1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
5 // Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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_CONSTANTS_H
12 #define EIGEN_CONSTANTS_H
13
14 namespace Eigen {
15
16 /** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is
17 * stored in some runtime variable.
18 *
19 * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
20 */
21 const int Dynamic = -1;
22
23 /** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value
24 * has to be specified at runtime.
25 */
26 const int DynamicIndex = 0xffffff;
27
28 /** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
29 * The value Infinity there means the L-infinity norm.
30 */
31 const int Infinity = -1;
32
33 /** This value means that the cost to evaluate an expression coefficient is either very expensive or
34 * cannot be known at compile time.
35 *
36 * This value has to be positive to (1) simplify cost computation, and (2) allow to distinguish between a very expensive and very very expensive expressions.
37 * It thus must also be large enough to make sure unrolling won't happen and that sub expressions will be evaluated, but not too large to avoid overflow.
38 */
39 const int HugeCost = 10000;
40
41 /** \defgroup flags Flags
42 * \ingroup Core_Module
43 *
44 * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
45 * expression.
46 *
47 * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
48 * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
49 * runtime overhead.
50 *
51 * \sa MatrixBase::Flags
52 */
53
54 /** \ingroup flags
55 *
56 * for a matrix, this means that the storage order is row-major.
57 * If this bit is not set, the storage order is column-major.
58 * For an expression, this determines the storage order of
59 * the matrix created by evaluation of that expression.
60 * \sa \blank \ref TopicStorageOrders */
61 const unsigned int RowMajorBit = 0x1;
62
63 /** \ingroup flags
64 * means the expression should be evaluated by the calling expression */
65 const unsigned int EvalBeforeNestingBit = 0x2;
66
67 /** \ingroup flags
68 * \deprecated
69 * means the expression should be evaluated before any assignment */
70 EIGEN_DEPRECATED
71 const unsigned int EvalBeforeAssigningBit = 0x4; // FIXME deprecated
72
73 /** \ingroup flags
74 *
75 * Short version: means the expression might be vectorized
76 *
77 * Long version: means that the coefficients can be handled by packets
78 * and start at a memory location whose alignment meets the requirements
79 * of the present CPU architecture for optimized packet access. In the fixed-size
80 * case, there is the additional condition that it be possible to access all the
81 * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,
82 * and that any nontrivial strides don't break the alignment). In the dynamic-size case,
83 * there is no such condition on the total size and strides, so it might not be possible to access
84 * all coeffs by packets.
85 *
86 * \note This bit can be set regardless of whether vectorization is actually enabled.
87 * To check for actual vectorizability, see \a ActualPacketAccessBit.
88 */
89 const unsigned int PacketAccessBit = 0x8;
90
91 #ifdef EIGEN_VECTORIZE
92 /** \ingroup flags
93 *
94 * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
95 * is set to the value \a PacketAccessBit.
96 *
97 * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
98 * is set to the value 0.
99 */
100 const unsigned int ActualPacketAccessBit = PacketAccessBit;
101 #else
102 const unsigned int ActualPacketAccessBit = 0x0;
103 #endif
104
105 /** \ingroup flags
106 *
107 * Short version: means the expression can be seen as 1D vector.
108 *
109 * Long version: means that one can access the coefficients
110 * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
111 * index-based access methods are guaranteed
112 * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
113 * is guaranteed that whenever it is available, index-based access is at least as fast as
114 * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
115 *
116 * If both PacketAccessBit and LinearAccessBit are set, then the
117 * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
118 * lvalue expression.
119 *
120 * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
121 * Product expressions don't have it, because it would be troublesome for vectorization, even when the
122 * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
123 * not index-based packet access, so they don't have the LinearAccessBit.
124 */
125 const unsigned int LinearAccessBit = 0x10;
126
127 /** \ingroup flags
128 *
129 * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.
130 * This rules out read-only expressions.
131 *
132 * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note
133 * the other:
134 * \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit
135 * \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit
136 *
137 * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.
138 */
139 const unsigned int LvalueBit = 0x20;
140
141 /** \ingroup flags
142 *
143 * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
144 * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
145 * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
146 * though referencable, do not have such a regular memory layout.
147 *
148 * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
149 */
150 const unsigned int DirectAccessBit = 0x40;
151
152 /** \deprecated \ingroup flags
153 *
154 * means the first coefficient packet is guaranteed to be aligned.
155 * An expression cannot has the AlignedBit without the PacketAccessBit flag.
156 * In other words, this means we are allow to perform an aligned packet access to the first element regardless
157 * of the expression kind:
158 * \code
159 * expression.packet<Aligned>(0);
160 * \endcode
161 */
162 EIGEN_DEPRECATED const unsigned int AlignedBit = 0x80;
163
164 const unsigned int NestByRefBit = 0x100;
165
166 /** \ingroup flags
167 *
168 * for an expression, this means that the storage order
169 * can be either row-major or column-major.
170 * The precise choice will be decided at evaluation time or when
171 * combined with other expressions.
172 * \sa \blank \ref RowMajorBit, \ref TopicStorageOrders */
173 const unsigned int NoPreferredStorageOrderBit = 0x200;
174
175 /** \ingroup flags
176 *
177 * Means that the underlying coefficients can be accessed through pointers to the sparse (un)compressed storage format,
178 * that is, the expression provides:
179 * \code
180 inline const Scalar* valuePtr() const;
181 inline const Index* innerIndexPtr() const;
182 inline const Index* outerIndexPtr() const;
183 inline const Index* innerNonZeroPtr() const;
184 \endcode
185 */
186 const unsigned int CompressedAccessBit = 0x400;
187
188
189 // list of flags that are inherited by default
190 const unsigned int HereditaryBits = RowMajorBit
191 | EvalBeforeNestingBit;
192
193 /** \defgroup enums Enumerations
194 * \ingroup Core_Module
195 *
196 * Various enumerations used in %Eigen. Many of these are used as template parameters.
197 */
198
199 /** \ingroup enums
200 * Enum containing possible values for the \c Mode or \c UpLo parameter of
201 * MatrixBase::selfadjointView() and MatrixBase::triangularView(), and selfadjoint solvers. */
202 enum UpLoType {
203 /** View matrix as a lower triangular matrix. */
204 Lower=0x1,
205 /** View matrix as an upper triangular matrix. */
206 Upper=0x2,
207 /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */
208 UnitDiag=0x4,
209 /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */
210 ZeroDiag=0x8,
211 /** View matrix as a lower triangular matrix with ones on the diagonal. */
212 UnitLower=UnitDiag|Lower,
213 /** View matrix as an upper triangular matrix with ones on the diagonal. */
214 UnitUpper=UnitDiag|Upper,
215 /** View matrix as a lower triangular matrix with zeros on the diagonal. */
216 StrictlyLower=ZeroDiag|Lower,
217 /** View matrix as an upper triangular matrix with zeros on the diagonal. */
218 StrictlyUpper=ZeroDiag|Upper,
219 /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */
220 SelfAdjoint=0x10,
221 /** Used to support symmetric, non-selfadjoint, complex matrices. */
222 Symmetric=0x20
223 };
224
225 /** \ingroup enums
226 * Enum for indicating whether a buffer is aligned or not. */
227 enum AlignmentType {
228 Unaligned=0, /**< Data pointer has no specific alignment. */
229 Aligned8=8, /**< Data pointer is aligned on a 8 bytes boundary. */
230 Aligned16=16, /**< Data pointer is aligned on a 16 bytes boundary. */
231 Aligned32=32, /**< Data pointer is aligned on a 32 bytes boundary. */
232 Aligned64=64, /**< Data pointer is aligned on a 64 bytes boundary. */
233 Aligned128=128, /**< Data pointer is aligned on a 128 bytes boundary. */
234 AlignedMask=255,
235 Aligned=16, /**< \deprecated Synonym for Aligned16. */
236 #if EIGEN_MAX_ALIGN_BYTES==128
237 AlignedMax = Aligned128
238 #elif EIGEN_MAX_ALIGN_BYTES==64
239 AlignedMax = Aligned64
240 #elif EIGEN_MAX_ALIGN_BYTES==32
241 AlignedMax = Aligned32
242 #elif EIGEN_MAX_ALIGN_BYTES==16
243 AlignedMax = Aligned16
244 #elif EIGEN_MAX_ALIGN_BYTES==8
245 AlignedMax = Aligned8
246 #elif EIGEN_MAX_ALIGN_BYTES==0
247 AlignedMax = Unaligned
248 #else
249 #error Invalid value for EIGEN_MAX_ALIGN_BYTES
250 #endif
251 };
252
253 /** \ingroup enums
254 * Enum used by DenseBase::corner() in Eigen2 compatibility mode. */
255 // FIXME after the corner() API change, this was not needed anymore, except by AlignedBox
256 // TODO: find out what to do with that. Adapt the AlignedBox API ?
257 enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
258
259 /** \ingroup enums
260 * Enum containing possible values for the \p Direction parameter of
261 * Reverse, PartialReduxExpr and VectorwiseOp. */
262 enum DirectionType {
263 /** For Reverse, all columns are reversed;
264 * for PartialReduxExpr and VectorwiseOp, act on columns. */
265 Vertical,
266 /** For Reverse, all rows are reversed;
267 * for PartialReduxExpr and VectorwiseOp, act on rows. */
268 Horizontal,
269 /** For Reverse, both rows and columns are reversed;
270 * not used for PartialReduxExpr and VectorwiseOp. */
271 BothDirections
272 };
273
274 /** \internal \ingroup enums
275 * Enum to specify how to traverse the entries of a matrix. */
276 enum TraversalType {
277 /** \internal Default traversal, no vectorization, no index-based access */
278 DefaultTraversal,
279 /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */
280 LinearTraversal,
281 /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
282 * and good size */
283 InnerVectorizedTraversal,
284 /** \internal Vectorization path using a single loop plus scalar loops for the
285 * unaligned boundaries */
286 LinearVectorizedTraversal,
287 /** \internal Generic vectorization path using one vectorized loop per row/column with some
288 * scalar loops to handle the unaligned boundaries */
289 SliceVectorizedTraversal,
290 /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/
291 InvalidTraversal,
292 /** \internal Evaluate all entries at once */
293 AllAtOnceTraversal
294 };
295
296 /** \internal \ingroup enums
297 * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */
298 enum UnrollingType {
299 /** \internal Do not unroll loops. */
300 NoUnrolling,
301 /** \internal Unroll only the inner loop, but not the outer loop. */
302 InnerUnrolling,
303 /** \internal Unroll both the inner and the outer loop. If there is only one loop,
304 * because linear traversal is used, then unroll that loop. */
305 CompleteUnrolling
306 };
307
308 /** \internal \ingroup enums
309 * Enum to specify whether to use the default (built-in) implementation or the specialization. */
310 enum SpecializedType {
311 Specialized,
312 BuiltIn
313 };
314
315 /** \ingroup enums
316 * Enum containing possible values for the \p _Options template parameter of
317 * Matrix, Array and BandMatrix. */
318 enum StorageOptions {
319 /** Storage order is column major (see \ref TopicStorageOrders). */
320 ColMajor = 0,
321 /** Storage order is row major (see \ref TopicStorageOrders). */
322 RowMajor = 0x1, // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
323 /** Align the matrix itself if it is vectorizable fixed-size */
324 AutoAlign = 0,
325 /** Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be requested to be aligned) */ // FIXME --- clarify the situation
326 DontAlign = 0x2
327 };
328
329 /** \ingroup enums
330 * Enum for specifying whether to apply or solve on the left or right. */
331 enum SideType {
332 /** Apply transformation on the left. */
333 OnTheLeft = 1,
334 /** Apply transformation on the right. */
335 OnTheRight = 2
336 };
337
338 /* the following used to be written as:
339 *
340 * struct NoChange_t {};
341 * namespace {
342 * EIGEN_UNUSED NoChange_t NoChange;
343 * }
344 *
345 * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.
346 * However, this leads to "variable declared but never referenced" warnings on Intel Composer XE,
347 * and we do not know how to get rid of them (bug 450).
348 */
349
350 enum NoChange_t { NoChange };
351 enum Sequential_t { Sequential };
352 enum Default_t { Default };
353
354 /** \internal \ingroup enums
355 * Used in AmbiVector. */
356 enum AmbiVectorMode {
357 IsDense = 0,
358 IsSparse
359 };
360
361 /** \ingroup enums
362 * Used as template parameter in DenseCoeffBase and MapBase to indicate
363 * which accessors should be provided. */
364 enum AccessorLevels {
365 /** Read-only access via a member function. */
366 ReadOnlyAccessors,
367 /** Read/write access via member functions. */
368 WriteAccessors,
369 /** Direct read-only access to the coefficients. */
370 DirectAccessors,
371 /** Direct read/write access to the coefficients. */
372 DirectWriteAccessors
373 };
374
375 /** \ingroup enums
376 * Enum with options to give to various decompositions. */
377 enum DecompositionOptions {
378 /** \internal Not used (meant for LDLT?). */
379 Pivoting = 0x01,
380 /** \internal Not used (meant for LDLT?). */
381 NoPivoting = 0x02,
382 /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */
383 ComputeFullU = 0x04,
384 /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */
385 ComputeThinU = 0x08,
386 /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */
387 ComputeFullV = 0x10,
388 /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */
389 ComputeThinV = 0x20,
390 /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
391 * that only the eigenvalues are to be computed and not the eigenvectors. */
392 EigenvaluesOnly = 0x40,
393 /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
394 * that both the eigenvalues and the eigenvectors are to be computed. */
395 ComputeEigenvectors = 0x80,
396 /** \internal */
397 EigVecMask = EigenvaluesOnly | ComputeEigenvectors,
398 /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
399 * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */
400 Ax_lBx = 0x100,
401 /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
402 * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */
403 ABx_lx = 0x200,
404 /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
405 * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */
406 BAx_lx = 0x400,
407 /** \internal */
408 GenEigMask = Ax_lBx | ABx_lx | BAx_lx
409 };
410
411 /** \ingroup enums
412 * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */
413 enum QRPreconditioners {
414 /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
415 NoQRPreconditioner,
416 /** Use a QR decomposition without pivoting as the first step. */
417 HouseholderQRPreconditioner,
418 /** Use a QR decomposition with column pivoting as the first step. */
419 ColPivHouseholderQRPreconditioner,
420 /** Use a QR decomposition with full pivoting as the first step. */
421 FullPivHouseholderQRPreconditioner
422 };
423
424 #ifdef Success
425 #error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h
426 #endif
427
428 /** \ingroup enums
429 * Enum for reporting the status of a computation. */
430 enum ComputationInfo {
431 /** Computation was successful. */
432 Success = 0,
433 /** The provided data did not satisfy the prerequisites. */
434 NumericalIssue = 1,
435 /** Iterative procedure did not converge. */
436 NoConvergence = 2,
437 /** The inputs are invalid, or the algorithm has been improperly called.
438 * When assertions are enabled, such errors trigger an assert. */
439 InvalidInput = 3
440 };
441
442 /** \ingroup enums
443 * Enum used to specify how a particular transformation is stored in a matrix.
444 * \sa Transform, Hyperplane::transform(). */
445 enum TransformTraits {
446 /** Transformation is an isometry. */
447 Isometry = 0x1,
448 /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is
449 * assumed to be [0 ... 0 1]. */
450 Affine = 0x2,
451 /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */
452 AffineCompact = 0x10 | Affine,
453 /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */
454 Projective = 0x20
455 };
456
457 /** \internal \ingroup enums
458 * Enum used to choose between implementation depending on the computer architecture. */
459 namespace Architecture
460 {
461 enum Type {
462 Generic = 0x0,
463 SSE = 0x1,
464 AltiVec = 0x2,
465 VSX = 0x3,
466 NEON = 0x4,
467 #if defined EIGEN_VECTORIZE_SSE
468 Target = SSE
469 #elif defined EIGEN_VECTORIZE_ALTIVEC
470 Target = AltiVec
471 #elif defined EIGEN_VECTORIZE_VSX
472 Target = VSX
473 #elif defined EIGEN_VECTORIZE_NEON
474 Target = NEON
475 #else
476 Target = Generic
477 #endif
478 };
479 }
480
481 /** \internal \ingroup enums
482 * Enum used as template parameter in Product and product evaluators. */
483 enum ProductImplType
484 { DefaultProduct=0, LazyProduct, AliasFreeProduct, CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
485
486 /** \internal \ingroup enums
487 * Enum used in experimental parallel implementation. */
488 enum Action {GetAction, SetAction};
489
490 /** The type used to identify a dense storage. */
491 struct Dense {};
492
493 /** The type used to identify a general sparse storage. */
494 struct Sparse {};
495
496 /** The type used to identify a general solver (factored) storage. */
497 struct SolverStorage {};
498
499 /** The type used to identify a permutation storage. */
500 struct PermutationStorage {};
501
502 /** The type used to identify a permutation storage. */
503 struct TranspositionsStorage {};
504
505 /** The type used to identify a matrix expression */
506 struct MatrixXpr {};
507
508 /** The type used to identify an array expression */
509 struct ArrayXpr {};
510
511 // An evaluator must define its shape. By default, it can be one of the following:
debugNameDenseShape512 struct DenseShape { static std::string debugName() { return "DenseShape"; } };
debugNameSolverShape513 struct SolverShape { static std::string debugName() { return "SolverShape"; } };
debugNameHomogeneousShape514 struct HomogeneousShape { static std::string debugName() { return "HomogeneousShape"; } };
debugNameDiagonalShape515 struct DiagonalShape { static std::string debugName() { return "DiagonalShape"; } };
debugNameBandShape516 struct BandShape { static std::string debugName() { return "BandShape"; } };
debugNameTriangularShape517 struct TriangularShape { static std::string debugName() { return "TriangularShape"; } };
debugNameSelfAdjointShape518 struct SelfAdjointShape { static std::string debugName() { return "SelfAdjointShape"; } };
debugNamePermutationShape519 struct PermutationShape { static std::string debugName() { return "PermutationShape"; } };
debugNameTranspositionsShape520 struct TranspositionsShape { static std::string debugName() { return "TranspositionsShape"; } };
debugNameSparseShape521 struct SparseShape { static std::string debugName() { return "SparseShape"; } };
522
523 namespace internal {
524
525 // random access iterators based on coeff*() accessors.
526 struct IndexBased {};
527
528 // evaluator based on iterators to access coefficients.
529 struct IteratorBased {};
530
531 /** \internal
532 * Constants for comparison functors
533 */
534 enum ComparisonName {
535 cmp_EQ = 0,
536 cmp_LT = 1,
537 cmp_LE = 2,
538 cmp_UNORD = 3,
539 cmp_NEQ = 4,
540 cmp_GT = 5,
541 cmp_GE = 6
542 };
543 } // end namespace internal
544
545 } // end namespace Eigen
546
547 #endif // EIGEN_CONSTANTS_H
548