// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com> // // Eigen is free software; you can redistribute it and/or // modify it under the terms of the GNU Lesser General Public // License as published by the Free Software Foundation; either // version 3 of the License, or (at your option) any later version. // // Alternatively, you can redistribute it and/or // modify it under the terms of the GNU General Public License as // published by the Free Software Foundation; either version 2 of // the License, or (at your option) any later version. // // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the // GNU General Public License for more details. // // You should have received a copy of the GNU Lesser General Public // License and a copy of the GNU General Public License along with // Eigen. If not, see <http://www.gnu.org/licenses/>. #ifndef EIGEN_CONSTANTS_H #define EIGEN_CONSTANTS_H /** This value means that a quantity is not known at compile-time, and that instead the value is * stored in some runtime variable. * * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix. */ const int Dynamic = -1; /** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>(). * The value Infinity there means the L-infinity norm. */ const int Infinity = -1; /** \defgroup flags Flags * \ingroup Core_Module * * These are the possible bits which can be OR'ed to constitute the flags of a matrix or * expression. * * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any * runtime overhead. * * \sa MatrixBase::Flags */ /** \ingroup flags * * for a matrix, this means that the storage order is row-major. * If this bit is not set, the storage order is column-major. * For an expression, this determines the storage order of * the matrix created by evaluation of that expression. * \sa \ref TopicStorageOrders */ 00061 const unsigned int RowMajorBit = 0x1; /** \ingroup flags * * means the expression should be evaluated by the calling expression */ 00066 const unsigned int EvalBeforeNestingBit = 0x2; /** \ingroup flags * * means the expression should be evaluated before any assignment */ 00071 const unsigned int EvalBeforeAssigningBit = 0x4; /** \ingroup flags * * Short version: means the expression might be vectorized * * Long version: means that the coefficients can be handled by packets * and start at a memory location whose alignment meets the requirements * of the present CPU architecture for optimized packet access. In the fixed-size * case, there is the additional condition that it be possible to access all the * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes, * and that any nontrivial strides don't break the alignment). In the dynamic-size case, * there is no such condition on the total size and strides, so it might not be possible to access * all coeffs by packets. * * \note This bit can be set regardless of whether vectorization is actually enabled. * To check for actual vectorizability, see \a ActualPacketAccessBit. */ 00089 const unsigned int PacketAccessBit = 0x8; #ifdef EIGEN_VECTORIZE /** \ingroup flags * * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant * is set to the value \a PacketAccessBit. * * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant * is set to the value 0. */ const unsigned int ActualPacketAccessBit = PacketAccessBit; #else const unsigned int ActualPacketAccessBit = 0x0; #endif /** \ingroup flags * * Short version: means the expression can be seen as 1D vector. * * Long version: means that one can access the coefficients * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These * index-based access methods are guaranteed * to not have to do any runtime computation of a (row, col)-pair from the index, so that it * is guaranteed that whenever it is available, index-based access is at least as fast as * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit. * * If both PacketAccessBit and LinearAccessBit are set, then the * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a * lvalue expression. * * Typically, all vector expressions have the LinearAccessBit, but there is one exception: * Product expressions don't have it, because it would be troublesome for vectorization, even when the * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but * not index-based packet access, so they don't have the LinearAccessBit. */ 00125 const unsigned int LinearAccessBit = 0x10; /** \ingroup flags * * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable. * This rules out read-only expressions. * * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note * the other: * \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit * \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit * * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value. */ 00139 const unsigned int LvalueBit = 0x20; /** \ingroup flags * * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout * of the array of coefficients must be exactly the natural one suggested by rows(), cols(), * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients, * though referencable, do not have such a regular memory layout. * * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal. */ 00150 const unsigned int DirectAccessBit = 0x40; /** \ingroup flags * * means the first coefficient packet is guaranteed to be aligned */ 00155 const unsigned int AlignedBit = 0x80; const unsigned int NestByRefBit = 0x100; // list of flags that are inherited by default const unsigned int HereditaryBits = RowMajorBit | EvalBeforeNestingBit | EvalBeforeAssigningBit; /** \defgroup enums Enumerations * \ingroup Core_Module * * Various enumerations used in %Eigen. Many of these are used as template parameters. */ /** \ingroup enums * Enum containing possible values for the \p Mode parameter of * MatrixBase::selfadjointView() and MatrixBase::triangularView(). */ enum { /** View matrix as a lower triangular matrix. */ 00175 Lower=0x1, /** View matrix as an upper triangular matrix. */ 00177 Upper=0x2, /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */ 00179 UnitDiag=0x4, /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */ 00181 ZeroDiag=0x8, /** View matrix as a lower triangular matrix with ones on the diagonal. */ 00183 UnitLower=UnitDiag|Lower, /** View matrix as an upper triangular matrix with ones on the diagonal. */ 00185 UnitUpper=UnitDiag|Upper, /** View matrix as a lower triangular matrix with zeros on the diagonal. */ 00187 StrictlyLower=ZeroDiag|Lower, /** View matrix as an upper triangular matrix with zeros on the diagonal. */ 00189 StrictlyUpper=ZeroDiag|Upper, /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */ 00191 SelfAdjoint=0x10 }; /** \ingroup enums * Enum for indicating whether an object is aligned or not. */ enum { /** Object is not correctly aligned for vectorization. */ 00198 Unaligned=0, /** Object is aligned for vectorization. */ 00200 Aligned=1 }; enum { ConditionalJumpCost = 5 }; /** \ingroup enums * Enum used by DenseBase::corner() in Eigen2 compatibility mode. */ // FIXME after the corner() API change, this was not needed anymore, except by AlignedBox // TODO: find out what to do with that. Adapt the AlignedBox API ? 00209 enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight }; /** \ingroup enums * Enum containing possible values for the \p Direction parameter of * Reverse, PartialReduxExpr and VectorwiseOp. */ 00214 enum DirectionType { /** For Reverse, all columns are reversed; * for PartialReduxExpr and VectorwiseOp, act on columns. */ 00217 Vertical, /** For Reverse, all rows are reversed; * for PartialReduxExpr and VectorwiseOp, act on rows. */ 00220 Horizontal, /** For Reverse, both rows and columns are reversed; * not used for PartialReduxExpr and VectorwiseOp. */ 00223 BothDirections }; enum ProductEvaluationMode { NormalProduct, CacheFriendlyProduct }; /** \internal \ingroup enums * Enum to specify how to traverse the entries of a matrix. */ enum { /** \internal Default traversal, no vectorization, no index-based access */ 00232 DefaultTraversal, /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */ 00234 LinearTraversal, /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment * and good size */ 00237 InnerVectorizedTraversal, /** \internal Vectorization path using a single loop plus scalar loops for the * unaligned boundaries */ 00240 LinearVectorizedTraversal, /** \internal Generic vectorization path using one vectorized loop per row/column with some * scalar loops to handle the unaligned boundaries */ 00243 SliceVectorizedTraversal, /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/ 00245 InvalidTraversal }; /** \internal \ingroup enums * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */ enum { /** \internal Do not unroll loops. */ 00252 NoUnrolling, /** \internal Unroll only the inner loop, but not the outer loop. */ 00254 InnerUnrolling, /** \internal Unroll both the inner and the outer loop. If there is only one loop, * because linear traversal is used, then unroll that loop. */ 00257 CompleteUnrolling }; /** \ingroup enums * Enum containing possible values for the \p _Options template parameter of * Matrix, Array and BandMatrix. */ enum { /** Storage order is column major (see \ref TopicStorageOrders). */ 00265 ColMajor = 0, /** Storage order is row major (see \ref TopicStorageOrders). */ 00267 RowMajor = 0x1, // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that /** \internal Align the matrix itself if it is vectorizable fixed-size */ 00269 AutoAlign = 0, /** \internal 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 00271 DontAlign = 0x2 }; /** \ingroup enums * Enum for specifying whether to apply or solve on the left or right. */ enum { /** Apply transformation on the left. */ 00278 OnTheLeft = 1, /** Apply transformation on the right. */ 00280 OnTheRight = 2 }; /* the following could as well be written: * enum NoChange_t { NoChange }; * but it feels dangerous to disambiguate overloaded functions on enum/integer types. * If on some platform it is really impossible to get rid of "unused variable" warnings, then * we can always come back to that solution. */ 00289 struct NoChange_t {}; namespace { EIGEN_UNUSED NoChange_t NoChange; } 00294 struct Sequential_t {}; namespace { EIGEN_UNUSED Sequential_t Sequential; } 00299 struct Default_t {}; namespace { EIGEN_UNUSED Default_t Default; } /** \internal \ingroup enums * Used in AmbiVector. */ enum { IsDense = 0, IsSparse }; /** \ingroup enums * Used as template parameter in DenseCoeffBase and MapBase to indicate * which accessors should be provided. */ 00314 enum AccessorLevels { /** Read-only access via a member function. */ 00316 ReadOnlyAccessors, /** Read/write access via member functions. */ 00318 WriteAccessors, /** Direct read-only access to the coefficients. */ 00320 DirectAccessors, /** Direct read/write access to the coefficients. */ 00322 DirectWriteAccessors }; /** \ingroup enums * Enum with options to give to various decompositions. */ 00327 enum DecompositionOptions { /** \internal Not used (meant for LDLT?). */ 00329 Pivoting = 0x01, /** \internal Not used (meant for LDLT?). */ 00331 NoPivoting = 0x02, /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */ 00333 ComputeFullU = 0x04, /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */ 00335 ComputeThinU = 0x08, /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */ 00337 ComputeFullV = 0x10, /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */ 00339 ComputeThinV = 0x20, /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify * that only the eigenvalues are to be computed and not the eigenvectors. */ 00342 EigenvaluesOnly = 0x40, /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify * that both the eigenvalues and the eigenvectors are to be computed. */ 00345 ComputeEigenvectors = 0x80, /** \internal */ EigVecMask = EigenvaluesOnly | ComputeEigenvectors, /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */ 00350 Ax_lBx = 0x100, /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */ 00353 ABx_lx = 0x200, /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */ 00356 BAx_lx = 0x400, /** \internal */ GenEigMask = Ax_lBx | ABx_lx | BAx_lx }; /** \ingroup enums * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */ 00363 enum QRPreconditioners { /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */ 00365 NoQRPreconditioner, /** Use a QR decomposition without pivoting as the first step. */ 00367 HouseholderQRPreconditioner, /** Use a QR decomposition with column pivoting as the first step. */ 00369 ColPivHouseholderQRPreconditioner, /** Use a QR decomposition with full pivoting as the first step. */ 00371 FullPivHouseholderQRPreconditioner }; #ifdef Success #error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h #endif /** \ingroups enums * Enum for reporting the status of a computation. */ enum ComputationInfo { /** Computation was successful. */ Success = 0, /** The provided data did not satisfy the prerequisites. */ NumericalIssue = 1, /** Iterative procedure did not converge. */ NoConvergence = 2 }; /** \ingroup enums * Enum used to specify how a particular transformation is stored in a matrix. * \sa Transform, Hyperplane::transform(). */ 00392 enum TransformTraits { /** Transformation is an isometry. */ 00394 Isometry = 0x1, /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is * assumed to be [0 ... 0 1]. */ 00397 Affine = 0x2, /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */ 00399 AffineCompact = 0x10 | Affine, /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */ 00401 Projective = 0x20 }; /** \internal \ingroup enums * Enum used to choose between implementation depending on the computer architecture. */ 00406 namespace Architecture { enum Type { Generic = 0x0, SSE = 0x1, AltiVec = 0x2, #if defined EIGEN_VECTORIZE_SSE Target = SSE #elif defined EIGEN_VECTORIZE_ALTIVEC Target = AltiVec #else Target = Generic #endif }; } /** \internal \ingroup enums * Enum used as template parameter in GeneralProduct. */ enum { CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct }; /** \internal \ingroup enums * Enum used in experimental parallel implementation. */ 00428 enum Action {GetAction, SetAction}; /** The type used to identify a dense storage. */ 00431 struct Dense {}; /** The type used to identify a matrix expression */ 00434 struct MatrixXpr {}; /** The type used to identify an array expression */ 00437 struct ArrayXpr {}; #endif // EIGEN_CONSTANTS_H

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