11#ifndef EIGEN_INVERSE_IMPL_H
12#define EIGEN_INVERSE_IMPL_H
22template<
typename MatrixType,
typename ResultType,
int Size = MatrixType::RowsAtCompileTime>
26 static inline void run(
const MatrixType& matrix, ResultType& result)
28 result = matrix.partialPivLu().inverse();
32template<
typename MatrixType,
typename ResultType,
int Size = MatrixType::RowsAtCompileTime>
33struct compute_inverse_and_det_with_check { };
39template<
typename MatrixType,
typename ResultType>
40struct compute_inverse<MatrixType, ResultType, 1>
43 static inline void run(
const MatrixType& matrix, ResultType& result)
45 typedef typename MatrixType::Scalar Scalar;
46 internal::evaluator<MatrixType> matrixEval(matrix);
47 result.coeffRef(0,0) = Scalar(1) / matrixEval.coeff(0,0);
51template<
typename MatrixType,
typename ResultType>
52struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
55 static inline void run(
56 const MatrixType& matrix,
57 const typename MatrixType::RealScalar& absDeterminantThreshold,
59 typename ResultType::Scalar& determinant,
64 determinant = matrix.coeff(0,0);
65 invertible = abs(determinant) > absDeterminantThreshold;
66 if(invertible) result.coeffRef(0,0) =
typename ResultType::Scalar(1) / determinant;
74template<
typename MatrixType,
typename ResultType>
76inline void compute_inverse_size2_helper(
77 const MatrixType& matrix,
const typename ResultType::Scalar& invdet,
80 typename ResultType::Scalar temp = matrix.coeff(0,0);
81 result.coeffRef(0,0) = matrix.coeff(1,1) * invdet;
82 result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
83 result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
84 result.coeffRef(1,1) = temp * invdet;
87template<
typename MatrixType,
typename ResultType>
88struct compute_inverse<MatrixType, ResultType, 2>
91 static inline void run(
const MatrixType& matrix, ResultType& result)
93 typedef typename ResultType::Scalar Scalar;
94 const Scalar invdet =
typename MatrixType::Scalar(1) / matrix.determinant();
95 compute_inverse_size2_helper(matrix, invdet, result);
99template<
typename MatrixType,
typename ResultType>
100struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
103 static inline void run(
104 const MatrixType& matrix,
105 const typename MatrixType::RealScalar& absDeterminantThreshold,
107 typename ResultType::Scalar& determinant,
112 typedef typename ResultType::Scalar Scalar;
113 determinant = matrix.determinant();
114 invertible = abs(determinant) > absDeterminantThreshold;
115 if(!invertible)
return;
116 const Scalar invdet = Scalar(1) / determinant;
117 compute_inverse_size2_helper(matrix, invdet, inverse);
125template<
typename MatrixType,
int i,
int j>
127inline typename MatrixType::Scalar cofactor_3x3(
const MatrixType& m)
135 return m.coeff(i1, j1) * m.coeff(i2, j2)
136 - m.coeff(i1, j2) * m.coeff(i2, j1);
139template<
typename MatrixType,
typename ResultType>
141inline void compute_inverse_size3_helper(
142 const MatrixType& matrix,
143 const typename ResultType::Scalar& invdet,
144 const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,
148 typedef typename ResultType::Scalar Scalar;
149 const Scalar c01 = cofactor_3x3<MatrixType,0,1>(matrix) * invdet;
150 const Scalar c11 = cofactor_3x3<MatrixType,1,1>(matrix) * invdet;
151 const Scalar c02 = cofactor_3x3<MatrixType,0,2>(matrix) * invdet;
152 result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet;
153 result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet;
154 result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet;
155 result.coeffRef(1,0) = c01;
156 result.coeffRef(1,1) = c11;
157 result.coeffRef(2,0) = c02;
158 result.row(0) = cofactors_col0 * invdet;
161template<
typename MatrixType,
typename ResultType>
162struct compute_inverse<MatrixType, ResultType, 3>
165 static inline void run(
const MatrixType& matrix, ResultType& result)
167 typedef typename ResultType::Scalar Scalar;
168 Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;
169 cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
170 cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
171 cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
172 const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
173 const Scalar invdet = Scalar(1) / det;
174 compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
178template<
typename MatrixType,
typename ResultType>
179struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
182 static inline void run(
183 const MatrixType& matrix,
184 const typename MatrixType::RealScalar& absDeterminantThreshold,
186 typename ResultType::Scalar& determinant,
190 typedef typename ResultType::Scalar Scalar;
191 Matrix<Scalar,3,1> cofactors_col0;
192 cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
193 cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
194 cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
195 determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
196 invertible = Eigen::numext::abs(determinant) > absDeterminantThreshold;
197 if(!invertible)
return;
198 const Scalar invdet = Scalar(1) / determinant;
199 compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
207template<
typename Derived>
209inline const typename Derived::Scalar general_det3_helper
210(
const MatrixBase<Derived>& matrix,
int i1,
int i2,
int i3,
int j1,
int j2,
int j3)
212 return matrix.coeff(i1,j1)
213 * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
216template<
typename MatrixType,
int i,
int j>
218inline typename MatrixType::Scalar cofactor_4x4(
const MatrixType& matrix)
228 return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
229 + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
230 + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
233template<
int Arch,
typename Scalar,
typename MatrixType,
typename ResultType>
234struct compute_inverse_size4
237 static void run(
const MatrixType& matrix, ResultType& result)
239 result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix);
240 result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);
241 result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix);
242 result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);
243 result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix);
244 result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);
245 result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix);
246 result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);
247 result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);
248 result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix);
249 result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);
250 result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix);
251 result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);
252 result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix);
253 result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);
254 result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix);
255 result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
259template<
typename MatrixType,
typename ResultType>
260struct compute_inverse<MatrixType, ResultType, 4>
261 : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,
262 MatrixType, ResultType>
266template<
typename MatrixType,
typename ResultType>
267struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
270 static inline void run(
271 const MatrixType& matrix,
272 const typename MatrixType::RealScalar& absDeterminantThreshold,
274 typename ResultType::Scalar& determinant,
279 determinant = matrix.determinant();
280 invertible = abs(determinant) > absDeterminantThreshold;
281 if(invertible && extract_data(matrix) != extract_data(inverse)) {
282 compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
284 else if(invertible) {
285 MatrixType matrix_t = matrix;
286 compute_inverse<MatrixType, ResultType>::run(matrix_t, inverse);
300template<
typename DstXprType,
typename XprType>
301struct Assignment<DstXprType, Inverse<XprType>, internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar>, Dense2Dense>
303 typedef Inverse<XprType> SrcXprType;
305 static void run(DstXprType &dst,
const SrcXprType &src,
const internal::assign_op<typename DstXprType::Scalar,typename XprType::Scalar> &)
307 Index dstRows = src.rows();
308 Index dstCols = src.cols();
309 if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
310 dst.resize(dstRows, dstCols);
312 const int Size = EIGEN_PLAIN_ENUM_MIN(XprType::ColsAtCompileTime,DstXprType::ColsAtCompileTime);
313 EIGEN_ONLY_USED_FOR_DEBUG(Size);
314 eigen_assert(( (Size<=1) || (Size>4) || (extract_data(src.nestedExpression())!=extract_data(dst)))
315 &&
"Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
317 typedef typename internal::nested_eval<XprType,XprType::ColsAtCompileTime>::type ActualXprType;
318 typedef typename internal::remove_all<ActualXprType>::type ActualXprTypeCleanded;
320 ActualXprType actual_xpr(src.nestedExpression());
322 compute_inverse<ActualXprTypeCleanded, DstXprType>::run(actual_xpr, dst);
346template<
typename Derived>
351 eigen_assert(rows() == cols());
375template<
typename Derived>
376template<
typename ResultType>
379 typename ResultType::Scalar& determinant,
381 const RealScalar& absDeterminantThreshold
385 eigen_assert(rows() == cols());
388 typedef typename internal::conditional<
389 RowsAtCompileTime == 2,
390 typename internal::remove_all<typename internal::nested_eval<Derived, 2>::type>::type,
393 internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run
394 (derived(), absDeterminantThreshold,
inverse, determinant, invertible);
416template<
typename Derived>
417template<
typename ResultType>
421 const RealScalar& absDeterminantThreshold
426 eigen_assert(rows() == cols());
427 computeInverseAndDetWithCheck(
inverse,determinant,invertible,absDeterminantThreshold);
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:66
Expression of the inverse of another expression.
Definition: Inverse.h:44
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Namespace containing all symbols from the Eigen library.
Definition: Core:141
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_inverse_op< typename Derived::Scalar >, const Derived > inverse(const Eigen::ArrayBase< Derived > &x)
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233