```/* <![CDATA[ */
2// for linear algebra.
3//
4// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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_GENERAL_PRODUCT_H
12#define EIGEN_GENERAL_PRODUCT_H
13
14namespace Eigen {
15
16/** \class GeneralProduct
17  * \ingroup Core_Module
18  *
19  * \brief Expression of the product of two general matrices or vectors
20  *
21  * \param LhsNested the type used to store the left-hand side
22  * \param RhsNested the type used to store the right-hand side
23  * \param ProductMode the type of the product
24  *
25  * This class represents an expression of the product of two general matrices.
26  * We call a general matrix, a dense matrix with full storage. For instance,
27  * This excludes triangular, selfadjoint, and sparse matrices.
28  * It is the return type of the operator* between general matrices. Its template
29  * arguments are determined automatically by ProductReturnType. Therefore,
30  * GeneralProduct should never be used direclty. To determine the result type of a
31  * function which involves a matrix product, use ProductReturnType::Type.
32  *
33  * \sa ProductReturnType, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
34  */
35template<typename Lhs, typename Rhs, int ProductType = internal::product_type<Lhs,Rhs>::value>
36class GeneralProduct;
37
38enum {
39  Large = 2,
40  Small = 3
41};
42
43namespace internal {
44
45template<int Rows, int Cols, int Depth> struct product_type_selector;
46
47template<int Size, int MaxSize> struct product_size_category
48{
49  enum { is_large = MaxSize == Dynamic ||
50                    Size >= EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD,
51         value = is_large  ? Large
52               : Size == 1 ? 1
53                           : Small
54  };
55};
56
57template<typename Lhs, typename Rhs> struct product_type
58{
59  typedef typename remove_all<Lhs>::type _Lhs;
60  typedef typename remove_all<Rhs>::type _Rhs;
61  enum {
62    MaxRows  = _Lhs::MaxRowsAtCompileTime,
63    Rows  = _Lhs::RowsAtCompileTime,
64    MaxCols  = _Rhs::MaxColsAtCompileTime,
65    Cols  = _Rhs::ColsAtCompileTime,
66    MaxDepth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::MaxColsAtCompileTime,
67                                           _Rhs::MaxRowsAtCompileTime),
68    Depth = EIGEN_SIZE_MIN_PREFER_FIXED(_Lhs::ColsAtCompileTime,
69                                        _Rhs::RowsAtCompileTime),
70    LargeThreshold = EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
71  };
72
73  // the splitting into different lines of code here, introducing the _select enums and the typedef below,
74  // is to work around an internal compiler error with gcc 4.1 and 4.2.
75private:
76  enum {
77    rows_select = product_size_category<Rows,MaxRows>::value,
78    cols_select = product_size_category<Cols,MaxCols>::value,
79    depth_select = product_size_category<Depth,MaxDepth>::value
80  };
81  typedef product_type_selector<rows_select, cols_select, depth_select> selector;
82
83public:
84  enum {
85    value = selector::ret
86  };
87#ifdef EIGEN_DEBUG_PRODUCT
88  static void debug()
89  {
90      EIGEN_DEBUG_VAR(Rows);
91      EIGEN_DEBUG_VAR(Cols);
92      EIGEN_DEBUG_VAR(Depth);
93      EIGEN_DEBUG_VAR(rows_select);
94      EIGEN_DEBUG_VAR(cols_select);
95      EIGEN_DEBUG_VAR(depth_select);
96      EIGEN_DEBUG_VAR(value);
97  }
98#endif
99};
100
101
102/* The following allows to select the kind of product at compile time
103 * based on the three dimensions of the product.
104 * This is a compile time mapping from {1,Small,Large}^3 -> {product types} */
105// FIXME I'm not sure the current mapping is the ideal one.
106template<int M, int N>  struct product_type_selector<M,N,1>              { enum { ret = OuterProduct }; };
107template<int Depth>     struct product_type_selector<1,    1,    Depth>  { enum { ret = InnerProduct }; };
108template<>              struct product_type_selector<1,    1,    1>      { enum { ret = InnerProduct }; };
109template<>              struct product_type_selector<Small,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
110template<>              struct product_type_selector<1,    Small,Small>  { enum { ret = CoeffBasedProductMode }; };
111template<>              struct product_type_selector<Small,Small,Small>  { enum { ret = CoeffBasedProductMode }; };
112template<>              struct product_type_selector<Small, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
113template<>              struct product_type_selector<Small, Large, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
114template<>              struct product_type_selector<Large, Small, 1>    { enum { ret = LazyCoeffBasedProductMode }; };
115template<>              struct product_type_selector<1,    Large,Small>  { enum { ret = CoeffBasedProductMode }; };
116template<>              struct product_type_selector<1,    Large,Large>  { enum { ret = GemvProduct }; };
117template<>              struct product_type_selector<1,    Small,Large>  { enum { ret = CoeffBasedProductMode }; };
118template<>              struct product_type_selector<Large,1,    Small>  { enum { ret = CoeffBasedProductMode }; };
119template<>              struct product_type_selector<Large,1,    Large>  { enum { ret = GemvProduct }; };
120template<>              struct product_type_selector<Small,1,    Large>  { enum { ret = CoeffBasedProductMode }; };
121template<>              struct product_type_selector<Small,Small,Large>  { enum { ret = GemmProduct }; };
122template<>              struct product_type_selector<Large,Small,Large>  { enum { ret = GemmProduct }; };
123template<>              struct product_type_selector<Small,Large,Large>  { enum { ret = GemmProduct }; };
124template<>              struct product_type_selector<Large,Large,Large>  { enum { ret = GemmProduct }; };
125template<>              struct product_type_selector<Large,Small,Small>  { enum { ret = GemmProduct }; };
126template<>              struct product_type_selector<Small,Large,Small>  { enum { ret = GemmProduct }; };
127template<>              struct product_type_selector<Large,Large,Small>  { enum { ret = GemmProduct }; };
128
129} // end namespace internal
130
131/** \class ProductReturnType
132  * \ingroup Core_Module
133  *
134  * \brief Helper class to get the correct and optimized returned type of operator*
135  *
136  * \param Lhs the type of the left-hand side
137  * \param Rhs the type of the right-hand side
138  * \param ProductMode the type of the product (determined automatically by internal::product_mode)
139  *
140  * This class defines the typename Type representing the optimized product expression
141  * between two matrix expressions. In practice, using ProductReturnType<Lhs,Rhs>::Type
142  * is the recommended way to define the result type of a function returning an expression
143  * which involve a matrix product. The class Product should never be
144  * used directly.
145  *
146  * \sa class Product, MatrixBase::operator*(const MatrixBase<OtherDerived>&)
147  */
148template<typename Lhs, typename Rhs, int ProductType>
149struct ProductReturnType
150{
151  // TODO use the nested type to reduce instanciations ????
152//   typedef typename internal::nested<Lhs,Rhs::ColsAtCompileTime>::type LhsNested;
153//   typedef typename internal::nested<Rhs,Lhs::RowsAtCompileTime>::type RhsNested;
154
155  typedef GeneralProduct<Lhs/*Nested*/, Rhs/*Nested*/, ProductType> Type;
156};
157
158template<typename Lhs, typename Rhs>
159struct ProductReturnType<Lhs,Rhs,CoeffBasedProductMode>
160{
161  typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
162  typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
163  typedef CoeffBasedProduct<LhsNested, RhsNested, EvalBeforeAssigningBit | EvalBeforeNestingBit> Type;
164};
165
166template<typename Lhs, typename Rhs>
167struct ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
168{
169  typedef typename internal::nested<Lhs, Rhs::ColsAtCompileTime, typename internal::plain_matrix_type<Lhs>::type >::type LhsNested;
170  typedef typename internal::nested<Rhs, Lhs::RowsAtCompileTime, typename internal::plain_matrix_type<Rhs>::type >::type RhsNested;
171  typedef CoeffBasedProduct<LhsNested, RhsNested, NestByRefBit> Type;
172};
173
174// this is a workaround for sun CC
175template<typename Lhs, typename Rhs>
176struct LazyProductReturnType : public ProductReturnType<Lhs,Rhs,LazyCoeffBasedProductMode>
177{};
178
179/***********************************************************************
180*  Implementation of Inner Vector Vector Product
181***********************************************************************/
182
183// FIXME : maybe the "inner product" could return a Scalar
184// instead of a 1x1 matrix ??
185// Pro: more natural for the user
186// Cons: this could be a problem if in a meta unrolled algorithm a matrix-matrix
187// product ends up to a row-vector times col-vector product... To tackle this use
188// case, we could have a specialization for Block<MatrixType,1,1> with: operator=(Scalar x);
189
190namespace internal {
191
192template<typename Lhs, typename Rhs>
193struct traits<GeneralProduct<Lhs,Rhs,InnerProduct> >
194 : traits<Matrix<typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> >
195{};
196
197}
198
199template<typename Lhs, typename Rhs>
200class GeneralProduct<Lhs, Rhs, InnerProduct>
201  : internal::no_assignment_operator,
202    public Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1>
203{
204    typedef Matrix<typename internal::scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType,1,1> Base;
205  public:
206    GeneralProduct(const Lhs& lhs, const Rhs& rhs)
207    {
208      EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
209        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
210
211      Base::coeffRef(0,0) = (lhs.transpose().cwiseProduct(rhs)).sum();
212    }
213
214    /** Convertion to scalar */
215    operator const typename Base::Scalar() const {
216      return Base::coeff(0,0);
217    }
218};
219
220/***********************************************************************
221*  Implementation of Outer Vector Vector Product
222***********************************************************************/
223
224namespace internal {
225
226// Column major
227template<typename ProductType, typename Dest, typename Func>
228EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const false_type&)
229{
230  typedef typename Dest::Index Index;
231  // FIXME make sure lhs is sequentially stored
232  // FIXME not very good if rhs is real and lhs complex while alpha is real too
233  const Index cols = dest.cols();
234  for (Index j=0; j<cols; ++j)
235    func(dest.col(j), prod.rhs().coeff(j) * prod.lhs());
236}
237
238// Row major
239template<typename ProductType, typename Dest, typename Func>
240EIGEN_DONT_INLINE void outer_product_selector_run(const ProductType& prod, Dest& dest, const Func& func, const true_type&) {
241  typedef typename Dest::Index Index;
242  // FIXME make sure rhs is sequentially stored
243  // FIXME not very good if lhs is real and rhs complex while alpha is real too
244  const Index rows = dest.rows();
245  for (Index i=0; i<rows; ++i)
246    func(dest.row(i), prod.lhs().coeff(i) * prod.rhs());
247}
248
249template<typename Lhs, typename Rhs>
250struct traits<GeneralProduct<Lhs,Rhs,OuterProduct> >
251 : traits<ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs> >
252{};
253
254}
255
256template<typename Lhs, typename Rhs>
257class GeneralProduct<Lhs, Rhs, OuterProduct>
258  : public ProductBase<GeneralProduct<Lhs,Rhs,OuterProduct>, Lhs, Rhs>
259{
260    template<typename T> struct IsRowMajor : internal::conditional<(int(T::Flags)&RowMajorBit), internal::true_type, internal::false_type>::type {};
261
262  public:
263    EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
264
265    GeneralProduct(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs)
266    {
267      EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::RealScalar, typename Rhs::RealScalar>::value),
268        YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
269    }
270
271    struct set  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived()  = src; } };
272    struct add  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() += src; } };
273    struct sub  { template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const { dst.const_cast_derived() -= src; } };
275      Scalar m_scale;
276      adds(const Scalar& s) : m_scale(s) {}
277      template<typename Dst, typename Src> void operator()(const Dst& dst, const Src& src) const {
278        dst.const_cast_derived() += m_scale * src;
279      }
280    };
281
282    template<typename Dest>
283    inline void evalTo(Dest& dest) const {
284      internal::outer_product_selector_run(*this, dest, set(), IsRowMajor<Dest>());
285    }
286
287    template<typename Dest>
288    inline void addTo(Dest& dest) const {
290    }
291
292    template<typename Dest>
293    inline void subTo(Dest& dest) const {
294      internal::outer_product_selector_run(*this, dest, sub(), IsRowMajor<Dest>());
295    }
296
297    template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
298    {
300    }
301};
302
303/***********************************************************************
304*  Implementation of General Matrix Vector Product
305***********************************************************************/
306
307/*  According to the shape/flags of the matrix we have to distinghish 3 different cases:
308 *   1 - the matrix is col-major, BLAS compatible and M is large => call fast BLAS-like colmajor routine
309 *   2 - the matrix is row-major, BLAS compatible and N is large => call fast BLAS-like rowmajor routine
310 *   3 - all other cases are handled using a simple loop along the outer-storage direction.
311 *  Therefore we need a lower level meta selector.
312 *  Furthermore, if the matrix is the rhs, then the product has to be transposed.
313 */
314namespace internal {
315
316template<typename Lhs, typename Rhs>
317struct traits<GeneralProduct<Lhs,Rhs,GemvProduct> >
318 : traits<ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs> >
319{};
320
321template<int Side, int StorageOrder, bool BlasCompatible>
322struct gemv_selector;
323
324} // end namespace internal
325
326template<typename Lhs, typename Rhs>
327class GeneralProduct<Lhs, Rhs, GemvProduct>
328  : public ProductBase<GeneralProduct<Lhs,Rhs,GemvProduct>, Lhs, Rhs>
329{
330  public:
331    EIGEN_PRODUCT_PUBLIC_INTERFACE(GeneralProduct)
332
333    typedef typename Lhs::Scalar LhsScalar;
334    typedef typename Rhs::Scalar RhsScalar;
335
336    GeneralProduct(const Lhs& a_lhs, const Rhs& a_rhs) : Base(a_lhs,a_rhs)
337    {
338//       EIGEN_STATIC_ASSERT((internal::is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value),
339//         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
340    }
341
342    enum { Side = Lhs::IsVectorAtCompileTime ? OnTheLeft : OnTheRight };
343    typedef typename internal::conditional<int(Side)==OnTheRight,_LhsNested,_RhsNested>::type MatrixType;
344
345    template<typename Dest> void scaleAndAddTo(Dest& dst, const Scalar& alpha) const
346    {
347      eigen_assert(m_lhs.rows() == dst.rows() && m_rhs.cols() == dst.cols());
348      internal::gemv_selector<Side,(int(MatrixType::Flags)&RowMajorBit) ? RowMajor : ColMajor,
349                       bool(internal::blas_traits<MatrixType>::HasUsableDirectAccess)>::run(*this, dst, alpha);
350    }
351};
352
353namespace internal {
354
355// The vector is on the left => transposition
356template<int StorageOrder, bool BlasCompatible>
357struct gemv_selector<OnTheLeft,StorageOrder,BlasCompatible>
358{
359  template<typename ProductType, typename Dest>
360  static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
361  {
362    Transpose<Dest> destT(dest);
363    enum { OtherStorageOrder = StorageOrder == RowMajor ? ColMajor : RowMajor };
364    gemv_selector<OnTheRight,OtherStorageOrder,BlasCompatible>
365      ::run(GeneralProduct<Transpose<const typename ProductType::_RhsNested>,Transpose<const typename ProductType::_LhsNested>, GemvProduct>
366        (prod.rhs().transpose(), prod.lhs().transpose()), destT, alpha);
367  }
368};
369
370template<typename Scalar,int Size,int MaxSize,bool Cond> struct gemv_static_vector_if;
371
372template<typename Scalar,int Size,int MaxSize>
373struct gemv_static_vector_if<Scalar,Size,MaxSize,false>
374{
375  EIGEN_STRONG_INLINE  Scalar* data() { eigen_internal_assert(false && "should never be called"); return 0; }
376};
377
378template<typename Scalar,int Size>
379struct gemv_static_vector_if<Scalar,Size,Dynamic,true>
380{
381  EIGEN_STRONG_INLINE Scalar* data() { return 0; }
382};
383
384template<typename Scalar,int Size,int MaxSize>
385struct gemv_static_vector_if<Scalar,Size,MaxSize,true>
386{
387  #if EIGEN_ALIGN_STATICALLY
388  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize),0> m_data;
389  EIGEN_STRONG_INLINE Scalar* data() { return m_data.array; }
390  #else
391  // Some architectures cannot align on the stack,
392  // => let's manually enforce alignment by allocating more data and return the address of the first aligned element.
393  enum {
394    ForceAlignment  = internal::packet_traits<Scalar>::Vectorizable,
395    PacketSize      = internal::packet_traits<Scalar>::size
396  };
397  internal::plain_array<Scalar,EIGEN_SIZE_MIN_PREFER_FIXED(Size,MaxSize)+(ForceAlignment?PacketSize:0),0> m_data;
398  EIGEN_STRONG_INLINE Scalar* data() {
399    return ForceAlignment
400            ? reinterpret_cast<Scalar*>((reinterpret_cast<size_t>(m_data.array) & ~(size_t(15))) + 16)
401            : m_data.array;
402  }
403  #endif
404};
405
406template<> struct gemv_selector<OnTheRight,ColMajor,true>
407{
408  template<typename ProductType, typename Dest>
409  static inline void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
410  {
411    typedef typename ProductType::Index Index;
412    typedef typename ProductType::LhsScalar   LhsScalar;
413    typedef typename ProductType::RhsScalar   RhsScalar;
414    typedef typename ProductType::Scalar      ResScalar;
415    typedef typename ProductType::RealScalar  RealScalar;
416    typedef typename ProductType::ActualLhsType ActualLhsType;
417    typedef typename ProductType::ActualRhsType ActualRhsType;
418    typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
419    typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
420    typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
421
422    ActualLhsType actualLhs = LhsBlasTraits::extract(prod.lhs());
423    ActualRhsType actualRhs = RhsBlasTraits::extract(prod.rhs());
424
425    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
426                                  * RhsBlasTraits::extractScalarFactor(prod.rhs());
427
428    enum {
429      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
430      // on, the other hand it is good for the cache to pack the vector anyways...
431      EvalToDestAtCompileTime = Dest::InnerStrideAtCompileTime==1,
432      ComplexByReal = (NumTraits<LhsScalar>::IsComplex) && (!NumTraits<RhsScalar>::IsComplex),
433      MightCannotUseDest = (Dest::InnerStrideAtCompileTime!=1) || ComplexByReal
434    };
435
436    gemv_static_vector_if<ResScalar,Dest::SizeAtCompileTime,Dest::MaxSizeAtCompileTime,MightCannotUseDest> static_dest;
437
438    bool alphaIsCompatible = (!ComplexByReal) || (numext::imag(actualAlpha)==RealScalar(0));
439    bool evalToDest = EvalToDestAtCompileTime && alphaIsCompatible;
440
441    RhsScalar compatibleAlpha = get_factor<ResScalar,RhsScalar>::run(actualAlpha);
442
443    ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
444                                                  evalToDest ? dest.data() : static_dest.data());
445
446    if(!evalToDest)
447    {
448      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
449      int size = dest.size();
450      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
451      #endif
452      if(!alphaIsCompatible)
453      {
454        MappedDest(actualDestPtr, dest.size()).setZero();
455        compatibleAlpha = RhsScalar(1);
456      }
457      else
458        MappedDest(actualDestPtr, dest.size()) = dest;
459    }
460
461    general_matrix_vector_product
462      <Index,LhsScalar,ColMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
463        actualLhs.rows(), actualLhs.cols(),
464        actualLhs.data(), actualLhs.outerStride(),
465        actualRhs.data(), actualRhs.innerStride(),
466        actualDestPtr, 1,
467        compatibleAlpha);
468
469    if (!evalToDest)
470    {
471      if(!alphaIsCompatible)
472        dest += actualAlpha * MappedDest(actualDestPtr, dest.size());
473      else
474        dest = MappedDest(actualDestPtr, dest.size());
475    }
476  }
477};
478
479template<> struct gemv_selector<OnTheRight,RowMajor,true>
480{
481  template<typename ProductType, typename Dest>
482  static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
483  {
484    typedef typename ProductType::LhsScalar LhsScalar;
485    typedef typename ProductType::RhsScalar RhsScalar;
486    typedef typename ProductType::Scalar    ResScalar;
487    typedef typename ProductType::Index Index;
488    typedef typename ProductType::ActualLhsType ActualLhsType;
489    typedef typename ProductType::ActualRhsType ActualRhsType;
490    typedef typename ProductType::_ActualRhsType _ActualRhsType;
491    typedef typename ProductType::LhsBlasTraits LhsBlasTraits;
492    typedef typename ProductType::RhsBlasTraits RhsBlasTraits;
493
494    typename add_const<ActualLhsType>::type actualLhs = LhsBlasTraits::extract(prod.lhs());
495    typename add_const<ActualRhsType>::type actualRhs = RhsBlasTraits::extract(prod.rhs());
496
497    ResScalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(prod.lhs())
498                                  * RhsBlasTraits::extractScalarFactor(prod.rhs());
499
500    enum {
501      // FIXME find a way to allow an inner stride on the result if packet_traits<Scalar>::size==1
502      // on, the other hand it is good for the cache to pack the vector anyways...
503      DirectlyUseRhs = _ActualRhsType::InnerStrideAtCompileTime==1
504    };
505
506    gemv_static_vector_if<RhsScalar,_ActualRhsType::SizeAtCompileTime,_ActualRhsType::MaxSizeAtCompileTime,!DirectlyUseRhs> static_rhs;
507
508    ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,actualRhs.size(),
509        DirectlyUseRhs ? const_cast<RhsScalar*>(actualRhs.data()) : static_rhs.data());
510
511    if(!DirectlyUseRhs)
512    {
513      #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
514      int size = actualRhs.size();
515      EIGEN_DENSE_STORAGE_CTOR_PLUGIN
516      #endif
517      Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, actualRhs.size()) = actualRhs;
518    }
519
520    general_matrix_vector_product
521      <Index,LhsScalar,RowMajor,LhsBlasTraits::NeedToConjugate,RhsScalar,RhsBlasTraits::NeedToConjugate>::run(
522        actualLhs.rows(), actualLhs.cols(),
523        actualLhs.data(), actualLhs.outerStride(),
524        actualRhsPtr, 1,
525        dest.data(), dest.innerStride(),
526        actualAlpha);
527  }
528};
529
530template<> struct gemv_selector<OnTheRight,ColMajor,false>
531{
532  template<typename ProductType, typename Dest>
533  static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
534  {
535    typedef typename Dest::Index Index;
536    // TODO makes sure dest is sequentially stored in memory, otherwise use a temp
537    const Index size = prod.rhs().rows();
538    for(Index k=0; k<size; ++k)
539      dest += (alpha*prod.rhs().coeff(k)) * prod.lhs().col(k);
540  }
541};
542
543template<> struct gemv_selector<OnTheRight,RowMajor,false>
544{
545  template<typename ProductType, typename Dest>
546  static void run(const ProductType& prod, Dest& dest, const typename ProductType::Scalar& alpha)
547  {
548    typedef typename Dest::Index Index;
549    // TODO makes sure rhs is sequentially stored in memory, otherwise use a temp
550    const Index rows = prod.rows();
551    for(Index i=0; i<rows; ++i)
552      dest.coeffRef(i) += alpha * (prod.lhs().row(i).cwiseProduct(prod.rhs().transpose())).sum();
553  }
554};
555
556} // end namespace internal
557
558/***************************************************************************
559* Implementation of matrix base methods
560***************************************************************************/
561
562/** \returns the matrix product of \c *this and \a other.
563  *
564  * \note If instead of the matrix product you want the coefficient-wise product, see Cwise::operator*().
565  *
566  * \sa lazyProduct(), operator*=(const MatrixBase&), Cwise::operator*()
567  */
568template<typename Derived>
569template<typename OtherDerived>
570inline const typename ProductReturnType<Derived, OtherDerived>::Type
571MatrixBase<Derived>::operator*(const MatrixBase<OtherDerived> &other) const
572{
573  // A note regarding the function declaration: In MSVC, this function will sometimes
574  // not be inlined since DenseStorage is an unwindable object for dynamic
575  // matrices and product types are holding a member to store the result.
576  // Thus it does not help tagging this function with EIGEN_STRONG_INLINE.
577  enum {
578    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
579                   || OtherDerived::RowsAtCompileTime==Dynamic
580                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
581    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
582    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
583  };
584  // note to the lost user:
585  //    * for a dot product use: v1.dot(v2)
586  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
587  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
588    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
589  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
590    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
591  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
592#ifdef EIGEN_DEBUG_PRODUCT
593  internal::product_type<Derived,OtherDerived>::debug();
594#endif
595  return typename ProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
596}
597
598/** \returns an expression of the matrix product of \c *this and \a other without implicit evaluation.
599  *
600  * The returned product will behave like any other expressions: the coefficients of the product will be
601  * computed once at a time as requested. This might be useful in some extremely rare cases when only
602  * a small and no coherent fraction of the result's coefficients have to be computed.
603  *
604  * \warning This version of the matrix product can be much much slower. So use it only if you know
605  * what you are doing and that you measured a true speed improvement.
606  *
607  * \sa operator*(const MatrixBase&)
608  */
609template<typename Derived>
610template<typename OtherDerived>
611const typename LazyProductReturnType<Derived,OtherDerived>::Type
612MatrixBase<Derived>::lazyProduct(const MatrixBase<OtherDerived> &other) const
613{
614  enum {
615    ProductIsValid =  Derived::ColsAtCompileTime==Dynamic
616                   || OtherDerived::RowsAtCompileTime==Dynamic
617                   || int(Derived::ColsAtCompileTime)==int(OtherDerived::RowsAtCompileTime),
618    AreVectors = Derived::IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime,
619    SameSizes = EIGEN_PREDICATE_SAME_MATRIX_SIZE(Derived,OtherDerived)
620  };
621  // note to the lost user:
622  //    * for a dot product use: v1.dot(v2)
623  //    * for a coeff-wise product use: v1.cwiseProduct(v2)
624  EIGEN_STATIC_ASSERT(ProductIsValid || !(AreVectors && SameSizes),
625    INVALID_VECTOR_VECTOR_PRODUCT__IF_YOU_WANTED_A_DOT_OR_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTIONS)
626  EIGEN_STATIC_ASSERT(ProductIsValid || !(SameSizes && !AreVectors),
627    INVALID_MATRIX_PRODUCT__IF_YOU_WANTED_A_COEFF_WISE_PRODUCT_YOU_MUST_USE_THE_EXPLICIT_FUNCTION)
628  EIGEN_STATIC_ASSERT(ProductIsValid || SameSizes, INVALID_MATRIX_PRODUCT)
629
630  return typename LazyProductReturnType<Derived,OtherDerived>::Type(derived(), other.derived());
631}
632
633} // end namespace Eigen
634
635#endif // EIGEN_PRODUCT_H
636```