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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2006-2008 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/>.


/** This value means that a quantity is not known at compile-time, and that instead the value is
  * stored in some runtime variable.
  * Explanation for the choice of this value:
  * - It should be positive and larger than any reasonable compile-time-fixed number of rows or columns.
  *   This allows to simplify many compile-time conditions throughout Eigen.
  * - It should be smaller than the sqrt of INT_MAX. Indeed, we often multiply a number of rows with a number
  *   of columns in order to compute a number of coefficients. Even if we guard that with an "if" checking whether
  *   the values are Dynamic, we still get a compiler warning "integer overflow". So the only way to get around
  *   it would be a meta-selector. Doing this everywhere would reduce code readability and lenghten compilation times.
  *   Also, disabling compiler warnings for integer overflow, sounds like a bad idea.
  * If you wish to port Eigen to a platform where sizeof(int)==2, it is perfectly possible to set Dynamic to, say, 100.
const int Dynamic = 10000;

/** 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. */
00069 const unsigned int RowMajorBit = 0x1;

/** \ingroup flags
  * means the expression should be evaluated by the calling expression */
00074 const unsigned int EvalBeforeNestingBit = 0x2;

/** \ingroup flags
  * means the expression should be evaluated before any assignement */
00079 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 the total size of the coefficients
  * array is a multiple of the packet size, so that it is possible to access all the
  * coefficients by packets. In the dynamic-size case, there is no such condition
  * on the total size, so it might not be possible to access the few last coeffs
  * by packets.
  * \note This bit can be set regardless of whether vectorization is actually enabled.
  *       To check for actual vectorizability, see \a ActualPacketAccessBit.
00097 const unsigned int PacketAccessBit = 0x8;

/** \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;
const unsigned int ActualPacketAccessBit = 0x0;

/** \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.
00133 const unsigned int LinearAccessBit = 0x10;

/** \ingroup flags
  * Means that the underlying array of coefficients can be directly accessed. This means two things.
  * First, references to the coefficients must be available through coeffRef(int, int). This rules out read-only
  * expressions whose coefficients are computed on demand by coeff(int, int). Second, the memory layout of the
  * array of coefficients must be exactly the natural one suggested by rows(), cols(), stride(), and the RowMajorBit.
  * This rules out expressions such as DiagonalCoeffs, whose coefficients, though referencable, do not have
  * such a regular memory layout.
00144 const unsigned int DirectAccessBit = 0x20;

/** \ingroup flags
  * means the first coefficient packet is guaranteed to be aligned */
00149 const unsigned int AlignedBit = 0x40;

/** \ingroup flags
  * means all diagonal coefficients are equal to 0 */
00154 const unsigned int ZeroDiagBit = 0x80;

/** \ingroup flags
  * means all diagonal coefficients are equal to 1 */
00159 const unsigned int UnitDiagBit = 0x100;

/** \ingroup flags
  * means the matrix is selfadjoint (M=M*). */
00164 const unsigned int SelfAdjointBit = 0x200;

/** \ingroup flags
  * means the strictly lower triangular part is 0 */
00169 const unsigned int UpperTriangularBit = 0x400;

/** \ingroup flags
  * means the strictly upper triangular part is 0 */
00174 const unsigned int LowerTriangularBit = 0x800;

/** \ingroup flags
  * means the expression includes sparse matrices and the sparse path has to be taken. */
00179 const unsigned int SparseBit = 0x1000;

// list of flags that are inherited by default
const unsigned int HereditaryBits = RowMajorBit
                                  | EvalBeforeNestingBit
                                  | EvalBeforeAssigningBit
                                  | SparseBit;

// Possible values for the Mode parameter of part() and of extract()
const unsigned int UpperTriangular = UpperTriangularBit;
const unsigned int StrictlyUpperTriangular = UpperTriangularBit | ZeroDiagBit;
const unsigned int LowerTriangular = LowerTriangularBit;
const unsigned int StrictlyLowerTriangular = LowerTriangularBit | ZeroDiagBit;
const unsigned int SelfAdjoint = SelfAdjointBit;

// additional possible values for the Mode parameter of extract()
const unsigned int UnitUpperTriangular = UpperTriangularBit | UnitDiagBit;
const unsigned int UnitLowerTriangular = LowerTriangularBit | UnitDiagBit;
const unsigned int Diagonal = UpperTriangular | LowerTriangular;

enum { Aligned, Unaligned };
enum { ForceAligned, AsRequested };
enum { ConditionalJumpCost = 5 };
enum CornerType { TopLeft, TopRight, BottomLeft, BottomRight };
enum DirectionType { Vertical, Horizontal };
enum ProductEvaluationMode { NormalProduct, CacheFriendlyProduct, DiagonalProduct, SparseTimeSparseProduct, SparseTimeDenseProduct, DenseTimeSparseProduct };

enum {
  /** \internal Equivalent to a slice vectorization for fixed-size matrices having good alignment
    * and good size */
  /** \internal Vectorization path using a single loop plus scalar loops for the
    * unaligned boundaries */
  /** \internal Generic vectorization path using one vectorized loop per row/column with some
    * scalar loops to handle the unaligned boundaries */

enum {

enum {
  ColMajor = 0,
  RowMajor = 0x1,  // it is only a coincidence that this is equal to RowMajorBit -- don't rely on that
  /** \internal Don't require alignment for the matrix itself (the array of coefficients, if dynamically allocated, may still be
                requested to be aligned) */
  DontAlign = 0,
  /** \internal Align the matrix itself if it is vectorizable fixed-size */
  AutoAlign = 0x2

enum {
  IsDense         = 0,
  IsSparse        = SparseBit,
  NoDirectAccess  = 0,
  HasDirectAccess = DirectAccessBit

const int EiArch_Generic = 0x0;
const int EiArch_SSE     = 0x1;
const int EiArch_AltiVec = 0x2;

  const int EiArch = EiArch_SSE;
  const int EiArch = EiArch_AltiVec;
  const int EiArch = EiArch_Generic;


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