1 /* 2 Copyright (c) 2011, Intel Corporation. All rights reserved. 3 4 Redistribution and use in source and binary forms, with or without modification, 5 are permitted provided that the following conditions are met: 6 7 * Redistributions of source code must retain the above copyright notice, this 8 list of conditions and the following disclaimer. 9 * Redistributions in binary form must reproduce the above copyright notice, 10 this list of conditions and the following disclaimer in the documentation 11 and/or other materials provided with the distribution. 12 * Neither the name of Intel Corporation nor the names of its contributors may 13 be used to endorse or promote products derived from this software without 14 specific prior written permission. 15 16 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND 17 ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 18 WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 19 DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR 20 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 21 (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 22 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON 23 ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 24 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 25 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 26 27 ******************************************************************************** 28 * Content : Eigen bindings to BLAS F77 29 * Triangular matrix * matrix product functionality based on ?TRMM. 30 ******************************************************************************** 31 */ 32 33 #ifndef EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H 34 #define EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_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, 1, BuiltIn> {}; 50 51 52 // try to go to BLAS specialization 53 #define EIGEN_BLAS_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,1,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 resIncr, Index resStride, Scalar alpha, level3_blocking<Scalar,Scalar>& blocking) { \ 61 EIGEN_ONLY_USED_FOR_DEBUG(resIncr); \ 62 eigen_assert(resIncr == 1); \ 63 product_triangular_matrix_matrix_trmm<Scalar,Index,Mode, \ 64 LhsIsTriangular,LhsStorageOrder,ConjugateLhs, \ 65 RhsStorageOrder, ConjugateRhs, ColMajor>::run( \ 66 _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, resStride, alpha, blocking); \ 67 } \ 68 }; 69 70 EIGEN_BLAS_TRMM_SPECIALIZE(double, true) 71 EIGEN_BLAS_TRMM_SPECIALIZE(double, false) 72 EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, true) 73 EIGEN_BLAS_TRMM_SPECIALIZE(dcomplex, false) 74 EIGEN_BLAS_TRMM_SPECIALIZE(float, true) 75 EIGEN_BLAS_TRMM_SPECIALIZE(float, false) 76 EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, true) 77 EIGEN_BLAS_TRMM_SPECIALIZE(scomplex, false) 78 79 // implements col-major += alpha * op(triangular) * op(general) 80 #define EIGEN_BLAS_TRMM_L(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \ 81 template <typename Index, int Mode, \ 82 int LhsStorageOrder, bool ConjugateLhs, \ 83 int RhsStorageOrder, bool ConjugateRhs> \ 84 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,true, \ 85 LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \ 86 { \ 87 enum { \ 88 IsLower = (Mode&Lower) == Lower, \ 89 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \ 90 IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \ 91 IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \ 92 LowUp = IsLower ? Lower : Upper, \ 93 conjA = ((LhsStorageOrder==ColMajor) && ConjugateLhs) ? 1 : 0 \ 94 }; \ 95 \ 96 static void run( \ 97 Index _rows, Index _cols, Index _depth, \ 98 const EIGTYPE* _lhs, Index lhsStride, \ 99 const EIGTYPE* _rhs, Index rhsStride, \ 100 EIGTYPE* res, Index resStride, \ 101 EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \ 102 { \ 103 Index diagSize = (std::min)(_rows,_depth); \ 104 Index rows = IsLower ? _rows : diagSize; \ 105 Index depth = IsLower ? diagSize : _depth; \ 106 Index cols = _cols; \ 107 \ 108 typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \ 109 typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \ 110 \ 111 /* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \ 112 if (rows != depth) { \ 113 \ 114 /* FIXME handle mkl_domain_get_max_threads */ \ 115 /*int nthr = mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS);*/ int nthr = 1;\ 116 \ 117 if (((nthr==1) && (((std::max)(rows,depth)-diagSize)/(double)diagSize < 0.5))) { \ 118 /* Most likely no benefit to call TRMM or GEMM from BLAS */ \ 119 product_triangular_matrix_matrix<EIGTYPE,Index,Mode,true, \ 120 LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \ 121 _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \ 122 /*std::cout << "TRMM_L: A is not square! Go to Eigen TRMM implementation!\n";*/ \ 123 } else { \ 124 /* Make sense to call GEMM */ \ 125 Map<const MatrixLhs, 0, OuterStride<> > lhsMap(_lhs,rows,depth,OuterStride<>(lhsStride)); \ 126 MatrixLhs aa_tmp=lhsMap.template triangularView<Mode>(); \ 127 BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \ 128 gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \ 129 general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \ 130 rows, cols, depth, aa_tmp.data(), aStride, _rhs, rhsStride, res, 1, resStride, alpha, gemm_blocking, 0); \ 131 \ 132 /*std::cout << "TRMM_L: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \ 133 } \ 134 return; \ 135 } \ 136 char side = 'L', transa, uplo, diag = 'N'; \ 137 EIGTYPE *b; \ 138 const EIGTYPE *a; \ 139 BlasIndex m, n, lda, ldb; \ 140 \ 141 /* Set m, n */ \ 142 m = convert_index<BlasIndex>(diagSize); \ 143 n = convert_index<BlasIndex>(cols); \ 144 \ 145 /* Set trans */ \ 146 transa = (LhsStorageOrder==RowMajor) ? ((ConjugateLhs) ? 'C' : 'T') : 'N'; \ 147 \ 148 /* Set b, ldb */ \ 149 Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols,OuterStride<>(rhsStride)); \ 150 MatrixX##EIGPREFIX b_tmp; \ 151 \ 152 if (ConjugateRhs) b_tmp = rhs.conjugate(); else b_tmp = rhs; \ 153 b = b_tmp.data(); \ 154 ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \ 155 \ 156 /* Set uplo */ \ 157 uplo = IsLower ? 'L' : 'U'; \ 158 if (LhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \ 159 /* Set a, lda */ \ 160 Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \ 161 MatrixLhs a_tmp; \ 162 \ 163 if ((conjA!=0) || (SetDiag==0)) { \ 164 if (conjA) a_tmp = lhs.conjugate(); else a_tmp = lhs; \ 165 if (IsZeroDiag) \ 166 a_tmp.diagonal().setZero(); \ 167 else if (IsUnitDiag) \ 168 a_tmp.diagonal().setOnes();\ 169 a = a_tmp.data(); \ 170 lda = convert_index<BlasIndex>(a_tmp.outerStride()); \ 171 } else { \ 172 a = _lhs; \ 173 lda = convert_index<BlasIndex>(lhsStride); \ 174 } \ 175 /*std::cout << "TRMM_L: A is square! Go to BLAS TRMM implementation! \n";*/ \ 176 /* call ?trmm*/ \ 177 BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \ 178 \ 179 /* Add op(a_triangular)*b into res*/ \ 180 Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \ 181 res_tmp=res_tmp+b_tmp; \ 182 } \ 183 }; 184 185 #ifdef EIGEN_USE_MKL 186 EIGEN_BLAS_TRMM_L(double, double, d, dtrmm) 187 EIGEN_BLAS_TRMM_L(dcomplex, MKL_Complex16, cd, ztrmm) 188 EIGEN_BLAS_TRMM_L(float, float, f, strmm) 189 EIGEN_BLAS_TRMM_L(scomplex, MKL_Complex8, cf, ctrmm) 190 #else 191 EIGEN_BLAS_TRMM_L(double, double, d, dtrmm_) 192 EIGEN_BLAS_TRMM_L(dcomplex, double, cd, ztrmm_) 193 EIGEN_BLAS_TRMM_L(float, float, f, strmm_) 194 EIGEN_BLAS_TRMM_L(scomplex, float, cf, ctrmm_) 195 #endif 196 197 // implements col-major += alpha * op(general) * op(triangular) 198 #define EIGEN_BLAS_TRMM_R(EIGTYPE, BLASTYPE, EIGPREFIX, BLASFUNC) \ 199 template <typename Index, int Mode, \ 200 int LhsStorageOrder, bool ConjugateLhs, \ 201 int RhsStorageOrder, bool ConjugateRhs> \ 202 struct product_triangular_matrix_matrix_trmm<EIGTYPE,Index,Mode,false, \ 203 LhsStorageOrder,ConjugateLhs,RhsStorageOrder,ConjugateRhs,ColMajor> \ 204 { \ 205 enum { \ 206 IsLower = (Mode&Lower) == Lower, \ 207 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \ 208 IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \ 209 IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \ 210 LowUp = IsLower ? Lower : Upper, \ 211 conjA = ((RhsStorageOrder==ColMajor) && ConjugateRhs) ? 1 : 0 \ 212 }; \ 213 \ 214 static void run( \ 215 Index _rows, Index _cols, Index _depth, \ 216 const EIGTYPE* _lhs, Index lhsStride, \ 217 const EIGTYPE* _rhs, Index rhsStride, \ 218 EIGTYPE* res, Index resStride, \ 219 EIGTYPE alpha, level3_blocking<EIGTYPE,EIGTYPE>& blocking) \ 220 { \ 221 Index diagSize = (std::min)(_cols,_depth); \ 222 Index rows = _rows; \ 223 Index depth = IsLower ? _depth : diagSize; \ 224 Index cols = IsLower ? diagSize : _cols; \ 225 \ 226 typedef Matrix<EIGTYPE, Dynamic, Dynamic, LhsStorageOrder> MatrixLhs; \ 227 typedef Matrix<EIGTYPE, Dynamic, Dynamic, RhsStorageOrder> MatrixRhs; \ 228 \ 229 /* Non-square case - doesn't fit to BLAS ?TRMM. Fall to default triangular product or call BLAS ?GEMM*/ \ 230 if (cols != depth) { \ 231 \ 232 int nthr = 1 /*mkl_domain_get_max_threads(EIGEN_BLAS_DOMAIN_BLAS)*/; \ 233 \ 234 if ((nthr==1) && (((std::max)(cols,depth)-diagSize)/(double)diagSize < 0.5)) { \ 235 /* Most likely no benefit to call TRMM or GEMM from BLAS*/ \ 236 product_triangular_matrix_matrix<EIGTYPE,Index,Mode,false, \ 237 LhsStorageOrder,ConjugateLhs, RhsStorageOrder, ConjugateRhs, ColMajor, 1, BuiltIn>::run( \ 238 _rows, _cols, _depth, _lhs, lhsStride, _rhs, rhsStride, res, 1, resStride, alpha, blocking); \ 239 /*std::cout << "TRMM_R: A is not square! Go to Eigen TRMM implementation!\n";*/ \ 240 } else { \ 241 /* Make sense to call GEMM */ \ 242 Map<const MatrixRhs, 0, OuterStride<> > rhsMap(_rhs,depth,cols, OuterStride<>(rhsStride)); \ 243 MatrixRhs aa_tmp=rhsMap.template triangularView<Mode>(); \ 244 BlasIndex aStride = convert_index<BlasIndex>(aa_tmp.outerStride()); \ 245 gemm_blocking_space<ColMajor,EIGTYPE,EIGTYPE,Dynamic,Dynamic,Dynamic> gemm_blocking(_rows,_cols,_depth, 1, true); \ 246 general_matrix_matrix_product<Index,EIGTYPE,LhsStorageOrder,ConjugateLhs,EIGTYPE,RhsStorageOrder,ConjugateRhs,ColMajor,1>::run( \ 247 rows, cols, depth, _lhs, lhsStride, aa_tmp.data(), aStride, res, 1, resStride, alpha, gemm_blocking, 0); \ 248 \ 249 /*std::cout << "TRMM_R: A is not square! Go to BLAS GEMM implementation! " << nthr<<" \n";*/ \ 250 } \ 251 return; \ 252 } \ 253 char side = 'R', transa, uplo, diag = 'N'; \ 254 EIGTYPE *b; \ 255 const EIGTYPE *a; \ 256 BlasIndex m, n, lda, ldb; \ 257 \ 258 /* Set m, n */ \ 259 m = convert_index<BlasIndex>(rows); \ 260 n = convert_index<BlasIndex>(diagSize); \ 261 \ 262 /* Set trans */ \ 263 transa = (RhsStorageOrder==RowMajor) ? ((ConjugateRhs) ? 'C' : 'T') : 'N'; \ 264 \ 265 /* Set b, ldb */ \ 266 Map<const MatrixLhs, 0, OuterStride<> > lhs(_lhs,rows,depth,OuterStride<>(lhsStride)); \ 267 MatrixX##EIGPREFIX b_tmp; \ 268 \ 269 if (ConjugateLhs) b_tmp = lhs.conjugate(); else b_tmp = lhs; \ 270 b = b_tmp.data(); \ 271 ldb = convert_index<BlasIndex>(b_tmp.outerStride()); \ 272 \ 273 /* Set uplo */ \ 274 uplo = IsLower ? 'L' : 'U'; \ 275 if (RhsStorageOrder==RowMajor) uplo = (uplo == 'L') ? 'U' : 'L'; \ 276 /* Set a, lda */ \ 277 Map<const MatrixRhs, 0, OuterStride<> > rhs(_rhs,depth,cols, OuterStride<>(rhsStride)); \ 278 MatrixRhs a_tmp; \ 279 \ 280 if ((conjA!=0) || (SetDiag==0)) { \ 281 if (conjA) a_tmp = rhs.conjugate(); else a_tmp = rhs; \ 282 if (IsZeroDiag) \ 283 a_tmp.diagonal().setZero(); \ 284 else if (IsUnitDiag) \ 285 a_tmp.diagonal().setOnes();\ 286 a = a_tmp.data(); \ 287 lda = convert_index<BlasIndex>(a_tmp.outerStride()); \ 288 } else { \ 289 a = _rhs; \ 290 lda = convert_index<BlasIndex>(rhsStride); \ 291 } \ 292 /*std::cout << "TRMM_R: A is square! Go to BLAS TRMM implementation! \n";*/ \ 293 /* call ?trmm*/ \ 294 BLASFUNC(&side, &uplo, &transa, &diag, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (BLASTYPE*)b, &ldb); \ 295 \ 296 /* Add op(a_triangular)*b into res*/ \ 297 Map<MatrixX##EIGPREFIX, 0, OuterStride<> > res_tmp(res,rows,cols,OuterStride<>(resStride)); \ 298 res_tmp=res_tmp+b_tmp; \ 299 } \ 300 }; 301 302 #ifdef EIGEN_USE_MKL 303 EIGEN_BLAS_TRMM_R(double, double, d, dtrmm) 304 EIGEN_BLAS_TRMM_R(dcomplex, MKL_Complex16, cd, ztrmm) 305 EIGEN_BLAS_TRMM_R(float, float, f, strmm) 306 EIGEN_BLAS_TRMM_R(scomplex, MKL_Complex8, cf, ctrmm) 307 #else 308 EIGEN_BLAS_TRMM_R(double, double, d, dtrmm_) 309 EIGEN_BLAS_TRMM_R(dcomplex, double, cd, ztrmm_) 310 EIGEN_BLAS_TRMM_R(float, float, f, strmm_) 311 EIGEN_BLAS_TRMM_R(scomplex, float, cf, ctrmm_) 312 #endif 313 } // end namespace internal 314 315 } // end namespace Eigen 316 317 #endif // EIGEN_TRIANGULAR_MATRIX_MATRIX_BLAS_H 318