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eigen/Eigen/src/Core/MatrixBase.h
Gael Guennebaud eb7b7b2cfc * remove Cross product expression: MatrixBase::cross() now returns a temporary 
which is even better optimized by the compiler.
* Quaternion no longer inherits MatrixBase. Instead it stores the coefficients
  using a Matrix<> and provides only relevant methods.
2008-06-07 13:18:29 +00:00

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_MATRIXBASE_H
#define EIGEN_MATRIXBASE_H
/** \class MatrixBase
*
* \brief Base class for all matrices, vectors, and expressions
*
* This class is the base that is inherited by all matrix, vector, and expression
* types. Most of the Eigen API is contained in this class.
*
* \param Derived is the derived type, e.g. a matrix type, or an expression, etc.
*
* When writing a function taking Eigen objects as argument, if you want your function
* to take as argument any matrix, vector, or expression, just let it take a
* MatrixBase argument. As an example, here is a function printFirstRow which, given
* a matrix, vector, or expression \a x, prints the first row of \a x.
*
* \code
template<typename Derived>
void printFirstRow(const Eigen::MatrixBase<Derived>& x)
{
cout << x.row(0) << endl;
}
* \endcode
*
* \nosubgrouping
*/
template<typename Derived> class MatrixBase : public ArrayBase<Derived>
{
struct CommaInitializer;
public:
typedef typename ei_traits<Derived>::Scalar Scalar;
typedef typename ei_packet_traits<Scalar>::type PacketScalar;
enum {
RowsAtCompileTime = ei_traits<Derived>::RowsAtCompileTime,
/**< The number of rows at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), ColsAtCompileTime, SizeAtCompileTime */
ColsAtCompileTime = ei_traits<Derived>::ColsAtCompileTime,
/**< The number of columns at compile-time. This is just a copy of the value provided
* by the \a Derived type. If a value is not known at compile-time,
* it is set to the \a Dynamic constant.
* \sa MatrixBase::rows(), MatrixBase::cols(), RowsAtCompileTime, SizeAtCompileTime */
SizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::RowsAtCompileTime,
ei_traits<Derived>::ColsAtCompileTime>::ret),
/**< This is equal to the number of coefficients, i.e. the number of
* rows times the number of columns, or to \a Dynamic if this is not
* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
MaxRowsAtCompileTime = ei_traits<Derived>::MaxRowsAtCompileTime,
/**< This value is equal to the maximum possible number of rows that this expression
* might have. If this expression might have an arbitrarily high number of rows,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa RowsAtCompileTime, MaxColsAtCompileTime, MaxSizeAtCompileTime
*/
MaxColsAtCompileTime = ei_traits<Derived>::MaxColsAtCompileTime,
/**< This value is equal to the maximum possible number of columns that this expression
* might have. If this expression might have an arbitrarily high number of columns,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa ColsAtCompileTime, MaxRowsAtCompileTime, MaxSizeAtCompileTime
*/
MaxSizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::MaxRowsAtCompileTime,
ei_traits<Derived>::MaxColsAtCompileTime>::ret),
/**< This value is equal to the maximum possible number of coefficients that this expression
* might have. If this expression might have an arbitrarily high number of coefficients,
* this value is set to \a Dynamic.
*
* This value is useful to know when evaluating an expression, in order to determine
* whether it is possible to avoid doing a dynamic memory allocation.
*
* \sa SizeAtCompileTime, MaxRowsAtCompileTime, MaxColsAtCompileTime
*/
IsVectorAtCompileTime = ei_traits<Derived>::RowsAtCompileTime == 1
|| ei_traits<Derived>::ColsAtCompileTime == 1,
/**< This is set to true if either the number of rows or the number of
* columns is known at compile-time to be equal to 1. Indeed, in that case,
* we are dealing with a column-vector (if there is only one column) or with
* a row-vector (if there is only one row). */
Flags = ei_traits<Derived>::Flags,
/**< This stores expression \ref flags flags which may or may not be inherited by new expressions
* constructed from this one. See the \ref flags "list of flags".
*/
CoeffReadCost = ei_traits<Derived>::CoeffReadCost
/**< This is a rough measure of how expensive it is to read one coefficient from
* this expression.
*/
};
/** Default constructor. Just checks at compile-time for self-consistency of the flags. */
MatrixBase()
{
ei_assert(ei_are_flags_consistent<Flags>::ret);
}
/** This is the "real scalar" type; if the \a Scalar type is already real numbers
* (e.g. int, float or double) then \a RealScalar is just the same as \a Scalar. If
* \a Scalar is \a std::complex<T> then RealScalar is \a T.
*
* \sa class NumTraits
*/
typedef typename NumTraits<Scalar>::Real RealScalar;
/** \returns the number of rows. \sa cols(), RowsAtCompileTime */
inline int rows() const { return derived()._rows(); }
/** \returns the number of columns. \sa row(), ColsAtCompileTime*/
inline int cols() const { return derived()._cols(); }
/** \returns the number of coefficients, which is \a rows()*cols().
* \sa rows(), cols(), SizeAtCompileTime. */
inline int size() const { return rows() * cols(); }
/** \returns true if either the number of rows or the number of columns is equal to 1.
* In other words, this function returns
* \code rows()==1 || cols()==1 \endcode
* \sa rows(), cols(), IsVectorAtCompileTime. */
inline bool isVector() const { return rows()==1 || cols()==1; }
/** Represents a constant matrix */
typedef CwiseNullaryOp<ei_scalar_constant_op<Scalar>,Derived> ConstantReturnType;
/** Represents a vector block of a matrix */
template<int Size> struct SubVectorReturnType
{
typedef Block<Derived, (ei_traits<Derived>::RowsAtCompileTime == 1 ? 1 : Size),
(ei_traits<Derived>::ColsAtCompileTime == 1 ? 1 : Size)> Type;
};
/** Represents a product scalar-matrix */
typedef CwiseUnaryOp<ei_scalar_multiple_op<Scalar>, Derived> ScalarMultipleReturnType;
/** */
template<typename OtherDerived>
struct ProductReturnType
{
typedef typename ei_meta_if<
(Derived::Flags & OtherDerived::Flags & ArrayBit),
CwiseBinaryOp<ei_scalar_product_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>,
Product<Derived,OtherDerived>
>::ret Type;
};
/** the return type of MatrixBase::conjugate() */
typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
CwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, Derived>,
Derived&
>::ret ConjugateReturnType;
/** the return type of MatrixBase::real() */
typedef CwiseUnaryOp<ei_scalar_real_op<Scalar>, Derived> RealReturnType;
/** the return type of MatrixBase::adjoint() */
typedef Transpose<NestByValue<typename ei_unref<ConjugateReturnType>::type> >
AdjointReturnType;
typedef Matrix<typename NumTraits<typename ei_traits<Derived>::Scalar>::Real, ei_traits<Derived>::ColsAtCompileTime, 1> EigenvaluesReturnType;
/** Copies \a other into *this. \returns a reference to *this. */
template<typename OtherDerived>
Derived& operator=(const MatrixBase<OtherDerived>& other);
/** Copies \a other into *this without evaluating other. \returns a reference to *this. */
template<typename OtherDerived>
Derived& lazyAssign(const MatrixBase<OtherDerived>& other);
/** Special case of the template operator=, in order to prevent the compiler
* from generating a default operator= (issue hit with g++ 4.1)
*/
inline Derived& operator=(const MatrixBase& other)
{
return this->operator=<Derived>(other);
}
/** Overloaded for optimal product evaluation */
template<typename Derived1, typename Derived2>
Derived& lazyAssign(const Product<Derived1,Derived2,CacheFriendlyProduct>& product);
CommaInitializer operator<< (const Scalar& s);
template<typename OtherDerived>
CommaInitializer operator<< (const MatrixBase<OtherDerived>& other);
const Scalar coeff(int row, int col) const;
const Scalar operator()(int row, int col) const;
Scalar& coeffRef(int row, int col);
Scalar& operator()(int row, int col);
const Scalar coeff(int index) const;
const Scalar operator[](int index) const;
Scalar& coeffRef(int index);
Scalar& operator[](int index);
template<int LoadMode>
PacketScalar packetCoeff(int row, int col) const;
template<int StoreMode>
void writePacketCoeff(int row, int col, const PacketScalar& x);
const Scalar x() const;
const Scalar y() const;
const Scalar z() const;
const Scalar w() const;
Scalar& x();
Scalar& y();
Scalar& z();
Scalar& w();
const CwiseUnaryOp<ei_scalar_opposite_op<typename ei_traits<Derived>::Scalar>,Derived> operator-() const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_sum_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
operator+(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_difference_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
operator-(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
Derived& operator+=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
Derived& operator-=(const MatrixBase<OtherDerived>& other);
template<typename Lhs,typename Rhs>
Derived& operator+=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProduct>, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>& other);
Derived& operator*=(const Scalar& other);
Derived& operator/=(const Scalar& other);
const ScalarMultipleReturnType operator*(const Scalar& scalar) const;
const CwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<Derived>::Scalar>, Derived>
operator/(const Scalar& scalar) const;
inline friend const CwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<Derived>::Scalar>, Derived>
operator*(const Scalar& scalar, const MatrixBase& matrix)
{ return matrix*scalar; }
template<typename OtherDerived>
const typename ProductReturnType<OtherDerived>::Type
operator*(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
Derived& operator*=(const MatrixBase<OtherDerived>& other);
template<typename OtherDerived>
typename OtherDerived::Eval inverseProduct(const MatrixBase<OtherDerived>& other) const;
template<typename OtherDerived>
Scalar dot(const MatrixBase<OtherDerived>& other) const;
RealScalar norm2() const;
RealScalar norm() const;
const ScalarMultipleReturnType normalized() const;
Transpose<Derived> transpose();
const Transpose<Derived> transpose() const;
const AdjointReturnType adjoint() const;
Block<Derived, 1, ei_traits<Derived>::ColsAtCompileTime> row(int i);
const Block<Derived, 1, ei_traits<Derived>::ColsAtCompileTime> row(int i) const;
Block<Derived, ei_traits<Derived>::RowsAtCompileTime, 1> col(int i);
const Block<Derived, ei_traits<Derived>::RowsAtCompileTime, 1> col(int i) const;
Minor<Derived> minor(int row, int col);
const Minor<Derived> minor(int row, int col) const;
Block<Derived> block(int startRow, int startCol, int blockRows, int blockCols);
const Block<Derived>
block(int startRow, int startCol, int blockRows, int blockCols) const;
Block<Derived> block(int start, int size);
const Block<Derived> block(int start, int size) const;
Block<Derived> start(int size);
const Block<Derived> start(int size) const;
Block<Derived> end(int size);
const Block<Derived> end(int size) const;
Block<Derived> corner(CornerType type, int cRows, int cCols);
const Block<Derived> corner(CornerType type, int cRows, int cCols) const;
template<int BlockRows, int BlockCols>
Block<Derived, BlockRows, BlockCols> block(int startRow, int startCol);
template<int BlockRows, int BlockCols>
const Block<Derived, BlockRows, BlockCols> block(int startRow, int startCol) const;
template<int CRows, int CCols> Block<Derived, CRows, CCols> corner(CornerType type);
template<int CRows, int CCols> const Block<Derived, CRows, CCols> corner(CornerType type) const;
template<int Size>
typename SubVectorReturnType<Size>::Type start(void);
template<int Size>
const typename SubVectorReturnType<Size>::Type start() const;
template<int Size>
typename SubVectorReturnType<Size>::Type end();
template<int Size>
const typename SubVectorReturnType<Size>::Type end() const;
DiagonalCoeffs<Derived> diagonal();
const DiagonalCoeffs<Derived> diagonal() const;
template<unsigned int Mode> Part<Derived, Mode> part();
template<unsigned int Mode> const Extract<Derived, Mode> extract() const;
static const ConstantReturnType
constant(int rows, int cols, const Scalar& value);
static const ConstantReturnType
constant(int size, const Scalar& value);
static const ConstantReturnType
constant(const Scalar& value);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
create(int rows, int cols, const CustomNullaryOp& func);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
create(int size, const CustomNullaryOp& func);
template<typename CustomNullaryOp>
static const CwiseNullaryOp<CustomNullaryOp, Derived>
create(const CustomNullaryOp& func);
static const ConstantReturnType zero(int rows, int cols);
static const ConstantReturnType zero(int size);
static const ConstantReturnType zero();
static const ConstantReturnType ones(int rows, int cols);
static const ConstantReturnType ones(int size);
static const ConstantReturnType ones();
static const CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> identity();
static const CwiseNullaryOp<ei_scalar_identity_op<Scalar>,Derived> identity(int rows, int cols);
const DiagonalMatrix<Derived> asDiagonal() const;
Derived& setConstant(const Scalar& value);
Derived& setZero();
Derived& setOnes();
Derived& setRandom();
Derived& setIdentity();
template<typename OtherDerived>
bool isApprox(const MatrixBase<OtherDerived>& other,
RealScalar prec = precision<Scalar>()) const;
bool isMuchSmallerThan(const RealScalar& other,
RealScalar prec = precision<Scalar>()) const;
template<typename OtherDerived>
bool isMuchSmallerThan(const MatrixBase<OtherDerived>& other,
RealScalar prec = precision<Scalar>()) const;
bool isApproxToConstant(const Scalar& value, RealScalar prec = precision<Scalar>()) const;
bool isZero(RealScalar prec = precision<Scalar>()) const;
bool isOnes(RealScalar prec = precision<Scalar>()) const;
bool isIdentity(RealScalar prec = precision<Scalar>()) const;
bool isDiagonal(RealScalar prec = precision<Scalar>()) const;
bool isUpper(RealScalar prec = precision<Scalar>()) const;
bool isLower(RealScalar prec = precision<Scalar>()) const;
template<typename OtherDerived>
bool isOrtho(const MatrixBase<OtherDerived>& other,
RealScalar prec = precision<Scalar>()) const;
bool isOrtho(RealScalar prec = precision<Scalar>()) const;
template<typename OtherDerived>
inline bool operator==(const MatrixBase<OtherDerived>& other) const
{ return derived().cwiseEqualTo(other.derived()).all(); }
template<typename OtherDerived>
inline bool operator!=(const MatrixBase<OtherDerived>& other) const
{ return derived().cwiseNotEqualTo(other.derived()).all(); }
template<typename NewType>
const CwiseUnaryOp<ei_scalar_cast_op<typename ei_traits<Derived>::Scalar, NewType>, Derived> cast() const;
EIGEN_ALWAYS_INLINE const typename ei_eval<Derived>::type eval() const
{
return typename ei_eval<Derived>::type(derived());
}
template<typename OtherDerived>
void swap(const MatrixBase<OtherDerived>& other);
template<unsigned int Added>
const Flagged<Derived, Added, 0> marked() const;
const Flagged<Derived, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit> lazy() const;
/** \returns number of elements to skip to pass from one row (resp. column) to another
* for a row-major (resp. column-major) matrix.
* Combined with coeffRef() and the \ref flags flags, it allows a direct access to the data
* of the underlying matrix.
*/
inline int stride(void) const { return derived()._stride(); }
inline const NestByValue<Derived> nestByValue() const;
const ConjugateReturnType conjugate() const;
const RealReturnType real() const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_product_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseProduct(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_quotient_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseQuotient(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_min_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseMin(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<ei_scalar_max_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseMax(const MatrixBase<OtherDerived> &other) const;
const CwiseUnaryOp<ei_scalar_abs_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseAbs() const;
const CwiseUnaryOp<ei_scalar_abs2_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseAbs2() const;
template<typename CustomUnaryOp>
const CwiseUnaryOp<CustomUnaryOp, Derived> cwise(const CustomUnaryOp& func = CustomUnaryOp()) const;
template<typename CustomBinaryOp, typename OtherDerived>
const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>
cwise(const MatrixBase<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const;
Scalar sum() const;
Scalar trace() const;
typename ei_traits<Derived>::Scalar minCoeff() const;
typename ei_traits<Derived>::Scalar maxCoeff() const;
typename ei_traits<Derived>::Scalar minCoeff(int* row, int* col = 0) const;
typename ei_traits<Derived>::Scalar maxCoeff(int* row, int* col = 0) const;
template<typename BinaryOp>
typename ei_result_of<BinaryOp(typename ei_traits<Derived>::Scalar)>::type
redux(const BinaryOp& func) const;
template<typename Visitor>
void visit(Visitor& func) const;
inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
inline Derived& derived() { return *static_cast<Derived*>(this); }
inline Derived& const_cast_derived() const
{ return *static_cast<Derived*>(const_cast<MatrixBase*>(this)); }
/////////// Array module ///////////
const CwiseUnaryOp<ei_scalar_sqrt_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseSqrt() const;
const CwiseUnaryOp<ei_scalar_exp_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseExp() const;
const CwiseUnaryOp<ei_scalar_log_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseLog() const;
const CwiseUnaryOp<ei_scalar_cos_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseCos() const;
const CwiseUnaryOp<ei_scalar_sin_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseSin() const;
const CwiseUnaryOp<ei_scalar_pow_op<typename ei_traits<Derived>::Scalar>, Derived>
cwisePow(const Scalar& exponent) const;
const CwiseUnaryOp<ei_scalar_inverse_op<typename ei_traits<Derived>::Scalar>, Derived> cwiseInverse() const;
template<typename OtherDerived>
const CwiseBinaryOp<std::less<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseLessThan(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<std::less_equal<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseLessEqual(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<std::greater<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseGreaterThan(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<std::greater_equal<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseGreaterEqual(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<std::equal_to<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseEqualTo(const MatrixBase<OtherDerived> &other) const;
template<typename OtherDerived>
const CwiseBinaryOp<std::not_equal_to<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
cwiseNotEqualTo(const MatrixBase<OtherDerived> &other) const;
bool all(void) const;
bool any(void) const;
template<typename BinaryOp>
const PartialRedux<Vertical, BinaryOp, Derived>
verticalRedux(const BinaryOp& func) const;
template<typename BinaryOp>
const PartialRedux<Horizontal, BinaryOp, Derived>
horizontalRedux(const BinaryOp& func) const;
static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> random(int rows, int cols);
static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> random(int size);
static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> random();
/////////// LU module ///////////
const Inverse<typename ei_eval<Derived>::type, true> inverse() const;
const Inverse<typename ei_eval<Derived>::type, false> quickInverse() const;
Scalar determinant() const;
/////////// QR module ///////////
const QR<typename ei_eval<Derived>::type> qr() const;
EigenvaluesReturnType eigenvalues() const;
RealScalar matrixNorm() const;
/////////// Geometry module ///////////
template<typename OtherDerived>
typename ei_eval<Derived>::type
cross(const MatrixBase<OtherDerived>& other) const;
};
#endif // EIGEN_MATRIXBASE_H
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