1 /*
2  Copyright (c) 2011, Intel Corporation. All rights reserved.
3 
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21  (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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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
310