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Eigen  3.3.90 (git rev ecb7bc9514b12051d050299234b2a74ac76b5a8e)
Eigen::VectorwiseOp Class Reference

Detailed Description

Pseudo expression providing broadcasting and partial reduction operations.

Template Parameters
ExpressionTypethe type of the object on which to do partial reductions
Directionindicates whether to operate on columns (Vertical) or rows (Horizontal)

This class represents a pseudo expression with broadcasting and 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 explicitly used.

To understand the logic of rowwise/colwise expression, let's consider a generic case A.colwise().foo() where foo is any method of VectorwiseOp. This expression is equivalent to applying foo() to each column of A and then re-assemble the outputs in a matrix expression:

[A.col(0).foo(), A.col(1).foo(), ..., A.col(A.cols()-1).foo()]

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

The begin() and end() methods are obviously exceptions to the previous rule as they return STL-compatible begin/end iterators to the rows or columns of the nested expression. Typical use cases include for-range-loop and calls to STL algorithms:

Example:

Matrix3i m = Matrix3i::Random();
cout << "Here is the initial matrix m:" << endl << m << endl;
int i = -1;
for(auto c: m.colwise()) {
c *= i;
++i;
}
cout << "Here is the matrix m after the for-range-loop:" << endl << m << endl;
auto cols = m.colwise();
auto it = std::find_if(cols.cbegin(), cols.cend(),
[](Matrix3i::ConstColXpr x) { return x.squaredNorm() == 0; });
cout << "The first empty column is: " << distance(cols.cbegin(),it) << endl;

Output:

Here is the initial matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the matrix m after the for-range-loop:
-7  0 -3
 2  0  6
-6  0 -5
The first empty column is: 1

For a partial reduction on an empty input, some rules apply. For the sake of clarity, let's consider a vertical reduction:

  • If the number of columns is zero, then a 1x0 row-major vector expression is returned.
  • Otherwise, if the number of rows is zero, then
    • a row vector of zeros is returned for sum-like reductions (sum, squaredNorm, norm, etc.)
    • a row vector of ones is returned for a product reduction (e.g., MatrixXd(n,0).colwise().prod())
    • an assert is triggered for all other reductions (minCoeff,maxCoeff,redux(bin_op))
See also
DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr

Public Types

typedef Eigen::Index Index
 

Public Member Functions

const AllReturnType all () const
 
const AnyReturnType any () const
 
iterator begin ()
 
const_iterator begin () const
 
const BlueNormReturnType blueNorm () const
 
const_iterator cbegin () const
 
const_iterator cend () const
 
const CountReturnType count () const
 
const_reverse_iterator crbegin () const
 
const_reverse_iterator crend () const
 
template<typename OtherDerived >
const CrossReturnType cross (const MatrixBase< OtherDerived > &other) const
 
iterator end ()
 
const_iterator end () const
 
const HNormalizedReturnType hnormalized () const
 column or row-wise homogeneous normalization More...
 
HomogeneousReturnType homogeneous () const
 
const HypotNormReturnType hypotNorm () const
 
template<int p>
const LpNormReturnType< p >::Type lpNorm () const
 
const MaxCoeffReturnType maxCoeff () const
 
const MeanReturnType mean () const
 
const MinCoeffReturnType minCoeff () const
 
const NormReturnType norm () const
 
void normalize ()
 
CwiseBinaryOp< internal::scalar_quotient_op< Scalar >, const ExpressionTypeNestedCleaned, const typename OppositeExtendedType< NormReturnType >::Type > normalized () 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, typename OtherDerived::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, typename OtherDerived::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 ProdReturnType prod () const
 
reverse_iterator rbegin ()
 
const_reverse_iterator rbegin () const
 
template<typename BinaryOp >
const ReduxReturnType< BinaryOp >::Type redux (const BinaryOp &func=BinaryOp()) const
 
reverse_iterator rend ()
 
const_reverse_iterator rend () const
 
const ReplicateReturnType replicate (Index factor) const
 
template<int Factor>
const Replicate< ExpressionType, isVertical *Factor+isHorizontal, isHorizontal *Factor+isVertical > replicate (Index factor=Factor) const
 
ReverseReturnType reverse ()
 
const ConstReverseReturnType reverse () const
 
void reverseInPlace ()
 
const SquaredNormReturnType squaredNorm () const
 
const StableNormReturnType stableNorm () const
 
const SumReturnType sum () const
 

Public Attributes

random_access_iterator_type const_iterator
 
random_access_iterator_type iterator
 

Member Typedef Documentation

◆ Index

Member Function Documentation

◆ all()

const AllReturnType Eigen::VectorwiseOp::all ( ) const
inline
Returns
a row (or column) vector expression representing whether all coefficients of each respective column (or row) are true. This expression can be assigned to a vector with entries of type bool.
See also
DenseBase::all()

◆ any()

const AnyReturnType Eigen::VectorwiseOp::any ( ) const
inline
Returns
a row (or column) vector expression representing whether at least one coefficient of each respective column (or row) is true. This expression can be assigned to a vector with entries of type bool.
See also
DenseBase::any()

◆ begin() [1/2]

iterator Eigen::VectorwiseOp::begin ( )
inline

returns an iterator to the first row (rowwise) or column (colwise) of the nested expression.

See also
end(), cbegin()

◆ begin() [2/2]

const_iterator Eigen::VectorwiseOp::begin ( ) const
inline

const version of begin()

◆ blueNorm()

const BlueNormReturnType Eigen::VectorwiseOp::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. This is a vector with real entries, even if the original matrix has complex entries.
See also
DenseBase::blueNorm()

◆ cbegin()

const_iterator Eigen::VectorwiseOp::cbegin ( ) const
inline

const version of begin()

◆ cend()

const_iterator Eigen::VectorwiseOp::cend ( ) const
inline

const version of end()

◆ count()

const CountReturnType Eigen::VectorwiseOp::count ( ) const
inline
Returns
a row (or column) vector expression representing the number of true coefficients of each respective column (or row). This expression can be assigned to a vector whose entries have the same type as is used to index entries of the original matrix; for dense matrices, this is std::ptrdiff_t .

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
Matrix<ptrdiff_t, 3, 1> res = (m.array() >= 0.5).rowwise().count();
cout << "Here is the count of elements larger or equal than 0.5 of each row:" << endl;
cout << res << 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()

◆ crbegin()

const_reverse_iterator Eigen::VectorwiseOp::crbegin ( ) const
inline

const version of rbegin()

◆ crend()

const_reverse_iterator Eigen::VectorwiseOp::crend ( ) const
inline

const version of rend()

◆ end() [1/2]

iterator Eigen::VectorwiseOp::end ( )
inline

returns an iterator to the row (resp. column) following the last row (resp. column) of the nested expression

See also
begin(), cend()

◆ end() [2/2]

const_iterator Eigen::VectorwiseOp::end ( ) const
inline

const version of end()

◆ hypotNorm()

const HypotNormReturnType Eigen::VectorwiseOp::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. This is a vector with real entries, even if the original matrix has complex entries.
See also
DenseBase::hypotNorm()

◆ lpNorm()

template<int p>
const LpNormReturnType<p>::Type Eigen::VectorwiseOp::lpNorm ( ) const
inline
Returns
a row (or column) vector expression of the norm of each column (or row) of the referenced expression. This is a vector with real entries, even if the original matrix has complex entries.

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()

◆ maxCoeff()

const MaxCoeffReturnType Eigen::VectorwiseOp::maxCoeff ( ) const
inline
Returns
a row (or column) vector expression of the largest coefficient of each column (or row) of the referenced expression.
Warning
the size along the reduction direction must be strictly positive, otherwise an assertion is triggered.
the result is undefined if *this contains NaN.

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()

const MeanReturnType Eigen::VectorwiseOp::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()

const MinCoeffReturnType Eigen::VectorwiseOp::minCoeff ( ) const
inline
Returns
a row (or column) vector expression of the smallest coefficient of each column (or row) of the referenced expression.
Warning
the size along the reduction direction must be strictly positive, otherwise an assertion is triggered.
the result is undefined if *this contains NaN.

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()

const NormReturnType Eigen::VectorwiseOp::norm ( ) const
inline
Returns
a row (or column) vector expression of the norm of each column (or row) of the referenced expression. This is a vector with real entries, even if the original matrix has complex entries.

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()

◆ normalize()

void Eigen::VectorwiseOp::normalize ( )
inline

Normalize in-place each row or columns of the referenced matrix.

See also
MatrixBase::normalize(), normalized()

◆ normalized()

CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const ExpressionTypeNestedCleaned, const typename OppositeExtendedType<NormReturnType>::Type> Eigen::VectorwiseOp::normalized ( ) const
inline
Returns
an expression where each column (or row) of the referenced matrix are normalized. The referenced matrix is not modified.
See also
MatrixBase::normalized(), normalize()

◆ operator*()

template<typename OtherDerived >
CwiseBinaryOp<internal::scalar_product_op<Scalar>, const ExpressionTypeNestedCleaned, const typename ExtendedType<OtherDerived>::Type> Eigen::VectorwiseOp::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 OtherDerived >
ExpressionType& Eigen::VectorwiseOp::operator*= ( const DenseBase< OtherDerived > &  other)
inline

Multiples each subvector of *this by the vector other

◆ operator+()

template<typename OtherDerived >
CwiseBinaryOp<internal::scalar_sum_op<Scalar,typename OtherDerived::Scalar>, const ExpressionTypeNestedCleaned, const typename ExtendedType<OtherDerived>::Type> Eigen::VectorwiseOp::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 OtherDerived >
ExpressionType& Eigen::VectorwiseOp::operator+= ( const DenseBase< OtherDerived > &  other)
inline

Adds the vector other to each subvector of *this

◆ operator-()

template<typename OtherDerived >
CwiseBinaryOp<internal::scalar_difference_op<Scalar,typename OtherDerived::Scalar>, const ExpressionTypeNestedCleaned, const typename ExtendedType<OtherDerived>::Type> Eigen::VectorwiseOp::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 OtherDerived >
ExpressionType& Eigen::VectorwiseOp::operator-= ( const DenseBase< OtherDerived > &  other)
inline

Substracts the vector other to each subvector of *this

◆ operator/()

template<typename OtherDerived >
CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const ExpressionTypeNestedCleaned, const typename ExtendedType<OtherDerived>::Type> Eigen::VectorwiseOp::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 OtherDerived >
ExpressionType& Eigen::VectorwiseOp::operator/= ( const DenseBase< OtherDerived > &  other)
inline

Divides each subvector of *this by the vector other

◆ operator=()

template<typename OtherDerived >
ExpressionType& Eigen::VectorwiseOp::operator= ( const DenseBase< OtherDerived > &  other)
inline

Copies the vector other to each subvector of *this

◆ prod()

const ProdReturnType Eigen::VectorwiseOp::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()

◆ rbegin() [1/2]

reverse_iterator Eigen::VectorwiseOp::rbegin ( )
inline

returns a reverse iterator to the last row (rowwise) or column (colwise) of the nested expression.

See also
rend(), crbegin()

◆ rbegin() [2/2]

const_reverse_iterator Eigen::VectorwiseOp::rbegin ( ) const
inline

const version of rbegin()

◆ redux()

template<typename BinaryOp >
const ReduxReturnType<BinaryOp>::Type Eigen::VectorwiseOp::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.

Warning
the size along the reduction direction must be strictly positive, otherwise an assertion is triggered.
See also
class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()

◆ rend() [1/2]

reverse_iterator Eigen::VectorwiseOp::rend ( )
inline

returns a reverse iterator to the row (resp. column) before the first row (resp. column) of the nested expression

See also
begin(), cend()

◆ rend() [2/2]

const_reverse_iterator Eigen::VectorwiseOp::rend ( ) const
inline

const version of rend()

◆ replicate() [1/2]

const VectorwiseOp< ExpressionType, Direction >::ReplicateReturnType Eigen::VectorwiseOp::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

◆ replicate() [2/2]

template<int Factor>
const Replicate<ExpressionType,isVertical*Factor+isHorizontal,isHorizontal*Factor+isVertical> Eigen::VectorwiseOp::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() [1/2]

ReverseReturnType Eigen::VectorwiseOp::reverse ( )
inline
Returns
a writable matrix expression where each column (or row) are reversed.
See also
reverse() const

◆ reverse() [2/2]

const ConstReverseReturnType Eigen::VectorwiseOp::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()

◆ reverseInPlace()

void Eigen::VectorwiseOp::reverseInPlace ( )
inline

This is the "in place" version of VectorwiseOp::reverse: it reverses each column or row of *this.

In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional benefits:

  • less error prone: doing the same operation with .reverse() requires special care:
    m = m.reverse().eval();
  • this API enables reverse operations without the need for a temporary
See also
DenseBase::reverseInPlace(), reverse()

◆ squaredNorm()

const SquaredNormReturnType Eigen::VectorwiseOp::squaredNorm ( ) const
inline
Returns
a row (or column) vector expression of the squared norm of each column (or row) of the referenced expression. This is a vector with real entries, even if the original matrix has complex entries.

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()

◆ stableNorm()

const StableNormReturnType Eigen::VectorwiseOp::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. This is a vector with real entries, even if the original matrix has complex entries.
See also
DenseBase::stableNorm()

◆ sum()

const SumReturnType Eigen::VectorwiseOp::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()

Member Data Documentation

◆ const_iterator

random_access_iterator_type Eigen::VectorwiseOp::const_iterator

This is the const version of iterator (aka read-only)

◆ iterator

random_access_iterator_type Eigen::VectorwiseOp::iterator

STL-like RandomAccessIterator iterator type over the columns or rows as returned by the begin() and end() methods.


The documentation for this class was generated from the following files:
Eigen::DenseBase::Random
static const RandomReturnType Random()
Definition: Random.h:113