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 (at) 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 78 EIGEN_STRONG_INLINE Index rows() const { return m_rows.value(); } 79 EIGEN_DEVICE_FUNC 80 EIGEN_STRONG_INLINE 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 const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject> 109 DenseBase<Derived>::NullaryExpr(Index rows, Index cols, const CustomNullaryOp& func) 110 { 111 return CwiseNullaryOp<CustomNullaryOp, PlainObject>(rows, cols, func); 112 } 113 114 /** \returns an expression of a matrix defined by a custom functor \a func 115 * 116 * The parameter \a size is the size of the returned vector. 117 * Must be compatible with this MatrixBase type. 118 * 119 * \only_for_vectors 120 * 121 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 122 * it is redundant to pass \a size as argument, so Zero() should be used 123 * instead. 124 * 125 * The template parameter \a CustomNullaryOp is the type of the functor. 126 * 127 * Here is an example with C++11 random generators: \include random_cpp11.cpp 128 * Output: \verbinclude random_cpp11.out 129 * 130 * \sa class CwiseNullaryOp 131 */ 132 template<typename Derived> 133 template<typename CustomNullaryOp> 134 EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject> 135 DenseBase<Derived>::NullaryExpr(Index size, const CustomNullaryOp& func) 136 { 137 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 138 if(RowsAtCompileTime == 1) return CwiseNullaryOp<CustomNullaryOp, PlainObject>(1, size, func); 139 else return CwiseNullaryOp<CustomNullaryOp, PlainObject>(size, 1, func); 140 } 141 142 /** \returns an expression of a matrix defined by a custom functor \a func 143 * 144 * This variant is only for fixed-size DenseBase types. For dynamic-size types, you 145 * need to use the variants taking size arguments. 146 * 147 * The template parameter \a CustomNullaryOp is the type of the functor. 148 * 149 * \sa class CwiseNullaryOp 150 */ 151 template<typename Derived> 152 template<typename CustomNullaryOp> 153 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const CwiseNullaryOp<CustomNullaryOp, typename DenseBase<Derived>::PlainObject> 154 DenseBase<Derived>::NullaryExpr(const CustomNullaryOp& func) 155 { 156 return CwiseNullaryOp<CustomNullaryOp, PlainObject>(RowsAtCompileTime, ColsAtCompileTime, func); 157 } 158 159 /** \returns an expression of a constant matrix of value \a value 160 * 161 * The parameters \a rows and \a cols are the number of rows and of columns of 162 * the returned matrix. Must be compatible with this DenseBase type. 163 * 164 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 165 * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used 166 * instead. 167 * 168 * The template parameter \a CustomNullaryOp is the type of the functor. 169 * 170 * \sa class CwiseNullaryOp 171 */ 172 template<typename Derived> 173 EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 174 DenseBase<Derived>::Constant(Index rows, Index cols, const Scalar& value) 175 { 176 return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_constant_op<Scalar>(value)); 177 } 178 179 /** \returns an expression of a constant matrix of value \a value 180 * 181 * The parameter \a size is the size of the returned vector. 182 * Must be compatible with this DenseBase type. 183 * 184 * \only_for_vectors 185 * 186 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 187 * it is redundant to pass \a size as argument, so Zero() should be used 188 * instead. 189 * 190 * The template parameter \a CustomNullaryOp is the type of the functor. 191 * 192 * \sa class CwiseNullaryOp 193 */ 194 template<typename Derived> 195 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 196 DenseBase<Derived>::Constant(Index size, const Scalar& value) 197 { 198 return DenseBase<Derived>::NullaryExpr(size, internal::scalar_constant_op<Scalar>(value)); 199 } 200 201 /** \returns an expression of a constant matrix of value \a value 202 * 203 * This variant is only for fixed-size DenseBase types. For dynamic-size types, you 204 * need to use the variants taking size arguments. 205 * 206 * The template parameter \a CustomNullaryOp is the type of the functor. 207 * 208 * \sa class CwiseNullaryOp 209 */ 210 template<typename Derived> 211 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 212 DenseBase<Derived>::Constant(const Scalar& value) 213 { 214 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 215 return DenseBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_constant_op<Scalar>(value)); 216 } 217 218 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(Index,const Scalar&,const Scalar&) 219 * 220 * \sa LinSpaced(Index,Scalar,Scalar), setLinSpaced(Index,const Scalar&,const Scalar&) 221 */ 222 template<typename Derived> 223 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 224 DenseBase<Derived>::LinSpaced(Sequential_t, Index size, const Scalar& low, const Scalar& high) 225 { 226 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 227 return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size)); 228 } 229 230 /** \deprecated because of accuracy loss. In Eigen 3.3, it is an alias for LinSpaced(const Scalar&,const Scalar&) 231 * 232 * \sa LinSpaced(Scalar,Scalar) 233 */ 234 template<typename Derived> 235 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 236 DenseBase<Derived>::LinSpaced(Sequential_t, const Scalar& low, const Scalar& high) 237 { 238 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 239 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 240 return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime)); 241 } 242 243 /** 244 * \brief Sets a linearly spaced vector. 245 * 246 * The function generates 'size' equally spaced values in the closed interval [low,high]. 247 * When size is set to 1, a vector of length 1 containing 'high' is returned. 248 * 249 * \only_for_vectors 250 * 251 * Example: \include DenseBase_LinSpaced.cpp 252 * Output: \verbinclude DenseBase_LinSpaced.out 253 * 254 * For integer scalar types, an even spacing is possible if and only if the length of the range, 255 * i.e., \c high-low is a scalar multiple of \c size-1, or if \c size is a scalar multiple of the 256 * number of values \c high-low+1 (meaning each value can be repeated the same number of time). 257 * If one of these two considions is not satisfied, then \c high is lowered to the largest value 258 * satisfying one of this constraint. 259 * Here are some examples: 260 * 261 * Example: \include DenseBase_LinSpacedInt.cpp 262 * Output: \verbinclude DenseBase_LinSpacedInt.out 263 * 264 * \sa setLinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp 265 */ 266 template<typename Derived> 267 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 268 DenseBase<Derived>::LinSpaced(Index size, const Scalar& low, const Scalar& high) 269 { 270 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 271 return DenseBase<Derived>::NullaryExpr(size, internal::linspaced_op<Scalar,PacketScalar>(low,high,size)); 272 } 273 274 /** 275 * \copydoc DenseBase::LinSpaced(Index, const Scalar&, const Scalar&) 276 * Special version for fixed size types which does not require the size parameter. 277 */ 278 template<typename Derived> 279 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::RandomAccessLinSpacedReturnType 280 DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high) 281 { 282 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 283 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 284 return DenseBase<Derived>::NullaryExpr(Derived::SizeAtCompileTime, internal::linspaced_op<Scalar,PacketScalar>(low,high,Derived::SizeAtCompileTime)); 285 } 286 287 /** \returns true if all coefficients in this matrix are approximately equal to \a val, to within precision \a prec */ 288 template<typename Derived> 289 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isApproxToConstant 290 (const Scalar& val, const RealScalar& prec) const 291 { 292 typename internal::nested_eval<Derived,1>::type self(derived()); 293 for(Index j = 0; j < cols(); ++j) 294 for(Index i = 0; i < rows(); ++i) 295 if(!internal::isApprox(self.coeff(i, j), val, prec)) 296 return false; 297 return true; 298 } 299 300 /** This is just an alias for isApproxToConstant(). 301 * 302 * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */ 303 template<typename Derived> 304 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isConstant 305 (const Scalar& val, const RealScalar& prec) const 306 { 307 return isApproxToConstant(val, prec); 308 } 309 310 /** Alias for setConstant(): sets all coefficients in this expression to \a val. 311 * 312 * \sa setConstant(), Constant(), class CwiseNullaryOp 313 */ 314 template<typename Derived> 315 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void DenseBase<Derived>::fill(const Scalar& val) 316 { 317 setConstant(val); 318 } 319 320 /** Sets all coefficients in this expression to value \a val. 321 * 322 * \sa fill(), setConstant(Index,const Scalar&), setConstant(Index,Index,const Scalar&), setZero(), setOnes(), Constant(), class CwiseNullaryOp, setZero(), setOnes() 323 */ 324 template<typename Derived> 325 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setConstant(const Scalar& val) 326 { 327 return derived() = Constant(rows(), cols(), val); 328 } 329 330 /** Resizes to the given \a size, and sets all coefficients in this expression to the given value \a val. 331 * 332 * \only_for_vectors 333 * 334 * Example: \include Matrix_setConstant_int.cpp 335 * Output: \verbinclude Matrix_setConstant_int.out 336 * 337 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 338 */ 339 template<typename Derived> 340 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 341 PlainObjectBase<Derived>::setConstant(Index size, const Scalar& val) 342 { 343 resize(size); 344 return setConstant(val); 345 } 346 347 /** Resizes to the given size, and sets all coefficients in this expression to the given value \a val. 348 * 349 * \param rows the new number of rows 350 * \param cols the new number of columns 351 * \param val the value to which all coefficients are set 352 * 353 * Example: \include Matrix_setConstant_int_int.cpp 354 * Output: \verbinclude Matrix_setConstant_int_int.out 355 * 356 * \sa MatrixBase::setConstant(const Scalar&), setConstant(Index,const Scalar&), class CwiseNullaryOp, MatrixBase::Constant(const Scalar&) 357 */ 358 template<typename Derived> 359 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 360 PlainObjectBase<Derived>::setConstant(Index rows, Index cols, const Scalar& val) 361 { 362 resize(rows, cols); 363 return setConstant(val); 364 } 365 366 /** 367 * \brief Sets a linearly spaced vector. 368 * 369 * The function generates 'size' equally spaced values in the closed interval [low,high]. 370 * When size is set to 1, a vector of length 1 containing 'high' is returned. 371 * 372 * \only_for_vectors 373 * 374 * Example: \include DenseBase_setLinSpaced.cpp 375 * Output: \verbinclude DenseBase_setLinSpaced.out 376 * 377 * For integer scalar types, do not miss the explanations on the definition 378 * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. 379 * 380 * \sa LinSpaced(Index,const Scalar&,const Scalar&), CwiseNullaryOp 381 */ 382 template<typename Derived> 383 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(Index newSize, const Scalar& low, const Scalar& high) 384 { 385 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 386 return derived() = Derived::NullaryExpr(newSize, internal::linspaced_op<Scalar,PacketScalar>(low,high,newSize)); 387 } 388 389 /** 390 * \brief Sets a linearly spaced vector. 391 * 392 * The function fills \c *this with equally spaced values in the closed interval [low,high]. 393 * When size is set to 1, a vector of length 1 containing 'high' is returned. 394 * 395 * \only_for_vectors 396 * 397 * For integer scalar types, do not miss the explanations on the definition 398 * of \link LinSpaced(Index,const Scalar&,const Scalar&) even spacing \endlink. 399 * 400 * \sa LinSpaced(Index,const Scalar&,const Scalar&), setLinSpaced(Index, const Scalar&, const Scalar&), CwiseNullaryOp 401 */ 402 template<typename Derived> 403 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setLinSpaced(const Scalar& low, const Scalar& high) 404 { 405 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 406 return setLinSpaced(size(), low, high); 407 } 408 409 // zero: 410 411 /** \returns an expression of a zero matrix. 412 * 413 * The parameters \a rows and \a cols are the number of rows and of columns of 414 * the returned matrix. Must be compatible with this MatrixBase type. 415 * 416 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 417 * it is redundant to pass \a rows and \a cols as arguments, so Zero() should be used 418 * instead. 419 * 420 * Example: \include MatrixBase_zero_int_int.cpp 421 * Output: \verbinclude MatrixBase_zero_int_int.out 422 * 423 * \sa Zero(), Zero(Index) 424 */ 425 template<typename Derived> 426 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 427 DenseBase<Derived>::Zero(Index rows, Index cols) 428 { 429 return Constant(rows, cols, Scalar(0)); 430 } 431 432 /** \returns an expression of a zero vector. 433 * 434 * The parameter \a size is the size of the returned vector. 435 * Must be compatible with this MatrixBase type. 436 * 437 * \only_for_vectors 438 * 439 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 440 * it is redundant to pass \a size as argument, so Zero() should be used 441 * instead. 442 * 443 * Example: \include MatrixBase_zero_int.cpp 444 * Output: \verbinclude MatrixBase_zero_int.out 445 * 446 * \sa Zero(), Zero(Index,Index) 447 */ 448 template<typename Derived> 449 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 450 DenseBase<Derived>::Zero(Index size) 451 { 452 return Constant(size, Scalar(0)); 453 } 454 455 /** \returns an expression of a fixed-size zero matrix or vector. 456 * 457 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 458 * need to use the variants taking size arguments. 459 * 460 * Example: \include MatrixBase_zero.cpp 461 * Output: \verbinclude MatrixBase_zero.out 462 * 463 * \sa Zero(Index), Zero(Index,Index) 464 */ 465 template<typename Derived> 466 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 467 DenseBase<Derived>::Zero() 468 { 469 return Constant(Scalar(0)); 470 } 471 472 /** \returns true if *this is approximately equal to the zero matrix, 473 * within the precision given by \a prec. 474 * 475 * Example: \include MatrixBase_isZero.cpp 476 * Output: \verbinclude MatrixBase_isZero.out 477 * 478 * \sa class CwiseNullaryOp, Zero() 479 */ 480 template<typename Derived> 481 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isZero(const RealScalar& prec) const 482 { 483 typename internal::nested_eval<Derived,1>::type self(derived()); 484 for(Index j = 0; j < cols(); ++j) 485 for(Index i = 0; i < rows(); ++i) 486 if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<Scalar>(1), prec)) 487 return false; 488 return true; 489 } 490 491 /** Sets all coefficients in this expression to zero. 492 * 493 * Example: \include MatrixBase_setZero.cpp 494 * Output: \verbinclude MatrixBase_setZero.out 495 * 496 * \sa class CwiseNullaryOp, Zero() 497 */ 498 template<typename Derived> 499 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setZero() 500 { 501 return setConstant(Scalar(0)); 502 } 503 504 /** Resizes to the given \a size, and sets all coefficients in this expression to zero. 505 * 506 * \only_for_vectors 507 * 508 * Example: \include Matrix_setZero_int.cpp 509 * Output: \verbinclude Matrix_setZero_int.out 510 * 511 * \sa DenseBase::setZero(), setZero(Index,Index), class CwiseNullaryOp, DenseBase::Zero() 512 */ 513 template<typename Derived> 514 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 515 PlainObjectBase<Derived>::setZero(Index newSize) 516 { 517 resize(newSize); 518 return setConstant(Scalar(0)); 519 } 520 521 /** Resizes to the given size, and sets all coefficients in this expression to zero. 522 * 523 * \param rows the new number of rows 524 * \param cols the new number of columns 525 * 526 * Example: \include Matrix_setZero_int_int.cpp 527 * Output: \verbinclude Matrix_setZero_int_int.out 528 * 529 * \sa DenseBase::setZero(), setZero(Index), class CwiseNullaryOp, DenseBase::Zero() 530 */ 531 template<typename Derived> 532 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 533 PlainObjectBase<Derived>::setZero(Index rows, Index cols) 534 { 535 resize(rows, cols); 536 return setConstant(Scalar(0)); 537 } 538 539 // ones: 540 541 /** \returns an expression of a matrix where all coefficients equal one. 542 * 543 * The parameters \a rows and \a cols are the number of rows and of columns of 544 * the returned matrix. Must be compatible with this MatrixBase type. 545 * 546 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 547 * it is redundant to pass \a rows and \a cols as arguments, so Ones() should be used 548 * instead. 549 * 550 * Example: \include MatrixBase_ones_int_int.cpp 551 * Output: \verbinclude MatrixBase_ones_int_int.out 552 * 553 * \sa Ones(), Ones(Index), isOnes(), class Ones 554 */ 555 template<typename Derived> 556 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 557 DenseBase<Derived>::Ones(Index rows, Index cols) 558 { 559 return Constant(rows, cols, Scalar(1)); 560 } 561 562 /** \returns an expression of a vector where all coefficients equal one. 563 * 564 * The parameter \a newSize is the size of the returned vector. 565 * Must be compatible with this MatrixBase type. 566 * 567 * \only_for_vectors 568 * 569 * This variant is meant to be used for dynamic-size vector types. For fixed-size types, 570 * it is redundant to pass \a size as argument, so Ones() should be used 571 * instead. 572 * 573 * Example: \include MatrixBase_ones_int.cpp 574 * Output: \verbinclude MatrixBase_ones_int.out 575 * 576 * \sa Ones(), Ones(Index,Index), isOnes(), class Ones 577 */ 578 template<typename Derived> 579 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 580 DenseBase<Derived>::Ones(Index newSize) 581 { 582 return Constant(newSize, Scalar(1)); 583 } 584 585 /** \returns an expression of a fixed-size matrix or vector where all coefficients equal one. 586 * 587 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 588 * need to use the variants taking size arguments. 589 * 590 * Example: \include MatrixBase_ones.cpp 591 * Output: \verbinclude MatrixBase_ones.out 592 * 593 * \sa Ones(Index), Ones(Index,Index), isOnes(), class Ones 594 */ 595 template<typename Derived> 596 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename DenseBase<Derived>::ConstantReturnType 597 DenseBase<Derived>::Ones() 598 { 599 return Constant(Scalar(1)); 600 } 601 602 /** \returns true if *this is approximately equal to the matrix where all coefficients 603 * are equal to 1, within the precision given by \a prec. 604 * 605 * Example: \include MatrixBase_isOnes.cpp 606 * Output: \verbinclude MatrixBase_isOnes.out 607 * 608 * \sa class CwiseNullaryOp, Ones() 609 */ 610 template<typename Derived> 611 EIGEN_DEVICE_FUNC bool DenseBase<Derived>::isOnes 612 (const RealScalar& prec) const 613 { 614 return isApproxToConstant(Scalar(1), prec); 615 } 616 617 /** Sets all coefficients in this expression to one. 618 * 619 * Example: \include MatrixBase_setOnes.cpp 620 * Output: \verbinclude MatrixBase_setOnes.out 621 * 622 * \sa class CwiseNullaryOp, Ones() 623 */ 624 template<typename Derived> 625 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& DenseBase<Derived>::setOnes() 626 { 627 return setConstant(Scalar(1)); 628 } 629 630 /** Resizes to the given \a newSize, and sets all coefficients in this expression to one. 631 * 632 * \only_for_vectors 633 * 634 * Example: \include Matrix_setOnes_int.cpp 635 * Output: \verbinclude Matrix_setOnes_int.out 636 * 637 * \sa MatrixBase::setOnes(), setOnes(Index,Index), class CwiseNullaryOp, MatrixBase::Ones() 638 */ 639 template<typename Derived> 640 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 641 PlainObjectBase<Derived>::setOnes(Index newSize) 642 { 643 resize(newSize); 644 return setConstant(Scalar(1)); 645 } 646 647 /** Resizes to the given size, and sets all coefficients in this expression to one. 648 * 649 * \param rows the new number of rows 650 * \param cols the new number of columns 651 * 652 * Example: \include Matrix_setOnes_int_int.cpp 653 * Output: \verbinclude Matrix_setOnes_int_int.out 654 * 655 * \sa MatrixBase::setOnes(), setOnes(Index), class CwiseNullaryOp, MatrixBase::Ones() 656 */ 657 template<typename Derived> 658 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& 659 PlainObjectBase<Derived>::setOnes(Index rows, Index cols) 660 { 661 resize(rows, cols); 662 return setConstant(Scalar(1)); 663 } 664 665 // Identity: 666 667 /** \returns an expression of the identity matrix (not necessarily square). 668 * 669 * The parameters \a rows and \a cols are the number of rows and of columns of 670 * the returned matrix. Must be compatible with this MatrixBase type. 671 * 672 * This variant is meant to be used for dynamic-size matrix types. For fixed-size types, 673 * it is redundant to pass \a rows and \a cols as arguments, so Identity() should be used 674 * instead. 675 * 676 * Example: \include MatrixBase_identity_int_int.cpp 677 * Output: \verbinclude MatrixBase_identity_int_int.out 678 * 679 * \sa Identity(), setIdentity(), isIdentity() 680 */ 681 template<typename Derived> 682 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType 683 MatrixBase<Derived>::Identity(Index rows, Index cols) 684 { 685 return DenseBase<Derived>::NullaryExpr(rows, cols, internal::scalar_identity_op<Scalar>()); 686 } 687 688 /** \returns an expression of the identity matrix (not necessarily square). 689 * 690 * This variant is only for fixed-size MatrixBase types. For dynamic-size types, you 691 * need to use the variant taking size arguments. 692 * 693 * Example: \include MatrixBase_identity.cpp 694 * Output: \verbinclude MatrixBase_identity.out 695 * 696 * \sa Identity(Index,Index), setIdentity(), isIdentity() 697 */ 698 template<typename Derived> 699 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::IdentityReturnType 700 MatrixBase<Derived>::Identity() 701 { 702 EIGEN_STATIC_ASSERT_FIXED_SIZE(Derived) 703 return MatrixBase<Derived>::NullaryExpr(RowsAtCompileTime, ColsAtCompileTime, internal::scalar_identity_op<Scalar>()); 704 } 705 706 /** \returns true if *this is approximately equal to the identity matrix 707 * (not necessarily square), 708 * within the precision given by \a prec. 709 * 710 * Example: \include MatrixBase_isIdentity.cpp 711 * Output: \verbinclude MatrixBase_isIdentity.out 712 * 713 * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), setIdentity() 714 */ 715 template<typename Derived> 716 bool MatrixBase<Derived>::isIdentity 717 (const RealScalar& prec) const 718 { 719 typename internal::nested_eval<Derived,1>::type self(derived()); 720 for(Index j = 0; j < cols(); ++j) 721 { 722 for(Index i = 0; i < rows(); ++i) 723 { 724 if(i == j) 725 { 726 if(!internal::isApprox(self.coeff(i, j), static_cast<Scalar>(1), prec)) 727 return false; 728 } 729 else 730 { 731 if(!internal::isMuchSmallerThan(self.coeff(i, j), static_cast<RealScalar>(1), prec)) 732 return false; 733 } 734 } 735 } 736 return true; 737 } 738 739 namespace internal { 740 741 template<typename Derived, bool Big = (Derived::SizeAtCompileTime>=16)> 742 struct setIdentity_impl 743 { 744 EIGEN_DEVICE_FUNC 745 static EIGEN_STRONG_INLINE Derived& run(Derived& m) 746 { 747 return m = Derived::Identity(m.rows(), m.cols()); 748 } 749 }; 750 751 template<typename Derived> 752 struct setIdentity_impl<Derived, true> 753 { 754 EIGEN_DEVICE_FUNC 755 static EIGEN_STRONG_INLINE Derived& run(Derived& m) 756 { 757 m.setZero(); 758 const Index size = numext::mini(m.rows(), m.cols()); 759 for(Index i = 0; i < size; ++i) m.coeffRef(i,i) = typename Derived::Scalar(1); 760 return m; 761 } 762 }; 763 764 } // end namespace internal 765 766 /** Writes the identity expression (not necessarily square) into *this. 767 * 768 * Example: \include MatrixBase_setIdentity.cpp 769 * Output: \verbinclude MatrixBase_setIdentity.out 770 * 771 * \sa class CwiseNullaryOp, Identity(), Identity(Index,Index), isIdentity() 772 */ 773 template<typename Derived> 774 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity() 775 { 776 return internal::setIdentity_impl<Derived>::run(derived()); 777 } 778 779 /** \brief Resizes to the given size, and writes the identity expression (not necessarily square) into *this. 780 * 781 * \param rows the new number of rows 782 * \param cols the new number of columns 783 * 784 * Example: \include Matrix_setIdentity_int_int.cpp 785 * Output: \verbinclude Matrix_setIdentity_int_int.out 786 * 787 * \sa MatrixBase::setIdentity(), class CwiseNullaryOp, MatrixBase::Identity() 788 */ 789 template<typename Derived> 790 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& MatrixBase<Derived>::setIdentity(Index rows, Index cols) 791 { 792 derived().resize(rows, cols); 793 return setIdentity(); 794 } 795 796 /** \returns an expression of the i-th unit (basis) vector. 797 * 798 * \only_for_vectors 799 * 800 * \sa MatrixBase::Unit(Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 801 */ 802 template<typename Derived> 803 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index newSize, Index i) 804 { 805 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 806 return BasisReturnType(SquareMatrixType::Identity(newSize,newSize), i); 807 } 808 809 /** \returns an expression of the i-th unit (basis) vector. 810 * 811 * \only_for_vectors 812 * 813 * This variant is for fixed-size vector only. 814 * 815 * \sa MatrixBase::Unit(Index,Index), MatrixBase::UnitX(), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 816 */ 817 template<typename Derived> 818 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::Unit(Index i) 819 { 820 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived) 821 return BasisReturnType(SquareMatrixType::Identity(),i); 822 } 823 824 /** \returns an expression of the X axis unit vector (1{,0}^*) 825 * 826 * \only_for_vectors 827 * 828 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 829 */ 830 template<typename Derived> 831 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitX() 832 { return Derived::Unit(0); } 833 834 /** \returns an expression of the Y axis unit vector (0,1{,0}^*) 835 * 836 * \only_for_vectors 837 * 838 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 839 */ 840 template<typename Derived> 841 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitY() 842 { return Derived::Unit(1); } 843 844 /** \returns an expression of the Z axis unit vector (0,0,1{,0}^*) 845 * 846 * \only_for_vectors 847 * 848 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 849 */ 850 template<typename Derived> 851 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitZ() 852 { return Derived::Unit(2); } 853 854 /** \returns an expression of the W axis unit vector (0,0,0,1) 855 * 856 * \only_for_vectors 857 * 858 * \sa MatrixBase::Unit(Index,Index), MatrixBase::Unit(Index), MatrixBase::UnitY(), MatrixBase::UnitZ(), MatrixBase::UnitW() 859 */ 860 template<typename Derived> 861 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename MatrixBase<Derived>::BasisReturnType MatrixBase<Derived>::UnitW() 862 { return Derived::Unit(3); } 863 864 } // end namespace Eigen 865 866 #endif // EIGEN_CWISE_NULLARY_OP_H 867
