VectorwiseOp< ExpressionType, Direction > Class Template Reference

Pseudo expression providing partial reduction operations. More...

#include <VectorwiseOp.h>

Public Member Functions
const ReturnType< internal::member_all >::Type	all () const
const ReturnType< internal::member_any >::Type	any () const
const ReturnType< internal::member_blueNorm, RealScalar >::Type	blueNorm () const
const PartialReduxExpr< ExpressionType, internal::member_count< Index >, Direction >	count () const
template<typename OtherDerived>
const CrossReturnType	cross (const MatrixBase< OtherDerived > &other) const
const HNormalizedReturnType	hnormalized () const
Homogeneous< ExpressionType, Direction >	homogeneous () const
const ReturnType< internal::member_hypotNorm, RealScalar >::Type	hypotNorm () const
const ReturnType< internal::member_maxCoeff >::Type	maxCoeff () const
const ReturnType< internal::member_mean >::Type	mean () const
const ReturnType< internal::member_minCoeff >::Type	minCoeff () const
const ReturnType< internal::member_norm, RealScalar >::Type	norm () const
template<typename OtherDerived>
CwiseBinaryOp< internal::scalar_product_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type >	operator* (const DenseBase< OtherDerived > &other) const
template<typename OtherDerived>
ExpressionType &	operator*= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived>
CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type >	operator+ (const DenseBase< OtherDerived > &other) const
template<typename OtherDerived>
ExpressionType &	operator+= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived>
CwiseBinaryOp< internal::scalar_difference_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type >	operator- (const DenseBase< OtherDerived > &other) const
template<typename OtherDerived>
ExpressionType &	operator-= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived>
CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type >	operator/ (const DenseBase< OtherDerived > &other) const
template<typename OtherDerived>
ExpressionType &	operator/= (const DenseBase< OtherDerived > &other)
template<typename OtherDerived>
ExpressionType &	operator= (const DenseBase< OtherDerived > &other)
const ReturnType< internal::member_prod >::Type	prod () const
template<typename BinaryOp>
const ReduxReturnType< BinaryOp >::Type	redux (const BinaryOp &func=BinaryOp()) const
const ReplicateReturnType	replicate (Index factor) const
template<int Factor>
const Replicate< ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)>	replicate (Index factor=Factor) const
const Reverse< ExpressionType, Direction >	reverse () const
const ReturnType< internal::member_squaredNorm, RealScalar >::Type	squaredNorm () const
const ReturnType< internal::member_stableNorm, RealScalar >::Type	stableNorm () const
const ReturnType< internal::member_sum >::Type	sum () const

Detailed Description

template<typename ExpressionType, int Direction>
class Eigen::VectorwiseOp< ExpressionType, Direction >

Pseudo expression providing partial reduction operations.

Parameters

ExpressionType	the type of the object on which to do partial reductions
Direction	indicates the direction of the redux (Vertical or Horizontal)

This class represents a pseudo expression with partial reduction features. It is the return type of DenseBase::colwise() and DenseBase::rowwise() and most of the time this is the only way it is used.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each column:" << endl << m.colwise().sum() << endl;
cout << "Here is the maximum absolute value of each column:"
     << endl << m.cwiseAbs().colwise().maxCoeff() << 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
Here is the sum of each column:
  1.04  0.815 -0.238
Here is the maximum absolute value of each column:
 0.68 0.823 0.536

See also

DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr

Member Function Documentation

all()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_all >::Type all ( ) const

inline

Returns

a row (or column) vector expression representing whether all coefficients of each respective column (or row) are true.

See also

DenseBase::all()

any()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_any >::Type any ( ) const

inline

Returns

a row (or column) vector expression representing whether at least one coefficient of each respective column (or row) is true.

See also

DenseBase::any()

blueNorm()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_blueNorm, RealScalar >::Type blueNorm ( ) const

inline

Returns

a row (or column) vector expression of the norm of each column (or row) of the referenced expression, using blue's algorithm.

See also

DenseBase::blueNorm()

count()

template<typename ExpressionType, int Direction>

const PartialReduxExpr< ExpressionType, internal::member_count< Index >, Direction > count ( ) const

inline

Returns

a row (or column) vector expression representing the number of true coefficients of each respective column (or row).

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the count of elements larger or equal than 0.5 of each row:" << endl << (m.array() >= 0.5).rowwise().count() << 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
Here is the count of elements larger or equal than 0.5 of each row:
2
2
1

See also

DenseBase::count()

cross()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

const VectorwiseOp< ExpressionType, Direction >::CrossReturnType cross

(

const MatrixBase< OtherDerived > &

other

)

const

Returns

a matrix expression of the cross product of each column or row of the referenced expression with the other vector.

The referenced matrix must have one dimension equal to 3. The result matrix has the same dimensions than the referenced one.

This is defined in the Geometry module.

#include <Eigen/Geometry> 

See also

MatrixBase::cross()

References DenseBase< Derived >::col(), DenseBase< Derived >::row(), and Eigen::Vertical.

hnormalized()

template<typename ExpressionType, int Direction>

const VectorwiseOp< ExpressionType, Direction >::HNormalizedReturnType hnormalized ( ) const

inline

This is defined in the Geometry module.

#include <Eigen/Geometry> 

Returns

an expression of the homogeneous normalized vector of *this

Example:

Output:

See also

MatrixBase::hnormalized()

References Eigen::Horizontal, and Eigen::Vertical.

homogeneous()

template<typename ExpressionType, int Direction>

Homogeneous< ExpressionType, Direction > homogeneous ( ) const

inline

This is defined in the Geometry module.

#include <Eigen/Geometry> 

Returns

a matrix expression of homogeneous column (or row) vectors

Example:

Output:

See also

MatrixBase::homogeneous()

hypotNorm()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_hypotNorm, RealScalar >::Type hypotNorm ( ) const

inline

Returns

a row (or column) vector expression of the norm of each column (or row) of the referenced expression, avoiding underflow and overflow using a concatenation of hypot() calls.

See also

DenseBase::hypotNorm()

maxCoeff()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_maxCoeff >::Type maxCoeff ( ) const

inline

Returns

a row (or column) vector expression of the largest coefficient of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the maximum of each column:" << endl << m.colwise().maxCoeff() << 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
Here is the maximum of each column:
 0.68 0.823 0.536

See also

DenseBase::maxCoeff()

mean()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_mean >::Type mean ( ) const

inline

Returns

a row (or column) vector expression of the mean of each column (or row) of the referenced expression.

See also

DenseBase::mean()

minCoeff()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_minCoeff >::Type minCoeff ( ) const

inline

Returns

a row (or column) vector expression of the smallest coefficient of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the minimum of each column:" << endl << m.colwise().minCoeff() << 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
Here is the minimum of each column:
-0.211 -0.605 -0.444

See also

DenseBase::minCoeff()

norm()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_norm, RealScalar >::Type norm ( ) const

inline

Returns

a row (or column) vector expression of the norm of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the norm of each column:" << endl << m.colwise().norm() << 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
Here is the norm of each column:
 0.91  1.18 0.771

See also

DenseBase::norm()

operator*()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

CwiseBinaryOp< internal::scalar_product_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type > operator* ( const DenseBase< OtherDerived > & other ) const

inline

Returns the expression where each subvector is the product of the vector other by the corresponding subvector of *this

operator*=()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

ExpressionType & operator*= ( const DenseBase< OtherDerived > & other )

inline

Multiples each subvector of *this by the vector other

operator+()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type > operator+ ( const DenseBase< OtherDerived > & other ) const

inline

Returns the expression of the sum of the vector other to each subvector of *this

operator+=()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

ExpressionType & operator+= ( const DenseBase< OtherDerived > & other )

inline

Adds the vector other to each subvector of *this

operator-()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

CwiseBinaryOp< internal::scalar_difference_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type > operator- ( const DenseBase< OtherDerived > & other ) const

inline

Returns the expression of the difference between each subvector of *this and the vector other

operator-=()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

ExpressionType & operator-= ( const DenseBase< OtherDerived > & other )

inline

Substracts the vector other to each subvector of *this

operator/()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const ExpressionTypeNestedCleaned, const typename ExtendedType< OtherDerived >::Type > operator/ ( const DenseBase< OtherDerived > & other ) const

inline

Returns the expression where each subvector is the quotient of the corresponding subvector of *this by the vector other

operator/=()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

ExpressionType & operator/= ( const DenseBase< OtherDerived > & other )

inline

Divides each subvector of *this by the vector other

operator=()

template<typename ExpressionType, int Direction>

template<typename OtherDerived>

ExpressionType & operator= ( const DenseBase< OtherDerived > & other )

inline

Copies the vector other to each subvector of *this

prod()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_prod >::Type prod ( ) const

inline

Returns

a row (or column) vector expression of the product of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the product of each row:" << endl << m.rowwise().prod() << 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
Here is the product of each row:
-0.134
-0.0933
0.152

See also

DenseBase::prod()

redux()

template<typename ExpressionType, int Direction>

template<typename BinaryOp>

const ReduxReturnType< BinaryOp >::Type redux ( const BinaryOp & func = BinaryOp() ) const

inline

Returns

a row or column vector expression of *this reduxed by func

The template parameter BinaryOp is the type of the functor of the custom redux operator. Note that func must be an associative operator.

See also

class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()

replicate() [1/2]

template<typename ExpressionType, int Direction>

const VectorwiseOp< ExpressionType, Direction >::ReplicateReturnType replicate

(

Index

factor

)

const

Returns

an expression of the replication of each column (or row) of *this

Example:

Vector3i v = Vector3i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "v.rowwise().replicate(5) = ..." << endl;
cout << v.rowwise().replicate(5) << endl;

Output:

Here is the vector v:
7
-2
6
v.rowwise().replicate(5) = ...
 7  7  7  7  7
-2 -2 -2 -2 -2
 6  6  6  6  6

See also

VectorwiseOp::replicate(), DenseBase::replicate(), class Replicate

References Eigen::Horizontal, and Eigen::Vertical.

replicate() [2/2]

template<typename ExpressionType, int Direction>

template<int Factor>

const Replicate< ExpressionType,(IsVertical?Factor:1),(IsHorizontal?Factor:1)> replicate ( Index factor = Factor ) const

inline

Returns

an expression of the replication of each column (or row) of *this

Example:

MatrixXi m = MatrixXi::Random(2,3);
cout << "Here is the matrix m:" << endl << m << endl;
cout << "m.colwise().replicate<3>() = ..." << endl;
cout << m.colwise().replicate<3>() << endl;

Output:

Here is the matrix m:
 7  6  9
-2  6 -6
m.colwise().replicate<3>() = ...
 7  6  9
-2  6 -6
 7  6  9
-2  6 -6
 7  6  9
-2  6 -6

See also

VectorwiseOp::replicate(Index), DenseBase::replicate(), class Replicate

reverse()

template<typename ExpressionType, int Direction>

const Reverse< ExpressionType, Direction > reverse ( ) const

inline

Returns

a matrix expression where each column (or row) are reversed.

Example:

MatrixXi m = MatrixXi::Random(3,4);
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the rowwise reverse of m:" << endl << m.rowwise().reverse() << endl;
cout << "Here is the colwise reverse of m:" << endl << m.colwise().reverse() << endl;
 
cout << "Here is the coefficient (1,0) in the rowise reverse of m:" << endl
<< m.rowwise().reverse()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 4." << endl;
//m.colwise().reverse()(1,0) = 4;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  6 -3  1
-2  9  6  0
 6 -6 -5  3
Here is the rowwise reverse of m:
 1 -3  6  7
 0  6  9 -2
 3 -5 -6  6
Here is the colwise reverse of m:
 6 -6 -5  3
-2  9  6  0
 7  6 -3  1
Here is the coefficient (1,0) in the rowise reverse of m:
0
Let us overwrite this coefficient with the value 4.
Now the matrix m is:
 7  6 -3  1
-2  9  6  0
 6 -6 -5  3

See also

DenseBase::reverse()

squaredNorm()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_squaredNorm, RealScalar >::Type squaredNorm ( ) const

inline

Returns

a row (or column) vector expression of the squared norm of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the square norm of each row:" << endl << m.rowwise().squaredNorm() << 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
Here is the square norm of each row:
0.928
1.01
0.884

See also

DenseBase::squaredNorm()

Referenced by Eigen::umeyama().

stableNorm()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_stableNorm, RealScalar >::Type stableNorm ( ) const

inline

Returns

a row (or column) vector expression of the norm of each column (or row) of the referenced expression, avoiding underflow and overflow.

See also

DenseBase::stableNorm()

sum()

template<typename ExpressionType, int Direction>

const ReturnType< internal::member_sum >::Type sum ( ) const

inline

Returns

a row (or column) vector expression of the sum of each column (or row) of the referenced expression.

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the sum of each row:" << endl << m.rowwise().sum() << 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
Here is the sum of each row:
0.948
1.15
-0.483

See also

DenseBase::sum()

Referenced by Eigen::umeyama().

---

The documentation for this class was generated from the following files:

• ForwardDeclarations.h
• VectorwiseOp.h
• Replicate.h
• Homogeneous.h
• OrthoMethods.h