Constants.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 // Copyright (C) 2007-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_CONSTANTS_H
00012 #define EIGEN_CONSTANTS_H
00013 
00014 namespace Eigen {
00015 
00016 /** This value means that a positive quantity (e.g., a size) is not known at compile-time, and that instead the value is
00017   * stored in some runtime variable.
00018   *
00019   * Changing the value of Dynamic breaks the ABI, as Dynamic is often used as a template parameter for Matrix.
00020   */
00021 const int Dynamic = -1;
00022 
00023 /** This value means that a signed quantity (e.g., a signed index) is not known at compile-time, and that instead its value
00024   * has to be specified at runtime.
00025   */
00026 const int DynamicIndex = 0xffffff;
00027 
00028 /** This value means +Infinity; it is currently used only as the p parameter to MatrixBase::lpNorm<int>().
00029   * The value Infinity there means the L-infinity norm.
00030   */
00031 const int Infinity = -1;
00032 
00033 /** \defgroup flags Flags
00034   * \ingroup Core_Module
00035   *
00036   * These are the possible bits which can be OR'ed to constitute the flags of a matrix or
00037   * expression.
00038   *
00039   * It is important to note that these flags are a purely compile-time notion. They are a compile-time property of
00040   * an expression type, implemented as enum's. They are not stored in memory at runtime, and they do not incur any
00041   * runtime overhead.
00042   *
00043   * \sa MatrixBase::Flags
00044   */
00045 
00046 /** \ingroup flags
00047   *
00048   * for a matrix, this means that the storage order is row-major.
00049   * If this bit is not set, the storage order is column-major.
00050   * For an expression, this determines the storage order of
00051   * the matrix created by evaluation of that expression. 
00052   * \sa \ref TopicStorageOrders */
00053 const unsigned int RowMajorBit = 0x1;
00054 
00055 /** \ingroup flags
00056   *
00057   * means the expression should be evaluated by the calling expression */
00058 const unsigned int EvalBeforeNestingBit = 0x2;
00059 
00060 /** \ingroup flags
00061   *
00062   * means the expression should be evaluated before any assignment */
00063 const unsigned int EvalBeforeAssigningBit = 0x4;
00064 
00065 /** \ingroup flags
00066   *
00067   * Short version: means the expression might be vectorized
00068   *
00069   * Long version: means that the coefficients can be handled by packets
00070   * and start at a memory location whose alignment meets the requirements
00071   * of the present CPU architecture for optimized packet access. In the fixed-size
00072   * case, there is the additional condition that it be possible to access all the
00073   * coefficients by packets (this implies the requirement that the size be a multiple of 16 bytes,
00074   * and that any nontrivial strides don't break the alignment). In the dynamic-size case,
00075   * there is no such condition on the total size and strides, so it might not be possible to access
00076   * all coeffs by packets.
00077   *
00078   * \note This bit can be set regardless of whether vectorization is actually enabled.
00079   *       To check for actual vectorizability, see \a ActualPacketAccessBit.
00080   */
00081 const unsigned int PacketAccessBit = 0x8;
00082 
00083 #ifdef EIGEN_VECTORIZE
00084 /** \ingroup flags
00085   *
00086   * If vectorization is enabled (EIGEN_VECTORIZE is defined) this constant
00087   * is set to the value \a PacketAccessBit.
00088   *
00089   * If vectorization is not enabled (EIGEN_VECTORIZE is not defined) this constant
00090   * is set to the value 0.
00091   */
00092 const unsigned int ActualPacketAccessBit = PacketAccessBit;
00093 #else
00094 const unsigned int ActualPacketAccessBit = 0x0;
00095 #endif
00096 
00097 /** \ingroup flags
00098   *
00099   * Short version: means the expression can be seen as 1D vector.
00100   *
00101   * Long version: means that one can access the coefficients
00102   * of this expression by coeff(int), and coeffRef(int) in the case of a lvalue expression. These
00103   * index-based access methods are guaranteed
00104   * to not have to do any runtime computation of a (row, col)-pair from the index, so that it
00105   * is guaranteed that whenever it is available, index-based access is at least as fast as
00106   * (row,col)-based access. Expressions for which that isn't possible don't have the LinearAccessBit.
00107   *
00108   * If both PacketAccessBit and LinearAccessBit are set, then the
00109   * packets of this expression can be accessed by packet(int), and writePacket(int) in the case of a
00110   * lvalue expression.
00111   *
00112   * Typically, all vector expressions have the LinearAccessBit, but there is one exception:
00113   * Product expressions don't have it, because it would be troublesome for vectorization, even when the
00114   * Product is a vector expression. Thus, vector Product expressions allow index-based coefficient access but
00115   * not index-based packet access, so they don't have the LinearAccessBit.
00116   */
00117 const unsigned int LinearAccessBit = 0x10;
00118 
00119 /** \ingroup flags
00120   *
00121   * Means the expression has a coeffRef() method, i.e. is writable as its individual coefficients are directly addressable.
00122   * This rules out read-only expressions.
00123   *
00124   * Note that DirectAccessBit and LvalueBit are mutually orthogonal, as there are examples of expression having one but note
00125   * the other:
00126   *   \li writable expressions that don't have a very simple memory layout as a strided array, have LvalueBit but not DirectAccessBit
00127   *   \li Map-to-const expressions, for example Map<const Matrix>, have DirectAccessBit but not LvalueBit
00128   *
00129   * Expressions having LvalueBit also have their coeff() method returning a const reference instead of returning a new value.
00130   */
00131 const unsigned int LvalueBit = 0x20;
00132 
00133 /** \ingroup flags
00134   *
00135   * Means that the underlying array of coefficients can be directly accessed as a plain strided array. The memory layout
00136   * of the array of coefficients must be exactly the natural one suggested by rows(), cols(),
00137   * outerStride(), innerStride(), and the RowMajorBit. This rules out expressions such as Diagonal, whose coefficients,
00138   * though referencable, do not have such a regular memory layout.
00139   *
00140   * See the comment on LvalueBit for an explanation of how LvalueBit and DirectAccessBit are mutually orthogonal.
00141   */
00142 const unsigned int DirectAccessBit = 0x40;
00143 
00144 /** \ingroup flags
00145   *
00146   * means the first coefficient packet is guaranteed to be aligned */
00147 const unsigned int AlignedBit = 0x80;
00148 
00149 const unsigned int NestByRefBit = 0x100;
00150 
00151 // list of flags that are inherited by default
00152 const unsigned int HereditaryBits = RowMajorBit
00153                                   | EvalBeforeNestingBit
00154                                   | EvalBeforeAssigningBit;
00155 
00156 /** \defgroup enums Enumerations
00157   * \ingroup Core_Module
00158   *
00159   * Various enumerations used in %Eigen. Many of these are used as template parameters.
00160   */
00161 
00162 /** \ingroup enums
00163   * Enum containing possible values for the \p Mode parameter of 
00164   * MatrixBase::selfadjointView() and MatrixBase::triangularView(). */
00165 enum {
00166   /** View matrix as a lower triangular matrix. */
00167   Lower=0x1,                      
00168   /** View matrix as an upper triangular matrix. */
00169   Upper=0x2,                      
00170   /** %Matrix has ones on the diagonal; to be used in combination with #Lower or #Upper. */
00171   UnitDiag=0x4, 
00172   /** %Matrix has zeros on the diagonal; to be used in combination with #Lower or #Upper. */
00173   ZeroDiag=0x8,
00174   /** View matrix as a lower triangular matrix with ones on the diagonal. */
00175   UnitLower=UnitDiag|Lower, 
00176   /** View matrix as an upper triangular matrix with ones on the diagonal. */
00177   UnitUpper=UnitDiag|Upper,
00178   /** View matrix as a lower triangular matrix with zeros on the diagonal. */
00179   StrictlyLower=ZeroDiag|Lower, 
00180   /** View matrix as an upper triangular matrix with zeros on the diagonal. */
00181   StrictlyUpper=ZeroDiag|Upper,
00182   /** Used in BandMatrix and SelfAdjointView to indicate that the matrix is self-adjoint. */
00183   SelfAdjoint=0x10,
00184   /** Used to support symmetric, non-selfadjoint, complex matrices. */
00185   Symmetric=0x20
00186 };
00187 
00188 /** \ingroup enums
00189   * Enum for indicating whether an object is aligned or not. */
00190 enum { 
00191   /** Object is not correctly aligned for vectorization. */
00192   Unaligned=0, 
00193   /** Object is aligned for vectorization. */
00194   Aligned=1 
00195 };
00196 
00197 /** \ingroup enums
00198  * Enum used by DenseBase::corner() in Eigen2 compatibility mode. */
00199 // FIXME after the corner() API change, this was not needed anymore, except by AlignedBox
00200 // TODO: find out what to do with that. Adapt the AlignedBox API ?
00201 enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
00202 
00203 /** \ingroup enums
00204   * Enum containing possible values for the \p Direction parameter of
00205   * Reverse, PartialReduxExpr and VectorwiseOp. */
00206 enum DirectionType { 
00207   /** For Reverse, all columns are reversed; 
00208     * for PartialReduxExpr and VectorwiseOp, act on columns. */
00209   Vertical, 
00210   /** For Reverse, all rows are reversed; 
00211     * for PartialReduxExpr and VectorwiseOp, act on rows. */
00212   Horizontal, 
00213   /** For Reverse, both rows and columns are reversed; 
00214     * not used for PartialReduxExpr and VectorwiseOp. */
00215   BothDirections 
00216 };
00217 
00218 /** \internal \ingroup enums
00219   * Enum to specify how to traverse the entries of a matrix. */
00220 enum {
00221   /** \internal Default traversal, no vectorization, no index-based access */
00222   DefaultTraversal,
00223   /** \internal No vectorization, use index-based access to have only one for loop instead of 2 nested loops */
00224   LinearTraversal,
00225   /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
00226     * and good size */
00227   InnerVectorizedTraversal,
00228   /** \internal Vectorization path using a single loop plus scalar loops for the
00229     * unaligned boundaries */
00230   LinearVectorizedTraversal,
00231   /** \internal Generic vectorization path using one vectorized loop per row/column with some
00232     * scalar loops to handle the unaligned boundaries */
00233   SliceVectorizedTraversal,
00234   /** \internal Special case to properly handle incompatible scalar types or other defecting cases*/
00235   InvalidTraversal,
00236   /** \internal Evaluate all entries at once */
00237   AllAtOnceTraversal
00238 };
00239 
00240 /** \internal \ingroup enums
00241   * Enum to specify whether to unroll loops when traversing over the entries of a matrix. */
00242 enum {
00243   /** \internal Do not unroll loops. */
00244   NoUnrolling,
00245   /** \internal Unroll only the inner loop, but not the outer loop. */
00246   InnerUnrolling,
00247   /** \internal Unroll both the inner and the outer loop. If there is only one loop, 
00248     * because linear traversal is used, then unroll that loop. */
00249   CompleteUnrolling
00250 };
00251 
00252 /** \internal \ingroup enums
00253   * Enum to specify whether to use the default (built-in) implementation or the specialization. */
00254 enum {
00255   Specialized,
00256   BuiltIn
00257 };
00258 
00259 /** \ingroup enums
00260   * Enum containing possible values for the \p _Options template parameter of
00261   * Matrix, Array and BandMatrix. */
00262 enum {
00263   /** Storage order is column major (see \ref TopicStorageOrders). */
00264   ColMajor = 0,
00265   /** Storage order is row major (see \ref TopicStorageOrders). */
00266   RowMajor = 0x1,  // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
00267   /** Align the matrix itself if it is vectorizable fixed-size */
00268   AutoAlign = 0,
00269   /** 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
00270   DontAlign = 0x2
00271 };
00272 
00273 /** \ingroup enums
00274   * Enum for specifying whether to apply or solve on the left or right. */
00275 enum {
00276   /** Apply transformation on the left. */
00277   OnTheLeft = 1,  
00278   /** Apply transformation on the right. */
00279   OnTheRight = 2  
00280 };
00281 
00282 /* the following used to be written as:
00283  *
00284  *   struct NoChange_t {};
00285  *   namespace {
00286  *     EIGEN_UNUSED NoChange_t NoChange;
00287  *   }
00288  *
00289  * on the ground that it feels dangerous to disambiguate overloaded functions on enum/integer types.  
00290  * However, this leads to "variable declared but never referenced" warnings on Intel Composer XE,
00291  * and we do not know how to get rid of them (bug 450).
00292  */
00293 
00294 enum NoChange_t   { NoChange };
00295 enum Sequential_t { Sequential };
00296 enum Default_t    { Default };
00297 
00298 /** \internal \ingroup enums
00299   * Used in AmbiVector. */
00300 enum {
00301   IsDense         = 0,
00302   IsSparse
00303 };
00304 
00305 /** \ingroup enums
00306   * Used as template parameter in DenseCoeffBase and MapBase to indicate 
00307   * which accessors should be provided. */
00308 enum AccessorLevels {
00309   /** Read-only access via a member function. */
00310   ReadOnlyAccessors, 
00311   /** Read/write access via member functions. */
00312   WriteAccessors, 
00313   /** Direct read-only access to the coefficients. */
00314   DirectAccessors, 
00315   /** Direct read/write access to the coefficients. */
00316   DirectWriteAccessors
00317 };
00318 
00319 /** \ingroup enums
00320   * Enum with options to give to various decompositions. */
00321 enum DecompositionOptions {
00322   /** \internal Not used (meant for LDLT?). */
00323   Pivoting            = 0x01, 
00324   /** \internal Not used (meant for LDLT?). */
00325   NoPivoting          = 0x02, 
00326   /** Used in JacobiSVD to indicate that the square matrix U is to be computed. */
00327   ComputeFullU        = 0x04,
00328   /** Used in JacobiSVD to indicate that the thin matrix U is to be computed. */
00329   ComputeThinU        = 0x08,
00330   /** Used in JacobiSVD to indicate that the square matrix V is to be computed. */
00331   ComputeFullV        = 0x10,
00332   /** Used in JacobiSVD to indicate that the thin matrix V is to be computed. */
00333   ComputeThinV        = 0x20,
00334   /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
00335     * that only the eigenvalues are to be computed and not the eigenvectors. */
00336   EigenvaluesOnly     = 0x40,
00337   /** Used in SelfAdjointEigenSolver and GeneralizedSelfAdjointEigenSolver to specify
00338     * that both the eigenvalues and the eigenvectors are to be computed. */
00339   ComputeEigenvectors = 0x80,
00340   /** \internal */
00341   EigVecMask = EigenvaluesOnly | ComputeEigenvectors,
00342   /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
00343     * solve the generalized eigenproblem \f$ Ax = \lambda B x \f$. */
00344   Ax_lBx              = 0x100,
00345   /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
00346     * solve the generalized eigenproblem \f$ ABx = \lambda x \f$. */
00347   ABx_lx              = 0x200,
00348   /** Used in GeneralizedSelfAdjointEigenSolver to indicate that it should
00349     * solve the generalized eigenproblem \f$ BAx = \lambda x \f$. */
00350   BAx_lx              = 0x400,
00351   /** \internal */
00352   GenEigMask = Ax_lBx | ABx_lx | BAx_lx
00353 };
00354 
00355 /** \ingroup enums
00356   * Possible values for the \p QRPreconditioner template parameter of JacobiSVD. */
00357 enum QRPreconditioners {
00358   /** Do not specify what is to be done if the SVD of a non-square matrix is asked for. */
00359   NoQRPreconditioner,
00360   /** Use a QR decomposition without pivoting as the first step. */
00361   HouseholderQRPreconditioner,
00362   /** Use a QR decomposition with column pivoting as the first step. */
00363   ColPivHouseholderQRPreconditioner,
00364   /** Use a QR decomposition with full pivoting as the first step. */
00365   FullPivHouseholderQRPreconditioner
00366 };
00367 
00368 #ifdef Success
00369 #error The preprocessor symbol 'Success' is defined, possibly by the X11 header file X.h
00370 #endif
00371 
00372 /** \ingroup enums
00373   * Enum for reporting the status of a computation. */
00374 enum ComputationInfo {
00375   /** Computation was successful. */
00376   Success = 0,        
00377   /** The provided data did not satisfy the prerequisites. */
00378   NumericalIssue = 1, 
00379   /** Iterative procedure did not converge. */
00380   NoConvergence = 2,
00381   /** The inputs are invalid, or the algorithm has been improperly called.
00382     * When assertions are enabled, such errors trigger an assert. */
00383   InvalidInput = 3
00384 };
00385 
00386 /** \ingroup enums
00387   * Enum used to specify how a particular transformation is stored in a matrix.
00388   * \sa Transform, Hyperplane::transform(). */
00389 enum TransformTraits {
00390   /** Transformation is an isometry. */
00391   Isometry      = 0x1,
00392   /** Transformation is an affine transformation stored as a (Dim+1)^2 matrix whose last row is 
00393     * assumed to be [0 ... 0 1]. */
00394   Affine        = 0x2,
00395   /** Transformation is an affine transformation stored as a (Dim) x (Dim+1) matrix. */
00396   AffineCompact = 0x10 | Affine,
00397   /** Transformation is a general projective transformation stored as a (Dim+1)^2 matrix. */
00398   Projective    = 0x20
00399 };
00400 
00401 /** \internal \ingroup enums
00402   * Enum used to choose between implementation depending on the computer architecture. */
00403 namespace Architecture
00404 {
00405   enum Type {
00406     Generic = 0x0,
00407     SSE = 0x1,
00408     AltiVec = 0x2,
00409 #if defined EIGEN_VECTORIZE_SSE
00410     Target = SSE
00411 #elif defined EIGEN_VECTORIZE_ALTIVEC
00412     Target = AltiVec
00413 #else
00414     Target = Generic
00415 #endif
00416   };
00417 }
00418 
00419 /** \internal \ingroup enums
00420   * Enum used as template parameter in GeneralProduct. */
00421 enum { CoeffBasedProductMode, LazyCoeffBasedProductMode, OuterProduct, InnerProduct, GemvProduct, GemmProduct };
00422 
00423 /** \internal \ingroup enums
00424   * Enum used in experimental parallel implementation. */
00425 enum Action {GetAction, SetAction};
00426 
00427 /** The type used to identify a dense storage. */
00428 struct Dense {};
00429 
00430 /** The type used to identify a matrix expression */
00431 struct MatrixXpr {};
00432 
00433 /** The type used to identify an array expression */
00434 struct ArrayXpr {};
00435 
00436 namespace internal {
00437   /** \internal
00438   * Constants for comparison functors
00439   */
00440   enum ComparisonName {
00441     cmp_EQ = 0,
00442     cmp_LT = 1,
00443     cmp_LE = 2,
00444     cmp_UNORD = 3,
00445     cmp_NEQ = 4
00446   };
00447 }
00448 
00449 } // end namespace Eigen
00450 
00451 #endif // EIGEN_CONSTANTS_H