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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