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

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

The plain array type corresponding to this expression.

See also

PlainObject

The plain matrix type corresponding to this expression.

See also

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&.

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

The type used to store indices.

This typedef is relevant for types that store multiple indices such as PermutationMatrix or Transpositions, otherwise it defaults to Eigen::Index

See also

Preprocessor directives, Eigen::Index, SparseMatrixBase.

The numeric type of the expression' coefficients, e.g. float, double, int or std::complex<float>, etc.

It is an alias for the Scalar type

Default constructor. Do nothing.

Returns

true if all coefficients are true

Example:

Vector3f boxMin(Vector3f::Zero()), boxMax(Vector3f::Ones());
Vector3f p0 = Vector3f::Random(), p1 = Vector3f::Random().cwiseAbs();
// let's check if p0 and p1 are inside the axis aligned box defined by the corners boxMin,boxMax:
cout << "Is (" << p0.transpose() << ") inside the box: "
     << ((boxMin.array()<p0.array()).all() && (boxMax.array()>p0.array()).all()) << endl;
cout << "Is (" << p1.transpose() << ") inside the box: "
     << ((boxMin.array()<p1.array()).all() && (boxMax.array()>p1.array()).all()) << endl;

Output:

Is (  0.68 -0.211  0.566) inside the box: 0
Is (0.597 0.823 0.605) inside the box: 1

See also

any(), Cwise::operator<()

Returns

true if *this contains only finite numbers, i.e., no NaN and no +/-INF values.

See also

hasNaN()

Returns

true if at least one coefficient is true

See also

all()

returns an iterator to the first element of the 1D vector or array 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

end(), cbegin()

const version of begin()

returns a read-only const_iterator to the first element of the 1D vector or array 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

cend(), begin()

returns a read-only const_iterator to the element following the last element of the 1D vector or array 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

begin(), cend()

Returns

a writable VectorwiseOp wrapper of *this providing additional partial reduction operations

See also

rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Returns

a VectorwiseOp wrapper of *this broadcasting and partial reductions

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

rowwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Returns

an expression of a constant matrix of value value

This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.

The template parameter CustomNullaryOp is the type of the functor.

See also

class CwiseNullaryOp

Returns

an expression of a constant matrix of value value

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase 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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also

class CwiseNullaryOp

Returns

an expression of a constant matrix of value value

The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also

class CwiseNullaryOp

Returns

the number of coefficients which evaluate to true

See also

all(), any()

returns an iterator to the element following the last element of the 1D vector or array 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

begin(), cend()

const version of end()

Returns

the matrix or vector obtained by evaluating this expression.

Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.

Warning

Be careful with eval() and the auto C++ keyword, as detailed in this page .

Alias for setConstant(): sets all coefficients in this expression to val.

See also

setConstant(), Constant(), class CwiseNullaryOp

Deprecated:

it now returns *this

Returns

a WithFormat proxy object allowing to print a matrix the with given format fmt.

See class IOFormat for some examples.

See also

class IOFormat, class WithFormat

Returns

true is *this contains at least one Not A Number (NaN).

See also

allFinite()

Returns

the inner size.

Note

For a vector, this is just the size. For a matrix (non-vector), this is the minor dimension with respect to the storage order, i.e., the number of rows for a column-major matrix, and the number of columns for a row-major matrix.

Returns

true if *this is approximately equal to other, within the precision determined by prec.

Note

The fuzzy compares are done multiplicatively. Two vectors \( v \) and \( w \) are considered to be approximately equal within precision \( p \) if

\[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \]

For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm L2 norm).

Because of the multiplicativeness of this comparison, one can't use this function to check whether *this is approximately equal to the zero matrix or vector. Indeed, isApprox(zero) returns false unless *this itself is exactly the zero matrix or vector. If you want to test whether *this is zero, use internal::isMuchSmallerThan(const RealScalar&, RealScalar) instead.

See also

internal::isMuchSmallerThan(const RealScalar&, RealScalar) const

Returns

true if all coefficients in this matrix are approximately equal to val, to within precision prec

This is just an alias for isApproxToConstant().

Returns

true if all coefficients in this matrix are approximately equal to value, to within precision prec

Returns

true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.

Note

The fuzzy compares are done multiplicatively. A vector \( v \) is considered to be much smaller than a vector \( w \) within precision \( p \) if

\[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \]

For matrices, the comparison is done using the Hilbert-Schmidt norm.

See also

isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const

Returns

true if the norm of *this is much smaller than other, within the precision determined by prec.

Note

The fuzzy compares are done multiplicatively. A vector \( v \) is considered to be much smaller than \( x \) within precision \( p \) if

\[ \Vert v \Vert \leqslant p\,\vert x\vert. \]

For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.

See also

isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const

Returns

true if *this is approximately equal to the matrix where all coefficients are equal to 1, within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
1 1 1
1 1 1
1 1 1
m.isOnes() returns: 0
m.isOnes(1e-3) returns: 1

See also

class CwiseNullaryOp, Ones()

Returns

true if *this is approximately equal to the zero matrix, within the precision given by prec.

Example:

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

Output:

Here's the matrix m:
     0      0 0.0001
     0      0      0
     0      0      0
m.isZero() returns: 0
m.isZero(1e-3) returns: 1

See also

class CwiseNullaryOp, Zero()

Deprecated:

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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 << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

cout << "Even spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,4).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,8).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,15).transpose() << endl;
cout << "Uneven spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,7).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,9).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,16).transpose() << endl;

Output:

Even spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
Uneven spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15

See also

setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp Special version for fixed size types which does not require the size parameter.

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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 << VectorXi::LinSpaced(4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

For integer scalar types, an even spacing is possible if and only if the length of the range, i.e., high-low is a scalar multiple of size-1, or if size is a scalar multiple of the number of values high-low+1 (meaning each value can be repeated the same number of time). If one of these two considions is not satisfied, then high is lowered to the largest value satisfying one of this constraint. Here are some examples:

Example:

cout << "Even spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,4).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,8).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,15).transpose() << endl;
cout << "Uneven spacing inputs:" << endl;
cout << VectorXi::LinSpaced(8,1,7).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,9).transpose() << endl;
cout << VectorXi::LinSpaced(8,1,16).transpose() << endl;

Output:

Even spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15
Uneven spacing inputs:
1 1 2 2 3 3 4 4
1 2 3 4 5 6 7 8
 1  3  5  7  9 11 13 15

See also

setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp

Deprecated:

because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&)

See also

LinSpaced(const Scalar&, const Scalar&)

Deprecated:

because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&)

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 << VectorXi::LinSpaced(Sequential,4,7,10).transpose() << endl;
cout << VectorXd::LinSpaced(Sequential,5,0.0,1.0).transpose() << endl;

Output:

 7  8  9 10
   0 0.25  0.5 0.75    1

See also

LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&)

Returns

the maximum of all coefficients of *this. In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

Returns

the maximum of all coefficients of *this and puts in *index its location.

In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

See also

DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visitor(), DenseBase::maxCoeff()

Returns

the maximum of all coefficients of *this and puts in *row and *col its location.

In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

See also

DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::maxCoeff()

Returns

the mean of all coefficients of *this

See also

trace(), prod(), sum()

Returns

the minimum of all coefficients of *this. In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is minimum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

Returns

the minimum of all coefficients of *this and puts in *index its location.

In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

See also

DenseBase::minCoeff(IndexType*,IndexType*), DenseBase::maxCoeff(IndexType*,IndexType*), DenseBase::visit(), DenseBase::minCoeff()

Returns

the minimum of all coefficients of *this and puts in *row and *col its location.

In case *this contains NaN, NaNPropagation determines the behavior: NaNPropagation == PropagateFast : undefined NaNPropagation == PropagateNaN : result is NaN NaNPropagation == PropagateNumbers : result is maximum of elements that are not NaN

Warning

the matrix must be not empty, otherwise an assertion is triggered.

See also

DenseBase::minCoeff(Index*), DenseBase::maxCoeff(Index*,Index*), DenseBase::visit(), DenseBase::minCoeff()

Returns

an expression of the temporary version of *this.

Returns

the number of nonzero coefficients which is in practice the number of stored coefficients.

Returns

an expression of a matrix defined by a custom functor func

This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.

The template parameter CustomNullaryOp is the type of the functor.

See also

class CwiseNullaryOp

Returns

an expression of a matrix defined by a custom functor func

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 Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

See also

class CwiseNullaryOp

Returns

an expression of a matrix defined by a custom functor func

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

The template parameter CustomNullaryOp is the type of the functor.

Here is an example with C++11 random generators:

#include <Eigen/Core>
#include <iostream>
#include <random>
 
using namespace Eigen;
 
int main() {
  std::default_random_engine generator;
  std::poisson_distribution<int> distribution(4.1);
  auto poisson = [&] () {return distribution(generator);};
 
  RowVectorXi v = RowVectorXi::NullaryExpr(10, poisson );
  std::cout << v << "\n";
}

Output:

2 3 1 4 3 4 4 3 2 3

See also

class CwiseNullaryOp

Returns

an expression of a fixed-size matrix or vector where all coefficients equal one.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << Matrix2d::Ones() << endl;
cout << 6 * RowVector4i::Ones() << endl;

Output:

1 1
1 1
6 6 6 6

See also

Ones(Index), Ones(Index,Index), isOnes(), class Ones

Returns

an expression of a matrix where all coefficients equal one.

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 Ones() should be used instead.

Example:

cout << MatrixXi::Ones(2,3) << endl;

Output:

1 1 1
1 1 1

See also

Ones(), Ones(Index), isOnes(), class Ones

Returns

an expression of a vector where all coefficients equal one.

The parameter newSize is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.

Example:

cout << 6 * RowVectorXi::Ones(4) << endl;
cout << VectorXf::Ones(2) << endl;

Output:

6 6 6 6
1
1

See also

Ones(), Ones(Index,Index), isOnes(), class Ones

See also

operator<<(const Scalar&)

Convenient operator to set the coefficients of a matrix.

The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.

Example:

Matrix3i m1;
m1 << 1, 2, 3,
      4, 5, 6,
      7, 8, 9;
cout << m1 << endl << endl;
Matrix3i m2 = Matrix3i::Identity();
m2.block(0,0, 2,2) << 10, 11, 12, 13;
cout << m2 << endl << endl;
Vector2i v1;
v1 << 14, 15;
m2 << v1.transpose(), 16,
      v1, m1.block(1,1,2,2);
cout << m2 << endl;

Output:

1 2 3
4 5 6
7 8 9

10 11  0
12 13  0
 0  0  1

14 15 16
14  5  6
15  8  9

Note

According the c++ standard, the argument expressions of this comma initializer are evaluated in arbitrary order.

See also

CommaInitializer::finished(), class CommaInitializer

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

Copies other into *this.

Returns

a reference to *this.

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.

Returns

the outer size.

Note

For a vector, this returns just 1. For a matrix (non-vector), this is the major dimension with respect to the storage order, i.e., the number of columns for a column-major matrix, and the number of rows for a row-major matrix.

Returns

the product of all coefficients of *this

Example:

Matrix3d m = Matrix3d::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the product of all the coefficients:" << endl << m.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 all the coefficients:
0.0019

See also

sum(), mean(), trace()

Returns

a fixed-size random matrix or vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << 100 * Matrix2i::Random() << endl;

Output:

 700  600
-200  600

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

Warning

This function is not re-entrant.

See also

DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random(Index)

Returns

a random matrix expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.

Warning

This function is not re-entrant.

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 Random() should be used instead.

Example:

cout << MatrixXi::Random(2,3) << endl;

Output:

 7  6  9
-2  6 -6

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See DenseBase::NullaryExpr(Index, const CustomNullaryOp&) for an example using C++11 random generators.

See also

DenseBase::setRandom(), DenseBase::Random(Index), DenseBase::Random()

Returns

a random vector expression

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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

This function is not re-entrant.

This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.

Example:

cout << VectorXi::Random(2) << endl;

Output:

 7
-2

This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.

See also

DenseBase::setRandom(), DenseBase::Random(Index,Index), DenseBase::Random()

Returns

the result of a full redux operation on the whole matrix or vector using func

The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current C++98 and C++11 functor styles are handled.

Warning

the matrix must be not empty, otherwise an assertion is triggered.

See also

DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()

Returns

an expression of the replication of *this

Example:

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

Output:

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

See also

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

Returns

an expression of the replication of *this

Example:

Vector3i v = Vector3i::Random();
cout << "Here is the vector v:" << endl << v << endl;
cout << "v.replicate(2,5) = ..." << endl;
cout << v.replicate(2,5) << endl;

Output:

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

See also

VectorwiseOp::replicate(), DenseBase::replicate<int,int>(), class Replicate

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

Only plain matrices/arrays, not expressions, may be resized; therefore the only useful resize methods are Matrix::resize() and Array::resize(). The present method only asserts that the new size equals the old size, and does nothing else.

Returns

an expression of the reverse of *this.

Example:

MatrixXi m = MatrixXi::Random(3,4);
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the reverse of m:" << endl << m.reverse() << endl;
cout << "Here is the coefficient (1,0) in the reverse of m:" << endl
     << m.reverse()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 4." << endl;
m.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 reverse of m:
 3 -5 -6  6
 0  6  9 -2
 1 -3  6  7
Here is the coefficient (1,0) in the 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  4
 6 -6 -5  3

This is the const version of reverse().

This is the "in place" version of reverse: it reverses *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
• it allows future optimizations (cache friendliness, etc.)

See also

VectorwiseOp::reverseInPlace(), reverse()

Returns

a writable VectorwiseOp wrapper of *this providing additional partial reduction operations

See also

colwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Returns

a VectorwiseOp wrapper of *this for broadcasting and partial reductions

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;
cout << "Here is the maximum absolute value of each row:"
     << endl << m.cwiseAbs().rowwise().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 row:
 0.948
  1.15
-0.483
Here is the maximum absolute value of each row:
 0.68
0.823
0.605

See also

colwise(), class VectorwiseOp, Reductions, visitors and broadcasting

Returns

a matrix where each coefficient (i,j) is equal to thenMatrix(i,j) if *this(i,j), and elseMatrix(i,j) otherwise.

Example:

MatrixXi m(3, 3);
m << 1, 2, 3,
     4, 5, 6,
     7, 8, 9;
m = (m.array() >= 5).select(-m, m);
cout << m << endl;

Output:

 1  2  3
 4 -5 -6
-7 -8 -9

See also

class Select

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.

See also

DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select

Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.

See also

DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select

Sets all coefficients in this expression to value val.

See also

fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes()

Sets a linearly spaced vector.

The function fills *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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.

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also

LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp

Sets a linearly spaced vector.

The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.

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:

VectorXf v;
v.setLinSpaced(5,0.5f,1.5f);
cout << v << endl;

Output:

 0.5
0.75
   1
1.25
 1.5

For integer scalar types, do not miss the explanations on the definition of even spacing .

See also

LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp

Sets all coefficients in this expression to one.

Example:

Matrix4i m = Matrix4i::Random();
m.row(1).setOnes();
cout << m << endl;

Output:

 7  9 -5 -3
 1  1  1  1
 6 -3  0  9
 6  6  3  9

See also

class CwiseNullaryOp, Ones()

Sets all coefficients in this expression to random values.

Numbers are uniformly spread through their whole definition range for integer types, and in the [-1:1] range for floating point scalar types.

Warning

This function is not re-entrant.

Example:

Matrix4i m = Matrix4i::Zero();
m.col(1).setRandom();
cout << m << endl;

Output:

 0  7  0  0
 0 -2  0  0
 0  6  0  0
 0  6  0  0

See also

class CwiseNullaryOp, setRandom(Index), setRandom(Index,Index)

Sets all coefficients in this expression to zero.

Example:

Matrix4i m = Matrix4i::Random();
m.row(1).setZero();
cout << m << endl;

Output:

 7  9 -5 -3
 0  0  0  0
 6 -3  0  9
 6  6  3  9

See also

class CwiseNullaryOp, Zero()

Returns

the sum of all coefficients of *this

If *this is empty, then the value 0 is returned.

See also

trace(), prod(), mean()

swaps *this with the expression other.

swaps *this with the matrix or array other.

Returns

an expression of the transpose of *this.

Example:

Matrix2i m = Matrix2i::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the transpose of m:" << endl << m.transpose() << endl;
cout << "Here is the coefficient (1,0) in the transpose of m:" << endl
     << m.transpose()(1,0) << endl;
cout << "Let us overwrite this coefficient with the value 0." << endl;
m.transpose()(1,0) = 0;
cout << "Now the matrix m is:" << endl << m << endl;

Output:

Here is the matrix m:
 7  6
-2  6
Here is the transpose of m:
 7 -2
 6  6
Here is the coefficient (1,0) in the transpose of m:
6
Let us overwrite this coefficient with the value 0.
Now the matrix m is:
 7  0
-2  6

Warning

If you want to replace a matrix by its own transpose, do NOT do this:

m = m.transpose(); // bug!!! caused by aliasing effect

Instead, use the transposeInPlace() method:

m.transposeInPlace();

which gives Eigen good opportunities for optimization, or alternatively you can also do:

m = m.transpose().eval();

See also

transposeInPlace(), adjoint()

This is the const version of transpose().

Make sure you read the warning for transpose() !

See also

transposeInPlace(), adjoint()

This is the "in place" version of transpose(): it replaces *this by its own transpose. Thus, doing

m.transposeInPlace();

has the same effect on m as doing

m = m.transpose().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 transpose. If you just need the transpose of a matrix, use transpose().

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(), adjointInPlace()

Returns

the unique coefficient of a 1x1 expression

Applies the visitor visitor to the whole coefficients of the matrix or vector.

The template parameter Visitor is the type of the visitor and provides the following interface:

struct MyVisitor {
  // called for the first coefficient
  void init(const Scalar& value, Index i, Index j);
  // called for all other coefficients
  void operator() (const Scalar& value, Index i, Index j);
};

Note

compared to one or two for loops, visitors offer automatic unrolling for small fixed size matrix.

if the matrix is empty, then the visitor is left unchanged.

See also

minCoeff(Index*,Index*), maxCoeff(Index*,Index*), DenseBase::redux()

Returns

an expression of a fixed-size zero matrix or vector.

This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.

Example:

cout << Matrix2d::Zero() << endl;
cout << RowVector4i::Zero() << endl;

Output:

0 0
0 0
0 0 0 0

See also

Zero(Index), Zero(Index,Index)

Returns

an expression of a zero matrix.

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 Zero() should be used instead.

Example:

cout << MatrixXi::Zero(2,3) << endl;

Output:

0 0 0
0 0 0

See also

Zero(), Zero(Index)

Returns

an expression of a zero vector.

The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.

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 meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.

Example:

cout << RowVectorXi::Zero(4) << endl;
cout << VectorXf::Zero(2) << endl;

Output:

0 0 0 0
0
0

See also

Zero(), Zero(Index,Index)

Outputs the matrix, to the given stream.

If you wish to print the matrix with a format different than the default, use DenseBase::format().

It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.

See also

DenseBase::format()