CwiseNullaryOp.h (36282B)
1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_CWISE_NULLARY_OP_H 11 #define EIGEN_CWISE_NULLARY_OP_H 12 13 namespace Eigen { 14 15 namespace internal { 16 template<typename NullaryOp, typename PlainObjectType> 17 struct traits<CwiseNullaryOp<NullaryOp, PlainObjectType> > : traits<PlainObjectType> 18 { 19 enum { 20 Flags = traits<PlainObjectType>::Flags & RowMajorBit 21 }; 22 }; 23 24 } // namespace internal 25 26 /** \class CwiseNullaryOp 27 * \ingroup Core_Module 28 * 29 * \brief Generic expression of a matrix where all coefficients are defined by a functor 30 * 31 * \tparam NullaryOp template functor implementing the operator 32 * \tparam PlainObjectType the underlying plain matrix/array type 33 * 34 * This class represents an expression of a generic nullary operator. 35 * It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods, 36 * and most of the time this is the only way it is used. 37 * 38 * However, if you want to write a function returning such an expression, you 39 * will need to use this class. 40 * 41 * The functor NullaryOp must expose one of the following method: 42 <table class="manual"> 43 <tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr> 44 <tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr> 45 <tr ><td>\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)</td></tr> 46 </table> 47 * It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors. 48 * 49 * See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding 50 * C++11 random number generators. 51 * 52 * A nullary expression can also be used to implement custom sophisticated matrix manipulations 53 * that cannot be covered by the existing set of natively supported matrix manipulations. 54 * See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations 55 * on the behavior of CwiseNullaryOp. 56 * 57 * \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr 58 */ 59 template<typename NullaryOp, typename PlainObjectType> 60 class CwiseNullaryOp : public internal::dense_xpr_base< CwiseNullaryOp<NullaryOp, PlainObjectType> >::type, internal::no_assignment_operator 61 { 62 public: 63 64 typedef typename internal::dense_xpr_base<CwiseNullaryOp>::type Base; 65 EIGEN_DENSE_PUBLIC_INTERFACE(CwiseNullaryOp) 66 67 EIGEN_DEVICE_FUNC 68 CwiseNullaryOp(Index rows, Index cols, const NullaryOp& func = NullaryOp()) 69 : m_rows(rows), m_cols(cols), m_functor(func) 70 { 71 eigen_assert(rows >= 0 72 && (RowsAtCompileTime == Dynamic || RowsAtCompileTime == rows) 73 && cols >= 0 74 && (ColsAtCompileTime == Dynamic || ColsAtCompileTime == cols)); 75 } 76 77 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR 78 Index rows() const { return m_rows.value(); } 79 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR 80 Index cols() const { return m_cols.value(); } 81 82 /** \returns the functor representing the nullary operation */ 83 EIGEN_DEVICE_FUNC 84 const NullaryOp& functor() const { return m_functor; } 85 86 protected: 87 const internal::variable_if_dynamic<Index, RowsAtCompileTime> m_rows; 88 const internal::variable_if_dynamic<Index, ColsAtCompileTime> m_cols; 89 const NullaryOp m_functor; 90 }; 91 92 93 /** \returns an expression of a matrix defined by a custom functor \a func 94 * 95 * The parameters \a rows and \a cols are the number of rows and of columns of 96 * the returned matrix. Must be compatible with this MatrixBase type. 97 * 98 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 99 * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used 100 * instead. 101 * 102 * The template parameter \a CustomNullaryOp is the type of the functor. 103 * 104 * \sa class CwiseNullaryOp 105 */ 106 template<typename Derived> 107 template<typename CustomNullaryOp> 108 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE 109 #ifndef EIGEN_PARSED_BY_DOXYGEN 110 const CwiseNullaryOp<CustomNullaryOp,typename DenseBase<Derived>::PlainObject> 111 #else 112 const CwiseNullaryOp<CustomNullaryOp,PlainObject> 113 #endif 114 DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func) 115 { 116 return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func); 117 } 118 119 /** \returns an expression of a matrix defined by a custom functor \a func 120 * 121 * The parameter \a size is the size of the returned vector. 122 * Must be compatible with this MatrixBase type. 123 * 124 * \only_for_vectors 125 * 126 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 127 * it is redundant to pass \a size as argument, so Zero() should be used 128 * instead. 129 * 130 * The template parameter \a CustomNullaryOp is the type of the functor. 131 * 132 * Here is an example with C++11 random generators: \include random_cpp11.cpp 133 * Output: \verbinclude random_cpp11.out 134 * 135 * \sa class CwiseNullaryOp 136 */ 137 template<typename Derived> 138 template<typename CustomNullaryOp> 139 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE 140 #ifndef EIGEN_PARSED_BY_DOXYGEN 141 const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject> 142 #else 143 const CwiseNullaryOp<CustomNullaryOp, PlainObject> 144 #endif 145 DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func) 146 { 147 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 148 if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func); 149 else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func); 150 } 151 152 /** \returns an expression of a matrix defined by a custom functor \a func 153 * 154 * This variant is only for fixed-size DenseBase types. For dynamic-size types, you 155 * need to use the variants taking size arguments. 156 * 157 * The template parameter \a CustomNullaryOp is the type of the functor. 158 * 159 * \sa class CwiseNullaryOp 160 */ 161 template<typename Derived> 162 template<typename CustomNullaryOp> 163 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE 164 #ifndef EIGEN_PARSED_BY_DOXYGEN 165 const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject> 166 #else 167 const CwiseNullaryOp<CustomNullaryOp, PlainObject> 168 #endif 169 DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func) 170 { 171 return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func); 172 } 173 174 /** \returns an expression of a constant matrix of value \a value 175 * 176 * The parameters \a rows and \a cols are the number of rows and of columns of 177 * the returned matrix. Must be compatible with this DenseBase type. 178 * 179 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 180 * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used 181 * instead. 182 * 183 * The template parameter \a CustomNullaryOp is the type of the functor. 184 * 185 * \sa class CwiseNullaryOp 186 */ 187 template<typename Derived> 188 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 189 DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) 190 { 191 return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value)); 192 } 193 194 /** \returns an expression of a constant matrix of value \a value 195 * 196 * The parameter \a size is the size of the returned vector. 197 * Must be compatible with this DenseBase type. 198 * 199 * \only_for_vectors 200 * 201 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 202 * it is redundant to pass \a size as argument, so Zero() should be used 203 * instead. 204 * 205 * The template parameter \a CustomNullaryOp is the type of the functor. 206 * 207 * \sa class CwiseNullaryOp 208 */ 209 template<typename Derived> 210 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 211 DenseBase<Derived>::Constant(Index size, const Scalar& value) 212 { 213 return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value)); 214 } 215 216 /** \returns an expression of a constant matrix of value \a value 217 * 218 * This variant is only for fixed-size DenseBase types. For dynamic-size types, you 219 * need to use the variants taking size arguments. 220 * 221 * The template parameter \a CustomNullaryOp is the type of the functor. 222 * 223 * \sa class CwiseNullaryOp 224 */ 225 template<typename Derived> 226 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 227 DenseBase<Derived>::Constant(const Scalar& value) 228 { 229 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 230 return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value)); 231 } 232 233 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&) 234 * 235 * \only_for_vectors 236 * 237 * Example: \include DenseBase_LinSpaced_seq_deprecated.cpp 238 * Output: \verbinclude DenseBase_LinSpaced_seq_deprecated.out 239 * 240 * \sa LinSpaced(Index,const Scalar&, const Scalar&), setLinSpaced(Index,const Scalar&,const Scalar&) 241 */ 242 template<typename Derived> 243 EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 244 DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) 245 { 246 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 247 return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low,high,size)); 248 } 249 250 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&) 251 * 252 * \sa LinSpaced(const Scalar&, const Scalar&) 253 */ 254 template<typename Derived> 255 EIGEN_DEPRECATED EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 256 DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) 257 { 258 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 259 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 260 return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar>(low,high,Derived::SizeAtCompileTime)); 261 } 262 263 /** 264 * \brief Sets a linearly spaced vector. 265 * 266 * The function generates 'size' equally spaced values in the closed interval [low,high]. 267 * When size is set to 1, a vector of length 1 containing 'high' is returned. 268 * 269 * \only_for_vectors 270 * 271 * Example: \include DenseBase_LinSpaced.cpp 272 * Output: \verbinclude DenseBase_LinSpaced.out 273 * 274 * For integer scalar types, an even spacing is possible if and only if the length of the range, 275 * i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the 276 * number of values \c high-low+1 (meaning each value can be repeated the same number of time). 277 * If one of these two considions is not satisfied, then \c high is lowered to the largest value 278 * satisfying one of this constraint. 279 * Here are some examples: 280 * 281 * Example: \include DenseBase_LinSpacedInt.cpp 282 * Output: \verbinclude DenseBase_LinSpacedInt.out 283 * 284 * \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp 285 */ 286 template<typename Derived> 287 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 288 DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high) 289 { 290 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 291 return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar>(low,high,size)); 292 } 293 294 /** 295 * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&) 296 * Special version for fixed size types which does not require the size parameter. 297 */ 298 template<typename Derived> 299 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 300 DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high) 301 { 302 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 303 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 304 return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar>(low,high,Derived::SizeAtCompileTime)); 305 } 306 307 /** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */ 308 template<typename Derived> 309 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant 310 (const Scalar& val, const RealScalar& prec) const 311 { 312 typename internal::nested_eval<Derived,1>::type self(derived()); 313 for(Index j = 0; j < cols(); ++j) 314 for(Index i = 0; i < rows(); ++i) 315 if(!internal::isApprox(self.coeff(i, j), val, prec)) 316 return false; 317 return true; 318 } 319 320 /** This is just an alias for isApproxToConstant(). 321 * 322 * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */ 323 template<typename Derived> 324 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant 325 (const Scalar& val, const RealScalar& prec) const 326 { 327 return isApproxToConstant(val, prec); 328 } 329 330 /** Alias for setConstant(): sets all coefficients in this expression to \a val. 331 * 332 * \sa setConstant(), Constant(), class CwiseNullaryOp 333 */ 334 template<typename Derived> 335 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val) 336 { 337 setConstant(val); 338 } 339 340 /** Sets all coefficients in this expression to value \a val. 341 * 342 * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes() 343 */ 344 template<typename Derived> 345 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val) 346 { 347 return derived() = Constant(rows(), cols(), val); 348 } 349 350 /** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val. 351 * 352 * \only_for_vectors 353 * 354 * Example: \include Matrix_setConstant_int.cpp 355 * Output: \verbinclude Matrix_setConstant_int.out 356 * 357 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 358 */ 359 template<typename Derived> 360 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 361 PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val) 362 { 363 resize(size); 364 return setConstant(val); 365 } 366 367 /** Resizes to the given size, and sets all coefficients in this expression to the given value \a val. 368 * 369 * \param rows the new number of rows 370 * \param cols the new number of columns 371 * \param val the value to which all coefficients are set 372 * 373 * Example: \include Matrix_setConstant_int_int.cpp 374 * Output: \verbinclude Matrix_setConstant_int_int.out 375 * 376 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 377 */ 378 template<typename Derived> 379 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 380 PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val) 381 { 382 resize(rows, cols); 383 return setConstant(val); 384 } 385 386 /** Resizes to the given size, changing only the number of columns, and sets all 387 * coefficients in this expression to the given value \a val. For the parameter 388 * of type NoChange_t, just pass the special value \c NoChange. 389 * 390 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 391 */ 392 template<typename Derived> 393 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 394 PlainObjectBase<Derived>::setConstant(NoChange_t, Index cols, const Scalar& val) 395 { 396 return setConstant(rows(), cols, val); 397 } 398 399 /** Resizes to the given size, changing only the number of rows, and sets all 400 * coefficients in this expression to the given value \a val. For the parameter 401 * of type NoChange_t, just pass the special value \c NoChange. 402 * 403 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 404 */ 405 template<typename Derived> 406 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 407 PlainObjectBase<Derived>::setConstant(Index rows, NoChange_t, const Scalar& val) 408 { 409 return setConstant(rows, cols(), val); 410 } 411 412 413 /** 414 * \brief Sets a linearly spaced vector. 415 * 416 * The function generates 'size' equally spaced values in the closed interval [low,high]. 417 * When size is set to 1, a vector of length 1 containing 'high' is returned. 418 * 419 * \only_for_vectors 420 * 421 * Example: \include DenseBase_setLinSpaced.cpp 422 * Output: \verbinclude DenseBase_setLinSpaced.out 423 * 424 * For integer scalar types, do not miss the explanations on the definition 425 * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. 426 * 427 * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp 428 */ 429 template<typename Derived> 430 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high) 431 { 432 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 433 return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar>(low,high,newSize)); 434 } 435 436 /** 437 * \brief Sets a linearly spaced vector. 438 * 439 * The function fills \c *this with equally spaced values in the closed interval [low,high]. 440 * When size is set to 1, a vector of length 1 containing 'high' is returned. 441 * 442 * \only_for_vectors 443 * 444 * For integer scalar types, do not miss the explanations on the definition 445 * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. 446 * 447 * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp 448 */ 449 template<typename Derived> 450 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high) 451 { 452 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 453 return setLinSpaced(size(), low, high); 454 } 455 456 // zero: 457 458 /** \returns an expression of a zero matrix. 459 * 460 * The parameters \a rows and \a cols are the number of rows and of columns of 461 * the returned matrix. Must be compatible with this MatrixBase type. 462 * 463 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 464 * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used 465 * instead. 466 * 467 * Example: \include MatrixBase_zero_int_int.cpp 468 * Output: \verbinclude MatrixBase_zero_int_int.out 469 * 470 * \sa Zero(), Zero(Index) 471 */ 472 template<typename Derived> 473 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 474 DenseBase<Derived>::Zero(Index rows, Index cols) 475 { 476 return Constant(rows, cols, Scalar(0)); 477 } 478 479 /** \returns an expression of a zero vector. 480 * 481 * The parameter \a size is the size of the returned vector. 482 * Must be compatible with this MatrixBase type. 483 * 484 * \only_for_vectors 485 * 486 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 487 * it is redundant to pass \a size as argument, so Zero() should be used 488 * instead. 489 * 490 * Example: \include MatrixBase_zero_int.cpp 491 * Output: \verbinclude MatrixBase_zero_int.out 492 * 493 * \sa Zero(), Zero(Index,Index) 494 */ 495 template<typename Derived> 496 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 497 DenseBase<Derived>::Zero(Index size) 498 { 499 return Constant(size, Scalar(0)); 500 } 501 502 /** \returns an expression of a fixed-size zero matrix or vector. 503 * 504 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 505 * need to use the variants taking size arguments. 506 * 507 * Example: \include MatrixBase_zero.cpp 508 * Output: \verbinclude MatrixBase_zero.out 509 * 510 * \sa Zero(Index), Zero(Index,Index) 511 */ 512 template<typename Derived> 513 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 514 DenseBase<Derived>::Zero() 515 { 516 return Constant(Scalar(0)); 517 } 518 519 /** \returns true if *this is approximately equal to the zero matrix, 520 * within the precision given by \a prec. 521 * 522 * Example: \include MatrixBase_isZero.cpp 523 * Output: \verbinclude MatrixBase_isZero.out 524 * 525 * \sa class CwiseNullaryOp, Zero() 526 */ 527 template<typename Derived> 528 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const 529 { 530 typename internal::nested_eval<Derived,1>::type self(derived()); 531 for(Index j = 0; j < cols(); ++j) 532 for(Index i = 0; i < rows(); ++i) 533 if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec)) 534 return false; 535 return true; 536 } 537 538 /** Sets all coefficients in this expression to zero. 539 * 540 * Example: \include MatrixBase_setZero.cpp 541 * Output: \verbinclude MatrixBase_setZero.out 542 * 543 * \sa class CwiseNullaryOp, Zero() 544 */ 545 template<typename Derived> 546 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() 547 { 548 return setConstant(Scalar(0)); 549 } 550 551 /** Resizes to the given \a size, and sets all coefficients in this expression to zero. 552 * 553 * \only_for_vectors 554 * 555 * Example: \include Matrix_setZero_int.cpp 556 * Output: \verbinclude Matrix_setZero_int.out 557 * 558 * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero() 559 */ 560 template<typename Derived> 561 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 562 PlainObjectBase<Derived>::setZero(Index newSize) 563 { 564 resize(newSize); 565 return setConstant(Scalar(0)); 566 } 567 568 /** Resizes to the given size, and sets all coefficients in this expression to zero. 569 * 570 * \param rows the new number of rows 571 * \param cols the new number of columns 572 * 573 * Example: \include Matrix_setZero_int_int.cpp 574 * Output: \verbinclude Matrix_setZero_int_int.out 575 * 576 * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero() 577 */ 578 template<typename Derived> 579 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 580 PlainObjectBase<Derived>::setZero(Index rows, Index cols) 581 { 582 resize(rows, cols); 583 return setConstant(Scalar(0)); 584 } 585 586 /** Resizes to the given size, changing only the number of columns, and sets all 587 * coefficients in this expression to zero. For the parameter of type NoChange_t, 588 * just pass the special value \c NoChange. 589 * 590 * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(Index, NoChange_t), class CwiseNullaryOp, DenseBase::Zero() 591 */ 592 template<typename Derived> 593 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 594 PlainObjectBase<Derived>::setZero(NoChange_t, Index cols) 595 { 596 return setZero(rows(), cols); 597 } 598 599 /** Resizes to the given size, changing only the number of rows, and sets all 600 * coefficients in this expression to zero. For the parameter of type NoChange_t, 601 * just pass the special value \c NoChange. 602 * 603 * \sa DenseBase::setZero(), setZero(Index), setZero(Index, Index), setZero(NoChange_t, Index), class CwiseNullaryOp, DenseBase::Zero() 604 */ 605 template<typename Derived> 606 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 607 PlainObjectBase<Derived>::setZero(Index rows, NoChange_t) 608 { 609 return setZero(rows, cols()); 610 } 611 612 // ones: 613 614 /** \returns an expression of a matrix where all coefficients equal one. 615 * 616 * The parameters \a rows and \a cols are the number of rows and of columns of 617 * the returned matrix. Must be compatible with this MatrixBase type. 618 * 619 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 620 * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used 621 * instead. 622 * 623 * Example: \include MatrixBase_ones_int_int.cpp 624 * Output: \verbinclude MatrixBase_ones_int_int.out 625 * 626 * \sa Ones(), Ones(Index), isOnes(), class Ones 627 */ 628 template<typename Derived> 629 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 630 DenseBase<Derived>::Ones(Index rows, Index cols) 631 { 632 return Constant(rows, cols, Scalar(1)); 633 } 634 635 /** \returns an expression of a vector where all coefficients equal one. 636 * 637 * The parameter \a newSize is the size of the returned vector. 638 * Must be compatible with this MatrixBase type. 639 * 640 * \only_for_vectors 641 * 642 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 643 * it is redundant to pass \a size as argument, so Ones() should be used 644 * instead. 645 * 646 * Example: \include MatrixBase_ones_int.cpp 647 * Output: \verbinclude MatrixBase_ones_int.out 648 * 649 * \sa Ones(), Ones(Index,Index), isOnes(), class Ones 650 */ 651 template<typename Derived> 652 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 653 DenseBase<Derived>::Ones(Index newSize) 654 { 655 return Constant(newSize, Scalar(1)); 656 } 657 658 /** \returns an expression of a fixed-size matrix or vector where all coefficients equal one. 659 * 660 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 661 * need to use the variants taking size arguments. 662 * 663 * Example: \include MatrixBase_ones.cpp 664 * Output: \verbinclude MatrixBase_ones.out 665 * 666 * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones 667 */ 668 template<typename Derived> 669 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 670 DenseBase<Derived>::Ones() 671 { 672 return Constant(Scalar(1)); 673 } 674 675 /** \returns true if *this is approximately equal to the matrix where all coefficients 676 * are equal to 1, within the precision given by \a prec. 677 * 678 * Example: \include MatrixBase_isOnes.cpp 679 * Output: \verbinclude MatrixBase_isOnes.out 680 * 681 * \sa class CwiseNullaryOp, Ones() 682 */ 683 template<typename Derived> 684 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes 685 (const RealScalar& prec) const 686 { 687 return isApproxToConstant(Scalar(1), prec); 688 } 689 690 /** Sets all coefficients in this expression to one. 691 * 692 * Example: \include MatrixBase_setOnes.cpp 693 * Output: \verbinclude MatrixBase_setOnes.out 694 * 695 * \sa class CwiseNullaryOp, Ones() 696 */ 697 template<typename Derived> 698 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes() 699 { 700 return setConstant(Scalar(1)); 701 } 702 703 /** Resizes to the given \a newSize, and sets all coefficients in this expression to one. 704 * 705 * \only_for_vectors 706 * 707 * Example: \include Matrix_setOnes_int.cpp 708 * Output: \verbinclude Matrix_setOnes_int.out 709 * 710 * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones() 711 */ 712 template<typename Derived> 713 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 714 PlainObjectBase<Derived>::setOnes(Index newSize) 715 { 716 resize(newSize); 717 return setConstant(Scalar(1)); 718 } 719 720 /** Resizes to the given size, and sets all coefficients in this expression to one. 721 * 722 * \param rows the new number of rows 723 * \param cols the new number of columns 724 * 725 * Example: \include Matrix_setOnes_int_int.cpp 726 * Output: \verbinclude Matrix_setOnes_int_int.out 727 * 728 * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones() 729 */ 730 template<typename Derived> 731 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 732 PlainObjectBase<Derived>::setOnes(Index rows, Index cols) 733 { 734 resize(rows, cols); 735 return setConstant(Scalar(1)); 736 } 737 738 /** Resizes to the given size, changing only the number of rows, and sets all 739 * coefficients in this expression to one. For the parameter of type NoChange_t, 740 * just pass the special value \c NoChange. 741 * 742 * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(NoChange_t, Index), class CwiseNullaryOp, MatrixBase::Ones() 743 */ 744 template<typename Derived> 745 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 746 PlainObjectBase<Derived>::setOnes(Index rows, NoChange_t) 747 { 748 return setOnes(rows, cols()); 749 } 750 751 /** Resizes to the given size, changing only the number of columns, and sets all 752 * coefficients in this expression to one. For the parameter of type NoChange_t, 753 * just pass the special value \c NoChange. 754 * 755 * \sa MatrixBase::setOnes(), setOnes(Index), setOnes(Index, Index), setOnes(Index, NoChange_t) class CwiseNullaryOp, MatrixBase::Ones() 756 */ 757 template<typename Derived> 758 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 759 PlainObjectBase<Derived>::setOnes(NoChange_t, Index cols) 760 { 761 return setOnes(rows(), cols); 762 } 763 764 // Identity: 765 766 /** \returns an expression of the identity matrix (not necessarily square). 767 * 768 * The parameters \a rows and \a cols are the number of rows and of columns of 769 * the returned matrix. Must be compatible with this MatrixBase type. 770 * 771 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 772 * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used 773 * instead. 774 * 775 * Example: \include MatrixBase_identity_int_int.cpp 776 * Output: \verbinclude MatrixBase_identity_int_int.out 777 * 778 * \sa Identity(), setIdentity(), isIdentity() 779 */ 780 template<typename Derived> 781 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType 782 MatrixBase<Derived>::Identity(Index rows, Index cols) 783 { 784 return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>()); 785 } 786 787 /** \returns an expression of the identity matrix (not necessarily square). 788 * 789 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 790 * need to use the variant taking size arguments. 791 * 792 * Example: \include MatrixBase_identity.cpp 793 * Output: \verbinclude MatrixBase_identity.out 794 * 795 * \sa Identity(Index,Index), setIdentity(), isIdentity() 796 */ 797 template<typename Derived> 798 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType 799 MatrixBase<Derived>::Identity() 800 { 801 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 802 return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>()); 803 } 804 805 /** \returns true if *this is approximately equal to the identity matrix 806 * (not necessarily square), 807 * within the precision given by \a prec. 808 * 809 * Example: \include MatrixBase_isIdentity.cpp 810 * Output: \verbinclude MatrixBase_isIdentity.out 811 * 812 * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity() 813 */ 814 template<typename Derived> 815 bool MatrixBase<Derived>::isIdentity 816 (const RealScalar& prec) const 817 { 818 typename internal::nested_eval<Derived,1>::type self(derived()); 819 for(Index j = 0; j < cols(); ++j) 820 { 821 for(Index i = 0; i < rows(); ++i) 822 { 823 if(i == j) 824 { 825 if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec)) 826 return false; 827 } 828 else 829 { 830 if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec)) 831 return false; 832 } 833 } 834 } 835 return true; 836 } 837 838 namespace internal { 839 840 template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)> 841 struct setIdentity_impl 842 { 843 EIGEN_DEVICE_FUNC 844 static EIGEN_STRONG_INLINE Derived& run(Derived& m) 845 { 846 return m = Derived::Identity(m.rows(), m.cols()); 847 } 848 }; 849 850 template<typename Derived> 851 struct setIdentity_impl<Derived, true> 852 { 853 EIGEN_DEVICE_FUNC 854 static EIGEN_STRONG_INLINE Derived& run(Derived& m) 855 { 856 m.setZero(); 857 const Index size = numext::mini(m.rows(), m.cols()); 858 for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1); 859 return m; 860 } 861 }; 862 863 } // end namespace internal 864 865 /** Writes the identity expression (not necessarily square) into *this. 866 * 867 * Example: \include MatrixBase_setIdentity.cpp 868 * Output: \verbinclude MatrixBase_setIdentity.out 869 * 870 * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity() 871 */ 872 template<typename Derived> 873 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity() 874 { 875 return internal::setIdentity_impl<Derived>::run(derived()); 876 } 877 878 /** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this. 879 * 880 * \param rows the new number of rows 881 * \param cols the new number of columns 882 * 883 * Example: \include Matrix_setIdentity_int_int.cpp 884 * Output: \verbinclude Matrix_setIdentity_int_int.out 885 * 886 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity() 887 */ 888 template<typename Derived> 889 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols) 890 { 891 derived().resize(rows, cols); 892 return setIdentity(); 893 } 894 895 /** \returns an expression of the i-th unit (basis) vector. 896 * 897 * \only_for_vectors 898 * 899 * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 900 */ 901 template<typename Derived> 902 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i) 903 { 904 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 905 return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i); 906 } 907 908 /** \returns an expression of the i-th unit (basis) vector. 909 * 910 * \only_for_vectors 911 * 912 * This variant is for fixed-size vector only. 913 * 914 * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 915 */ 916 template<typename Derived> 917 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i) 918 { 919 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 920 return BasisReturnType(SquareMatrixType::Identity(),i); 921 } 922 923 /** \returns an expression of the X axis unit vector (1{,0}^*) 924 * 925 * \only_for_vectors 926 * 927 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 928 */ 929 template<typename Derived> 930 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX() 931 { return Derived::Unit(0); } 932 933 /** \returns an expression of the Y axis unit vector (0,1{,0}^*) 934 * 935 * \only_for_vectors 936 * 937 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 938 */ 939 template<typename Derived> 940 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY() 941 { return Derived::Unit(1); } 942 943 /** \returns an expression of the Z axis unit vector (0,0,1{,0}^*) 944 * 945 * \only_for_vectors 946 * 947 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 948 */ 949 template<typename Derived> 950 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ() 951 { return Derived::Unit(2); } 952 953 /** \returns an expression of the W axis unit vector (0,0,0,1) 954 * 955 * \only_for_vectors 956 * 957 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 958 */ 959 template<typename Derived> 960 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW() 961 { return Derived::Unit(3); } 962 963 /** \brief Set the coefficients of \c *this to the i-th unit (basis) vector 964 * 965 * \param i index of the unique coefficient to be set to 1 966 * 967 * \only_for_vectors 968 * 969 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index) 970 */ 971 template<typename Derived> 972 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index i) 973 { 974 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived); 975 eigen_assert(i<size()); 976 derived().setZero(); 977 derived().coeffRef(i) = Scalar(1); 978 return derived(); 979 } 980 981 /** \brief Resizes to the given \a newSize, and writes the i-th unit (basis) vector into *this. 982 * 983 * \param newSize the new size of the vector 984 * \param i index of the unique coefficient to be set to 1 985 * 986 * \only_for_vectors 987 * 988 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Unit(Index,Index) 989 */ 990 template<typename Derived> 991 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setUnit(Index newSize, Index i) 992 { 993 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived); 994 eigen_assert(i<newSize); 995 derived().resize(newSize); 996 return setUnit(i); 997 } 998 999 } // end namespace Eigen 1000 1001 #endif // EIGEN_CWISE_NULLARY_OP_H