TriangularMatrixMatrix_MKL.h
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26 
27  ********************************************************************************
28  * Content : Eigen bindings to Intel(R) MKL
29  * Triangular matrix * matrix product functionality based on ?TRMM.
30  ********************************************************************************
31 */
32 
33 #ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
34 #define EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
35 
36 namespace Eigen {
37 
38 namespace internal {
39 
40 
41 template <typename Scalar, typename Index,
42  int Mode, bool LhsIsTriangular,
43  int LhsStorageOrder, bool ConjugateLhs,
44  int RhsStorageOrder, bool ConjugateRhs,
45  int ResStorageOrder>
46 struct product_triangular_matrix_matrix_trmm :
47  product_triangular_matrix_matrix<Scalar,Index,Mode,
48  LhsIsTriangular,LhsStorageOrder,ConjugateLhs,
49  RhsStorageOrder, ConjugateRhs, ResStorageOrder, BuiltIn> {};
50 
51 
52 // try to go to BLAS specialization
53 #define EIGEN_MKL_TRMM_SPECIALIZE(Scalar, LhsIsTriangular) \
54 template <typename Index, int Mode, \
55  int LhsStorageOrder, bool ConjugateLhs, \
56  int RhsStorageOrder, bool ConjugateRhs> \
57 struct product_triangular_matrix_matrix<Scalar,Index, Mode, LhsIsTriangular, \
58  LhsStorageOrder,ConjugateLhs, RhsStorageOrder,ConjugateRhs,ColMajor,Specialized> { \
59  static inline void run(Index _rows, Index _cols, Index _depth, const Scalar* _lhs, Index lhsStride,\
60  const Scalar* _rhs, Index rhsStride, Scalar* res, Index resStride, Scalar alpha) { \
61  product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \
62  LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \
63  RhsStorageOrder, ConjugateRhs, ColMajor>::run( \
64  _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
65  } \
66 };
67 
68 EIGEN_MKL_TRMM_SPECIALIZE(double, true)
69 EIGEN_MKL_TRMM_SPECIALIZE(double, false)
70 EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, true)
71 EIGEN_MKL_TRMM_SPECIALIZE(dcomplex, false)
72 EIGEN_MKL_TRMM_SPECIALIZE(float, true)
73 EIGEN_MKL_TRMM_SPECIALIZE(float, false)
74 EIGEN_MKL_TRMM_SPECIALIZE(scomplex, true)
75 EIGEN_MKL_TRMM_SPECIALIZE(scomplex, false)
76 
77 // implements col-major += alpha * op(triangular) * op(general)
78 #define EIGEN_MKL_TRMM_L(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
79 template <typename Index, int Mode, \
80  int LhsStorageOrder, bool ConjugateLhs, \
81  int RhsStorageOrder, bool ConjugateRhs> \
82 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \
83  LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
84 { \
85  enum { \
86  IsLower = (Mode&Lower) == Lower, \
87  SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
88  IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
89  IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
90  LowUp = IsLower ? Lower : Upper, \
91  conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \
92  }; \
93 \
94  static EIGEN_DONT_INLINE void run( \
95  Index _rows, Index _cols, Index _depth, \
96  const EIGTYPE* _lhs, Index lhsStride, \
97  const EIGTYPE* _rhs, Index rhsStride, \
98  EIGTYPE* res, Index resStride, \
99  EIGTYPE alpha) \
100  { \
101  Index diagSize = (std::min)(_rows,_depth); \
102  Index rows = IsLower ? _rows : diagSize; \
103  Index depth = IsLower ? diagSize : _depth; \
104  Index cols = _cols; \
105 \
106  typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
107  typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
108 \
109 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
110  if (rows != depth) { \
111 \
112  int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
113 \
114  if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \
115  /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
116  product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \
117  LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
118  _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
119  /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \
120  } else { \
121  /* Make sense to call GEMM */ \
122  Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \
123  MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \
124  MKL_INT aStride = aa_tmp.outerStride(); \
125  gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> blocking(_rows,_cols,_depth); \
126  general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
127  rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, resStride, alpha, blocking, 0); \
128 \
129  /*std::cout << "TRMM_L: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
130  } \
131  return; \
132  } \
133  char side = 'L', transa, uplo, diag = 'N'; \
134  EIGTYPE *b; \
135  const EIGTYPE *a; \
136  MKL_INT m, n, lda, ldb; \
137  MKLTYPE alpha_; \
138 \
139 /* Set alpha_*/ \
140  assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
141 \
142 /* Set m, n */ \
143  m = (MKL_INT)diagSize; \
144  n = (MKL_INT)cols; \
145 \
146 /* Set trans */ \
147  transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \
148 \
149 /* Set b, ldb */ \
150  Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \
151  MatrixX##EIGPREFIX b_tmp; \
152 \
153  if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \
154  b = b_tmp.data(); \
155  ldb = b_tmp.outerStride(); \
156 \
157 /* Set uplo */ \
158  uplo = IsLower ? 'L' : 'U'; \
159  if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
160 /* Set a, lda */ \
161  Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
162  MatrixLhs a_tmp; \
163 \
164  if ((conjA!=0) || (SetDiag==0)) { \
165  if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \
166  if (IsZeroDiag) \
167  a_tmp.diagonal().setZero(); \
168  else if (IsUnitDiag) \
169  a_tmp.diagonal().setOnes();\
170  a = a_tmp.data(); \
171  lda = a_tmp.outerStride(); \
172  } else { \
173  a = _lhs; \
174  lda = lhsStride; \
175  } \
176  /*std::cout << "TRMM_L: A is square! Go to MKL TRMM implementation! \n";*/ \
177 /* call ?trmm*/ \
178  MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
179 \
180 /* Add op(a_triangular)*b into res*/ \
181  Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
182  res_tmp=res_tmp+b_tmp; \
183  } \
184 };
185 
186 EIGEN_MKL_TRMM_L(double, double, d, d)
187 EIGEN_MKL_TRMM_L(dcomplex, MKL_Complex16, cd, z)
188 EIGEN_MKL_TRMM_L(float, float, f, s)
189 EIGEN_MKL_TRMM_L(scomplex, MKL_Complex8, cf, c)
190 
191 // implements col-major += alpha * op(general) * op(triangular)
192 #define EIGEN_MKL_TRMM_R(EIGTYPE, MKLTYPE, EIGPREFIX, MKLPREFIX) \
193 template <typename Index, int Mode, \
194  int LhsStorageOrder, bool ConjugateLhs, \
195  int RhsStorageOrder, bool ConjugateRhs> \
196 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \
197  LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \
198 { \
199  enum { \
200  IsLower = (Mode&Lower) == Lower, \
201  SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \
202  IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \
203  IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \
204  LowUp = IsLower ? Lower : Upper, \
205  conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \
206  }; \
207 \
208  static EIGEN_DONT_INLINE void run( \
209  Index _rows, Index _cols, Index _depth, \
210  const EIGTYPE* _lhs, Index lhsStride, \
211  const EIGTYPE* _rhs, Index rhsStride, \
212  EIGTYPE* res, Index resStride, \
213  EIGTYPE alpha) \
214  { \
215  Index diagSize = (std::min)(_cols,_depth); \
216  Index rows = _rows; \
217  Index depth = IsLower ? _depth : diagSize; \
218  Index cols = IsLower ? diagSize : _cols; \
219 \
220  typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \
221  typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \
222 \
223 /* Non-square case - doesn't fit to MKL ?TRMM. Fall to default triangular product or call MKL ?GEMM*/ \
224  if (cols != depth) { \
225 \
226  int nthr = mkl_domain_get_max_threads(MKL_BLAS); \
227 \
228  if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \
229  /* Most likely no benefit to call TRMM or GEMM from MKL*/ \
230  product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \
231  LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, BuiltIn>::run( \
232  _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha); \
233  /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \
234  } else { \
235  /* Make sense to call GEMM */ \
236  Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \
237  MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \
238  MKL_INT aStride = aa_tmp.outerStride(); \
239  gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> blocking(_rows,_cols,_depth); \
240  general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor>::run( \
241  rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, resStride, alpha, blocking, 0); \
242 \
243  /*std::cout << "TRMM_R: A is not square! Go to MKL GEMM implementation! " << nthr<<" \n";*/ \
244  } \
245  return; \
246  } \
247  char side = 'R', transa, uplo, diag = 'N'; \
248  EIGTYPE *b; \
249  const EIGTYPE *a; \
250  MKL_INT m, n, lda, ldb; \
251  MKLTYPE alpha_; \
252 \
253 /* Set alpha_*/ \
254  assign_scalar_eig2mkl<MKLTYPE, EIGTYPE>(alpha_, alpha); \
255 \
256 /* Set m, n */ \
257  m = (MKL_INT)rows; \
258  n = (MKL_INT)diagSize; \
259 \
260 /* Set trans */ \
261  transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \
262 \
263 /* Set b, ldb */ \
264  Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \
265  MatrixX##EIGPREFIX b_tmp; \
266 \
267  if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \
268  b = b_tmp.data(); \
269  ldb = b_tmp.outerStride(); \
270 \
271 /* Set uplo */ \
272  uplo = IsLower ? 'L' : 'U'; \
273  if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \
274 /* Set a, lda */ \
275  Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \
276  MatrixRhs a_tmp; \
277 \
278  if ((conjA!=0) || (SetDiag==0)) { \
279  if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \
280  if (IsZeroDiag) \
281  a_tmp.diagonal().setZero(); \
282  else if (IsUnitDiag) \
283  a_tmp.diagonal().setOnes();\
284  a = a_tmp.data(); \
285  lda = a_tmp.outerStride(); \
286  } else { \
287  a = _rhs; \
288  lda = rhsStride; \
289  } \
290  /*std::cout << "TRMM_R: A is square! Go to MKL TRMM implementation! \n";*/ \
291 /* call ?trmm*/ \
292  MKLPREFIX##trmm(&side, &uplo, &transa, &diag, &m, &n, &alpha_, (const MKLTYPE*)a, &lda, (MKLTYPE*)b, &ldb); \
293 \
294 /* Add op(a_triangular)*b into res*/ \
295  Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \
296  res_tmp=res_tmp+b_tmp; \
297  } \
298 };
299 
300 EIGEN_MKL_TRMM_R(double, double, d, d)
301 EIGEN_MKL_TRMM_R(dcomplex, MKL_Complex16, cd, z)
302 EIGEN_MKL_TRMM_R(float, float, f, s)
303 EIGEN_MKL_TRMM_R(scomplex, MKL_Complex8, cf, c)
304 
305 } // end namespace internal
306 
307 } // end namespace Eigen
308 
309 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_MKL_H
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