endl; */
Output:
const CwiseUnaryOp<CustomUnaryOp, const Derived> unaryExpr | ( | const CustomUnaryOp & | func = CustomUnaryOp() |
) | const [inline] |
Apply a unary operator coefficient-wise.
[in] | func | Functor implementing the unary operator |
CustomUnaryOp | Type of func |
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
const CwiseUnaryView<CustomViewOp, const Derived> unaryViewExpr | ( | const CustomViewOp & | func = CustomViewOp() |
) | const [inline] |
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
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | i | ) | [inline, static] |
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.
const MatrixBase< Derived >::BasisReturnType Unit | ( | Index | size, | |
Index | i | |||
) | [inline, static] |
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.
MatrixBase< Derived >::PlainObject unitOrthogonal | ( | void | ) | const |
*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().
const MatrixBase< Derived >::BasisReturnType UnitW | ( | ) | [inline, static] |
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.
const MatrixBase< Derived >::BasisReturnType UnitX | ( | ) | [inline, static] |
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.
const MatrixBase< Derived >::BasisReturnType UnitY | ( | ) | [inline, static] |
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.
const MatrixBase< Derived >::BasisReturnType UnitZ | ( | ) | [inline, static] |
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.