template<typename Derived>

Eigen::MatrixBase class

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_abs2_op<Scalar>, const Derived> Eigen::MatrixBase<Derived>::CwiseAbs2ReturnType

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_abs_op<Scalar>, const Derived> Eigen::MatrixBase<Derived>::CwiseAbsReturnType

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_inverse_op<Scalar>, const Derived> Eigen::MatrixBase<Derived>::CwiseInverseReturnType

template<typename Derived>

typedef CwiseBinaryOp<internal::scalar_cmp_op<Scalar, Scalar, internal::cmp_EQ>, const Derived, const ConstantReturnType> Eigen::MatrixBase<Derived>::CwiseScalarEqualReturnType

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_sign_op<Scalar>, const Derived> Eigen::MatrixBase<Derived>::CwiseSignReturnType

template<typename Derived>

typedef CwiseUnaryOp<internal::scalar_sqrt_op<Scalar>, const Derived> Eigen::MatrixBase<Derived>::CwiseSqrtReturnType

template<typename Derived>

static const IdentityReturnType Eigen::MatrixBase<Derived>::Identity()

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

template<typename Derived>

static const IdentityReturnType Eigen::MatrixBase<Derived>::Identity(Index rows, Index cols)

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

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::Unit(Index size, Index i)

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.

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::Unit(Index i)

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.

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::UnitW()

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.

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::UnitX()

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.

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::UnitY()

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.

template<typename Derived>

static const BasisReturnType Eigen::MatrixBase<Derived>::UnitZ()

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.

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::acosh() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::acosh .

template<typename Derived>

const AdjointReturnType Eigen::MatrixBase<Derived>::adjoint() const

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)

template<typename Derived>

void Eigen::MatrixBase<Derived>::adjointInPlace()

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().

template<typename Derived> template<typename EssentialPart>

void Eigen::MatrixBase<Derived>::applyHouseholderOnTheLeft(const EssentialPart& essential, const Scalar& tau, Scalar* workspace)

Apply the elementary reflector H given by with from the left to a vector or matrix.

On input:

template<typename Derived> template<typename EssentialPart>

void Eigen::MatrixBase<Derived>::applyHouseholderOnTheRight(const EssentialPart& essential, const Scalar& tau, Scalar* workspace)

Apply the elementary reflector H given by with from the right to a vector or matrix.

On input:

template<typename Derived> template<typename OtherDerived>

void Eigen::MatrixBase<Derived>::applyOnTheLeft(const EigenBase<OtherDerived>& other)

replaces *this by other * *this.

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After applyOnTheLeft, A = 
-0.211  0.823  0.536
 0.566 -0.605 -0.444
  0.68  0.597  -0.33

template<typename Derived> template<typename OtherScalar>

void Eigen::MatrixBase<Derived>::applyOnTheLeft(Index p, Index q, const JacobiRotation<OtherScalar>& j)

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 .

template<typename Derived> template<typename OtherDerived>

void Eigen::MatrixBase<Derived>::applyOnTheRight(const EigenBase<OtherDerived>& other)

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

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566

template<typename Derived>

ArrayWrapper<Derived> Eigen::MatrixBase<Derived>::array()

template<typename Derived>

const ArrayWrapper<const Derived> Eigen::MatrixBase<Derived>::array() const

template<typename Derived>

const DiagonalWrapper<const Derived> Eigen::MatrixBase<Derived>::asDiagonal() 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.

Example:

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

Output:

2 0 0
0 5 0
0 0 6

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::asinh() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic sine use ArrayBase::asinh .

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::atanh() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise inverse hyperbolic cosine use ArrayBase::atanh .

template<typename Derived>

BDCSVD<PlainObject> Eigen::MatrixBase<Derived>::bdcSvd(unsigned int computationOptions = 0) const

This is defined in the SVD module. #include <Eigen/SVD>

template<typename Derived> template<typename CustomBinaryOp, typename OtherDerived>

const CwiseBinaryOp<CustomBinaryOp, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::binaryExpr(const Eigen::MatrixBase<OtherDerived>& other, const CustomBinaryOp& func = CustomBinaryOp()) const

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)

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::blueNorm() const

For architecture/scalar types without vectorization, this version is much faster than stableNorm(). Otherwise the stableNorm() is faster.

template<typename Derived>

const ColPivHouseholderQR<PlainObject> Eigen::MatrixBase<Derived>::colPivHouseholderQr() const

template<typename Derived>

const CompleteOrthogonalDecomposition<PlainObject> Eigen::MatrixBase<Derived>::completeOrthogonalDecomposition() const

template<typename Derived> template<typename ResultType>

void Eigen::MatrixBase<Derived>::computeInverseAndDetWithCheck(ResultType& inverse, typename ResultType::Scalar& determinant, bool& invertible, const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const

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.

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

template<typename Derived> template<typename ResultType>

void Eigen::MatrixBase<Derived>::computeInverseWithCheck(ResultType& inverse, bool& invertible, const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision()) const

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.

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

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::cos() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise cosine use ArrayBase::cos .

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::cosh() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic cosine use ArrayBase::cosh .

template<typename Derived>

const CwiseAbsReturnType Eigen::MatrixBase<Derived>::cwiseAbs() const

Example:

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

Output:

cwiseAbs2()

template<typename Derived>

const CwiseAbs2ReturnType Eigen::MatrixBase<Derived>::cwiseAbs2() const

Example:

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

Output:

cwiseAbs()

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<std::equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseEqual(const Eigen::MatrixBase<OtherDerived>& other) const

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;
Index 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

template<typename Derived>

const CwiseScalarEqualReturnType Eigen::MatrixBase<Derived>::cwiseEqual(const Scalar& s) const

template<typename Derived>

const CwiseInverseReturnType Eigen::MatrixBase<Derived>::cwiseInverse() const

Example:

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

Output:

cwiseProduct()

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_max_op<Scalar, Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseMax(const Eigen::MatrixBase<OtherDerived>& other) const

Example:

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

Output:

4
3
4

template<typename Derived>

const CwiseBinaryOp<internal::scalar_max_op<Scalar, Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase<Derived>::cwiseMax(const Scalar& other) const

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_min_op<Scalar, Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseMin(const Eigen::MatrixBase<OtherDerived>& other) const

Example:

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

Output:

2
2
3

template<typename Derived>

const CwiseBinaryOp<internal::scalar_min_op<Scalar, Scalar>, const Derived, const ConstantReturnType> Eigen::MatrixBase<Derived>::cwiseMin(const Scalar& other) const

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<std::not_equal_to<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseNotEqual(const Eigen::MatrixBase<OtherDerived>& other) const

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;
Index 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

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_product_op<Derived ::Scalar, OtherDerived ::Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseProduct(const Eigen::MatrixBase<OtherDerived>& other) const

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

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::cwiseQuotient(const Eigen::MatrixBase<OtherDerived>& other) const

Example:

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

Output:

 0.5
 1.5
1.33

template<typename Derived>

const CwiseSignReturnType Eigen::MatrixBase<Derived>::cwiseSign() const

Example:

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

Output:

 1 -1  1
-1  1  0

template<typename Derived>

const CwiseSqrtReturnType Eigen::MatrixBase<Derived>::cwiseSqrt() const

Example:

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

Output:

cwisePow(), cwiseSquare()

template<typename Derived>

Scalar Eigen::MatrixBase<Derived>::determinant() const

This is defined in the LU module. #include <Eigen/LU>

template<typename Derived>

DiagonalReturnType Eigen::MatrixBase<Derived>::diagonal()

*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 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

template<typename Derived>

ConstDiagonalReturnType Eigen::MatrixBase<Derived>::diagonal() const

This is the const version of diagonal().

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

template<typename Derived>

DiagonalDynamicIndexReturnType Eigen::MatrixBase<Derived>::diagonal(Index index)

*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

template<typename Derived>

ConstDiagonalDynamicIndexReturnType Eigen::MatrixBase<Derived>::diagonal(Index index) const

This is the const version of diagonal(Index).

template<typename Derived>

Index Eigen::MatrixBase<Derived>::diagonalSize() const

template<typename Derived> template<typename OtherDerived>

ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar, typename internal::traits<OtherDerived>::Scalar>::ReturnType Eigen::MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const

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.

template<typename Derived>

EigenvaluesReturnType Eigen::MatrixBase<Derived>::eigenvalues() const

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)

template<typename Derived>

const MatrixExponentialReturnValue<Derived> Eigen::MatrixBase<Derived>::exp() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise exponential use ArrayBase::exp .

template<typename Derived>

const Derived& Eigen::MatrixBase<Derived>::forceAlignedAccess() const

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::forceAlignedAccess()

template<typename Derived> template<bool Enable>

internal::add_const_on_value_type<typename internal::conditional<Enable, ForceAlignedAccess<Derived>, Derived&>::type>::type Eigen::MatrixBase<Derived>::forceAlignedAccessIf() const

template<typename Derived> template<bool Enable>

internal::conditional<Enable, ForceAlignedAccess<Derived>, Derived&>::type Eigen::MatrixBase<Derived>::forceAlignedAccessIf()

template<typename Derived>

const FullPivHouseholderQR<PlainObject> Eigen::MatrixBase<Derived>::fullPivHouseholderQr() const

template<typename Derived>

const FullPivLU<PlainObject> Eigen::MatrixBase<Derived>::fullPivLu() const

This is defined in the LU module. #include <Eigen/LU>

template<typename Derived>

const HouseholderQR<PlainObject> Eigen::MatrixBase<Derived>::householderQr() const

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::hypotNorm() const

template<typename Derived>

const Inverse<Derived> Eigen::MatrixBase<Derived>::inverse() const

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.

template<typename Derived>

bool Eigen::MatrixBase<Derived>::isDiagonal(const 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

template<typename Derived>

bool Eigen::MatrixBase<Derived>::isIdentity(const 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

template<typename Derived>

bool Eigen::MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const

template<typename Derived> template<typename OtherDerived>

bool Eigen::MatrixBase<Derived>::isOrthogonal(const MatrixBase<OtherDerived>& other, const 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

template<typename Derived>

bool Eigen::MatrixBase<Derived>::isUnitary(const 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.isUnitary() returns: " << m.isUnitary() << endl;
cout << "m.isUnitary(1e-3) returns: " << m.isUnitary(1e-3) << endl;

Output:

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

template<typename Derived>

bool Eigen::MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const

template<typename Derived>

JacobiSVD<PlainObject> Eigen::MatrixBase<Derived>::jacobiSvd(unsigned int computationOptions = 0) const

This is defined in the SVD module. #include <Eigen/SVD>

template<typename Derived> template<typename OtherDerived>

const Product<Derived, OtherDerived, LazyProduct> Eigen::MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived>& other) const

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.

template<typename Derived>

const LDLT<PlainObject> Eigen::MatrixBase<Derived>::ldlt() const

This is defined in the Cholesky module. #include <Eigen/Cholesky>

template<typename Derived>

const LLT<PlainObject> Eigen::MatrixBase<Derived>::llt() const

This is defined in the Cholesky module. #include <Eigen/Cholesky>

template<typename Derived>

const MatrixLogarithmReturnValue<Derived> Eigen::MatrixBase<Derived>::log() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise logarithm use ArrayBase::log .

template<typename Derived> template<int p>

RealScalar Eigen::MatrixBase<Derived>::lpNorm() const

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

template<typename Derived>

const PartialPivLU<PlainObject> Eigen::MatrixBase<Derived>::lu() const

This is defined in the LU module. #include <Eigen/LU>

Synonym of partialPivLu().

template<typename Derived> template<typename EssentialPart>

void Eigen::MatrixBase<Derived>::makeHouseholder(EssentialPart& essential, Scalar& tau, RealScalar& beta) const

Computes the elementary reflector H such that: where the transformation H is: and the vector v is:

On output:

template<typename Derived>

void Eigen::MatrixBase<Derived>::makeHouseholderInPlace(Scalar& tau, RealScalar& beta)

Computes the elementary reflector H such that: where the transformation H is: and the vector v is:

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

On output:

template<typename Derived>

NoAlias<Derived, Eigen::MatrixBase> Eigen::MatrixBase<Derived>::noalias()

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 useful when the source expression contains a matrix product.

Here are some examples where noalias is useful:

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;

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::norm() const

template<typename Derived>

void Eigen::MatrixBase<Derived>::normalize()

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.

template<typename Derived>

const PlainObject Eigen::MatrixBase<Derived>::normalized() 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.

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_boolean_and_op, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::operator&&(const Eigen::MatrixBase<OtherDerived>& other) const

Example:

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

Output:

0
0
0

template<typename Derived> template<typename T>

const CwiseBinaryOp<internal::scalar_product_op<Scalar, T>, Derived, Constant<T>> Eigen::MatrixBase<Derived>::operator*(const T& scalar) const

template<typename Derived> template<typename OtherDerived>

const Product<Derived, OtherDerived> Eigen::MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived>& other) const

template<typename Derived> template<typename DiagonalDerived>

const Product<Derived, DiagonalDerived, LazyProduct> Eigen::MatrixBase<Derived>::operator*(const DiagonalBase<DiagonalDerived>& diagonal) const

template<typename Derived> template<typename OtherDerived>

Derived& Eigen::MatrixBase<Derived>::operator*=(const EigenBase<OtherDerived>& other)

replaces *this by *this * other.

Example:

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

Output:

At start, A = 
  0.68  0.597  -0.33
-0.211  0.823  0.536
 0.566 -0.605 -0.444
After A *= B, A = 
 -0.33   0.68  0.597
 0.536 -0.211  0.823
-0.444  0.566 -0.605
After applyOnTheRight, A = 
 0.597  -0.33   0.68
 0.823  0.536 -0.211
-0.605 -0.444  0.566

template<typename Derived> template<typename OtherDerived>

bool Eigen::MatrixBase<Derived>::operator!=(const MatrixBase<OtherDerived>& other) const

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<sum<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::operator+(const Eigen::MatrixBase<OtherDerived>& other) const

template<typename Derived> template<typename OtherDerived>

Derived& Eigen::MatrixBase<Derived>::operator+=(const MatrixBase<OtherDerived>& other)

replaces *this by *this + other.

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<difference<Scalar>, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::operator-(const Eigen::MatrixBase<OtherDerived>& other) const

template<typename Derived> template<typename OtherDerived>

Derived& Eigen::MatrixBase<Derived>::operator-=(const MatrixBase<OtherDerived>& other)

replaces *this by *this - other.

template<typename Derived> template<typename T>

const CwiseBinaryOp<internal::scalar_quotient_op<Scalar, T>, Derived, Constant<T>> Eigen::MatrixBase<Derived>::operator/(const T& scalar) const

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::operator=(const MatrixBase& other)

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

template<typename Derived> template<typename OtherDerived>

bool Eigen::MatrixBase<Derived>::operator==(const MatrixBase<OtherDerived>& other) const

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::operatorNorm() const

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

template<typename Derived> template<typename OtherDerived>

const CwiseBinaryOp<internal::scalar_boolean_or_op, const Derived, const OtherDerived> Eigen::MatrixBase<Derived>::operator||(const Eigen::MatrixBase<OtherDerived>& other) const

Example:

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

Output:

1
0
1

template<typename Derived>

const PartialPivLU<PlainObject> Eigen::MatrixBase<Derived>::partialPivLu() const

This is defined in the LU module. #include <Eigen/LU>

template<typename Derived>

const MatrixPowerReturnValue<Derived> Eigen::MatrixBase<Derived>::pow(const RealScalar& p) const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

template<typename Derived>

const MatrixComplexPowerReturnValue<Derived> Eigen::MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise power to p use ArrayBase::pow .

template<typename Derived> template<unsigned int UpLo>

MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase<Derived>::selfadjointView() const

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

template<typename Derived> template<unsigned int UpLo>

MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type Eigen::MatrixBase<Derived>::selfadjointView()

The parameter UpLo can be either Upper or Lower

Example:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the symmetric matrix extracted from the upper part of m:
 7  6 -3
 6  9  6
-3  6 -5
Here is the symmetric matrix extracted from the lower part of m:
 7 -2  6
-2  9 -6
 6 -6 -5

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::setIdentity()

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

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::setIdentity(Index rows, Index cols)

Resizes to the given size, and writes the identity expression (not necessarily square) into *this.

Example:

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

Output:

1 0 0
0 1 0
0 0 1

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::setUnit(Index i)

Set the coefficients of *this to the i-th unit (basis) vector.

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

template<typename Derived>

Derived& Eigen::MatrixBase<Derived>::setUnit(Index newSize, Index i)

Resizes to the given newSize, and writes the i-th unit (basis) vector into *this.

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.

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::sin() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise sine use ArrayBase::sin .

template<typename Derived>

const MatrixFunctionReturnValue<Derived> Eigen::MatrixBase<Derived>::sinh() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise hyperbolic sine use ArrayBase::sinh .

template<typename Derived>

const MatrixSquareRootReturnValue<Derived> Eigen::MatrixBase<Derived>::sqrt() const

This function requires the unsupported MatrixFunctions module. To compute the coefficient-wise square root use ArrayBase::sqrt .

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::squaredNorm() const

template<typename Derived>

RealScalar Eigen::MatrixBase<Derived>::stableNorm() const

For architecture/scalar types supporting vectorization, this version is faster than blueNorm(). Otherwise the blueNorm() is much faster.

template<typename Derived>

void Eigen::MatrixBase<Derived>::stableNormalize()

Normalizes the vector while avoid underflow and overflow

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

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

template<typename Derived>

const PlainObject Eigen::MatrixBase<Derived>::stableNormalized() 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.

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

template<typename Derived>

Scalar Eigen::MatrixBase<Derived>::trace() const

*this can be any matrix, not necessarily square.

template<typename Derived> template<unsigned int Mode>

MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type Eigen::MatrixBase<Derived>::triangularView()

The parameter Mode can have the following values: Upper, StrictlyUpper, UnitUpper, Lower, StrictlyLower, UnitLower.

Example:

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

Output:

Here is the matrix m:
 7  6 -3
-2  9  6
 6 -6 -5
Here is the upper-triangular matrix extracted from m:
 7  6 -3
 0  9  6
 0  0 -5
Here is the strictly-upper-triangular matrix extracted from m:
 0  6 -3
 0  0  6
 0  0  0
Here is the unit-lower-triangular matrix extracted from m:
 1  0  0
-2  1  0
 6 -6  1

template<typename Derived> template<unsigned int Mode>

MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type Eigen::MatrixBase<Derived>::triangularView() const

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

template<typename Derived> template<typename T>

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