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-vector product functionality based on ?TRMV. 30 ******************************************************************************** 31 */ 32 33 #ifndef EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H 34 #define EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H 35 36 namespace Eigen { 37 38 namespace internal { 39 40 /********************************************************************** 41 * This file implements triangular matrix-vector multiplication using BLAS 42 **********************************************************************/ 43 44 // trmv/hemv specialization 45 46 template<typename Index, int Mode, typename LhsScalar, bool ConjLhs, typename RhsScalar, bool ConjRhs, int StorageOrder> 47 struct triangular_matrix_vector_product_trmv : 48 triangular_matrix_vector_product<Index,Mode,LhsScalar,ConjLhs,RhsScalar,ConjRhs,StorageOrder,BuiltIn> {}; 49 50 #define EIGEN_BLAS_TRMV_SPECIALIZE(Scalar) \ 51 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \ 52 struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor,Specialized> { \ 53 static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \ 54 const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \ 55 triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,ColMajor>::run( \ 56 _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \ 57 } \ 58 }; \ 59 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \ 60 struct triangular_matrix_vector_product<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor,Specialized> { \ 61 static void run(Index _rows, Index _cols, const Scalar* _lhs, Index lhsStride, \ 62 const Scalar* _rhs, Index rhsIncr, Scalar* _res, Index resIncr, Scalar alpha) { \ 63 triangular_matrix_vector_product_trmv<Index,Mode,Scalar,ConjLhs,Scalar,ConjRhs,RowMajor>::run( \ 64 _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \ 65 } \ 66 }; 67 68 EIGEN_BLAS_TRMV_SPECIALIZE(double) 69 EIGEN_BLAS_TRMV_SPECIALIZE(float) 70 EIGEN_BLAS_TRMV_SPECIALIZE(dcomplex) 71 EIGEN_BLAS_TRMV_SPECIALIZE(scomplex) 72 73 // implements col-major: res += alpha * op(triangular) * vector 74 #define EIGEN_BLAS_TRMV_CM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \ 75 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \ 76 struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor> { \ 77 enum { \ 78 IsLower = (Mode&Lower) == Lower, \ 79 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \ 80 IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \ 81 IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \ 82 LowUp = IsLower ? Lower : Upper \ 83 }; \ 84 static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \ 85 const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \ 86 { \ 87 if (ConjLhs || IsZeroDiag) { \ 88 triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,ColMajor,BuiltIn>::run( \ 89 _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \ 90 return; \ 91 }\ 92 Index size = (std::min)(_rows,_cols); \ 93 Index rows = IsLower ? _rows : size; \ 94 Index cols = IsLower ? size : _cols; \ 95 \ 96 typedef VectorX##EIGPREFIX VectorRhs; \ 97 EIGTYPE *x, *y;\ 98 \ 99 /* Set x*/ \ 100 Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \ 101 VectorRhs x_tmp; \ 102 if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \ 103 x = x_tmp.data(); \ 104 \ 105 /* Square part handling */\ 106 \ 107 char trans, uplo, diag; \ 108 BlasIndex m, n, lda, incx, incy; \ 109 EIGTYPE const *a; \ 110 EIGTYPE beta(1); \ 111 \ 112 /* Set m, n */ \ 113 n = convert_index<BlasIndex>(size); \ 114 lda = convert_index<BlasIndex>(lhsStride); \ 115 incx = 1; \ 116 incy = convert_index<BlasIndex>(resIncr); \ 117 \ 118 /* Set uplo, trans and diag*/ \ 119 trans = 'N'; \ 120 uplo = IsLower ? 'L' : 'U'; \ 121 diag = IsUnitDiag ? 'U' : 'N'; \ 122 \ 123 /* call ?TRMV*/ \ 124 BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \ 125 \ 126 /* Add op(a_tr)rhs into res*/ \ 127 BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \ 128 /* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \ 129 if (size<(std::max)(rows,cols)) { \ 130 if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \ 131 x = x_tmp.data(); \ 132 if (size<rows) { \ 133 y = _res + size*resIncr; \ 134 a = _lhs + size; \ 135 m = convert_index<BlasIndex>(rows-size); \ 136 n = convert_index<BlasIndex>(size); \ 137 } \ 138 else { \ 139 x += size; \ 140 y = _res; \ 141 a = _lhs + size*lda; \ 142 m = convert_index<BlasIndex>(size); \ 143 n = convert_index<BlasIndex>(cols-size); \ 144 } \ 145 BLASPREFIX##gemv##BLASPOSTFIX(&trans, &m, &n, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \ 146 } \ 147 } \ 148 }; 149 150 #ifdef EIGEN_USE_MKL 151 EIGEN_BLAS_TRMV_CM(double, double, d, d,) 152 EIGEN_BLAS_TRMV_CM(dcomplex, MKL_Complex16, cd, z,) 153 EIGEN_BLAS_TRMV_CM(float, float, f, s,) 154 EIGEN_BLAS_TRMV_CM(scomplex, MKL_Complex8, cf, c,) 155 #else 156 EIGEN_BLAS_TRMV_CM(double, double, d, d, _) 157 EIGEN_BLAS_TRMV_CM(dcomplex, double, cd, z, _) 158 EIGEN_BLAS_TRMV_CM(float, float, f, s, _) 159 EIGEN_BLAS_TRMV_CM(scomplex, float, cf, c, _) 160 #endif 161 162 // implements row-major: res += alpha * op(triangular) * vector 163 #define EIGEN_BLAS_TRMV_RM(EIGTYPE, BLASTYPE, EIGPREFIX, BLASPREFIX, BLASPOSTFIX) \ 164 template<typename Index, int Mode, bool ConjLhs, bool ConjRhs> \ 165 struct triangular_matrix_vector_product_trmv<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor> { \ 166 enum { \ 167 IsLower = (Mode&Lower) == Lower, \ 168 SetDiag = (Mode&(ZeroDiag|UnitDiag)) ? 0 : 1, \ 169 IsUnitDiag = (Mode&UnitDiag) ? 1 : 0, \ 170 IsZeroDiag = (Mode&ZeroDiag) ? 1 : 0, \ 171 LowUp = IsLower ? Lower : Upper \ 172 }; \ 173 static void run(Index _rows, Index _cols, const EIGTYPE* _lhs, Index lhsStride, \ 174 const EIGTYPE* _rhs, Index rhsIncr, EIGTYPE* _res, Index resIncr, EIGTYPE alpha) \ 175 { \ 176 if (IsZeroDiag) { \ 177 triangular_matrix_vector_product<Index,Mode,EIGTYPE,ConjLhs,EIGTYPE,ConjRhs,RowMajor,BuiltIn>::run( \ 178 _rows, _cols, _lhs, lhsStride, _rhs, rhsIncr, _res, resIncr, alpha); \ 179 return; \ 180 }\ 181 Index size = (std::min)(_rows,_cols); \ 182 Index rows = IsLower ? _rows : size; \ 183 Index cols = IsLower ? size : _cols; \ 184 \ 185 typedef VectorX##EIGPREFIX VectorRhs; \ 186 EIGTYPE *x, *y;\ 187 \ 188 /* Set x*/ \ 189 Map<const VectorRhs, 0, InnerStride<> > rhs(_rhs,cols,InnerStride<>(rhsIncr)); \ 190 VectorRhs x_tmp; \ 191 if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \ 192 x = x_tmp.data(); \ 193 \ 194 /* Square part handling */\ 195 \ 196 char trans, uplo, diag; \ 197 BlasIndex m, n, lda, incx, incy; \ 198 EIGTYPE const *a; \ 199 EIGTYPE beta(1); \ 200 \ 201 /* Set m, n */ \ 202 n = convert_index<BlasIndex>(size); \ 203 lda = convert_index<BlasIndex>(lhsStride); \ 204 incx = 1; \ 205 incy = convert_index<BlasIndex>(resIncr); \ 206 \ 207 /* Set uplo, trans and diag*/ \ 208 trans = ConjLhs ? 'C' : 'T'; \ 209 uplo = IsLower ? 'U' : 'L'; \ 210 diag = IsUnitDiag ? 'U' : 'N'; \ 211 \ 212 /* call ?TRMV*/ \ 213 BLASPREFIX##trmv##BLASPOSTFIX(&uplo, &trans, &diag, &n, (const BLASTYPE*)_lhs, &lda, (BLASTYPE*)x, &incx); \ 214 \ 215 /* Add op(a_tr)rhs into res*/ \ 216 BLASPREFIX##axpy##BLASPOSTFIX(&n, (const BLASTYPE*)&numext::real_ref(alpha),(const BLASTYPE*)x, &incx, (BLASTYPE*)_res, &incy); \ 217 /* Non-square case - doesn't fit to BLAS ?TRMV. Fall to default triangular product*/ \ 218 if (size<(std::max)(rows,cols)) { \ 219 if (ConjRhs) x_tmp = rhs.conjugate(); else x_tmp = rhs; \ 220 x = x_tmp.data(); \ 221 if (size<rows) { \ 222 y = _res + size*resIncr; \ 223 a = _lhs + size*lda; \ 224 m = convert_index<BlasIndex>(rows-size); \ 225 n = convert_index<BlasIndex>(size); \ 226 } \ 227 else { \ 228 x += size; \ 229 y = _res; \ 230 a = _lhs + size; \ 231 m = convert_index<BlasIndex>(size); \ 232 n = convert_index<BlasIndex>(cols-size); \ 233 } \ 234 BLASPREFIX##gemv##BLASPOSTFIX(&trans, &n, &m, (const BLASTYPE*)&numext::real_ref(alpha), (const BLASTYPE*)a, &lda, (const BLASTYPE*)x, &incx, (const BLASTYPE*)&numext::real_ref(beta), (BLASTYPE*)y, &incy); \ 235 } \ 236 } \ 237 }; 238 239 #ifdef EIGEN_USE_MKL 240 EIGEN_BLAS_TRMV_RM(double, double, d, d,) 241 EIGEN_BLAS_TRMV_RM(dcomplex, MKL_Complex16, cd, z,) 242 EIGEN_BLAS_TRMV_RM(float, float, f, s,) 243 EIGEN_BLAS_TRMV_RM(scomplex, MKL_Complex8, cf, c,) 244 #else 245 EIGEN_BLAS_TRMV_RM(double, double, d, d,_) 246 EIGEN_BLAS_TRMV_RM(dcomplex, double, cd, z,_) 247 EIGEN_BLAS_TRMV_RM(float, float, f, s,_) 248 EIGEN_BLAS_TRMV_RM(scomplex, float, cf, c,_) 249 #endif 250 251 } // end namespase internal 252 253 } // end namespace Eigen 254 255 #endif // EIGEN_TRIANGULAR_MATRIX_VECTOR_BLAS_H 256