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|
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2008-2016 National ICT Australia (NICTA)
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------
//! \addtogroup gemv
//! @{
//! for tiny square matrices, size <= 4x4
template<const bool do_trans_A=false, const bool use_alpha=false, const bool use_beta=false>
class gemv_emul_tinysq
{
public:
template<const uword row, const uword col>
struct pos
{
static constexpr uword n2 = (do_trans_A == false) ? (row + col*2) : (col + row*2);
static constexpr uword n3 = (do_trans_A == false) ? (row + col*3) : (col + row*3);
static constexpr uword n4 = (do_trans_A == false) ? (row + col*4) : (col + row*4);
};
template<typename eT, const uword i>
arma_inline
static
void
assign(eT* y, const eT acc, const eT alpha, const eT beta)
{
if(use_beta == false)
{
y[i] = (use_alpha == false) ? acc : alpha*acc;
}
else
{
const eT tmp = y[i];
y[i] = beta*tmp + ( (use_alpha == false) ? acc : alpha*acc );
}
}
template<typename eT, typename TA>
arma_cold
inline
static
void
apply( eT* y, const TA& A, const eT* x, const eT alpha = eT(1), const eT beta = eT(0) )
{
arma_extra_debug_sigprint();
const eT* Am = A.memptr();
switch(A.n_rows)
{
case 1:
{
const eT acc = Am[0] * x[0];
assign<eT, 0>(y, acc, alpha, beta);
}
break;
case 2:
{
const eT x0 = x[0];
const eT x1 = x[1];
const eT acc0 = Am[pos<0,0>::n2]*x0 + Am[pos<0,1>::n2]*x1;
const eT acc1 = Am[pos<1,0>::n2]*x0 + Am[pos<1,1>::n2]*x1;
assign<eT, 0>(y, acc0, alpha, beta);
assign<eT, 1>(y, acc1, alpha, beta);
}
break;
case 3:
{
const eT x0 = x[0];
const eT x1 = x[1];
const eT x2 = x[2];
const eT acc0 = Am[pos<0,0>::n3]*x0 + Am[pos<0,1>::n3]*x1 + Am[pos<0,2>::n3]*x2;
const eT acc1 = Am[pos<1,0>::n3]*x0 + Am[pos<1,1>::n3]*x1 + Am[pos<1,2>::n3]*x2;
const eT acc2 = Am[pos<2,0>::n3]*x0 + Am[pos<2,1>::n3]*x1 + Am[pos<2,2>::n3]*x2;
assign<eT, 0>(y, acc0, alpha, beta);
assign<eT, 1>(y, acc1, alpha, beta);
assign<eT, 2>(y, acc2, alpha, beta);
}
break;
case 4:
{
const eT x0 = x[0];
const eT x1 = x[1];
const eT x2 = x[2];
const eT x3 = x[3];
const eT acc0 = Am[pos<0,0>::n4]*x0 + Am[pos<0,1>::n4]*x1 + Am[pos<0,2>::n4]*x2 + Am[pos<0,3>::n4]*x3;
const eT acc1 = Am[pos<1,0>::n4]*x0 + Am[pos<1,1>::n4]*x1 + Am[pos<1,2>::n4]*x2 + Am[pos<1,3>::n4]*x3;
const eT acc2 = Am[pos<2,0>::n4]*x0 + Am[pos<2,1>::n4]*x1 + Am[pos<2,2>::n4]*x2 + Am[pos<2,3>::n4]*x3;
const eT acc3 = Am[pos<3,0>::n4]*x0 + Am[pos<3,1>::n4]*x1 + Am[pos<3,2>::n4]*x2 + Am[pos<3,3>::n4]*x3;
assign<eT, 0>(y, acc0, alpha, beta);
assign<eT, 1>(y, acc1, alpha, beta);
assign<eT, 2>(y, acc2, alpha, beta);
assign<eT, 3>(y, acc3, alpha, beta);
}
break;
default:
;
}
}
};
class gemv_emul_helper
{
public:
template<typename eT, typename TA>
arma_hot
inline
static
typename arma_not_cx<eT>::result
dot_row_col( const TA& A, const eT* x, const uword row, const uword N )
{
eT acc1 = eT(0);
eT acc2 = eT(0);
uword i,j;
for(i=0, j=1; j < N; i+=2, j+=2)
{
const eT xi = x[i];
const eT xj = x[j];
acc1 += A.at(row,i) * xi;
acc2 += A.at(row,j) * xj;
}
if(i < N)
{
acc1 += A.at(row,i) * x[i];
}
return (acc1 + acc2);
}
template<typename eT, typename TA>
arma_hot
inline
static
typename arma_cx_only<eT>::result
dot_row_col( const TA& A, const eT* x, const uword row, const uword N )
{
typedef typename get_pod_type<eT>::result T;
T val_real = T(0);
T val_imag = T(0);
for(uword i=0; i<N; ++i)
{
const std::complex<T>& Ai = A.at(row,i);
const std::complex<T>& xi = x[i];
const T a = Ai.real();
const T b = Ai.imag();
const T c = xi.real();
const T d = xi.imag();
val_real += (a*c) - (b*d);
val_imag += (a*d) + (b*c);
}
return std::complex<T>(val_real, val_imag);
}
};
//! \brief
//! Partial emulation of ATLAS/BLAS gemv().
//! 'y' is assumed to have been set to the correct size (i.e. taking into account the transpose)
template<const bool do_trans_A=false, const bool use_alpha=false, const bool use_beta=false>
class gemv_emul
{
public:
template<typename eT, typename TA>
arma_hot
inline
static
void
apply( eT* y, const TA& A, const eT* x, const eT alpha = eT(1), const eT beta = eT(0) )
{
arma_extra_debug_sigprint();
const uword A_n_rows = A.n_rows;
const uword A_n_cols = A.n_cols;
if(do_trans_A == false)
{
if(A_n_rows == 1)
{
const eT acc = op_dot::direct_dot_arma(A_n_cols, A.memptr(), x);
if( (use_alpha == false) && (use_beta == false) ) { y[0] = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { y[0] = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { y[0] = acc + beta*y[0]; }
else if( (use_alpha == true ) && (use_beta == true ) ) { y[0] = alpha*acc + beta*y[0]; }
}
else
for(uword row=0; row < A_n_rows; ++row)
{
const eT acc = gemv_emul_helper::dot_row_col(A, x, row, A_n_cols);
if( (use_alpha == false) && (use_beta == false) ) { y[row] = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { y[row] = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { y[row] = acc + beta*y[row]; }
else if( (use_alpha == true ) && (use_beta == true ) ) { y[row] = alpha*acc + beta*y[row]; }
}
}
else
if(do_trans_A == true)
{
if(is_cx<eT>::no)
{
for(uword col=0; col < A_n_cols; ++col)
{
// col is interpreted as row when storing the results in 'y'
// const eT* A_coldata = A.colptr(col);
//
// eT acc = eT(0);
// for(uword row=0; row < A_n_rows; ++row)
// {
// acc += A_coldata[row] * x[row];
// }
const eT acc = op_dot::direct_dot_arma(A_n_rows, A.colptr(col), x);
if( (use_alpha == false) && (use_beta == false) ) { y[col] = acc; }
else if( (use_alpha == true ) && (use_beta == false) ) { y[col] = alpha*acc; }
else if( (use_alpha == false) && (use_beta == true ) ) { y[col] = acc + beta*y[col]; }
else if( (use_alpha == true ) && (use_beta == true ) ) { y[col] = alpha*acc + beta*y[col]; }
}
}
else
{
Mat<eT> AA;
op_htrans::apply_mat_noalias(AA, A);
gemv_emul<false, use_alpha, use_beta>::apply(y, AA, x, alpha, beta);
}
}
}
};
//! \brief
//! Wrapper for ATLAS/BLAS gemv function, using template arguments to control the arguments passed to gemv.
//! 'y' is assumed to have been set to the correct size (i.e. taking into account the transpose)
template<const bool do_trans_A=false, const bool use_alpha=false, const bool use_beta=false>
class gemv
{
public:
template<typename eT, typename TA>
inline
static
void
apply_blas_type( eT* y, const TA& A, const eT* x, const eT alpha = eT(1), const eT beta = eT(0) )
{
arma_extra_debug_sigprint();
if( (A.n_rows <= 4) && (A.n_rows == A.n_cols) && (is_cx<eT>::no) )
{
gemv_emul_tinysq<do_trans_A, use_alpha, use_beta>::apply(y, A, x, alpha, beta);
}
else
{
#if defined(ARMA_USE_ATLAS)
{
arma_debug_assert_atlas_size(A);
if(is_cx<eT>::no)
{
// use gemm() instead of gemv() to work around a speed issue in Atlas 3.8.4
arma_extra_debug_print("atlas::cblas_gemm()");
atlas::cblas_gemm<eT>
(
atlas::CblasColMajor,
(do_trans_A) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
atlas::CblasNoTrans,
(do_trans_A) ? A.n_cols : A.n_rows,
1,
(do_trans_A) ? A.n_rows : A.n_cols,
(use_alpha) ? alpha : eT(1),
A.mem,
A.n_rows,
x,
(do_trans_A) ? A.n_rows : A.n_cols,
(use_beta) ? beta : eT(0),
y,
(do_trans_A) ? A.n_cols : A.n_rows
);
}
else
{
arma_extra_debug_print("atlas::cblas_gemv()");
atlas::cblas_gemv<eT>
(
atlas::CblasColMajor,
(do_trans_A) ? ( is_cx<eT>::yes ? CblasConjTrans : atlas::CblasTrans ) : atlas::CblasNoTrans,
A.n_rows,
A.n_cols,
(use_alpha) ? alpha : eT(1),
A.mem,
A.n_rows,
x,
1,
(use_beta) ? beta : eT(0),
y,
1
);
}
}
#elif defined(ARMA_USE_BLAS)
{
arma_extra_debug_print("blas::gemv()");
arma_debug_assert_blas_size(A);
const char trans_A = (do_trans_A) ? ( is_cx<eT>::yes ? 'C' : 'T' ) : 'N';
const blas_int m = blas_int(A.n_rows);
const blas_int n = blas_int(A.n_cols);
const eT local_alpha = (use_alpha) ? alpha : eT(1);
//const blas_int lda = A.n_rows;
const blas_int inc = blas_int(1);
const eT local_beta = (use_beta) ? beta : eT(0);
arma_extra_debug_print( arma_str::format("blas::gemv(): trans_A = %c") % trans_A );
blas::gemv<eT>
(
&trans_A,
&m,
&n,
&local_alpha,
A.mem,
&m, // lda
x,
&inc,
&local_beta,
y,
&inc
);
}
#else
{
gemv_emul<do_trans_A, use_alpha, use_beta>::apply(y,A,x,alpha,beta);
}
#endif
}
}
template<typename eT, typename TA>
arma_inline
static
void
apply( eT* y, const TA& A, const eT* x, const eT alpha = eT(1), const eT beta = eT(0) )
{
gemv_emul<do_trans_A, use_alpha, use_beta>::apply(y,A,x,alpha,beta);
}
template<typename TA>
arma_inline
static
void
apply
(
float* y,
const TA& A,
const float* x,
const float alpha = float(1),
const float beta = float(0)
)
{
gemv<do_trans_A, use_alpha, use_beta>::apply_blas_type(y,A,x,alpha,beta);
}
template<typename TA>
arma_inline
static
void
apply
(
double* y,
const TA& A,
const double* x,
const double alpha = double(1),
const double beta = double(0)
)
{
gemv<do_trans_A, use_alpha, use_beta>::apply_blas_type(y,A,x,alpha,beta);
}
template<typename TA>
arma_inline
static
void
apply
(
std::complex<float>* y,
const TA& A,
const std::complex<float>* x,
const std::complex<float> alpha = std::complex<float>(1),
const std::complex<float> beta = std::complex<float>(0)
)
{
gemv<do_trans_A, use_alpha, use_beta>::apply_blas_type(y,A,x,alpha,beta);
}
template<typename TA>
arma_inline
static
void
apply
(
std::complex<double>* y,
const TA& A,
const std::complex<double>* x,
const std::complex<double> alpha = std::complex<double>(1),
const std::complex<double> beta = std::complex<double>(0)
)
{
gemv<do_trans_A, use_alpha, use_beta>::apply_blas_type(y,A,x,alpha,beta);
}
};
//! @}
|
