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eigen/Eigen/src/LU/InverseImpl.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>
// Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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_IMPL_H
#define EIGEN_INVERSE_IMPL_H
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace internal {
/**********************************
*** General case implementation ***
**********************************/
template <typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
struct compute_inverse {
EIGEN_DEVICE_FUNC 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> {
EIGEN_DEVICE_FUNC static inline void run(const MatrixType& matrix, ResultType& result) {
typedef typename MatrixType::Scalar Scalar;
internal::evaluator<MatrixType> matrixEval(matrix);
result.coeffRef(0, 0) = Scalar(1) / matrixEval.coeff(0, 0);
}
};
template <typename MatrixType, typename ResultType>
struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1> {
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC inline void compute_inverse_size2_helper(const MatrixType& matrix,
const typename ResultType::Scalar& invdet,
ResultType& result) {
typename ResultType::Scalar temp = matrix.coeff(0, 0);
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) = temp * invdet;
}
template <typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 2> {
EIGEN_DEVICE_FUNC 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> {
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC 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) {
// Compute cofactors in a way that avoids aliasing issues.
typedef typename ResultType::Scalar Scalar;
const Scalar c01 = cofactor_3x3<MatrixType, 0, 1>(matrix) * invdet;
const Scalar c11 = cofactor_3x3<MatrixType, 1, 1>(matrix) * invdet;
const Scalar c02 = cofactor_3x3<MatrixType, 0, 2>(matrix) * invdet;
result.coeffRef(1, 2) = cofactor_3x3<MatrixType, 2, 1>(matrix) * invdet;
result.coeffRef(2, 1) = cofactor_3x3<MatrixType, 1, 2>(matrix) * invdet;
result.coeffRef(2, 2) = cofactor_3x3<MatrixType, 2, 2>(matrix) * invdet;
result.coeffRef(1, 0) = c01;
result.coeffRef(1, 1) = c11;
result.coeffRef(2, 0) = c02;
result.row(0) = cofactors_col0 * invdet;
}
template <typename MatrixType, typename ResultType>
struct compute_inverse<MatrixType, ResultType, 3> {
EIGEN_DEVICE_FUNC 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> {
EIGEN_DEVICE_FUNC static inline void run(const MatrixType& matrix,
const typename MatrixType::RealScalar& absDeterminantThreshold,
ResultType& inverse, typename ResultType::Scalar& determinant,
bool& invertible) {
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 = Eigen::numext::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>
EIGEN_DEVICE_FUNC 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>
EIGEN_DEVICE_FUNC 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 {
EIGEN_DEVICE_FUNC 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> {
EIGEN_DEVICE_FUNC 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 && extract_data(matrix) != extract_data(inverse)) {
compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
} else if (invertible) {
MatrixType matrix_t = matrix;
compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse);
}
}
};
/*************************
*** MatrixBase methods ***
*************************/
} // end namespace internal
namespace internal {
// Specialization for "dense = dense_xpr.inverse()"
template <typename DstXprType, typename XprType>
struct Assignment<DstXprType, Inverse<XprType>,
internal::assign_op<typename DstXprType::Scalar, typename XprType::Scalar>, Dense2Dense> {
typedef Inverse<XprType> SrcXprType;
EIGEN_DEVICE_FUNC static void run(DstXprType& dst, const SrcXprType& src,
const internal::assign_op<typename DstXprType::Scalar, typename XprType::Scalar>&) {
Index dstRows = src.rows();
Index dstCols = src.cols();
if ((dst.rows() != dstRows) || (dst.cols() != dstCols)) dst.resize(dstRows, dstCols);
const int Size = plain_enum_min(XprType::ColsAtCompileTime, DstXprType::ColsAtCompileTime);
EIGEN_ONLY_USED_FOR_DEBUG(Size);
eigen_assert(((Size <= 1) || (Size > 4) || (extract_data(src.nestedExpression()) != extract_data(dst))) &&
"Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
typedef typename internal::nested_eval<XprType, XprType::ColsAtCompileTime>::type ActualXprType;
typedef internal::remove_all_t<ActualXprType> ActualXprTypeCleanded;
ActualXprType actual_xpr(src.nestedExpression());
compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, 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 PartialPivLU.
*
* Example: \include MatrixBase_inverse.cpp
* Output: \verbinclude MatrixBase_inverse.out
*
* \sa computeInverseAndDetWithCheck()
*/
template <typename Derived>
EIGEN_DEVICE_FUNC inline const Inverse<Derived> MatrixBase<Derived>::inverse() const {
EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
eigen_assert(rows() == cols());
return Inverse<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.
*
* Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
*
* \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 std::conditional_t<RowsAtCompileTime == 2,
internal::remove_all_t<typename internal::nested_eval<Derived, 2>::type>, PlainObject>
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.
*
* Notice that it will trigger a copy of input matrix when trying to do the inverse in place.
*
* \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 {
Scalar 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_IMPL_H
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