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Inverse.h
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Inverse.h
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_INVERSE_H
#define EIGEN_INVERSE_H
namespace Eigen {
namespace internal {
/**********************************
*** General case implementation ***
**********************************/
template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
struct compute_inverse
{
static inline void run(const MatrixType& matrix, ResultType& result)
{
result = matrix.partialPivLu().inverse();
}
};
template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
struct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ };
/****************************
*** Size 1 implementation ***
****************************/
template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 1>
{
static inline void run(const MatrixType& matrix, ResultType& result)
{
typedef typename MatrixType::Scalar Scalar;
result.coeffRef(0,0) = Scalar(1) / matrix.coeff(0,0);
}
};
template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
{
static inline void run(
const MatrixType& matrix,
const typename MatrixType::RealScalar& absDeterminantThreshold,
ResultType& result,
typename ResultType::Scalar& determinant,
bool& invertible
)
{
using std::abs;
determinant = matrix.coeff(0,0);
invertible = abs(determinant) > absDeterminantThreshold;
if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;
}
};
/****************************
*** Size 2 implementation ***
****************************/
template<typename MatrixType, typename ResultType>
inline void compute_inverse_size2_helper(
const MatrixType& matrix, const typename ResultType::Scalar& invdet,
ResultType& result)
{
result.coeffRef(0,0) = matrix.coeff(1,1) * invdet;
result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
result.coeffRef(1,1) = matrix.coeff(0,0) * invdet;
}
template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 2>
{
static inline void run(const MatrixType& matrix, ResultType& result)
{
typedef typename ResultType::Scalar Scalar;
const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();
compute_inverse_size2_helper(matrix, invdet, result);
}
};
template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
{
static inline void run(
const MatrixType& matrix,
const typename MatrixType::RealScalar& absDeterminantThreshold,
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible
)
{
using std::abs;
typedef typename ResultType::Scalar Scalar;
determinant = matrix.determinant();
invertible = abs(determinant) > absDeterminantThreshold;
if(!invertible) return;
const Scalar invdet = Scalar(1) / determinant;
compute_inverse_size2_helper(matrix, invdet, inverse);
}
};
/****************************
*** Size 3 implementation ***
****************************/
template<typename MatrixType, int i, int j>
inline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m)
{
enum {
i1 = (i+1) % 3,
i2 = (i+2) % 3,
j1 = (j+1) % 3,
j2 = (j+2) % 3
};
return m.coeff(i1, j1) * m.coeff(i2, j2)
- m.coeff(i1, j2) * m.coeff(i2, j1);
}
template<typename MatrixType, typename ResultType>
inline void compute_inverse_size3_helper(
const MatrixType& matrix,
const typename ResultType::Scalar& invdet,
const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,
ResultType& result)
{
result.row(0) = cofactors_col0 * invdet;
result.coeffRef(1,0) = cofactor_3x3<MatrixType,0,1>(matrix) * invdet;
result.coeffRef(1,1) = cofactor_3x3<MatrixType,1,1>(matrix) * invdet;
result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet;
result.coeffRef(2,0) = cofactor_3x3<MatrixType,0,2>(matrix) * invdet;
result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet;
result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet;
}
template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 3>
{
static inline void run(const MatrixType& matrix, ResultType& result)
{
typedef typename ResultType::Scalar Scalar;
Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;
cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
const Scalar invdet = Scalar(1) / det;
compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
}
};
template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
{
static inline void run(
const MatrixType& matrix,
const typename MatrixType::RealScalar& absDeterminantThreshold,
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible
)
{
using std::abs;
typedef typename ResultType::Scalar Scalar;
Matrix<Scalar,3,1> cofactors_col0;
cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
invertible = abs(determinant) > absDeterminantThreshold;
if(!invertible) return;
const Scalar invdet = Scalar(1) / determinant;
compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
}
};
/****************************
*** Size 4 implementation ***
****************************/
template<typename Derived>
inline const typename Derived::Scalar general_det3_helper
(const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
{
return matrix.coeff(i1,j1)
* (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
}
template<typename MatrixType, int i, int j>
inline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix)
{
enum {
i1 = (i+1) % 4,
i2 = (i+2) % 4,
i3 = (i+3) % 4,
j1 = (j+1) % 4,
j2 = (j+2) % 4,
j3 = (j+3) % 4
};
return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
+ general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
+ general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
}
template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
struct compute_inverse_size4
{
static void run(const MatrixType& matrix, ResultType& result)
{
result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix);
result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);
result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix);
result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);
result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix);
result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);
result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix);
result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);
result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);
result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix);
result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);
result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix);
result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);
result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix);
result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);
result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix);
result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
}
};
template<typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 4>
: compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,
MatrixType, ResultType>
{
};
template<typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
{
static inline void run(
const MatrixType& matrix,
const typename MatrixType::RealScalar& absDeterminantThreshold,
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible
)
{
using std::abs;
determinant = matrix.determinant();
invertible = abs(determinant) > absDeterminantThreshold;
if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
}
};
/*************************
*** MatrixBase methods ***
*************************/
template<typename MatrixType>
struct traits<inverse_impl<MatrixType> >
{
typedef typename MatrixType::PlainObject ReturnType;
};
template<typename MatrixType>
struct inverse_impl : public ReturnByValue<inverse_impl<MatrixType> >
{
typedef typename MatrixType::Index Index;
typedef typename internal::eval<MatrixType>::type MatrixTypeNested;
typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
MatrixTypeNested m_matrix;
inverse_impl(const MatrixType& matrix)
: m_matrix(matrix)
{}
inline Index rows() const { return m_matrix.rows(); }
inline Index cols() const { return m_matrix.cols(); }
template<typename Dest> inline void evalTo(Dest& dst) const
{
const int Size = EIGEN_PLAIN_ENUM_MIN(MatrixType::ColsAtCompileTime,Dest::ColsAtCompileTime);
EIGEN_ONLY_USED_FOR_DEBUG(Size);
eigen_assert(( (Size<=1) || (Size>4) || (extract_data(m_matrix)!=extract_data(dst)))
&& "Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
compute_inverse<MatrixTypeNestedCleaned, Dest>::run(m_matrix, dst);
}
};
} // end namespace internal
/** \lu_module
*
* \returns the matrix inverse of this matrix.
*
* For small fixed sizes up to 4x4, this method uses cofactors.
* In the general case, this method uses class PartialPivLU.
*
* \note This matrix must be invertible, otherwise the result is undefined. If you need an
* invertibility check, do the following:
* \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
* \li for the general case, use class FullPivLU.
*
* Example: \include MatrixBase_inverse.cpp
* Output: \verbinclude MatrixBase_inverse.out
*
* \sa computeInverseAndDetWithCheck()
*/
template<typename Derived>
inline const internal::inverse_impl<Derived> MatrixBase<Derived>::inverse() const
{
EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
eigen_assert(rows() == cols());
return internal::inverse_impl<Derived>(derived());
}
/** \lu_module
*
* Computation of matrix inverse and determinant, with invertibility check.
*
* This is only for fixed-size square matrices of size up to 4x4.
*
* \param inverse Reference to the matrix in which to store the inverse.
* \param determinant Reference to the variable in which to store the determinant.
* \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
* \param absDeterminantThreshold Optional parameter controlling the invertibility check.
* The matrix will be declared invertible if the absolute value of its
* determinant is greater than this threshold.
*
* Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
* Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
*
* \sa inverse(), computeInverseWithCheck()
*/
template<typename Derived>
template<typename ResultType>
inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
ResultType& inverse,
typename ResultType::Scalar& determinant,
bool& invertible,
const RealScalar& absDeterminantThreshold
) const
{
// i'd love to put some static assertions there, but SFINAE means that they have no effect...
eigen_assert(rows() == cols());
// for 2x2, it's worth giving a chance to avoid evaluating.
// for larger sizes, evaluating has negligible cost and limits code size.
typedef typename internal::conditional<
RowsAtCompileTime == 2,
typename internal::remove_all<typename internal::nested<Derived, 2>::type>::type,
PlainObject
>::type MatrixType;
internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run
(derived(), absDeterminantThreshold, inverse, determinant, invertible);
}
/** \lu_module
*
* Computation of matrix inverse, with invertibility check.
*
* This is only for fixed-size square matrices of size up to 4x4.
*
* \param inverse Reference to the matrix in which to store the inverse.
* \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
* \param absDeterminantThreshold Optional parameter controlling the invertibility check.
* The matrix will be declared invertible if the absolute value of its
* determinant is greater than this threshold.
*
* Example: \include MatrixBase_computeInverseWithCheck.cpp
* Output: \verbinclude MatrixBase_computeInverseWithCheck.out
*
* \sa inverse(), computeInverseAndDetWithCheck()
*/
template<typename Derived>
template<typename ResultType>
inline void MatrixBase<Derived>::computeInverseWithCheck(
ResultType& inverse,
bool& invertible,
const RealScalar& absDeterminantThreshold
) const
{
RealScalar determinant;
// i'd love to put some static assertions there, but SFINAE means that they have no effect...
eigen_assert(rows() == cols());
computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold);
}
} // end namespace Eigen
#endif // EIGEN_INVERSE_H

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