Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> |
| 5 | // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> |
| 6 | // |
| 7 | // This Source Code Form is subject to the terms of the Mozilla |
| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| 10 | |
| 11 | #ifndef EIGEN_TRIANGULARMATRIX_H |
| 12 | #define EIGEN_TRIANGULARMATRIX_H |
| 13 | |
| 14 | namespace Eigen { |
| 15 | |
| 16 | namespace internal { |
| 17 | |
| 18 | template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval; |
| 19 | |
| 20 | } |
| 21 | |
| 22 | /** \internal |
| 23 | * |
| 24 | * \class TriangularBase |
| 25 | * \ingroup Core_Module |
| 26 | * |
| 27 | * \brief Base class for triangular part in a matrix |
| 28 | */ |
| 29 | template<typename Derived> class TriangularBase : public EigenBase<Derived> |
| 30 | { |
| 31 | public: |
| 32 | |
| 33 | enum { |
| 34 | Mode = internal::traits<Derived>::Mode, |
| 35 | CoeffReadCost = internal::traits<Derived>::CoeffReadCost, |
| 36 | RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime, |
| 37 | ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime, |
| 38 | MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime, |
| 39 | MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime |
| 40 | }; |
| 41 | typedef typename internal::traits<Derived>::Scalar Scalar; |
| 42 | typedef typename internal::traits<Derived>::StorageKind StorageKind; |
| 43 | typedef typename internal::traits<Derived>::Index Index; |
| 44 | typedef typename internal::traits<Derived>::DenseMatrixType DenseMatrixType; |
| 45 | typedef DenseMatrixType DenseType; |
| 46 | |
| 47 | inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); } |
| 48 | |
| 49 | inline Index rows() const { return derived().rows(); } |
| 50 | inline Index cols() const { return derived().cols(); } |
| 51 | inline Index outerStride() const { return derived().outerStride(); } |
| 52 | inline Index innerStride() const { return derived().innerStride(); } |
| 53 | |
| 54 | inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); } |
| 55 | inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); } |
| 56 | |
| 57 | /** \see MatrixBase::copyCoeff(row,col) |
| 58 | */ |
| 59 | template<typename Other> |
| 60 | EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other) |
| 61 | { |
| 62 | derived().coeffRef(row, col) = other.coeff(row, col); |
| 63 | } |
| 64 | |
| 65 | inline Scalar operator()(Index row, Index col) const |
| 66 | { |
| 67 | check_coordinates(row, col); |
| 68 | return coeff(row,col); |
| 69 | } |
| 70 | inline Scalar& operator()(Index row, Index col) |
| 71 | { |
| 72 | check_coordinates(row, col); |
| 73 | return coeffRef(row,col); |
| 74 | } |
| 75 | |
| 76 | #ifndef EIGEN_PARSED_BY_DOXYGEN |
| 77 | inline const Derived& derived() const { return *static_cast<const Derived*>(this); } |
| 78 | inline Derived& derived() { return *static_cast<Derived*>(this); } |
| 79 | #endif // not EIGEN_PARSED_BY_DOXYGEN |
| 80 | |
| 81 | template<typename DenseDerived> |
| 82 | void evalTo(MatrixBase<DenseDerived> &other) const; |
| 83 | template<typename DenseDerived> |
| 84 | void evalToLazy(MatrixBase<DenseDerived> &other) const; |
| 85 | |
| 86 | DenseMatrixType toDenseMatrix() const |
| 87 | { |
| 88 | DenseMatrixType res(rows(), cols()); |
| 89 | evalToLazy(res); |
| 90 | return res; |
| 91 | } |
| 92 | |
| 93 | protected: |
| 94 | |
| 95 | void check_coordinates(Index row, Index col) const |
| 96 | { |
| 97 | EIGEN_ONLY_USED_FOR_DEBUG(row); |
| 98 | EIGEN_ONLY_USED_FOR_DEBUG(col); |
| 99 | eigen_assert(col>=0 && col<cols() && row>=0 && row<rows()); |
| 100 | const int mode = int(Mode) & ~SelfAdjoint; |
| 101 | EIGEN_ONLY_USED_FOR_DEBUG(mode); |
| 102 | eigen_assert((mode==Upper && col>=row) |
| 103 | || (mode==Lower && col<=row) |
| 104 | || ((mode==StrictlyUpper || mode==UnitUpper) && col>row) |
| 105 | || ((mode==StrictlyLower || mode==UnitLower) && col<row)); |
| 106 | } |
| 107 | |
| 108 | #ifdef EIGEN_INTERNAL_DEBUGGING |
| 109 | void check_coordinates_internal(Index row, Index col) const |
| 110 | { |
| 111 | check_coordinates(row, col); |
| 112 | } |
| 113 | #else |
| 114 | void check_coordinates_internal(Index , Index ) const {} |
| 115 | #endif |
| 116 | |
| 117 | }; |
| 118 | |
| 119 | /** \class TriangularView |
| 120 | * \ingroup Core_Module |
| 121 | * |
| 122 | * \brief Base class for triangular part in a matrix |
| 123 | * |
| 124 | * \param MatrixType the type of the object in which we are taking the triangular part |
| 125 | * \param Mode the kind of triangular matrix expression to construct. Can be #Upper, |
| 126 | * #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower. |
| 127 | * This is in fact a bit field; it must have either #Upper or #Lower, |
| 128 | * and additionnaly it may have #UnitDiag or #ZeroDiag or neither. |
| 129 | * |
| 130 | * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular |
| 131 | * matrices one should speak of "trapezoid" parts. This class is the return type |
| 132 | * of MatrixBase::triangularView() and most of the time this is the only way it is used. |
| 133 | * |
| 134 | * \sa MatrixBase::triangularView() |
| 135 | */ |
| 136 | namespace internal { |
| 137 | template<typename MatrixType, unsigned int _Mode> |
| 138 | struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType> |
| 139 | { |
| 140 | typedef typename nested<MatrixType>::type MatrixTypeNested; |
| 141 | typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef; |
| 142 | typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned; |
| 143 | typedef MatrixType ExpressionType; |
| 144 | typedef typename MatrixType::PlainObject DenseMatrixType; |
| 145 | enum { |
| 146 | Mode = _Mode, |
| 147 | Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit))) | Mode, |
| 148 | CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost |
| 149 | }; |
| 150 | }; |
| 151 | } |
| 152 | |
| 153 | template<int Mode, bool LhsIsTriangular, |
| 154 | typename Lhs, bool LhsIsVector, |
| 155 | typename Rhs, bool RhsIsVector> |
| 156 | struct TriangularProduct; |
| 157 | |
| 158 | template<typename _MatrixType, unsigned int _Mode> class TriangularView |
| 159 | : public TriangularBase<TriangularView<_MatrixType, _Mode> > |
| 160 | { |
| 161 | public: |
| 162 | |
| 163 | typedef TriangularBase<TriangularView> Base; |
| 164 | typedef typename internal::traits<TriangularView>::Scalar Scalar; |
| 165 | |
| 166 | typedef _MatrixType MatrixType; |
| 167 | typedef typename internal::traits<TriangularView>::DenseMatrixType DenseMatrixType; |
| 168 | typedef DenseMatrixType PlainObject; |
| 169 | |
| 170 | protected: |
| 171 | typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested; |
| 172 | typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef; |
| 173 | typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned; |
| 174 | |
| 175 | typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType; |
| 176 | |
| 177 | public: |
| 178 | using Base::evalToLazy; |
| 179 | |
| 180 | |
| 181 | typedef typename internal::traits<TriangularView>::StorageKind StorageKind; |
| 182 | typedef typename internal::traits<TriangularView>::Index Index; |
| 183 | |
| 184 | enum { |
| 185 | Mode = _Mode, |
| 186 | TransposeMode = (Mode & Upper ? Lower : 0) |
| 187 | | (Mode & Lower ? Upper : 0) |
| 188 | | (Mode & (UnitDiag)) |
| 189 | | (Mode & (ZeroDiag)) |
| 190 | }; |
| 191 | |
| 192 | inline TriangularView(const MatrixType& matrix) : m_matrix(matrix) |
| 193 | {} |
| 194 | |
| 195 | inline Index rows() const { return m_matrix.rows(); } |
| 196 | inline Index cols() const { return m_matrix.cols(); } |
| 197 | inline Index outerStride() const { return m_matrix.outerStride(); } |
| 198 | inline Index innerStride() const { return m_matrix.innerStride(); } |
| 199 | |
| 200 | /** \sa MatrixBase::operator+=() */ |
| 201 | template<typename Other> TriangularView& operator+=(const DenseBase<Other>& other) { return *this = m_matrix + other.derived(); } |
| 202 | /** \sa MatrixBase::operator-=() */ |
| 203 | template<typename Other> TriangularView& operator-=(const DenseBase<Other>& other) { return *this = m_matrix - other.derived(); } |
| 204 | /** \sa MatrixBase::operator*=() */ |
| 205 | TriangularView& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix * other; } |
| 206 | /** \sa MatrixBase::operator/=() */ |
| 207 | TriangularView& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = m_matrix / other; } |
| 208 | |
| 209 | /** \sa MatrixBase::fill() */ |
| 210 | void fill(const Scalar& value) { setConstant(value); } |
| 211 | /** \sa MatrixBase::setConstant() */ |
| 212 | TriangularView& setConstant(const Scalar& value) |
| 213 | { return *this = MatrixType::Constant(rows(), cols(), value); } |
| 214 | /** \sa MatrixBase::setZero() */ |
| 215 | TriangularView& setZero() { return setConstant(Scalar(0)); } |
| 216 | /** \sa MatrixBase::setOnes() */ |
| 217 | TriangularView& setOnes() { return setConstant(Scalar(1)); } |
| 218 | |
| 219 | /** \sa MatrixBase::coeff() |
| 220 | * \warning the coordinates must fit into the referenced triangular part |
| 221 | */ |
| 222 | inline Scalar coeff(Index row, Index col) const |
| 223 | { |
| 224 | Base::check_coordinates_internal(row, col); |
| 225 | return m_matrix.coeff(row, col); |
| 226 | } |
| 227 | |
| 228 | /** \sa MatrixBase::coeffRef() |
| 229 | * \warning the coordinates must fit into the referenced triangular part |
| 230 | */ |
| 231 | inline Scalar& coeffRef(Index row, Index col) |
| 232 | { |
| 233 | Base::check_coordinates_internal(row, col); |
| 234 | return m_matrix.const_cast_derived().coeffRef(row, col); |
| 235 | } |
| 236 | |
| 237 | const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; } |
| 238 | MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); } |
| 239 | |
| 240 | /** Assigns a triangular matrix to a triangular part of a dense matrix */ |
| 241 | template<typename OtherDerived> |
| 242 | TriangularView& operator=(const TriangularBase<OtherDerived>& other); |
| 243 | |
| 244 | template<typename OtherDerived> |
| 245 | TriangularView& operator=(const MatrixBase<OtherDerived>& other); |
| 246 | |
| 247 | TriangularView& operator=(const TriangularView& other) |
| 248 | { return *this = other.nestedExpression(); } |
| 249 | |
| 250 | template<typename OtherDerived> |
| 251 | void lazyAssign(const TriangularBase<OtherDerived>& other); |
| 252 | |
| 253 | template<typename OtherDerived> |
| 254 | void lazyAssign(const MatrixBase<OtherDerived>& other); |
| 255 | |
| 256 | /** \sa MatrixBase::conjugate() */ |
| 257 | inline TriangularView<MatrixConjugateReturnType,Mode> conjugate() |
| 258 | { return m_matrix.conjugate(); } |
| 259 | /** \sa MatrixBase::conjugate() const */ |
| 260 | inline const TriangularView<MatrixConjugateReturnType,Mode> conjugate() const |
| 261 | { return m_matrix.conjugate(); } |
| 262 | |
| 263 | /** \sa MatrixBase::adjoint() const */ |
| 264 | inline const TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> adjoint() const |
| 265 | { return m_matrix.adjoint(); } |
| 266 | |
| 267 | /** \sa MatrixBase::transpose() */ |
| 268 | inline TriangularView<Transpose<MatrixType>,TransposeMode> transpose() |
| 269 | { |
| 270 | EIGEN_STATIC_ASSERT_LVALUE(MatrixType) |
| 271 | return m_matrix.const_cast_derived().transpose(); |
| 272 | } |
| 273 | /** \sa MatrixBase::transpose() const */ |
| 274 | inline const TriangularView<Transpose<MatrixType>,TransposeMode> transpose() const |
| 275 | { |
| 276 | return m_matrix.transpose(); |
| 277 | } |
| 278 | |
| 279 | /** Efficient triangular matrix times vector/matrix product */ |
| 280 | template<typename OtherDerived> |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 281 | TriangularProduct<Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1> |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 282 | operator*(const MatrixBase<OtherDerived>& rhs) const |
| 283 | { |
| 284 | return TriangularProduct |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 285 | <Mode, true, MatrixType, false, OtherDerived, OtherDerived::ColsAtCompileTime==1> |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 286 | (m_matrix, rhs.derived()); |
| 287 | } |
| 288 | |
| 289 | /** Efficient vector/matrix times triangular matrix product */ |
| 290 | template<typename OtherDerived> friend |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 291 | TriangularProduct<Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false> |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 292 | operator*(const MatrixBase<OtherDerived>& lhs, const TriangularView& rhs) |
| 293 | { |
| 294 | return TriangularProduct |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 295 | <Mode, false, OtherDerived, OtherDerived::RowsAtCompileTime==1, MatrixType, false> |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 296 | (lhs.derived(),rhs.m_matrix); |
| 297 | } |
| 298 | |
| 299 | #ifdef EIGEN2_SUPPORT |
| 300 | template<typename OtherDerived> |
| 301 | struct eigen2_product_return_type |
| 302 | { |
| 303 | typedef typename TriangularView<MatrixType,Mode>::DenseMatrixType DenseMatrixType; |
| 304 | typedef typename OtherDerived::PlainObject::DenseType OtherPlainObject; |
| 305 | typedef typename ProductReturnType<DenseMatrixType, OtherPlainObject>::Type ProdRetType; |
| 306 | typedef typename ProdRetType::PlainObject type; |
| 307 | }; |
| 308 | template<typename OtherDerived> |
| 309 | const typename eigen2_product_return_type<OtherDerived>::type |
| 310 | operator*(const EigenBase<OtherDerived>& rhs) const |
| 311 | { |
| 312 | typename OtherDerived::PlainObject::DenseType rhsPlainObject; |
| 313 | rhs.evalTo(rhsPlainObject); |
| 314 | return this->toDenseMatrix() * rhsPlainObject; |
| 315 | } |
| 316 | template<typename OtherMatrixType> |
| 317 | bool isApprox(const TriangularView<OtherMatrixType, Mode>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const |
| 318 | { |
| 319 | return this->toDenseMatrix().isApprox(other.toDenseMatrix(), precision); |
| 320 | } |
| 321 | template<typename OtherDerived> |
| 322 | bool isApprox(const MatrixBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const |
| 323 | { |
| 324 | return this->toDenseMatrix().isApprox(other, precision); |
| 325 | } |
| 326 | #endif // EIGEN2_SUPPORT |
| 327 | |
| 328 | template<int Side, typename Other> |
| 329 | inline const internal::triangular_solve_retval<Side,TriangularView, Other> |
| 330 | solve(const MatrixBase<Other>& other) const; |
| 331 | |
| 332 | template<int Side, typename OtherDerived> |
| 333 | void solveInPlace(const MatrixBase<OtherDerived>& other) const; |
| 334 | |
| 335 | template<typename Other> |
| 336 | inline const internal::triangular_solve_retval<OnTheLeft,TriangularView, Other> |
| 337 | solve(const MatrixBase<Other>& other) const |
| 338 | { return solve<OnTheLeft>(other); } |
| 339 | |
| 340 | template<typename OtherDerived> |
| 341 | void solveInPlace(const MatrixBase<OtherDerived>& other) const |
| 342 | { return solveInPlace<OnTheLeft>(other); } |
| 343 | |
| 344 | const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const |
| 345 | { |
| 346 | EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR); |
| 347 | return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix); |
| 348 | } |
| 349 | SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() |
| 350 | { |
| 351 | EIGEN_STATIC_ASSERT((Mode&UnitDiag)==0,PROGRAMMING_ERROR); |
| 352 | return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix); |
| 353 | } |
| 354 | |
| 355 | template<typename OtherDerived> |
| 356 | void swap(TriangularBase<OtherDerived> const & other) |
| 357 | { |
| 358 | TriangularView<SwapWrapper<MatrixType>,Mode>(const_cast<MatrixType&>(m_matrix)).lazyAssign(other.derived()); |
| 359 | } |
| 360 | |
| 361 | template<typename OtherDerived> |
| 362 | void swap(MatrixBase<OtherDerived> const & other) |
| 363 | { |
| 364 | SwapWrapper<MatrixType> swaper(const_cast<MatrixType&>(m_matrix)); |
| 365 | TriangularView<SwapWrapper<MatrixType>,Mode>(swaper).lazyAssign(other.derived()); |
| 366 | } |
| 367 | |
| 368 | Scalar determinant() const |
| 369 | { |
| 370 | if (Mode & UnitDiag) |
| 371 | return 1; |
| 372 | else if (Mode & ZeroDiag) |
| 373 | return 0; |
| 374 | else |
| 375 | return m_matrix.diagonal().prod(); |
| 376 | } |
| 377 | |
| 378 | // TODO simplify the following: |
| 379 | template<typename ProductDerived, typename Lhs, typename Rhs> |
| 380 | EIGEN_STRONG_INLINE TriangularView& operator=(const ProductBase<ProductDerived, Lhs,Rhs>& other) |
| 381 | { |
| 382 | setZero(); |
| 383 | return assignProduct(other,1); |
| 384 | } |
| 385 | |
| 386 | template<typename ProductDerived, typename Lhs, typename Rhs> |
| 387 | EIGEN_STRONG_INLINE TriangularView& operator+=(const ProductBase<ProductDerived, Lhs,Rhs>& other) |
| 388 | { |
| 389 | return assignProduct(other,1); |
| 390 | } |
| 391 | |
| 392 | template<typename ProductDerived, typename Lhs, typename Rhs> |
| 393 | EIGEN_STRONG_INLINE TriangularView& operator-=(const ProductBase<ProductDerived, Lhs,Rhs>& other) |
| 394 | { |
| 395 | return assignProduct(other,-1); |
| 396 | } |
| 397 | |
| 398 | |
| 399 | template<typename ProductDerived> |
| 400 | EIGEN_STRONG_INLINE TriangularView& operator=(const ScaledProduct<ProductDerived>& other) |
| 401 | { |
| 402 | setZero(); |
| 403 | return assignProduct(other,other.alpha()); |
| 404 | } |
| 405 | |
| 406 | template<typename ProductDerived> |
| 407 | EIGEN_STRONG_INLINE TriangularView& operator+=(const ScaledProduct<ProductDerived>& other) |
| 408 | { |
| 409 | return assignProduct(other,other.alpha()); |
| 410 | } |
| 411 | |
| 412 | template<typename ProductDerived> |
| 413 | EIGEN_STRONG_INLINE TriangularView& operator-=(const ScaledProduct<ProductDerived>& other) |
| 414 | { |
| 415 | return assignProduct(other,-other.alpha()); |
| 416 | } |
| 417 | |
| 418 | protected: |
| 419 | |
| 420 | template<typename ProductDerived, typename Lhs, typename Rhs> |
| 421 | EIGEN_STRONG_INLINE TriangularView& assignProduct(const ProductBase<ProductDerived, Lhs,Rhs>& prod, const Scalar& alpha); |
| 422 | |
| 423 | MatrixTypeNested m_matrix; |
| 424 | }; |
| 425 | |
| 426 | /*************************************************************************** |
| 427 | * Implementation of triangular evaluation/assignment |
| 428 | ***************************************************************************/ |
| 429 | |
| 430 | namespace internal { |
| 431 | |
| 432 | template<typename Derived1, typename Derived2, unsigned int Mode, int UnrollCount, bool ClearOpposite> |
| 433 | struct triangular_assignment_selector |
| 434 | { |
| 435 | enum { |
| 436 | col = (UnrollCount-1) / Derived1::RowsAtCompileTime, |
| 437 | row = (UnrollCount-1) % Derived1::RowsAtCompileTime |
| 438 | }; |
| 439 | |
| 440 | typedef typename Derived1::Scalar Scalar; |
| 441 | |
| 442 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 443 | { |
| 444 | triangular_assignment_selector<Derived1, Derived2, Mode, UnrollCount-1, ClearOpposite>::run(dst, src); |
| 445 | |
| 446 | eigen_assert( Mode == Upper || Mode == Lower |
| 447 | || Mode == StrictlyUpper || Mode == StrictlyLower |
| 448 | || Mode == UnitUpper || Mode == UnitLower); |
| 449 | if((Mode == Upper && row <= col) |
| 450 | || (Mode == Lower && row >= col) |
| 451 | || (Mode == StrictlyUpper && row < col) |
| 452 | || (Mode == StrictlyLower && row > col) |
| 453 | || (Mode == UnitUpper && row < col) |
| 454 | || (Mode == UnitLower && row > col)) |
| 455 | dst.copyCoeff(row, col, src); |
| 456 | else if(ClearOpposite) |
| 457 | { |
| 458 | if (Mode&UnitDiag && row==col) |
| 459 | dst.coeffRef(row, col) = Scalar(1); |
| 460 | else |
| 461 | dst.coeffRef(row, col) = Scalar(0); |
| 462 | } |
| 463 | } |
| 464 | }; |
| 465 | |
| 466 | // prevent buggy user code from causing an infinite recursion |
| 467 | template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite> |
| 468 | struct triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite> |
| 469 | { |
| 470 | static inline void run(Derived1 &, const Derived2 &) {} |
| 471 | }; |
| 472 | |
| 473 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 474 | struct triangular_assignment_selector<Derived1, Derived2, Upper, Dynamic, ClearOpposite> |
| 475 | { |
| 476 | typedef typename Derived1::Index Index; |
| 477 | typedef typename Derived1::Scalar Scalar; |
| 478 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 479 | { |
| 480 | for(Index j = 0; j < dst.cols(); ++j) |
| 481 | { |
| 482 | Index maxi = (std::min)(j, dst.rows()-1); |
| 483 | for(Index i = 0; i <= maxi; ++i) |
| 484 | dst.copyCoeff(i, j, src); |
| 485 | if (ClearOpposite) |
| 486 | for(Index i = maxi+1; i < dst.rows(); ++i) |
| 487 | dst.coeffRef(i, j) = Scalar(0); |
| 488 | } |
| 489 | } |
| 490 | }; |
| 491 | |
| 492 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 493 | struct triangular_assignment_selector<Derived1, Derived2, Lower, Dynamic, ClearOpposite> |
| 494 | { |
| 495 | typedef typename Derived1::Index Index; |
| 496 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 497 | { |
| 498 | for(Index j = 0; j < dst.cols(); ++j) |
| 499 | { |
| 500 | for(Index i = j; i < dst.rows(); ++i) |
| 501 | dst.copyCoeff(i, j, src); |
| 502 | Index maxi = (std::min)(j, dst.rows()); |
| 503 | if (ClearOpposite) |
| 504 | for(Index i = 0; i < maxi; ++i) |
| 505 | dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0); |
| 506 | } |
| 507 | } |
| 508 | }; |
| 509 | |
| 510 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 511 | struct triangular_assignment_selector<Derived1, Derived2, StrictlyUpper, Dynamic, ClearOpposite> |
| 512 | { |
| 513 | typedef typename Derived1::Index Index; |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 514 | typedef typename Derived1::Scalar Scalar; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 515 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 516 | { |
| 517 | for(Index j = 0; j < dst.cols(); ++j) |
| 518 | { |
| 519 | Index maxi = (std::min)(j, dst.rows()); |
| 520 | for(Index i = 0; i < maxi; ++i) |
| 521 | dst.copyCoeff(i, j, src); |
| 522 | if (ClearOpposite) |
| 523 | for(Index i = maxi; i < dst.rows(); ++i) |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 524 | dst.coeffRef(i, j) = Scalar(0); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 525 | } |
| 526 | } |
| 527 | }; |
| 528 | |
| 529 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 530 | struct triangular_assignment_selector<Derived1, Derived2, StrictlyLower, Dynamic, ClearOpposite> |
| 531 | { |
| 532 | typedef typename Derived1::Index Index; |
| 533 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 534 | { |
| 535 | for(Index j = 0; j < dst.cols(); ++j) |
| 536 | { |
| 537 | for(Index i = j+1; i < dst.rows(); ++i) |
| 538 | dst.copyCoeff(i, j, src); |
| 539 | Index maxi = (std::min)(j, dst.rows()-1); |
| 540 | if (ClearOpposite) |
| 541 | for(Index i = 0; i <= maxi; ++i) |
| 542 | dst.coeffRef(i, j) = static_cast<typename Derived1::Scalar>(0); |
| 543 | } |
| 544 | } |
| 545 | }; |
| 546 | |
| 547 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 548 | struct triangular_assignment_selector<Derived1, Derived2, UnitUpper, Dynamic, ClearOpposite> |
| 549 | { |
| 550 | typedef typename Derived1::Index Index; |
| 551 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 552 | { |
| 553 | for(Index j = 0; j < dst.cols(); ++j) |
| 554 | { |
| 555 | Index maxi = (std::min)(j, dst.rows()); |
| 556 | for(Index i = 0; i < maxi; ++i) |
| 557 | dst.copyCoeff(i, j, src); |
| 558 | if (ClearOpposite) |
| 559 | { |
| 560 | for(Index i = maxi+1; i < dst.rows(); ++i) |
| 561 | dst.coeffRef(i, j) = 0; |
| 562 | } |
| 563 | } |
| 564 | dst.diagonal().setOnes(); |
| 565 | } |
| 566 | }; |
| 567 | template<typename Derived1, typename Derived2, bool ClearOpposite> |
| 568 | struct triangular_assignment_selector<Derived1, Derived2, UnitLower, Dynamic, ClearOpposite> |
| 569 | { |
| 570 | typedef typename Derived1::Index Index; |
| 571 | static inline void run(Derived1 &dst, const Derived2 &src) |
| 572 | { |
| 573 | for(Index j = 0; j < dst.cols(); ++j) |
| 574 | { |
| 575 | Index maxi = (std::min)(j, dst.rows()); |
| 576 | for(Index i = maxi+1; i < dst.rows(); ++i) |
| 577 | dst.copyCoeff(i, j, src); |
| 578 | if (ClearOpposite) |
| 579 | { |
| 580 | for(Index i = 0; i < maxi; ++i) |
| 581 | dst.coeffRef(i, j) = 0; |
| 582 | } |
| 583 | } |
| 584 | dst.diagonal().setOnes(); |
| 585 | } |
| 586 | }; |
| 587 | |
| 588 | } // end namespace internal |
| 589 | |
| 590 | // FIXME should we keep that possibility |
| 591 | template<typename MatrixType, unsigned int Mode> |
| 592 | template<typename OtherDerived> |
| 593 | inline TriangularView<MatrixType, Mode>& |
| 594 | TriangularView<MatrixType, Mode>::operator=(const MatrixBase<OtherDerived>& other) |
| 595 | { |
| 596 | if(OtherDerived::Flags & EvalBeforeAssigningBit) |
| 597 | { |
| 598 | typename internal::plain_matrix_type<OtherDerived>::type other_evaluated(other.rows(), other.cols()); |
| 599 | other_evaluated.template triangularView<Mode>().lazyAssign(other.derived()); |
| 600 | lazyAssign(other_evaluated); |
| 601 | } |
| 602 | else |
| 603 | lazyAssign(other.derived()); |
| 604 | return *this; |
| 605 | } |
| 606 | |
| 607 | // FIXME should we keep that possibility |
| 608 | template<typename MatrixType, unsigned int Mode> |
| 609 | template<typename OtherDerived> |
| 610 | void TriangularView<MatrixType, Mode>::lazyAssign(const MatrixBase<OtherDerived>& other) |
| 611 | { |
| 612 | enum { |
| 613 | unroll = MatrixType::SizeAtCompileTime != Dynamic |
| 614 | && internal::traits<OtherDerived>::CoeffReadCost != Dynamic |
| 615 | && MatrixType::SizeAtCompileTime*internal::traits<OtherDerived>::CoeffReadCost/2 <= EIGEN_UNROLLING_LIMIT |
| 616 | }; |
| 617 | eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols()); |
| 618 | |
| 619 | internal::triangular_assignment_selector |
| 620 | <MatrixType, OtherDerived, int(Mode), |
| 621 | unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic, |
| 622 | false // do not change the opposite triangular part |
| 623 | >::run(m_matrix.const_cast_derived(), other.derived()); |
| 624 | } |
| 625 | |
| 626 | |
| 627 | |
| 628 | template<typename MatrixType, unsigned int Mode> |
| 629 | template<typename OtherDerived> |
| 630 | inline TriangularView<MatrixType, Mode>& |
| 631 | TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>& other) |
| 632 | { |
| 633 | eigen_assert(Mode == int(OtherDerived::Mode)); |
| 634 | if(internal::traits<OtherDerived>::Flags & EvalBeforeAssigningBit) |
| 635 | { |
| 636 | typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols()); |
| 637 | other_evaluated.template triangularView<Mode>().lazyAssign(other.derived().nestedExpression()); |
| 638 | lazyAssign(other_evaluated); |
| 639 | } |
| 640 | else |
| 641 | lazyAssign(other.derived().nestedExpression()); |
| 642 | return *this; |
| 643 | } |
| 644 | |
| 645 | template<typename MatrixType, unsigned int Mode> |
| 646 | template<typename OtherDerived> |
| 647 | void TriangularView<MatrixType, Mode>::lazyAssign(const TriangularBase<OtherDerived>& other) |
| 648 | { |
| 649 | enum { |
| 650 | unroll = MatrixType::SizeAtCompileTime != Dynamic |
| 651 | && internal::traits<OtherDerived>::CoeffReadCost != Dynamic |
| 652 | && MatrixType::SizeAtCompileTime * internal::traits<OtherDerived>::CoeffReadCost / 2 |
| 653 | <= EIGEN_UNROLLING_LIMIT |
| 654 | }; |
| 655 | eigen_assert(m_matrix.rows() == other.rows() && m_matrix.cols() == other.cols()); |
| 656 | |
| 657 | internal::triangular_assignment_selector |
| 658 | <MatrixType, OtherDerived, int(Mode), |
| 659 | unroll ? int(MatrixType::SizeAtCompileTime) : Dynamic, |
| 660 | false // preserve the opposite triangular part |
| 661 | >::run(m_matrix.const_cast_derived(), other.derived().nestedExpression()); |
| 662 | } |
| 663 | |
| 664 | /*************************************************************************** |
| 665 | * Implementation of TriangularBase methods |
| 666 | ***************************************************************************/ |
| 667 | |
| 668 | /** Assigns a triangular or selfadjoint matrix to a dense matrix. |
| 669 | * If the matrix is triangular, the opposite part is set to zero. */ |
| 670 | template<typename Derived> |
| 671 | template<typename DenseDerived> |
| 672 | void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const |
| 673 | { |
| 674 | if(internal::traits<Derived>::Flags & EvalBeforeAssigningBit) |
| 675 | { |
| 676 | typename internal::plain_matrix_type<Derived>::type other_evaluated(rows(), cols()); |
| 677 | evalToLazy(other_evaluated); |
| 678 | other.derived().swap(other_evaluated); |
| 679 | } |
| 680 | else |
| 681 | evalToLazy(other.derived()); |
| 682 | } |
| 683 | |
| 684 | /** Assigns a triangular or selfadjoint matrix to a dense matrix. |
| 685 | * If the matrix is triangular, the opposite part is set to zero. */ |
| 686 | template<typename Derived> |
| 687 | template<typename DenseDerived> |
| 688 | void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const |
| 689 | { |
| 690 | enum { |
| 691 | unroll = DenseDerived::SizeAtCompileTime != Dynamic |
| 692 | && internal::traits<Derived>::CoeffReadCost != Dynamic |
| 693 | && DenseDerived::SizeAtCompileTime * internal::traits<Derived>::CoeffReadCost / 2 |
| 694 | <= EIGEN_UNROLLING_LIMIT |
| 695 | }; |
| 696 | other.derived().resize(this->rows(), this->cols()); |
| 697 | |
| 698 | internal::triangular_assignment_selector |
| 699 | <DenseDerived, typename internal::traits<Derived>::MatrixTypeNestedCleaned, Derived::Mode, |
| 700 | unroll ? int(DenseDerived::SizeAtCompileTime) : Dynamic, |
| 701 | true // clear the opposite triangular part |
| 702 | >::run(other.derived(), derived().nestedExpression()); |
| 703 | } |
| 704 | |
| 705 | /*************************************************************************** |
| 706 | * Implementation of TriangularView methods |
| 707 | ***************************************************************************/ |
| 708 | |
| 709 | /*************************************************************************** |
| 710 | * Implementation of MatrixBase methods |
| 711 | ***************************************************************************/ |
| 712 | |
| 713 | #ifdef EIGEN2_SUPPORT |
| 714 | |
| 715 | // implementation of part<>(), including the SelfAdjoint case. |
| 716 | |
| 717 | namespace internal { |
| 718 | template<typename MatrixType, unsigned int Mode> |
| 719 | struct eigen2_part_return_type |
| 720 | { |
| 721 | typedef TriangularView<MatrixType, Mode> type; |
| 722 | }; |
| 723 | |
| 724 | template<typename MatrixType> |
| 725 | struct eigen2_part_return_type<MatrixType, SelfAdjoint> |
| 726 | { |
| 727 | typedef SelfAdjointView<MatrixType, Upper> type; |
| 728 | }; |
| 729 | } |
| 730 | |
| 731 | /** \deprecated use MatrixBase::triangularView() */ |
| 732 | template<typename Derived> |
| 733 | template<unsigned int Mode> |
| 734 | const typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part() const |
| 735 | { |
| 736 | return derived(); |
| 737 | } |
| 738 | |
| 739 | /** \deprecated use MatrixBase::triangularView() */ |
| 740 | template<typename Derived> |
| 741 | template<unsigned int Mode> |
| 742 | typename internal::eigen2_part_return_type<Derived, Mode>::type MatrixBase<Derived>::part() |
| 743 | { |
| 744 | return derived(); |
| 745 | } |
| 746 | #endif |
| 747 | |
| 748 | /** |
| 749 | * \returns an expression of a triangular view extracted from the current matrix |
| 750 | * |
| 751 | * The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper, |
| 752 | * \c #Lower, \c #StrictlyLower, \c #UnitLower. |
| 753 | * |
| 754 | * Example: \include MatrixBase_extract.cpp |
| 755 | * Output: \verbinclude MatrixBase_extract.out |
| 756 | * |
| 757 | * \sa class TriangularView |
| 758 | */ |
| 759 | template<typename Derived> |
| 760 | template<unsigned int Mode> |
| 761 | typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type |
| 762 | MatrixBase<Derived>::triangularView() |
| 763 | { |
| 764 | return derived(); |
| 765 | } |
| 766 | |
| 767 | /** This is the const version of MatrixBase::triangularView() */ |
| 768 | template<typename Derived> |
| 769 | template<unsigned int Mode> |
| 770 | typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type |
| 771 | MatrixBase<Derived>::triangularView() const |
| 772 | { |
| 773 | return derived(); |
| 774 | } |
| 775 | |
| 776 | /** \returns true if *this is approximately equal to an upper triangular matrix, |
| 777 | * within the precision given by \a prec. |
| 778 | * |
| 779 | * \sa isLowerTriangular() |
| 780 | */ |
| 781 | template<typename Derived> |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 782 | bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 783 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 784 | using std::abs; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 785 | RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1); |
| 786 | for(Index j = 0; j < cols(); ++j) |
| 787 | { |
| 788 | Index maxi = (std::min)(j, rows()-1); |
| 789 | for(Index i = 0; i <= maxi; ++i) |
| 790 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 791 | RealScalar absValue = abs(coeff(i,j)); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 792 | if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue; |
| 793 | } |
| 794 | } |
| 795 | RealScalar threshold = maxAbsOnUpperPart * prec; |
| 796 | for(Index j = 0; j < cols(); ++j) |
| 797 | for(Index i = j+1; i < rows(); ++i) |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 798 | if(abs(coeff(i, j)) > threshold) return false; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 799 | return true; |
| 800 | } |
| 801 | |
| 802 | /** \returns true if *this is approximately equal to a lower triangular matrix, |
| 803 | * within the precision given by \a prec. |
| 804 | * |
| 805 | * \sa isUpperTriangular() |
| 806 | */ |
| 807 | template<typename Derived> |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 808 | bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 809 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 810 | using std::abs; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 811 | RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1); |
| 812 | for(Index j = 0; j < cols(); ++j) |
| 813 | for(Index i = j; i < rows(); ++i) |
| 814 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 815 | RealScalar absValue = abs(coeff(i,j)); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 816 | if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue; |
| 817 | } |
| 818 | RealScalar threshold = maxAbsOnLowerPart * prec; |
| 819 | for(Index j = 1; j < cols(); ++j) |
| 820 | { |
| 821 | Index maxi = (std::min)(j, rows()-1); |
| 822 | for(Index i = 0; i < maxi; ++i) |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 823 | if(abs(coeff(i, j)) > threshold) return false; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 824 | } |
| 825 | return true; |
| 826 | } |
| 827 | |
| 828 | } // end namespace Eigen |
| 829 | |
| 830 | #endif // EIGEN_TRIANGULARMATRIX_H |