diff --git a/master/eigensolver_2reduction__to__band_2impl_8h_source.html b/master/eigensolver_2reduction__to__band_2impl_8h_source.html index 1b8bf4ebe2..12c84dad4e 100644 --- a/master/eigensolver_2reduction__to__band_2impl_8h_source.html +++ b/master/eigensolver_2reduction__to__band_2impl_8h_source.html @@ -170,1295 +170,1298 @@
99 template <Device D, class T>
100 T computeReflectorAndTau(const bool has_head, const std::vector<matrix::Tile<T, D>>& panel,
101  const SizeType j, std::array<T, 2> x0_and_squares) {
-
102  const T norm = std::sqrt(x0_and_squares[1]);
-
103  const T x0 = x0_and_squares[0];
-
104  const T y = std::signbit(std::real(x0_and_squares[0])) ? norm : -norm;
-
105  const T tau = (y - x0) / y;
-
106 
-
107  auto it_begin = panel.begin();
-
108  auto it_end = panel.end();
+
102  if (x0_and_squares[1] == T(0))
+
103  return T(0);
+
104 
+
105  const T norm = std::sqrt(x0_and_squares[1]);
+
106  const T x0 = x0_and_squares[0];
+
107  const T y = std::signbit(std::real(x0_and_squares[0])) ? norm : -norm;
+
108  const T tau = (y - x0) / y;
109 
-
110  common::internal::SingleThreadedBlasScope single;
-
111 
-
112  if (has_head) {
-
113  const auto& tile_v0 = *it_begin++;
+
110  auto it_begin = panel.begin();
+
111  auto it_end = panel.end();
+
112 
+
113  common::internal::SingleThreadedBlasScope single;
114 
-
115  const TileElementIndex idx_x0(j, j);
-
116  tile_v0(idx_x0) = y;
+
115  if (has_head) {
+
116  const auto& tile_v0 = *it_begin++;
117 
-
118  if (j + 1 < tile_v0.size().rows()) {
-
119  T* v = tile_v0.ptr({j + 1, j});
-
120  blas::scal(tile_v0.size().rows() - (j + 1), T(1) / (x0 - y), v, 1);
-
121  }
-
122  }
-
123 
-
124  for (auto it = it_begin; it != it_end; ++it) {
-
125  auto& tile_v = *it;
-
126  T* v = tile_v.ptr({0, j});
-
127  blas::scal(tile_v.size().rows(), T(1) / (x0 - y), v, 1);
-
128  }
-
129 
-
130  return tau;
-
131 }
+
118  const TileElementIndex idx_x0(j, j);
+
119  tile_v0(idx_x0) = y;
+
120 
+
121  if (j + 1 < tile_v0.size().rows()) {
+
122  T* v = tile_v0.ptr({j + 1, j});
+
123  blas::scal(tile_v0.size().rows() - (j + 1), T(1) / (x0 - y), v, 1);
+
124  }
+
125  }
+
126 
+
127  for (auto it = it_begin; it != it_end; ++it) {
+
128  auto& tile_v = *it;
+
129  T* v = tile_v.ptr({0, j});
+
130  blas::scal(tile_v.size().rows(), T(1) / (x0 - y), v, 1);
+
131  }
132 
-
133 template <Device D, class T>
-
134 void computeWTrailingPanel(const bool has_head, const std::vector<matrix::Tile<T, D>>& panel,
-
135  common::internal::vector<T>& w, SizeType j, const SizeType pt_cols,
-
136  const std::size_t begin, const std::size_t end) {
-
137  // for each tile in the panel, consider just the trailing panel
-
138  // i.e. all rows (height = reflector), just columns to the right of the current reflector
-
139  if (!(pt_cols > 0))
-
140  return;
-
141 
-
142  const TileElementIndex index_el_x0(j, j);
-
143  bool has_first_component = has_head;
+
133  return tau;
+
134 }
+
135 
+
136 template <Device D, class T>
+
137 void computeWTrailingPanel(const bool has_head, const std::vector<matrix::Tile<T, D>>& panel,
+
138  common::internal::vector<T>& w, SizeType j, const SizeType pt_cols,
+
139  const std::size_t begin, const std::size_t end) {
+
140  // for each tile in the panel, consider just the trailing panel
+
141  // i.e. all rows (height = reflector), just columns to the right of the current reflector
+
142  if (!(pt_cols > 0))
+
143  return;
144 
-
145  common::internal::SingleThreadedBlasScope single;
-
146 
-
147  // W = Pt* . V
-
148  for (auto index = begin; index < end; ++index) {
-
149  const matrix::Tile<const T, D>& tile_a = panel[index];
-
150  const SizeType first_element = has_first_component ? index_el_x0.row() : 0;
-
151 
-
152  TileElementIndex pt_start{first_element, index_el_x0.col() + 1};
-
153  TileElementSize pt_size{tile_a.size().rows() - pt_start.row(), pt_cols};
-
154  TileElementIndex v_start{first_element, index_el_x0.col()};
-
155 
-
156  if (has_first_component) {
-
157  const TileElementSize offset{1, 0};
+
145  const TileElementIndex index_el_x0(j, j);
+
146  bool has_first_component = has_head;
+
147 
+
148  common::internal::SingleThreadedBlasScope single;
+
149 
+
150  // W = Pt* . V
+
151  for (auto index = begin; index < end; ++index) {
+
152  const matrix::Tile<const T, D>& tile_a = panel[index];
+
153  const SizeType first_element = has_first_component ? index_el_x0.row() : 0;
+
154 
+
155  TileElementIndex pt_start{first_element, index_el_x0.col() + 1};
+
156  TileElementSize pt_size{tile_a.size().rows() - pt_start.row(), pt_cols};
+
157  TileElementIndex v_start{first_element, index_el_x0.col()};
158 
-
159  const T fake_v = 1;
-
160  blas::gemv(blas::Layout::ColMajor, blas::Op::ConjTrans, offset.rows(), pt_size.cols(), T(1),
-
161  tile_a.ptr(pt_start), tile_a.ld(), &fake_v, 1, T(0), w.data(), 1);
-
162 
-
163  pt_start = pt_start + offset;
-
164  v_start = v_start + offset;
-
165  pt_size = pt_size - offset;
-
166 
-
167  has_first_component = false;
-
168  }
+
159  if (has_first_component) {
+
160  const TileElementSize offset{1, 0};
+
161 
+
162  const T fake_v = 1;
+
163  blas::gemv(blas::Layout::ColMajor, blas::Op::ConjTrans, offset.rows(), pt_size.cols(), T(1),
+
164  tile_a.ptr(pt_start), tile_a.ld(), &fake_v, 1, T(0), w.data(), 1);
+
165 
+
166  pt_start = pt_start + offset;
+
167  v_start = v_start + offset;
+
168  pt_size = pt_size - offset;
169 
-
170  if (pt_start.isIn(tile_a.size())) {
-
171  // W += 1 . A* . V
-
172  blas::gemv(blas::Layout::ColMajor, blas::Op::ConjTrans, pt_size.rows(), pt_size.cols(), T(1),
-
173  tile_a.ptr(pt_start), tile_a.ld(), tile_a.ptr(v_start), 1, T(1), w.data(), 1);
-
174  }
-
175  }
-
176 }
-
177 
-
178 template <Device D, class T>
-
179 void updateTrailingPanel(const bool has_head, const std::vector<matrix::Tile<T, D>>& panel, SizeType j,
-
180  const std::vector<T>& w, const T tau, const std::size_t begin,
-
181  const std::size_t end) {
-
182  const TileElementIndex index_el_x0(j, j);
-
183 
-
184  bool has_first_component = has_head;
-
185 
-
186  common::internal::SingleThreadedBlasScope single;
-
187 
-
188  // GER Pt = Pt - tau . v . w*
-
189  for (auto index = begin; index < end; ++index) {
-
190  const matrix::Tile<T, D>& tile_a = panel[index];
-
191  const SizeType first_element = has_first_component ? index_el_x0.row() : 0;
-
192 
-
193  TileElementIndex pt_start{first_element, index_el_x0.col() + 1};
-
194  TileElementSize pt_size{tile_a.size().rows() - pt_start.row(),
-
195  tile_a.size().cols() - pt_start.col()};
-
196  TileElementIndex v_start{first_element, index_el_x0.col()};
-
197 
-
198  if (has_first_component) {
-
199  const TileElementSize offset{1, 0};
+
170  has_first_component = false;
+
171  }
+
172 
+
173  if (pt_start.isIn(tile_a.size())) {
+
174  // W += 1 . A* . V
+
175  blas::gemv(blas::Layout::ColMajor, blas::Op::ConjTrans, pt_size.rows(), pt_size.cols(), T(1),
+
176  tile_a.ptr(pt_start), tile_a.ld(), tile_a.ptr(v_start), 1, T(1), w.data(), 1);
+
177  }
+
178  }
+
179 }
+
180 
+
181 template <Device D, class T>
+
182 void updateTrailingPanel(const bool has_head, const std::vector<matrix::Tile<T, D>>& panel, SizeType j,
+
183  const std::vector<T>& w, const T tau, const std::size_t begin,
+
184  const std::size_t end) {
+
185  const TileElementIndex index_el_x0(j, j);
+
186 
+
187  bool has_first_component = has_head;
+
188 
+
189  common::internal::SingleThreadedBlasScope single;
+
190 
+
191  // GER Pt = Pt - tau . v . w*
+
192  for (auto index = begin; index < end; ++index) {
+
193  const matrix::Tile<T, D>& tile_a = panel[index];
+
194  const SizeType first_element = has_first_component ? index_el_x0.row() : 0;
+
195 
+
196  TileElementIndex pt_start{first_element, index_el_x0.col() + 1};
+
197  TileElementSize pt_size{tile_a.size().rows() - pt_start.row(),
+
198  tile_a.size().cols() - pt_start.col()};
+
199  TileElementIndex v_start{first_element, index_el_x0.col()};
200 
-
201  // Pt = Pt - tau * v[0] * w*
-
202  const T fake_v = 1;
-
203  blas::ger(blas::Layout::ColMajor, 1, pt_size.cols(), -dlaf::conj(tau), &fake_v, 1, w.data(), 1,
-
204  tile_a.ptr(pt_start), tile_a.ld());
-
205 
-
206  pt_start = pt_start + offset;
-
207  v_start = v_start + offset;
-
208  pt_size = pt_size - offset;
-
209 
-
210  has_first_component = false;
-
211  }
+
201  if (has_first_component) {
+
202  const TileElementSize offset{1, 0};
+
203 
+
204  // Pt = Pt - tau * v[0] * w*
+
205  const T fake_v = 1;
+
206  blas::ger(blas::Layout::ColMajor, 1, pt_size.cols(), -dlaf::conj(tau), &fake_v, 1, w.data(), 1,
+
207  tile_a.ptr(pt_start), tile_a.ld());
+
208 
+
209  pt_start = pt_start + offset;
+
210  v_start = v_start + offset;
+
211  pt_size = pt_size - offset;
212 
-
213  if (pt_start.isIn(tile_a.size())) {
-
214  // Pt = Pt - tau * v * w*
-
215  blas::ger(blas::Layout::ColMajor, pt_size.rows(), pt_size.cols(), -dlaf::conj(tau),
-
216  tile_a.ptr(v_start), 1, w.data(), 1, tile_a.ptr(pt_start), tile_a.ld());
-
217  }
-
218  }
-
219 }
-
220 
-
221 template <Backend B, typename ASender, typename WSender, typename XSender>
-
222 void hemmDiag(pika::execution::thread_priority priority, ASender&& tile_a, WSender&& tile_w,
-
223  XSender&& tile_x) {
-
224  using T = dlaf::internal::SenderElementType<ASender>;
-
225  pika::execution::experimental::start_detached(
-
226  dlaf::internal::whenAllLift(blas::Side::Left, blas::Uplo::Lower, T(1),
-
227  std::forward<ASender>(tile_a), std::forward<WSender>(tile_w), T(1),
-
228  std::forward<XSender>(tile_x)) |
-
229  tile::hemm(dlaf::internal::Policy<B>(priority)));
-
230 }
-
231 
-
232 // X += op(A) * W
-
233 template <Backend B, typename ASender, typename WSender, typename XSender>
-
234 void hemmOffDiag(pika::execution::thread_priority priority, blas::Op op, ASender&& tile_a,
-
235  WSender&& tile_w, XSender&& tile_x) {
-
236  using T = dlaf::internal::SenderElementType<ASender>;
-
237  pika::execution::experimental::start_detached(
-
238  dlaf::internal::whenAllLift(op, blas::Op::NoTrans, T(1), std::forward<ASender>(tile_a),
-
239  std::forward<WSender>(tile_w), T(1), std::forward<XSender>(tile_x)) |
-
240  tile::gemm(dlaf::internal::Policy<B>(priority)));
-
241 }
-
242 
-
243 template <Backend B, typename VSender, typename XSender, typename ASender>
-
244 void her2kDiag(pika::execution::thread_priority priority, VSender&& tile_v, XSender&& tile_x,
-
245  ASender&& tile_a) {
-
246  using T = dlaf::internal::SenderElementType<VSender>;
-
247  pika::execution::experimental::start_detached(
-
248  dlaf::internal::whenAllLift(blas::Uplo::Lower, blas::Op::NoTrans, T(-1),
-
249  std::forward<VSender>(tile_v), std::forward<XSender>(tile_x),
-
250  BaseType<T>(1), std::forward<ASender>(tile_a)) |
-
251  tile::her2k(dlaf::internal::Policy<B>(priority)));
-
252 }
-
253 
-
254 // C -= A . B*
-
255 template <Backend B, typename ASender, typename BSender, typename CSender>
-
256 void her2kOffDiag(pika::execution::thread_priority priority, ASender&& tile_a, BSender&& tile_b,
-
257  CSender&& tile_c) {
-
258  using T = dlaf::internal::SenderElementType<ASender>;
-
259  pika::execution::experimental::start_detached(
-
260  dlaf::internal::whenAllLift(blas::Op::NoTrans, blas::Op::ConjTrans, T(-1),
-
261  std::forward<ASender>(tile_a), std::forward<BSender>(tile_b), T(1),
-
262  std::forward<CSender>(tile_c)) |
-
263  tile::gemm(dlaf::internal::Policy<B>(priority)));
-
264 }
-
265 
-
266 namespace local {
-
267 
-
268 template <Device D, class T>
-
269 T computeReflector(const std::vector<matrix::Tile<T, D>>& panel, SizeType j) {
-
270  constexpr bool has_head = true;
-
271 
-
272  std::array<T, 2> x0_and_squares = computeX0AndSquares(has_head, panel, j);
-
273 
-
274  auto tau = computeReflectorAndTau(has_head, panel, j, std::move(x0_and_squares));
-
275 
-
276  return tau;
-
277 }
+
213  has_first_component = false;
+
214  }
+
215 
+
216  if (pt_start.isIn(tile_a.size())) {
+
217  // Pt = Pt - tau * v * w*
+
218  blas::ger(blas::Layout::ColMajor, pt_size.rows(), pt_size.cols(), -dlaf::conj(tau),
+
219  tile_a.ptr(v_start), 1, w.data(), 1, tile_a.ptr(pt_start), tile_a.ld());
+
220  }
+
221  }
+
222 }
+
223 
+
224 template <Backend B, typename ASender, typename WSender, typename XSender>
+
225 void hemmDiag(pika::execution::thread_priority priority, ASender&& tile_a, WSender&& tile_w,
+
226  XSender&& tile_x) {
+
227  using T = dlaf::internal::SenderElementType<ASender>;
+
228  pika::execution::experimental::start_detached(
+
229  dlaf::internal::whenAllLift(blas::Side::Left, blas::Uplo::Lower, T(1),
+
230  std::forward<ASender>(tile_a), std::forward<WSender>(tile_w), T(1),
+
231  std::forward<XSender>(tile_x)) |
+
232  tile::hemm(dlaf::internal::Policy<B>(priority)));
+
233 }
+
234 
+
235 // X += op(A) * W
+
236 template <Backend B, typename ASender, typename WSender, typename XSender>
+
237 void hemmOffDiag(pika::execution::thread_priority priority, blas::Op op, ASender&& tile_a,
+
238  WSender&& tile_w, XSender&& tile_x) {
+
239  using T = dlaf::internal::SenderElementType<ASender>;
+
240  pika::execution::experimental::start_detached(
+
241  dlaf::internal::whenAllLift(op, blas::Op::NoTrans, T(1), std::forward<ASender>(tile_a),
+
242  std::forward<WSender>(tile_w), T(1), std::forward<XSender>(tile_x)) |
+
243  tile::gemm(dlaf::internal::Policy<B>(priority)));
+
244 }
+
245 
+
246 template <Backend B, typename VSender, typename XSender, typename ASender>
+
247 void her2kDiag(pika::execution::thread_priority priority, VSender&& tile_v, XSender&& tile_x,
+
248  ASender&& tile_a) {
+
249  using T = dlaf::internal::SenderElementType<VSender>;
+
250  pika::execution::experimental::start_detached(
+
251  dlaf::internal::whenAllLift(blas::Uplo::Lower, blas::Op::NoTrans, T(-1),
+
252  std::forward<VSender>(tile_v), std::forward<XSender>(tile_x),
+
253  BaseType<T>(1), std::forward<ASender>(tile_a)) |
+
254  tile::her2k(dlaf::internal::Policy<B>(priority)));
+
255 }
+
256 
+
257 // C -= A . B*
+
258 template <Backend B, typename ASender, typename BSender, typename CSender>
+
259 void her2kOffDiag(pika::execution::thread_priority priority, ASender&& tile_a, BSender&& tile_b,
+
260  CSender&& tile_c) {
+
261  using T = dlaf::internal::SenderElementType<ASender>;
+
262  pika::execution::experimental::start_detached(
+
263  dlaf::internal::whenAllLift(blas::Op::NoTrans, blas::Op::ConjTrans, T(-1),
+
264  std::forward<ASender>(tile_a), std::forward<BSender>(tile_b), T(1),
+
265  std::forward<CSender>(tile_c)) |
+
266  tile::gemm(dlaf::internal::Policy<B>(priority)));
+
267 }
+
268 
+
269 namespace local {
+
270 
+
271 template <Device D, class T>
+
272 T computeReflector(const std::vector<matrix::Tile<T, D>>& panel, SizeType j) {
+
273  constexpr bool has_head = true;
+
274 
+
275  std::array<T, 2> x0_and_squares = computeX0AndSquares(has_head, panel, j);
+
276 
+
277  auto tau = computeReflectorAndTau(has_head, panel, j, std::move(x0_and_squares));
278 
-
279 template <class MatrixLikeA, class MatrixLikeTaus>
-
280 void computePanelReflectors(MatrixLikeA& mat_a, MatrixLikeTaus& mat_taus, const SizeType j_sub,
-
281  const matrix::SubPanelView& panel_view) {
-
282  static Device constexpr D = MatrixLikeA::device;
-
283  using T = typename MatrixLikeA::ElementType;
-
284  namespace ex = pika::execution::experimental;
-
285  namespace di = dlaf::internal;
-
286 
-
287  std::vector<matrix::ReadWriteTileSender<T, D>> panel_tiles;
-
288  panel_tiles.reserve(to_sizet(std::distance(panel_view.iteratorLocal().begin(),
-
289  panel_view.iteratorLocal().end())));
-
290  for (const auto& i : panel_view.iteratorLocal()) {
-
291  const matrix::SubTileSpec& spec = panel_view(i);
-
292  panel_tiles.emplace_back(matrix::splitTile(mat_a.readwrite(i), spec));
-
293  }
-
294 
-
295  const std::size_t nthreads = getReductionToBandPanelNWorkers();
-
296  auto s =
-
297  ex::when_all(ex::just(std::make_unique<pika::barrier<>>(nthreads),
-
298  std::vector<common::internal::vector<T>>{}), // w (internally required)
-
299  mat_taus.readwrite(LocalTileIndex(j_sub, 0)),
-
300  ex::when_all_vector(std::move(panel_tiles))) |
-
301  ex::transfer(di::getBackendScheduler<Backend::MC>(pika::execution::thread_priority::high)) |
-
302  ex::bulk(nthreads, [nthreads, cols = panel_view.cols()](const std::size_t index, auto& barrier_ptr,
-
303  auto& w, auto& taus, auto& tiles) {
-
304  const auto barrier_busy_wait = getReductionToBandBarrierBusyWait();
-
305  const std::size_t batch_size = util::ceilDiv(tiles.size(), nthreads);
-
306  const std::size_t begin = index * batch_size;
-
307  const std::size_t end = std::min(index * batch_size + batch_size, tiles.size());
-
308  const SizeType nrefls = taus.size().rows();
-
309 
-
310  if (index == 0) {
-
311  w.resize(nthreads);
-
312  }
-
313 
-
314  for (SizeType j = 0; j < nrefls; ++j) {
-
315  // STEP1: compute tau and reflector (single-thread)
-
316  if (index == 0) {
-
317  taus({j, 0}) = computeReflector(tiles, j);
-
318  }
-
319 
-
320  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
321 
-
322  // STEP2a: compute w (multi-threaded)
-
323  const SizeType pt_cols = cols - (j + 1);
-
324  if (pt_cols == 0)
-
325  break;
-
326  const bool has_head = (index == 0);
-
327 
-
328  w[index] = common::internal::vector<T>(pt_cols, 0);
-
329  computeWTrailingPanel(has_head, tiles, w[index], j, pt_cols, begin, end);
-
330  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
331 
-
332  // STEP2b: reduce w results (single-threaded)
-
333  if (index == 0)
-
334  dlaf::eigensolver::internal::reduceColumnVectors(w);
-
335  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
336 
-
337  // STEP3: update trailing panel (multi-threaded)
-
338  updateTrailingPanel(has_head, tiles, j, w[0], taus({j, 0}), begin, end);
-
339  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
340  }
-
341  });
-
342  ex::start_detached(std::move(s));
-
343 }
-
344 
-
345 template <Backend B, Device D, class T>
-
346 void setupReflectorPanelV(bool has_head, const matrix::SubPanelView& panel_view, const SizeType nrefls,
-
347  matrix::Panel<Coord::Col, T, D>& v, matrix::Matrix<const T, D>& mat_a,
-
348  bool force_copy = false) {
-
349  namespace ex = pika::execution::experimental;
-
350 
-
351  using pika::execution::thread_priority;
-
352 
-
353  // Note:
-
354  // Reflectors are stored in the lower triangular part of the A matrix leading to sharing memory
-
355  // between reflectors and results, which are in the upper triangular part. The problem exists only
-
356  // for the first tile (of the V, i.e. band excluded). Since refelectors will be used in next
-
357  // computations, they should be well-formed, i.e. a unit lower trapezoidal matrix. For this reason,
-
358  // a support tile is used, where just the reflectors values are copied, the diagonal is set to 1
-
359  // and the rest is zeroed out.
-
360  auto it_begin = panel_view.iteratorLocal().begin();
-
361  auto it_end = panel_view.iteratorLocal().end();
-
362 
-
363  if (has_head) {
-
364  const LocalTileIndex i = *it_begin;
-
365  matrix::SubTileSpec spec = panel_view(i);
-
366 
-
367  // Note:
-
368  // If the number of reflectors are limited by height (|reflector| > 1), the panel is narrower than
-
369  // the blocksize, leading to just using a part of A (first full nrefls columns)
-
370  spec.size = {spec.size.rows(), std::min(nrefls, spec.size.cols())};
-
371 
-
372  // Note:
-
373  // copy + laset is done in two independent tasks, but it could be theoretically merged to into a
-
374  // single task doing both.
-
375  const auto p = dlaf::internal::Policy<B>(thread_priority::high);
-
376  ex::start_detached(dlaf::internal::whenAllLift(splitTile(mat_a.read(i), spec), v.readwrite(i)) |
-
377  matrix::copy(p));
-
378  ex::start_detached(dlaf::internal::whenAllLift(blas::Uplo::Upper, T(0), T(1), v.readwrite(i)) |
-
379  tile::laset(p));
-
380 
-
381  ++it_begin;
-
382  }
+
279  return tau;
+
280 }
+
281 
+
282 template <class MatrixLikeA, class MatrixLikeTaus>
+
283 void computePanelReflectors(MatrixLikeA& mat_a, MatrixLikeTaus& mat_taus, const SizeType j_sub,
+
284  const matrix::SubPanelView& panel_view) {
+
285  static Device constexpr D = MatrixLikeA::device;
+
286  using T = typename MatrixLikeA::ElementType;
+
287  namespace ex = pika::execution::experimental;
+
288  namespace di = dlaf::internal;
+
289 
+
290  std::vector<matrix::ReadWriteTileSender<T, D>> panel_tiles;
+
291  panel_tiles.reserve(to_sizet(std::distance(panel_view.iteratorLocal().begin(),
+
292  panel_view.iteratorLocal().end())));
+
293  for (const auto& i : panel_view.iteratorLocal()) {
+
294  const matrix::SubTileSpec& spec = panel_view(i);
+
295  panel_tiles.emplace_back(matrix::splitTile(mat_a.readwrite(i), spec));
+
296  }
+
297 
+
298  const std::size_t nthreads = getReductionToBandPanelNWorkers();
+
299  auto s =
+
300  ex::when_all(ex::just(std::make_unique<pika::barrier<>>(nthreads),
+
301  std::vector<common::internal::vector<T>>{}), // w (internally required)
+
302  mat_taus.readwrite(LocalTileIndex(j_sub, 0)),
+
303  ex::when_all_vector(std::move(panel_tiles))) |
+
304  ex::transfer(di::getBackendScheduler<Backend::MC>(pika::execution::thread_priority::high)) |
+
305  ex::bulk(nthreads, [nthreads, cols = panel_view.cols()](const std::size_t index, auto& barrier_ptr,
+
306  auto& w, auto& taus, auto& tiles) {
+
307  const auto barrier_busy_wait = getReductionToBandBarrierBusyWait();
+
308  const std::size_t batch_size = util::ceilDiv(tiles.size(), nthreads);
+
309  const std::size_t begin = index * batch_size;
+
310  const std::size_t end = std::min(index * batch_size + batch_size, tiles.size());
+
311  const SizeType nrefls = taus.size().rows();
+
312 
+
313  if (index == 0) {
+
314  w.resize(nthreads);
+
315  }
+
316 
+
317  for (SizeType j = 0; j < nrefls; ++j) {
+
318  // STEP1: compute tau and reflector (single-thread)
+
319  if (index == 0) {
+
320  taus({j, 0}) = computeReflector(tiles, j);
+
321  }
+
322 
+
323  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
324 
+
325  // STEP2a: compute w (multi-threaded)
+
326  const SizeType pt_cols = cols - (j + 1);
+
327  if (pt_cols == 0)
+
328  break;
+
329  const bool has_head = (index == 0);
+
330 
+
331  w[index] = common::internal::vector<T>(pt_cols, 0);
+
332  computeWTrailingPanel(has_head, tiles, w[index], j, pt_cols, begin, end);
+
333  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
334 
+
335  // STEP2b: reduce w results (single-threaded)
+
336  if (index == 0)
+
337  dlaf::eigensolver::internal::reduceColumnVectors(w);
+
338  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
339 
+
340  // STEP3: update trailing panel (multi-threaded)
+
341  updateTrailingPanel(has_head, tiles, j, w[0], taus({j, 0}), begin, end);
+
342  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
343  }
+
344  });
+
345  ex::start_detached(std::move(s));
+
346 }
+
347 
+
348 template <Backend B, Device D, class T>
+
349 void setupReflectorPanelV(bool has_head, const matrix::SubPanelView& panel_view, const SizeType nrefls,
+
350  matrix::Panel<Coord::Col, T, D>& v, matrix::Matrix<const T, D>& mat_a,
+
351  bool force_copy = false) {
+
352  namespace ex = pika::execution::experimental;
+
353 
+
354  using pika::execution::thread_priority;
+
355 
+
356  // Note:
+
357  // Reflectors are stored in the lower triangular part of the A matrix leading to sharing memory
+
358  // between reflectors and results, which are in the upper triangular part. The problem exists only
+
359  // for the first tile (of the V, i.e. band excluded). Since refelectors will be used in next
+
360  // computations, they should be well-formed, i.e. a unit lower trapezoidal matrix. For this reason,
+
361  // a support tile is used, where just the reflectors values are copied, the diagonal is set to 1
+
362  // and the rest is zeroed out.
+
363  auto it_begin = panel_view.iteratorLocal().begin();
+
364  auto it_end = panel_view.iteratorLocal().end();
+
365 
+
366  if (has_head) {
+
367  const LocalTileIndex i = *it_begin;
+
368  matrix::SubTileSpec spec = panel_view(i);
+
369 
+
370  // Note:
+
371  // If the number of reflectors are limited by height (|reflector| > 1), the panel is narrower than
+
372  // the blocksize, leading to just using a part of A (first full nrefls columns)
+
373  spec.size = {spec.size.rows(), std::min(nrefls, spec.size.cols())};
+
374 
+
375  // Note:
+
376  // copy + laset is done in two independent tasks, but it could be theoretically merged to into a
+
377  // single task doing both.
+
378  const auto p = dlaf::internal::Policy<B>(thread_priority::high);
+
379  ex::start_detached(dlaf::internal::whenAllLift(splitTile(mat_a.read(i), spec), v.readwrite(i)) |
+
380  matrix::copy(p));
+
381  ex::start_detached(dlaf::internal::whenAllLift(blas::Uplo::Upper, T(0), T(1), v.readwrite(i)) |
+
382  tile::laset(p));
383 
-
384  // The rest of the V panel of reflectors can just point to the values in A, since they are
-
385  // well formed in-place.
-
386  for (auto it = it_begin; it < it_end; ++it) {
-
387  const LocalTileIndex idx = *it;
-
388  const matrix::SubTileSpec& spec = panel_view(idx);
-
389 
-
390  // Note: This is a workaround for the deadlock problem with sub-tiles.
-
391  // Without this copy, during matrix update the same tile would get accessed at the same
-
392  // time both in readonly mode (for reflectors) and in readwrite mode (for updating the
-
393  // matrix). This would result in a deadlock, so instead of linking the panel to an external
-
394  // tile, memory provided internally by the panel is used as support. In this way, the two
-
395  // subtiles used in the operation belong to different tiles.
-
396  if (force_copy)
-
397  ex::start_detached(ex::when_all(matrix::splitTile(mat_a.read(idx), spec), v.readwrite(idx)) |
-
398  matrix::copy(dlaf::internal::Policy<B>(thread_priority::high)));
-
399  else
-
400  v.setTile(idx, matrix::splitTile(mat_a.read(idx), spec));
-
401  }
-
402 }
-
403 
-
404 template <Backend B, Device D, class T>
-
405 void trmmComputeW(matrix::Panel<Coord::Col, T, D>& w, matrix::Panel<Coord::Col, T, D>& v,
-
406  matrix::ReadOnlyTileSender<T, D> tile_t) {
-
407  namespace ex = pika::execution::experimental;
-
408 
-
409  using pika::execution::thread_priority;
-
410  using namespace blas;
+
384  ++it_begin;
+
385  }
+
386 
+
387  // The rest of the V panel of reflectors can just point to the values in A, since they are
+
388  // well formed in-place.
+
389  for (auto it = it_begin; it < it_end; ++it) {
+
390  const LocalTileIndex idx = *it;
+
391  const matrix::SubTileSpec& spec = panel_view(idx);
+
392 
+
393  // Note: This is a workaround for the deadlock problem with sub-tiles.
+
394  // Without this copy, during matrix update the same tile would get accessed at the same
+
395  // time both in readonly mode (for reflectors) and in readwrite mode (for updating the
+
396  // matrix). This would result in a deadlock, so instead of linking the panel to an external
+
397  // tile, memory provided internally by the panel is used as support. In this way, the two
+
398  // subtiles used in the operation belong to different tiles.
+
399  if (force_copy)
+
400  ex::start_detached(ex::when_all(matrix::splitTile(mat_a.read(idx), spec), v.readwrite(idx)) |
+
401  matrix::copy(dlaf::internal::Policy<B>(thread_priority::high)));
+
402  else
+
403  v.setTile(idx, matrix::splitTile(mat_a.read(idx), spec));
+
404  }
+
405 }
+
406 
+
407 template <Backend B, Device D, class T>
+
408 void trmmComputeW(matrix::Panel<Coord::Col, T, D>& w, matrix::Panel<Coord::Col, T, D>& v,
+
409  matrix::ReadOnlyTileSender<T, D> tile_t) {
+
410  namespace ex = pika::execution::experimental;
411 
-
412  auto it = w.iteratorLocal();
-
413 
-
414  for (const auto& index_i : it) {
-
415  ex::start_detached(dlaf::internal::whenAllLift(Side::Right, Uplo::Upper, Op::NoTrans, Diag::NonUnit,
-
416  T(1), tile_t, v.read(index_i), w.readwrite(index_i)) |
-
417  tile::trmm3(dlaf::internal::Policy<B>(thread_priority::high)));
-
418  }
-
419 
-
420  if (it.empty()) {
-
421  ex::start_detached(std::move(tile_t));
-
422  }
-
423 }
-
424 
-
425 template <Backend B, Device D, class T>
-
426 void gemmUpdateX(matrix::Panel<Coord::Col, T, D>& x, matrix::Matrix<const T, D>& w2,
-
427  matrix::Panel<Coord::Col, const T, D>& v) {
-
428  namespace ex = pika::execution::experimental;
-
429 
-
430  using pika::execution::thread_priority;
-
431  using namespace blas;
+
412  using pika::execution::thread_priority;
+
413  using namespace blas;
+
414 
+
415  auto it = w.iteratorLocal();
+
416 
+
417  for (const auto& index_i : it) {
+
418  ex::start_detached(dlaf::internal::whenAllLift(Side::Right, Uplo::Upper, Op::NoTrans, Diag::NonUnit,
+
419  T(1), tile_t, v.read(index_i), w.readwrite(index_i)) |
+
420  tile::trmm3(dlaf::internal::Policy<B>(thread_priority::high)));
+
421  }
+
422 
+
423  if (it.empty()) {
+
424  ex::start_detached(std::move(tile_t));
+
425  }
+
426 }
+
427 
+
428 template <Backend B, Device D, class T>
+
429 void gemmUpdateX(matrix::Panel<Coord::Col, T, D>& x, matrix::Matrix<const T, D>& w2,
+
430  matrix::Panel<Coord::Col, const T, D>& v) {
+
431  namespace ex = pika::execution::experimental;
432 
-
433  // GEMM X = X - 0.5 . V . W2
-
434  for (const auto& index_i : v.iteratorLocal())
-
435  ex::start_detached(dlaf::internal::whenAllLift(Op::NoTrans, Op::NoTrans, T(-0.5), v.read(index_i),
-
436  w2.read(LocalTileIndex(0, 0)), T(1),
-
437  x.readwrite(index_i)) |
-
438  tile::gemm(dlaf::internal::Policy<B>(thread_priority::high)));
-
439 }
-
440 
-
441 template <Backend B, Device D, class T>
-
442 void hemmComputeX(matrix::Panel<Coord::Col, T, D>& x, const matrix::SubMatrixView& view,
-
443  matrix::Matrix<const T, D>& a, matrix::Panel<Coord::Col, const T, D>& w) {
-
444  namespace ex = pika::execution::experimental;
-
445 
-
446  using pika::execution::thread_priority;
-
447 
-
448  const auto dist = a.distribution();
-
449 
-
450  // Note:
-
451  // They have to be set to zero, because all tiles are going to be reduced, and some tiles may not get
-
452  // "initialized" during computation, so they should not contribute with any spurious value to the final
-
453  // result.
-
454  matrix::util::set0<B>(thread_priority::high, x);
-
455 
-
456  const LocalTileIndex at_offset = view.begin();
-
457 
-
458  for (SizeType i = at_offset.row(); i < dist.localNrTiles().rows(); ++i) {
-
459  const auto limit = i + 1;
-
460  for (SizeType j = limit - 1; j >= at_offset.col(); --j) {
-
461  const LocalTileIndex ij{i, j};
-
462 
-
463  const bool is_diagonal_tile = (ij.row() == ij.col());
-
464 
-
465  const auto& tile_a = splitTile(a.read(ij), view(ij));
-
466 
-
467  if (is_diagonal_tile) {
-
468  hemmDiag<B>(thread_priority::high, tile_a, w.read(ij), x.readwrite(ij));
-
469  }
-
470  else {
-
471  // Note:
-
472  // Because A is hermitian and just the lower part contains the data, for each a(ij) not
-
473  // on the diagonal, two computations are done:
-
474  // - using a(ij) in its position;
-
475  // - using a(ij) in its "transposed" position (applying the ConjTrans to its data)
-
476 
-
477  {
-
478  const LocalTileIndex index_x(Coord::Row, ij.row());
-
479  const LocalTileIndex index_w(Coord::Row, ij.col());
-
480  hemmOffDiag<B>(thread_priority::high, blas::Op::NoTrans, tile_a, w.read(index_w),
-
481  x.readwrite(index_x));
-
482  }
-
483 
-
484  {
-
485  const LocalTileIndex index_pretended = transposed(ij);
-
486  const LocalTileIndex index_x(Coord::Row, index_pretended.row());
-
487  const LocalTileIndex index_w(Coord::Row, index_pretended.col());
-
488  hemmOffDiag<B>(thread_priority::high, blas::Op::ConjTrans, tile_a, w.read(index_w),
-
489  x.readwrite(index_x));
-
490  }
-
491  }
-
492  }
-
493  }
-
494 }
-
495 
-
496 template <Backend B, Device D, class T>
-
497 void gemmComputeW2(matrix::Matrix<T, D>& w2, matrix::Panel<Coord::Col, const T, D>& w,
-
498  matrix::Panel<Coord::Col, const T, D>& x) {
-
499  using pika::execution::thread_priority;
-
500 
-
501  namespace ex = pika::execution::experimental;
-
502 
-
503  // Note:
-
504  // Not all ranks in the column always hold at least a tile in the panel Ai, but all ranks in
-
505  // the column are going to participate to the reduce. For them, it is important to set the
-
506  // partial result W2 to zero.
-
507  ex::start_detached(w2.readwrite(LocalTileIndex(0, 0)) |
-
508  tile::set0(dlaf::internal::Policy<B>(thread_priority::high)));
-
509 
-
510  using namespace blas;
-
511  // GEMM W2 = W* . X
-
512  for (const auto& index_tile : w.iteratorLocal())
-
513  ex::start_detached(dlaf::internal::whenAllLift(Op::ConjTrans, Op::NoTrans, T(1), w.read(index_tile),
-
514  x.read(index_tile), T(1),
-
515  w2.readwrite(LocalTileIndex(0, 0))) |
-
516  tile::gemm(dlaf::internal::Policy<B>(thread_priority::high)));
-
517 }
-
518 
-
519 template <Backend B, Device D, class T>
-
520 void her2kUpdateTrailingMatrix(const matrix::SubMatrixView& view, matrix::Matrix<T, D>& a,
-
521  matrix::Panel<Coord::Col, const T, D>& x,
-
522  matrix::Panel<Coord::Col, const T, D>& v) {
-
523  static_assert(std::is_signed_v<BaseType<T>>, "alpha in computations requires to be -1");
-
524 
-
525  using pika::execution::thread_priority;
-
526 
-
527  const auto dist = a.distribution();
-
528 
-
529  const LocalTileIndex at_start = view.begin();
-
530 
-
531  for (SizeType i = at_start.row(); i < dist.localNrTiles().rows(); ++i) {
-
532  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
-
533  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
-
534  for (SizeType j = at_start.col(); j < limit; ++j) {
-
535  const LocalTileIndex ij_local{i, j};
-
536  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
-
537 
-
538  const bool is_diagonal_tile = (ij.row() == ij.col());
-
539 
-
540  auto getSubA = [&a, &view, ij_local]() {
-
541  return splitTile(a.readwrite(ij_local), view(ij_local));
-
542  };
-
543 
-
544  // The first column of the trailing matrix (except for the very first global tile) has to be
-
545  // updated first, in order to unlock the next iteration as soon as possible.
-
546  const auto priority = (j == at_start.col()) ? thread_priority::high : thread_priority::normal;
-
547 
-
548  if (is_diagonal_tile) {
-
549  her2kDiag<B>(priority, v.read(ij_local), x.read(ij_local), getSubA());
-
550  }
-
551  else {
-
552  // A -= X . V*
-
553  her2kOffDiag<B>(priority, x.read(ij_local), v.read(transposed(ij_local)), getSubA());
-
554 
-
555  // A -= V . X*
-
556  her2kOffDiag<B>(priority, v.read(ij_local), x.read(transposed(ij_local)), getSubA());
-
557  }
-
558  }
-
559  }
-
560 }
-
561 
-
562 }
-
563 
-
564 namespace distributed {
-
565 template <Device D, class T>
-
566 T computeReflector(const bool has_head, comm::Communicator& communicator,
-
567  const std::vector<matrix::Tile<T, D>>& panel, SizeType j) {
-
568  std::array<T, 2> x0_and_squares = computeX0AndSquares(has_head, panel, j);
-
569 
-
570  // Note:
-
571  // This is an optimization for grouping two separate low bandwidth communications, respectively
-
572  // bcast(x0) and reduce(norm), where the latency was degrading performances.
-
573  //
-
574  // In particular this allReduce allows to:
-
575  // - bcast x0, since for all ranks is 0 and just the root rank has the real value;
-
576  // - allReduce squares for the norm computation.
-
577  //
-
578  // Moreover, by all-reducing squares and broadcasting x0, all ranks have all the information to
-
579  // update locally the reflectors (section they have). This is more efficient than computing params
-
580  // (e.g. norm, y, tau) just on the root rank and then having to broadcast them (i.e. additional
-
581  // communication).
-
582  comm::sync::allReduceInPlace(communicator, MPI_SUM,
-
583  common::make_data(x0_and_squares.data(),
-
584  to_SizeType(x0_and_squares.size())));
-
585 
-
586  auto tau = computeReflectorAndTau(has_head, panel, j, std::move(x0_and_squares));
-
587 
-
588  return tau;
-
589 }
+
433  using pika::execution::thread_priority;
+
434  using namespace blas;
+
435 
+
436  // GEMM X = X - 0.5 . V . W2
+
437  for (const auto& index_i : v.iteratorLocal())
+
438  ex::start_detached(dlaf::internal::whenAllLift(Op::NoTrans, Op::NoTrans, T(-0.5), v.read(index_i),
+
439  w2.read(LocalTileIndex(0, 0)), T(1),
+
440  x.readwrite(index_i)) |
+
441  tile::gemm(dlaf::internal::Policy<B>(thread_priority::high)));
+
442 }
+
443 
+
444 template <Backend B, Device D, class T>
+
445 void hemmComputeX(matrix::Panel<Coord::Col, T, D>& x, const matrix::SubMatrixView& view,
+
446  matrix::Matrix<const T, D>& a, matrix::Panel<Coord::Col, const T, D>& w) {
+
447  namespace ex = pika::execution::experimental;
+
448 
+
449  using pika::execution::thread_priority;
+
450 
+
451  const auto dist = a.distribution();
+
452 
+
453  // Note:
+
454  // They have to be set to zero, because all tiles are going to be reduced, and some tiles may not get
+
455  // "initialized" during computation, so they should not contribute with any spurious value to the final
+
456  // result.
+
457  matrix::util::set0<B>(thread_priority::high, x);
+
458 
+
459  const LocalTileIndex at_offset = view.begin();
+
460 
+
461  for (SizeType i = at_offset.row(); i < dist.localNrTiles().rows(); ++i) {
+
462  const auto limit = i + 1;
+
463  for (SizeType j = limit - 1; j >= at_offset.col(); --j) {
+
464  const LocalTileIndex ij{i, j};
+
465 
+
466  const bool is_diagonal_tile = (ij.row() == ij.col());
+
467 
+
468  const auto& tile_a = splitTile(a.read(ij), view(ij));
+
469 
+
470  if (is_diagonal_tile) {
+
471  hemmDiag<B>(thread_priority::high, tile_a, w.read(ij), x.readwrite(ij));
+
472  }
+
473  else {
+
474  // Note:
+
475  // Because A is hermitian and just the lower part contains the data, for each a(ij) not
+
476  // on the diagonal, two computations are done:
+
477  // - using a(ij) in its position;
+
478  // - using a(ij) in its "transposed" position (applying the ConjTrans to its data)
+
479 
+
480  {
+
481  const LocalTileIndex index_x(Coord::Row, ij.row());
+
482  const LocalTileIndex index_w(Coord::Row, ij.col());
+
483  hemmOffDiag<B>(thread_priority::high, blas::Op::NoTrans, tile_a, w.read(index_w),
+
484  x.readwrite(index_x));
+
485  }
+
486 
+
487  {
+
488  const LocalTileIndex index_pretended = transposed(ij);
+
489  const LocalTileIndex index_x(Coord::Row, index_pretended.row());
+
490  const LocalTileIndex index_w(Coord::Row, index_pretended.col());
+
491  hemmOffDiag<B>(thread_priority::high, blas::Op::ConjTrans, tile_a, w.read(index_w),
+
492  x.readwrite(index_x));
+
493  }
+
494  }
+
495  }
+
496  }
+
497 }
+
498 
+
499 template <Backend B, Device D, class T>
+
500 void gemmComputeW2(matrix::Matrix<T, D>& w2, matrix::Panel<Coord::Col, const T, D>& w,
+
501  matrix::Panel<Coord::Col, const T, D>& x) {
+
502  using pika::execution::thread_priority;
+
503 
+
504  namespace ex = pika::execution::experimental;
+
505 
+
506  // Note:
+
507  // Not all ranks in the column always hold at least a tile in the panel Ai, but all ranks in
+
508  // the column are going to participate to the reduce. For them, it is important to set the
+
509  // partial result W2 to zero.
+
510  ex::start_detached(w2.readwrite(LocalTileIndex(0, 0)) |
+
511  tile::set0(dlaf::internal::Policy<B>(thread_priority::high)));
+
512 
+
513  using namespace blas;
+
514  // GEMM W2 = W* . X
+
515  for (const auto& index_tile : w.iteratorLocal())
+
516  ex::start_detached(dlaf::internal::whenAllLift(Op::ConjTrans, Op::NoTrans, T(1), w.read(index_tile),
+
517  x.read(index_tile), T(1),
+
518  w2.readwrite(LocalTileIndex(0, 0))) |
+
519  tile::gemm(dlaf::internal::Policy<B>(thread_priority::high)));
+
520 }
+
521 
+
522 template <Backend B, Device D, class T>
+
523 void her2kUpdateTrailingMatrix(const matrix::SubMatrixView& view, matrix::Matrix<T, D>& a,
+
524  matrix::Panel<Coord::Col, const T, D>& x,
+
525  matrix::Panel<Coord::Col, const T, D>& v) {
+
526  static_assert(std::is_signed_v<BaseType<T>>, "alpha in computations requires to be -1");
+
527 
+
528  using pika::execution::thread_priority;
+
529 
+
530  const auto dist = a.distribution();
+
531 
+
532  const LocalTileIndex at_start = view.begin();
+
533 
+
534  for (SizeType i = at_start.row(); i < dist.localNrTiles().rows(); ++i) {
+
535  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
+
536  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
+
537  for (SizeType j = at_start.col(); j < limit; ++j) {
+
538  const LocalTileIndex ij_local{i, j};
+
539  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
+
540 
+
541  const bool is_diagonal_tile = (ij.row() == ij.col());
+
542 
+
543  auto getSubA = [&a, &view, ij_local]() {
+
544  return splitTile(a.readwrite(ij_local), view(ij_local));
+
545  };
+
546 
+
547  // The first column of the trailing matrix (except for the very first global tile) has to be
+
548  // updated first, in order to unlock the next iteration as soon as possible.
+
549  const auto priority = (j == at_start.col()) ? thread_priority::high : thread_priority::normal;
+
550 
+
551  if (is_diagonal_tile) {
+
552  her2kDiag<B>(priority, v.read(ij_local), x.read(ij_local), getSubA());
+
553  }
+
554  else {
+
555  // A -= X . V*
+
556  her2kOffDiag<B>(priority, x.read(ij_local), v.read(transposed(ij_local)), getSubA());
+
557 
+
558  // A -= V . X*
+
559  her2kOffDiag<B>(priority, v.read(ij_local), x.read(transposed(ij_local)), getSubA());
+
560  }
+
561  }
+
562  }
+
563 }
+
564 
+
565 }
+
566 
+
567 namespace distributed {
+
568 template <Device D, class T>
+
569 T computeReflector(const bool has_head, comm::Communicator& communicator,
+
570  const std::vector<matrix::Tile<T, D>>& panel, SizeType j) {
+
571  std::array<T, 2> x0_and_squares = computeX0AndSquares(has_head, panel, j);
+
572 
+
573  // Note:
+
574  // This is an optimization for grouping two separate low bandwidth communications, respectively
+
575  // bcast(x0) and reduce(norm), where the latency was degrading performances.
+
576  //
+
577  // In particular this allReduce allows to:
+
578  // - bcast x0, since for all ranks is 0 and just the root rank has the real value;
+
579  // - allReduce squares for the norm computation.
+
580  //
+
581  // Moreover, by all-reducing squares and broadcasting x0, all ranks have all the information to
+
582  // update locally the reflectors (section they have). This is more efficient than computing params
+
583  // (e.g. norm, y, tau) just on the root rank and then having to broadcast them (i.e. additional
+
584  // communication).
+
585  comm::sync::allReduceInPlace(communicator, MPI_SUM,
+
586  common::make_data(x0_and_squares.data(),
+
587  to_SizeType(x0_and_squares.size())));
+
588 
+
589  auto tau = computeReflectorAndTau(has_head, panel, j, std::move(x0_and_squares));
590 
-
591 template <class MatrixLikeA, class MatrixLikeTaus, class TriggerSender, class CommSender>
-
592 void computePanelReflectors(TriggerSender&& trigger, comm::IndexT_MPI rank_v0,
-
593  CommSender&& mpi_col_chain_panel, MatrixLikeA& mat_a,
-
594  MatrixLikeTaus& mat_taus, SizeType j_sub,
-
595  const matrix::SubPanelView& panel_view) {
-
596  static Device constexpr D = MatrixLikeA::device;
-
597  using T = typename MatrixLikeA::ElementType;
-
598  namespace ex = pika::execution::experimental;
-
599  namespace di = dlaf::internal;
-
600 
-
601  std::vector<matrix::ReadWriteTileSender<T, D>> panel_tiles;
-
602  panel_tiles.reserve(to_sizet(std::distance(panel_view.iteratorLocal().begin(),
-
603  panel_view.iteratorLocal().end())));
-
604  for (const auto& i : panel_view.iteratorLocal()) {
-
605  const matrix::SubTileSpec& spec = panel_view(i);
-
606  panel_tiles.emplace_back(matrix::splitTile(mat_a.readwrite(i), spec));
-
607  }
-
608 
-
609  const std::size_t nthreads = getReductionToBandPanelNWorkers();
-
610  auto s =
-
611  ex::when_all(ex::just(std::make_unique<pika::barrier<>>(nthreads),
-
612  std::vector<common::internal::vector<T>>{}), // w (internally required)
-
613  mat_taus.readwrite(GlobalTileIndex(j_sub, 0)),
-
614  ex::when_all_vector(std::move(panel_tiles)),
-
615  std::forward<CommSender>(mpi_col_chain_panel), std::forward<TriggerSender>(trigger)) |
-
616  ex::transfer(di::getBackendScheduler<Backend::MC>(pika::execution::thread_priority::high)) |
-
617  ex::bulk(nthreads, [nthreads, rank_v0,
-
618  cols = panel_view.cols()](const std::size_t index, auto& barrier_ptr, auto& w,
-
619  auto& taus, auto& tiles, auto&& pcomm) {
-
620  const bool rankHasHead = rank_v0 == pcomm.get().rank();
-
621 
-
622  const auto barrier_busy_wait = getReductionToBandBarrierBusyWait();
-
623  const std::size_t batch_size = util::ceilDiv(tiles.size(), nthreads);
-
624  const std::size_t begin = index * batch_size;
-
625  const std::size_t end = std::min(index * batch_size + batch_size, tiles.size());
-
626  const SizeType nrefls = taus.size().rows();
-
627 
-
628  if (index == 0) {
-
629  w.resize(nthreads);
-
630  }
-
631 
-
632  for (SizeType j = 0; j < nrefls; ++j) {
-
633  // STEP1: compute tau and reflector (single-thread)
-
634  if (index == 0) {
-
635  const bool has_head = rankHasHead;
-
636  taus({j, 0}) = computeReflector(has_head, pcomm.get(), tiles, j);
-
637  }
-
638  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
639 
-
640  // STEP2a: compute w (multi-threaded)
-
641  const SizeType pt_cols = cols - (j + 1);
-
642  if (pt_cols == 0)
-
643  break;
-
644 
-
645  const bool has_head = rankHasHead && (index == 0);
-
646 
-
647  w[index] = common::internal::vector<T>(pt_cols, 0);
-
648  computeWTrailingPanel(has_head, tiles, w[index], j, pt_cols, begin, end);
-
649  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
650 
-
651  // STEP2b: reduce w results (single-threaded)
-
652  if (index == 0) {
-
653  dlaf::eigensolver::internal::reduceColumnVectors(w);
-
654  comm::sync::allReduceInPlace(pcomm.get(), MPI_SUM, common::make_data(w[0].data(), pt_cols));
-
655  }
-
656  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
657 
-
658  // STEP3: update trailing panel (multi-threaded)
-
659  updateTrailingPanel(has_head, tiles, j, w[0], taus({j, 0}), begin, end);
-
660  barrier_ptr->arrive_and_wait(barrier_busy_wait);
-
661  }
-
662  });
-
663  ex::start_detached(std::move(s));
-
664 }
-
665 
-
666 template <Backend B, Device D, class T>
-
667 void hemmComputeX(comm::IndexT_MPI reducer_col, matrix::Panel<Coord::Col, T, D>& x,
-
668  matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>& xt,
-
669  const matrix::SubMatrixView& view, matrix::Matrix<const T, D>& a,
-
670  matrix::Panel<Coord::Col, const T, D>& w,
-
671  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& wt,
-
672  common::Pipeline<comm::Communicator>& mpi_row_chain,
-
673  common::Pipeline<comm::Communicator>& mpi_col_chain) {
-
674  namespace ex = pika::execution::experimental;
-
675 
-
676  using pika::execution::thread_priority;
-
677 
-
678  const auto dist = a.distribution();
-
679  const auto rank = dist.rankIndex();
+
591  return tau;
+
592 }
+
593 
+
594 template <class MatrixLikeA, class MatrixLikeTaus, class TriggerSender, class CommSender>
+
595 void computePanelReflectors(TriggerSender&& trigger, comm::IndexT_MPI rank_v0,
+
596  CommSender&& mpi_col_chain_panel, MatrixLikeA& mat_a,
+
597  MatrixLikeTaus& mat_taus, SizeType j_sub,
+
598  const matrix::SubPanelView& panel_view) {
+
599  static Device constexpr D = MatrixLikeA::device;
+
600  using T = typename MatrixLikeA::ElementType;
+
601  namespace ex = pika::execution::experimental;
+
602  namespace di = dlaf::internal;
+
603 
+
604  std::vector<matrix::ReadWriteTileSender<T, D>> panel_tiles;
+
605  panel_tiles.reserve(to_sizet(std::distance(panel_view.iteratorLocal().begin(),
+
606  panel_view.iteratorLocal().end())));
+
607  for (const auto& i : panel_view.iteratorLocal()) {
+
608  const matrix::SubTileSpec& spec = panel_view(i);
+
609  panel_tiles.emplace_back(matrix::splitTile(mat_a.readwrite(i), spec));
+
610  }
+
611 
+
612  const std::size_t nthreads = getReductionToBandPanelNWorkers();
+
613  auto s =
+
614  ex::when_all(ex::just(std::make_unique<pika::barrier<>>(nthreads),
+
615  std::vector<common::internal::vector<T>>{}), // w (internally required)
+
616  mat_taus.readwrite(GlobalTileIndex(j_sub, 0)),
+
617  ex::when_all_vector(std::move(panel_tiles)),
+
618  std::forward<CommSender>(mpi_col_chain_panel), std::forward<TriggerSender>(trigger)) |
+
619  ex::transfer(di::getBackendScheduler<Backend::MC>(pika::execution::thread_priority::high)) |
+
620  ex::bulk(nthreads, [nthreads, rank_v0,
+
621  cols = panel_view.cols()](const std::size_t index, auto& barrier_ptr, auto& w,
+
622  auto& taus, auto& tiles, auto&& pcomm) {
+
623  const bool rankHasHead = rank_v0 == pcomm.get().rank();
+
624 
+
625  const auto barrier_busy_wait = getReductionToBandBarrierBusyWait();
+
626  const std::size_t batch_size = util::ceilDiv(tiles.size(), nthreads);
+
627  const std::size_t begin = index * batch_size;
+
628  const std::size_t end = std::min(index * batch_size + batch_size, tiles.size());
+
629  const SizeType nrefls = taus.size().rows();
+
630 
+
631  if (index == 0) {
+
632  w.resize(nthreads);
+
633  }
+
634 
+
635  for (SizeType j = 0; j < nrefls; ++j) {
+
636  // STEP1: compute tau and reflector (single-thread)
+
637  if (index == 0) {
+
638  const bool has_head = rankHasHead;
+
639  taus({j, 0}) = computeReflector(has_head, pcomm.get(), tiles, j);
+
640  }
+
641  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
642 
+
643  // STEP2a: compute w (multi-threaded)
+
644  const SizeType pt_cols = cols - (j + 1);
+
645  if (pt_cols == 0)
+
646  break;
+
647 
+
648  const bool has_head = rankHasHead && (index == 0);
+
649 
+
650  w[index] = common::internal::vector<T>(pt_cols, 0);
+
651  computeWTrailingPanel(has_head, tiles, w[index], j, pt_cols, begin, end);
+
652  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
653 
+
654  // STEP2b: reduce w results (single-threaded)
+
655  if (index == 0) {
+
656  dlaf::eigensolver::internal::reduceColumnVectors(w);
+
657  comm::sync::allReduceInPlace(pcomm.get(), MPI_SUM, common::make_data(w[0].data(), pt_cols));
+
658  }
+
659  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
660 
+
661  // STEP3: update trailing panel (multi-threaded)
+
662  updateTrailingPanel(has_head, tiles, j, w[0], taus({j, 0}), begin, end);
+
663  barrier_ptr->arrive_and_wait(barrier_busy_wait);
+
664  }
+
665  });
+
666  ex::start_detached(std::move(s));
+
667 }
+
668 
+
669 template <Backend B, Device D, class T>
+
670 void hemmComputeX(comm::IndexT_MPI reducer_col, matrix::Panel<Coord::Col, T, D>& x,
+
671  matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>& xt,
+
672  const matrix::SubMatrixView& view, matrix::Matrix<const T, D>& a,
+
673  matrix::Panel<Coord::Col, const T, D>& w,
+
674  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& wt,
+
675  common::Pipeline<comm::Communicator>& mpi_row_chain,
+
676  common::Pipeline<comm::Communicator>& mpi_col_chain) {
+
677  namespace ex = pika::execution::experimental;
+
678 
+
679  using pika::execution::thread_priority;
680 
-
681  // Note:
-
682  // They have to be set to zero, because all tiles are going to be reduced, and some tiles may not get
-
683  // "initialized" during computation, so they should not contribute with any spurious value to the final
-
684  // result.
-
685  matrix::util::set0<B>(thread_priority::high, x);
-
686  matrix::util::set0<B>(thread_priority::high, xt);
-
687 
-
688  const LocalTileIndex at_offset = view.begin();
-
689 
-
690  for (SizeType i = at_offset.row(); i < dist.localNrTiles().rows(); ++i) {
-
691  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
-
692  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
-
693  for (SizeType j = limit - 1; j >= at_offset.col(); --j) {
-
694  const LocalTileIndex ij_local{i, j};
-
695  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
-
696 
-
697  const bool is_diagonal_tile = (ij.row() == ij.col());
-
698 
-
699  auto tile_a = splitTile(a.read(ij), view(ij_local));
-
700 
-
701  if (is_diagonal_tile) {
-
702  hemmDiag<B>(thread_priority::high, std::move(tile_a), w.read(ij_local), x.readwrite(ij_local));
-
703  }
-
704  else {
-
705  // Note:
-
706  // Since it is not a diagonal tile, otherwise it would have been managed in the previous
-
707  // branch, the second operand is not available in W but it is accessible through the
-
708  // support panel Wt.
-
709  // However, since we are still computing the "straight" part, the result can be stored
-
710  // in the "local" panel X.
-
711  hemmOffDiag<B>(thread_priority::high, blas::Op::NoTrans, tile_a, wt.read(ij_local),
-
712  x.readwrite(ij_local));
-
713 
-
714  // Note:
-
715  // Here we are considering the hermitian part of A, so coordinates have to be "mirrored".
-
716  // So, first step is identifying the mirrored cell coordinate, i.e. swap row/col, together
-
717  // with realizing if the new coord lays on an owned row or not.
-
718  // If yes, the result can be stored in the X, otherwise Xt support panel will be used.
-
719  // For what concerns the second operand, it can be found for sure in W. In fact, the
-
720  // multiplication requires matching col(A) == row(W), but since coordinates are mirrored,
-
721  // we are matching row(A) == row(W), so it is local by construction.
-
722  const auto owner = dist.template rankGlobalTile<Coord::Row>(ij.col());
-
723 
-
724  const LocalTileIndex index_x{dist.template localTileFromGlobalTile<Coord::Row>(ij.col()), 0};
-
725  const LocalTileIndex index_xt{0, ij_local.col()};
+
681  const auto dist = a.distribution();
+
682  const auto rank = dist.rankIndex();
+
683 
+
684  // Note:
+
685  // They have to be set to zero, because all tiles are going to be reduced, and some tiles may not get
+
686  // "initialized" during computation, so they should not contribute with any spurious value to the final
+
687  // result.
+
688  matrix::util::set0<B>(thread_priority::high, x);
+
689  matrix::util::set0<B>(thread_priority::high, xt);
+
690 
+
691  const LocalTileIndex at_offset = view.begin();
+
692 
+
693  for (SizeType i = at_offset.row(); i < dist.localNrTiles().rows(); ++i) {
+
694  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
+
695  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
+
696  for (SizeType j = limit - 1; j >= at_offset.col(); --j) {
+
697  const LocalTileIndex ij_local{i, j};
+
698  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
+
699 
+
700  const bool is_diagonal_tile = (ij.row() == ij.col());
+
701 
+
702  auto tile_a = splitTile(a.read(ij), view(ij_local));
+
703 
+
704  if (is_diagonal_tile) {
+
705  hemmDiag<B>(thread_priority::high, std::move(tile_a), w.read(ij_local), x.readwrite(ij_local));
+
706  }
+
707  else {
+
708  // Note:
+
709  // Since it is not a diagonal tile, otherwise it would have been managed in the previous
+
710  // branch, the second operand is not available in W but it is accessible through the
+
711  // support panel Wt.
+
712  // However, since we are still computing the "straight" part, the result can be stored
+
713  // in the "local" panel X.
+
714  hemmOffDiag<B>(thread_priority::high, blas::Op::NoTrans, tile_a, wt.read(ij_local),
+
715  x.readwrite(ij_local));
+
716 
+
717  // Note:
+
718  // Here we are considering the hermitian part of A, so coordinates have to be "mirrored".
+
719  // So, first step is identifying the mirrored cell coordinate, i.e. swap row/col, together
+
720  // with realizing if the new coord lays on an owned row or not.
+
721  // If yes, the result can be stored in the X, otherwise Xt support panel will be used.
+
722  // For what concerns the second operand, it can be found for sure in W. In fact, the
+
723  // multiplication requires matching col(A) == row(W), but since coordinates are mirrored,
+
724  // we are matching row(A) == row(W), so it is local by construction.
+
725  const auto owner = dist.template rankGlobalTile<Coord::Row>(ij.col());
726 
-
727  auto tile_x = (dist.rankIndex().row() == owner) ? x.readwrite(index_x) : xt.readwrite(index_xt);
-
728 
-
729  hemmOffDiag<B>(thread_priority::high, blas::Op::ConjTrans, std::move(tile_a), w.read(ij_local),
-
730  std::move(tile_x));
-
731  }
-
732  }
-
733  }
-
734 
-
735  // Note:
-
736  // At this point, partial results of X and Xt are available in the panels, and they have to be reduced,
-
737  // both row-wise and col-wise.
-
738  // The final X result will be available just on Ai panel column.
-
739 
-
740  // Note:
-
741  // The first step in reducing partial results distributed over X and Xt, it is to reduce the row
-
742  // panel Xt col-wise, by collecting all Xt results on the rank which can "mirror" the result on its
-
743  // rows (i.e. diagonal). So, for each tile of the row panel, select who is the "diagonal" rank that can
-
744  // mirror and reduce on it.
-
745  for (const auto& index_xt : xt.iteratorLocal()) {
-
746  const auto index_k = dist.template globalTileFromLocalTile<Coord::Col>(index_xt.col());
-
747  const auto rank_owner_row = dist.template rankGlobalTile<Coord::Row>(index_k);
-
748 
-
749  if (rank_owner_row == rank.row()) {
-
750  // Note:
-
751  // Since it is the owner, it has to perform the "mirroring" of the results from columns to
-
752  // rows.
-
753  //
-
754  // Moreover, it reduces in place because the owner of the diagonal stores the partial result
-
755  // directly in x (without using xt)
-
756  const auto i = dist.template localTileFromGlobalTile<Coord::Row>(index_k);
-
757  ex::start_detached(comm::scheduleReduceRecvInPlace(mpi_col_chain(), MPI_SUM, x.readwrite({i, 0})));
-
758  }
-
759  else {
-
760  ex::start_detached(comm::scheduleReduceSend(mpi_col_chain(), rank_owner_row, MPI_SUM,
-
761  xt.read(index_xt)));
-
762  }
-
763  }
-
764 
-
765  // Note:
-
766  // At this point partial results are all collected in X (Xt has been embedded in previous step),
-
767  // so the last step needed is to reduce these last partial results in the final results.
-
768  // The result is needed just on the column with reflectors.
-
769  for (const auto& index_x : x.iteratorLocal()) {
-
770  if (reducer_col == rank.col())
-
771  ex::start_detached(comm::scheduleReduceRecvInPlace(mpi_row_chain(), MPI_SUM,
-
772  x.readwrite(index_x)));
-
773  else
-
774  ex::start_detached(comm::scheduleReduceSend(mpi_row_chain(), reducer_col, MPI_SUM,
-
775  x.read(index_x)));
-
776  }
-
777 }
-
778 
-
779 template <Backend B, Device D, class T>
-
780 void her2kUpdateTrailingMatrix(const matrix::SubMatrixView& view, Matrix<T, D>& a,
-
781  matrix::Panel<Coord::Col, const T, D>& x,
-
782  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& vt,
-
783  matrix::Panel<Coord::Col, const T, D>& v,
-
784  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& xt) {
-
785  static_assert(std::is_signed_v<BaseType<T>>, "alpha in computations requires to be -1");
-
786 
-
787  using pika::execution::thread_priority;
-
788 
-
789  const auto dist = a.distribution();
-
790 
-
791  const LocalTileIndex at_start = view.begin();
-
792 
-
793  for (SizeType i = at_start.row(); i < dist.localNrTiles().rows(); ++i) {
-
794  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
-
795  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
-
796  for (SizeType j = at_start.col(); j < limit; ++j) {
-
797  const LocalTileIndex ij_local{i, j};
-
798  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
-
799 
-
800  const bool is_diagonal_tile = (ij.row() == ij.col());
-
801 
-
802  auto getSubA = [&a, &view, ij_local]() {
-
803  return splitTile(a.readwrite(ij_local), view(ij_local));
-
804  };
-
805 
-
806  // The first column of the trailing matrix (except for the very first global tile) has to be
-
807  // updated first, in order to unlock the next iteration as soon as possible.
-
808  const auto priority = (j == at_start.col()) ? thread_priority::high : thread_priority::normal;
-
809 
-
810  if (is_diagonal_tile) {
-
811  her2kDiag<B>(priority, v.read(ij_local), x.read(ij_local), getSubA());
-
812  }
-
813  else {
-
814  // A -= X . V*
-
815  her2kOffDiag<B>(priority, x.read(ij_local), vt.read(ij_local), getSubA());
-
816 
-
817  // A -= V . X*
-
818  her2kOffDiag<B>(priority, v.read(ij_local), xt.read(ij_local), getSubA());
-
819  }
-
820  }
-
821  }
-
822 }
-
823 }
-
824 
-
825 template <Backend B, Device D, class T>
-
826 struct ComputePanelHelper;
+
727  const LocalTileIndex index_x{dist.template localTileFromGlobalTile<Coord::Row>(ij.col()), 0};
+
728  const LocalTileIndex index_xt{0, ij_local.col()};
+
729 
+
730  auto tile_x = (dist.rankIndex().row() == owner) ? x.readwrite(index_x) : xt.readwrite(index_xt);
+
731 
+
732  hemmOffDiag<B>(thread_priority::high, blas::Op::ConjTrans, std::move(tile_a), w.read(ij_local),
+
733  std::move(tile_x));
+
734  }
+
735  }
+
736  }
+
737 
+
738  // Note:
+
739  // At this point, partial results of X and Xt are available in the panels, and they have to be reduced,
+
740  // both row-wise and col-wise.
+
741  // The final X result will be available just on Ai panel column.
+
742 
+
743  // Note:
+
744  // The first step in reducing partial results distributed over X and Xt, it is to reduce the row
+
745  // panel Xt col-wise, by collecting all Xt results on the rank which can "mirror" the result on its
+
746  // rows (i.e. diagonal). So, for each tile of the row panel, select who is the "diagonal" rank that can
+
747  // mirror and reduce on it.
+
748  for (const auto& index_xt : xt.iteratorLocal()) {
+
749  const auto index_k = dist.template globalTileFromLocalTile<Coord::Col>(index_xt.col());
+
750  const auto rank_owner_row = dist.template rankGlobalTile<Coord::Row>(index_k);
+
751 
+
752  if (rank_owner_row == rank.row()) {
+
753  // Note:
+
754  // Since it is the owner, it has to perform the "mirroring" of the results from columns to
+
755  // rows.
+
756  //
+
757  // Moreover, it reduces in place because the owner of the diagonal stores the partial result
+
758  // directly in x (without using xt)
+
759  const auto i = dist.template localTileFromGlobalTile<Coord::Row>(index_k);
+
760  ex::start_detached(comm::scheduleReduceRecvInPlace(mpi_col_chain(), MPI_SUM, x.readwrite({i, 0})));
+
761  }
+
762  else {
+
763  ex::start_detached(comm::scheduleReduceSend(mpi_col_chain(), rank_owner_row, MPI_SUM,
+
764  xt.read(index_xt)));
+
765  }
+
766  }
+
767 
+
768  // Note:
+
769  // At this point partial results are all collected in X (Xt has been embedded in previous step),
+
770  // so the last step needed is to reduce these last partial results in the final results.
+
771  // The result is needed just on the column with reflectors.
+
772  for (const auto& index_x : x.iteratorLocal()) {
+
773  if (reducer_col == rank.col())
+
774  ex::start_detached(comm::scheduleReduceRecvInPlace(mpi_row_chain(), MPI_SUM,
+
775  x.readwrite(index_x)));
+
776  else
+
777  ex::start_detached(comm::scheduleReduceSend(mpi_row_chain(), reducer_col, MPI_SUM,
+
778  x.read(index_x)));
+
779  }
+
780 }
+
781 
+
782 template <Backend B, Device D, class T>
+
783 void her2kUpdateTrailingMatrix(const matrix::SubMatrixView& view, Matrix<T, D>& a,
+
784  matrix::Panel<Coord::Col, const T, D>& x,
+
785  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& vt,
+
786  matrix::Panel<Coord::Col, const T, D>& v,
+
787  matrix::Panel<Coord::Row, const T, D, matrix::StoreTransposed::Yes>& xt) {
+
788  static_assert(std::is_signed_v<BaseType<T>>, "alpha in computations requires to be -1");
+
789 
+
790  using pika::execution::thread_priority;
+
791 
+
792  const auto dist = a.distribution();
+
793 
+
794  const LocalTileIndex at_start = view.begin();
+
795 
+
796  for (SizeType i = at_start.row(); i < dist.localNrTiles().rows(); ++i) {
+
797  const auto limit = dist.template nextLocalTileFromGlobalTile<Coord::Col>(
+
798  dist.template globalTileFromLocalTile<Coord::Row>(i) + 1);
+
799  for (SizeType j = at_start.col(); j < limit; ++j) {
+
800  const LocalTileIndex ij_local{i, j};
+
801  const GlobalTileIndex ij = dist.globalTileIndex(ij_local);
+
802 
+
803  const bool is_diagonal_tile = (ij.row() == ij.col());
+
804 
+
805  auto getSubA = [&a, &view, ij_local]() {
+
806  return splitTile(a.readwrite(ij_local), view(ij_local));
+
807  };
+
808 
+
809  // The first column of the trailing matrix (except for the very first global tile) has to be
+
810  // updated first, in order to unlock the next iteration as soon as possible.
+
811  const auto priority = (j == at_start.col()) ? thread_priority::high : thread_priority::normal;
+
812 
+
813  if (is_diagonal_tile) {
+
814  her2kDiag<B>(priority, v.read(ij_local), x.read(ij_local), getSubA());
+
815  }
+
816  else {
+
817  // A -= X . V*
+
818  her2kOffDiag<B>(priority, x.read(ij_local), vt.read(ij_local), getSubA());
+
819 
+
820  // A -= V . X*
+
821  her2kOffDiag<B>(priority, v.read(ij_local), xt.read(ij_local), getSubA());
+
822  }
+
823  }
+
824  }
+
825 }
+
826 }
827 
-
828 template <class T>
-
829 struct ComputePanelHelper<Backend::MC, Device::CPU, T> {
-
830  ComputePanelHelper(const std::size_t, matrix::Distribution) {}
-
831 
-
832  void call(Matrix<T, Device::CPU>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
-
833  const matrix::SubPanelView& panel_view) {
-
834  using red2band::local::computePanelReflectors;
-
835  computePanelReflectors(mat_a, mat_taus, j_sub, panel_view);
-
836  }
-
837 
-
838  template <Device D, class CommSender, class TriggerSender>
-
839  void call(TriggerSender&& trigger, comm::IndexT_MPI rank_v0, CommSender&& mpi_col_chain_panel,
-
840  Matrix<T, D>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
-
841  const matrix::SubPanelView& panel_view) {
-
842  using red2band::distributed::computePanelReflectors;
-
843  computePanelReflectors(std::forward<TriggerSender>(trigger), rank_v0,
-
844  std::forward<CommSender>(mpi_col_chain_panel), mat_a, mat_taus, j_sub,
-
845  panel_view);
-
846  }
-
847 };
-
848 
-
849 #ifdef DLAF_WITH_GPU
-
850 template <class T>
-
851 struct ComputePanelHelper<Backend::GPU, Device::GPU, T> {
-
852  ComputePanelHelper(const std::size_t n_workspaces, matrix::Distribution dist_a)
-
853  : panels_v(n_workspaces, dist_a) {}
-
854 
-
855  void call(Matrix<T, Device::GPU>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
-
856  const matrix::SubPanelView& panel_view) {
-
857  using red2band::local::computePanelReflectors;
-
858 
-
859  namespace ex = pika::execution::experimental;
-
860 
-
861  // Note:
-
862  // - copy panel_view from GPU to CPU
-
863  // - computePanelReflectors on CPU (on a matrix like, with just a panel)
-
864  // - copy back matrix "panel" from CPU to GPU
-
865 
-
866  auto& v = panels_v.nextResource();
-
867 
-
868  copyToCPU(panel_view, mat_a, v);
-
869  computePanelReflectors(v, mat_taus, j_sub, panel_view);
-
870  copyFromCPU(panel_view, v, mat_a);
-
871  }
-
872 
-
873  template <Device D, class CommSender, class TriggerSender>
-
874  void call(TriggerSender&& trigger, comm::IndexT_MPI rank_v0, CommSender&& mpi_col_chain_panel,
-
875  Matrix<T, D>& mat_a, Matrix<T, Device::CPU>& mat_taus, SizeType j_sub,
-
876  const matrix::SubPanelView& panel_view) {
-
877  auto& v = panels_v.nextResource();
-
878 
-
879  // copy to CPU
-
880  copyToCPU(panel_view, mat_a, v);
+
828 template <Backend B, Device D, class T>
+
829 struct ComputePanelHelper;
+
830 
+
831 template <class T>
+
832 struct ComputePanelHelper<Backend::MC, Device::CPU, T> {
+
833  ComputePanelHelper(const std::size_t, matrix::Distribution) {}
+
834 
+
835  void call(Matrix<T, Device::CPU>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
+
836  const matrix::SubPanelView& panel_view) {
+
837  using red2band::local::computePanelReflectors;
+
838  computePanelReflectors(mat_a, mat_taus, j_sub, panel_view);
+
839  }
+
840 
+
841  template <Device D, class CommSender, class TriggerSender>
+
842  void call(TriggerSender&& trigger, comm::IndexT_MPI rank_v0, CommSender&& mpi_col_chain_panel,
+
843  Matrix<T, D>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
+
844  const matrix::SubPanelView& panel_view) {
+
845  using red2band::distributed::computePanelReflectors;
+
846  computePanelReflectors(std::forward<TriggerSender>(trigger), rank_v0,
+
847  std::forward<CommSender>(mpi_col_chain_panel), mat_a, mat_taus, j_sub,
+
848  panel_view);
+
849  }
+
850 };
+
851 
+
852 #ifdef DLAF_WITH_GPU
+
853 template <class T>
+
854 struct ComputePanelHelper<Backend::GPU, Device::GPU, T> {
+
855  ComputePanelHelper(const std::size_t n_workspaces, matrix::Distribution dist_a)
+
856  : panels_v(n_workspaces, dist_a) {}
+
857 
+
858  void call(Matrix<T, Device::GPU>& mat_a, Matrix<T, Device::CPU>& mat_taus, const SizeType j_sub,
+
859  const matrix::SubPanelView& panel_view) {
+
860  using red2band::local::computePanelReflectors;
+
861 
+
862  namespace ex = pika::execution::experimental;
+
863 
+
864  // Note:
+
865  // - copy panel_view from GPU to CPU
+
866  // - computePanelReflectors on CPU (on a matrix like, with just a panel)
+
867  // - copy back matrix "panel" from CPU to GPU
+
868 
+
869  auto& v = panels_v.nextResource();
+
870 
+
871  copyToCPU(panel_view, mat_a, v);
+
872  computePanelReflectors(v, mat_taus, j_sub, panel_view);
+
873  copyFromCPU(panel_view, v, mat_a);
+
874  }
+
875 
+
876  template <Device D, class CommSender, class TriggerSender>
+
877  void call(TriggerSender&& trigger, comm::IndexT_MPI rank_v0, CommSender&& mpi_col_chain_panel,
+
878  Matrix<T, D>& mat_a, Matrix<T, Device::CPU>& mat_taus, SizeType j_sub,
+
879  const matrix::SubPanelView& panel_view) {
+
880  auto& v = panels_v.nextResource();
881 
-
882  // compute on CPU
-
883  using dlaf::eigensolver::internal::red2band::distributed::computePanelReflectors;
-
884  computePanelReflectors(std::forward<TriggerSender>(trigger), rank_v0,
-
885  std::forward<CommSender>(mpi_col_chain_panel), v, mat_taus, j_sub,
-
886  panel_view);
-
887 
-
888  // copy back to GPU
-
889  copyFromCPU(panel_view, v, mat_a);
-
890  }
-
891 
-
892 protected:
-
893  common::RoundRobin<matrix::Panel<Coord::Col, T, Device::CPU>> panels_v;
+
882  // copy to CPU
+
883  copyToCPU(panel_view, mat_a, v);
+
884 
+
885  // compute on CPU
+
886  using dlaf::eigensolver::internal::red2band::distributed::computePanelReflectors;
+
887  computePanelReflectors(std::forward<TriggerSender>(trigger), rank_v0,
+
888  std::forward<CommSender>(mpi_col_chain_panel), v, mat_taus, j_sub,
+
889  panel_view);
+
890 
+
891  // copy back to GPU
+
892  copyFromCPU(panel_view, v, mat_a);
+
893  }
894 
-
895  void copyToCPU(const matrix::SubPanelView panel_view, matrix::Matrix<T, Device::GPU>& mat_a,
-
896  matrix::Panel<Coord::Col, T, Device::CPU>& v) {
-
897  namespace ex = pika::execution::experimental;
-
898 
-
899  using dlaf::internal::Policy;
-
900  using dlaf::matrix::internal::CopyBackend_v;
-
901  using pika::execution::thread_priority;
-
902 
-
903  for (const auto& i : panel_view.iteratorLocal()) {
-
904  auto spec = panel_view(i);
-
905  auto tmp_tile = v.readwrite(i);
-
906  ex::start_detached(
-
907  ex::when_all(splitTile(mat_a.read(i), spec), splitTile(std::move(tmp_tile), spec)) |
-
908  matrix::copy(Policy<CopyBackend_v<Device::GPU, Device::CPU>>(thread_priority::high)));
-
909  }
-
910  }
-
911 
-
912  void copyFromCPU(const matrix::SubPanelView panel_view, matrix::Panel<Coord::Col, T, Device::CPU>& v,
-
913  matrix::Matrix<T, Device::GPU>& mat_a) {
-
914  namespace ex = pika::execution::experimental;
-
915 
-
916  using dlaf::internal::Policy;
-
917  using dlaf::matrix::internal::CopyBackend_v;
-
918  using pika::execution::thread_priority;
-
919 
-
920  for (const auto& i : panel_view.iteratorLocal()) {
-
921  auto spec = panel_view(i);
-
922  auto tile_a = mat_a.readwrite(i);
-
923  ex::start_detached(
-
924  ex::when_all(splitTile(v.read(i), spec), splitTile(std::move(tile_a), spec)) |
-
925  matrix::copy(Policy<CopyBackend_v<Device::CPU, Device::GPU>>(thread_priority::high)));
-
926  }
-
927  }
-
928 };
-
929 #endif
-
930 
-
931 }
-
932 
-
933 // Local implementation of reduction to band
-
934 template <Backend B, Device D, class T>
-
935 Matrix<T, Device::CPU> ReductionToBand<B, D, T>::call(Matrix<T, D>& mat_a, const SizeType band_size) {
-
936  using dlaf::matrix::Matrix;
-
937  using dlaf::matrix::Panel;
-
938 
-
939  using namespace red2band::local;
-
940 
-
941  using common::iterate_range2d;
-
942  using factorization::internal::computeTFactor;
+
895 protected:
+
896  common::RoundRobin<matrix::Panel<Coord::Col, T, Device::CPU>> panels_v;
+
897 
+
898  void copyToCPU(const matrix::SubPanelView panel_view, matrix::Matrix<T, Device::GPU>& mat_a,
+
899  matrix::Panel<Coord::Col, T, Device::CPU>& v) {
+
900  namespace ex = pika::execution::experimental;
+
901 
+
902  using dlaf::internal::Policy;
+
903  using dlaf::matrix::internal::CopyBackend_v;
+
904  using pika::execution::thread_priority;
+
905 
+
906  for (const auto& i : panel_view.iteratorLocal()) {
+
907  auto spec = panel_view(i);
+
908  auto tmp_tile = v.readwrite(i);
+
909  ex::start_detached(
+
910  ex::when_all(splitTile(mat_a.read(i), spec), splitTile(std::move(tmp_tile), spec)) |
+
911  matrix::copy(Policy<CopyBackend_v<Device::GPU, Device::CPU>>(thread_priority::high)));
+
912  }
+
913  }
+
914 
+
915  void copyFromCPU(const matrix::SubPanelView panel_view, matrix::Panel<Coord::Col, T, Device::CPU>& v,
+
916  matrix::Matrix<T, Device::GPU>& mat_a) {
+
917  namespace ex = pika::execution::experimental;
+
918 
+
919  using dlaf::internal::Policy;
+
920  using dlaf::matrix::internal::CopyBackend_v;
+
921  using pika::execution::thread_priority;
+
922 
+
923  for (const auto& i : panel_view.iteratorLocal()) {
+
924  auto spec = panel_view(i);
+
925  auto tile_a = mat_a.readwrite(i);
+
926  ex::start_detached(
+
927  ex::when_all(splitTile(v.read(i), spec), splitTile(std::move(tile_a), spec)) |
+
928  matrix::copy(Policy<CopyBackend_v<Device::CPU, Device::GPU>>(thread_priority::high)));
+
929  }
+
930  }
+
931 };
+
932 #endif
+
933 
+
934 }
+
935 
+
936 // Local implementation of reduction to band
+
937 template <Backend B, Device D, class T>
+
938 Matrix<T, Device::CPU> ReductionToBand<B, D, T>::call(Matrix<T, D>& mat_a, const SizeType band_size) {
+
939  using dlaf::matrix::Matrix;
+
940  using dlaf::matrix::Panel;
+
941 
+
942  using namespace red2band::local;
943 
-
944  using pika::execution::experimental::any_sender;
-
945 
-
946  const auto dist_a = mat_a.distribution();
-
947  const matrix::Distribution dist({mat_a.size().rows(), band_size},
-
948  {dist_a.blockSize().rows(), band_size});
-
949 
-
950  // Note:
-
951  // Reflector of size = 1 is not considered whatever T is (i.e. neither real nor complex)
-
952  const SizeType nrefls = std::max<SizeType>(0, dist_a.size().rows() - band_size - 1);
-
953 
-
954  // Row-vector that is distributed over columns, but exists locally on all rows of the grid
-
955  DLAF_ASSERT(mat_a.blockSize().cols() % band_size == 0, mat_a.blockSize().cols(), band_size);
-
956  Matrix<T, Device::CPU> mat_taus(matrix::Distribution(GlobalElementSize(nrefls, 1),
-
957  TileElementSize(mat_a.blockSize().cols(), 1),
-
958  comm::Size2D(mat_a.commGridSize().cols(), 1),
-
959  comm::Index2D(mat_a.rankIndex().col(), 0),
-
960  comm::Index2D(mat_a.sourceRankIndex().col(), 0)));
-
961 
-
962  if (nrefls == 0)
-
963  return mat_taus;
+
944  using common::iterate_range2d;
+
945  using factorization::internal::computeTFactor;
+
946 
+
947  using pika::execution::experimental::any_sender;
+
948 
+
949  const auto dist_a = mat_a.distribution();
+
950  const matrix::Distribution dist({mat_a.size().rows(), band_size},
+
951  {dist_a.blockSize().rows(), band_size});
+
952 
+
953  // Note:
+
954  // Reflector of size = 1 is not considered whatever T is (i.e. neither real nor complex)
+
955  const SizeType nrefls = std::max<SizeType>(0, dist_a.size().rows() - band_size - 1);
+
956 
+
957  // Row-vector that is distributed over columns, but exists locally on all rows of the grid
+
958  DLAF_ASSERT(mat_a.blockSize().cols() % band_size == 0, mat_a.blockSize().cols(), band_size);
+
959  Matrix<T, Device::CPU> mat_taus(matrix::Distribution(GlobalElementSize(nrefls, 1),
+
960  TileElementSize(mat_a.blockSize().cols(), 1),
+
961  comm::Size2D(mat_a.commGridSize().cols(), 1),
+
962  comm::Index2D(mat_a.rankIndex().col(), 0),
+
963  comm::Index2D(mat_a.sourceRankIndex().col(), 0)));
964 
-
965  Matrix<T, Device::CPU> mat_taus_retiled =
-
966  mat_taus.retiledSubPipeline(LocalTileSize(mat_a.blockSize().cols() / band_size, 1));
+
965  if (nrefls == 0)
+
966  return mat_taus;
967 
-
968  const SizeType ntiles = (nrefls - 1) / band_size + 1;
-
969  DLAF_ASSERT(ntiles == mat_taus_retiled.nrTiles().rows(), ntiles, mat_taus_retiled.nrTiles().rows());
+
968  Matrix<T, Device::CPU> mat_taus_retiled =
+
969  mat_taus.retiledSubPipeline(LocalTileSize(mat_a.blockSize().cols() / band_size, 1));
970 
-
971  const bool is_full_band = (band_size == dist_a.blockSize().cols());
-
972 
-
973  constexpr std::size_t n_workspaces = 2;
-
974  common::RoundRobin<Panel<Coord::Col, T, D>> panels_v(n_workspaces, dist);
-
975  common::RoundRobin<Panel<Coord::Col, T, D>> panels_w(n_workspaces, dist);
-
976  common::RoundRobin<Panel<Coord::Col, T, D>> panels_x(n_workspaces, dist);
-
977 
-
978  // Note:
-
979  // Here dist_a is given with full panel size instead of dist with just the part actually needeed,
-
980  // because the GPU Helper internally exploits Panel data-structure. Indeed, the full size panel is
-
981  // needed in order to mimick Matrix with Panel, so it is possible to apply a SubPanelView to it.
-
982  //
-
983  // It is a bit hacky usage, because SubPanelView is not meant to be used with Panel, but just with
-
984  // Matrix. This results in a variable waste of memory, depending no the ratio band_size/nb.
-
985  red2band::ComputePanelHelper<B, D, T> compute_panel_helper(n_workspaces, dist_a);
-
986 
-
987  for (SizeType j_sub = 0; j_sub < ntiles; ++j_sub) {
-
988  const auto i_sub = j_sub + 1;
+
971  const SizeType ntiles = (nrefls - 1) / band_size + 1;
+
972  DLAF_ASSERT(ntiles == mat_taus_retiled.nrTiles().rows(), ntiles, mat_taus_retiled.nrTiles().rows());
+
973 
+
974  const bool is_full_band = (band_size == dist_a.blockSize().cols());
+
975 
+
976  constexpr std::size_t n_workspaces = 2;
+
977  common::RoundRobin<Panel<Coord::Col, T, D>> panels_v(n_workspaces, dist);
+
978  common::RoundRobin<Panel<Coord::Col, T, D>> panels_w(n_workspaces, dist);
+
979  common::RoundRobin<Panel<Coord::Col, T, D>> panels_x(n_workspaces, dist);
+
980 
+
981  // Note:
+
982  // Here dist_a is given with full panel size instead of dist with just the part actually needeed,
+
983  // because the GPU Helper internally exploits Panel data-structure. Indeed, the full size panel is
+
984  // needed in order to mimick Matrix with Panel, so it is possible to apply a SubPanelView to it.
+
985  //
+
986  // It is a bit hacky usage, because SubPanelView is not meant to be used with Panel, but just with
+
987  // Matrix. This results in a variable waste of memory, depending no the ratio band_size/nb.
+
988  red2band::ComputePanelHelper<B, D, T> compute_panel_helper(n_workspaces, dist_a);
989 
-
990  const GlobalElementIndex ij_offset(i_sub * band_size, j_sub * band_size);
-
991 
-
992  const SizeType nrefls_tile = mat_taus_retiled.tileSize(GlobalTileIndex(j_sub, 0)).rows();
-
993 
-
994  const bool isPanelIncomplete = (nrefls_tile != band_size);
-
995 
-
996  // Note: if this is running, it must have at least one valid reflector (i.e. with size > 1)
-
997  DLAF_ASSERT_HEAVY(nrefls_tile != 0, nrefls_tile);
+
990  for (SizeType j_sub = 0; j_sub < ntiles; ++j_sub) {
+
991  const auto i_sub = j_sub + 1;
+
992 
+
993  const GlobalElementIndex ij_offset(i_sub * band_size, j_sub * band_size);
+
994 
+
995  const SizeType nrefls_tile = mat_taus_retiled.tileSize(GlobalTileIndex(j_sub, 0)).rows();
+
996 
+
997  const bool isPanelIncomplete = (nrefls_tile != band_size);
998 
-
999  // Note: SubPanelView is (at most) band_size wide, but it may contain a smaller number of
-
1000  // reflectors (i.e. at the end when last reflector size is 1)
-
1001  const matrix::SubPanelView panel_view(dist_a, ij_offset, band_size);
-
1002 
-
1003  Panel<Coord::Col, T, D>& v = panels_v.nextResource();
-
1004  v.setRangeStart(ij_offset);
-
1005  if (isPanelIncomplete)
-
1006  v.setWidth(nrefls_tile);
-
1007 
-
1008  // PANEL
-
1009  compute_panel_helper.call(mat_a, mat_taus_retiled, j_sub, panel_view);
+
999  // Note: if this is running, it must have at least one valid reflector (i.e. with size > 1)
+
1000  DLAF_ASSERT_HEAVY(nrefls_tile != 0, nrefls_tile);
+
1001 
+
1002  // Note: SubPanelView is (at most) band_size wide, but it may contain a smaller number of
+
1003  // reflectors (i.e. at the end when last reflector size is 1)
+
1004  const matrix::SubPanelView panel_view(dist_a, ij_offset, band_size);
+
1005 
+
1006  Panel<Coord::Col, T, D>& v = panels_v.nextResource();
+
1007  v.setRangeStart(ij_offset);
+
1008  if (isPanelIncomplete)
+
1009  v.setWidth(nrefls_tile);
1010 
-
1011  // Note:
-
1012  // - has_reflector_head tells if this rank owns the first tile of the panel (being local, always true)
-
1013  // - if !is_full_band it has to force copy as a workaround, otherwise in update matrix it would deadlock
-
1014  // due to tile shared between panel and trailing matrix
-
1015  constexpr bool has_reflector_head = true;
-
1016  setupReflectorPanelV<B, D, T>(has_reflector_head, panel_view, nrefls_tile, v, mat_a, !is_full_band);
-
1017 
-
1018  const LocalTileIndex t_idx(0, 0);
-
1019  // TODO used just by the column, maybe we can re-use a panel tile?
-
1020  // TODO probably the first one in any panel is ok?
-
1021  Matrix<T, D> t({nrefls_tile, nrefls_tile}, dist.blockSize());
-
1022 
-
1023  computeTFactor<B>(v, mat_taus_retiled.read(GlobalTileIndex(j_sub, 0)), t.readwrite(t_idx));
-
1024 
-
1025  // PREPARATION FOR TRAILING MATRIX UPDATE
-
1026  const GlobalElementIndex at_offset(ij_offset + GlobalElementSize(0, band_size));
+
1011  // PANEL
+
1012  compute_panel_helper.call(mat_a, mat_taus_retiled, j_sub, panel_view);
+
1013 
+
1014  // Note:
+
1015  // - has_reflector_head tells if this rank owns the first tile of the panel (being local, always true)
+
1016  // - if !is_full_band it has to force copy as a workaround, otherwise in update matrix it would deadlock
+
1017  // due to tile shared between panel and trailing matrix
+
1018  constexpr bool has_reflector_head = true;
+
1019  setupReflectorPanelV<B, D, T>(has_reflector_head, panel_view, nrefls_tile, v, mat_a, !is_full_band);
+
1020 
+
1021  const LocalTileIndex t_idx(0, 0);
+
1022  // TODO used just by the column, maybe we can re-use a panel tile?
+
1023  // TODO probably the first one in any panel is ok?
+
1024  Matrix<T, D> t({nrefls_tile, nrefls_tile}, dist.blockSize());
+
1025 
+
1026  computeTFactor<B>(v, mat_taus_retiled.read(GlobalTileIndex(j_sub, 0)), t.readwrite(t_idx));
1027 
-
1028  // Note: if there is no trailing matrix, algorithm has finised
-
1029  if (!at_offset.isIn(mat_a.size()))
-
1030  break;
-
1031 
-
1032  const matrix::SubMatrixView trailing_matrix_view(dist_a, at_offset);
-
1033 
-
1034  // W = V . T
-
1035  Panel<Coord::Col, T, D>& w = panels_w.nextResource();
-
1036  w.setRangeStart(at_offset);
-
1037  if (isPanelIncomplete)
-
1038  w.setWidth(nrefls_tile);
-
1039 
-
1040  trmmComputeW<B>(w, v, t.read(t_idx));
-
1041 
-
1042  // X = At . W
-
1043  Panel<Coord::Col, T, D>& x = panels_x.nextResource();
-
1044  x.setRangeStart(at_offset);
-
1045  if (isPanelIncomplete)
-
1046  x.setWidth(nrefls_tile);
-
1047 
-
1048  // Note:
-
1049  // Since At is hermitian, just the lower part is referenced.
-
1050  // When the tile is not part of the main diagonal, the same tile has to be used for two computations
-
1051  // that will contribute to two different rows of X: the ones indexed with row and col.
-
1052  hemmComputeX<B>(x, trailing_matrix_view, mat_a, w);
-
1053 
-
1054  // In the next section the next two operations are performed
-
1055  // A) W2 = W* . X
-
1056  // B) X -= 1/2 . V . W2
-
1057 
-
1058  // Note:
-
1059  // T can be re-used because it is not needed anymore in this step and it has the same shape
-
1060  Matrix<T, D> w2 = std::move(t);
-
1061 
-
1062  gemmComputeW2<B>(w2, w, x);
-
1063  gemmUpdateX<B>(x, w2, v);
+
1028  // PREPARATION FOR TRAILING MATRIX UPDATE
+
1029  const GlobalElementIndex at_offset(ij_offset + GlobalElementSize(0, band_size));
+
1030 
+
1031  // Note: if there is no trailing matrix, algorithm has finised
+
1032  if (!at_offset.isIn(mat_a.size()))
+
1033  break;
+
1034 
+
1035  const matrix::SubMatrixView trailing_matrix_view(dist_a, at_offset);
+
1036 
+
1037  // W = V . T
+
1038  Panel<Coord::Col, T, D>& w = panels_w.nextResource();
+
1039  w.setRangeStart(at_offset);
+
1040  if (isPanelIncomplete)
+
1041  w.setWidth(nrefls_tile);
+
1042 
+
1043  trmmComputeW<B>(w, v, t.read(t_idx));
+
1044 
+
1045  // X = At . W
+
1046  Panel<Coord::Col, T, D>& x = panels_x.nextResource();
+
1047  x.setRangeStart(at_offset);
+
1048  if (isPanelIncomplete)
+
1049  x.setWidth(nrefls_tile);
+
1050 
+
1051  // Note:
+
1052  // Since At is hermitian, just the lower part is referenced.
+
1053  // When the tile is not part of the main diagonal, the same tile has to be used for two computations
+
1054  // that will contribute to two different rows of X: the ones indexed with row and col.
+
1055  hemmComputeX<B>(x, trailing_matrix_view, mat_a, w);
+
1056 
+
1057  // In the next section the next two operations are performed
+
1058  // A) W2 = W* . X
+
1059  // B) X -= 1/2 . V . W2
+
1060 
+
1061  // Note:
+
1062  // T can be re-used because it is not needed anymore in this step and it has the same shape
+
1063  Matrix<T, D> w2 = std::move(t);
1064 
-
1065  // TRAILING MATRIX UPDATE
-
1066 
-
1067  // At -= X . V* + V . X*
-
1068  her2kUpdateTrailingMatrix<B>(trailing_matrix_view, mat_a, x, v);
+
1065  gemmComputeW2<B>(w2, w, x);
+
1066  gemmUpdateX<B>(x, w2, v);
+
1067 
+
1068  // TRAILING MATRIX UPDATE
1069 
-
1070  x.reset();
-
1071  w.reset();
-
1072  v.reset();
-
1073  }
-
1074 
-
1075  return mat_taus;
-
1076 }
+
1070  // At -= X . V* + V . X*
+
1071  her2kUpdateTrailingMatrix<B>(trailing_matrix_view, mat_a, x, v);
+
1072 
+
1073  x.reset();
+
1074  w.reset();
+
1075  v.reset();
+
1076  }
1077 
-
1078 // Distributed implementation of reduction to band
-
1079 template <Backend B, Device D, class T>
-
1080 Matrix<T, Device::CPU> ReductionToBand<B, D, T>::call(comm::CommunicatorGrid grid, Matrix<T, D>& mat_a,
-
1081  const SizeType band_size) {
-
1082  using namespace red2band::distributed;
-
1083 
-
1084  using common::iterate_range2d;
-
1085  using factorization::internal::computeTFactor;
+
1078  return mat_taus;
+
1079 }
+
1080 
+
1081 // Distributed implementation of reduction to band
+
1082 template <Backend B, Device D, class T>
+
1083 Matrix<T, Device::CPU> ReductionToBand<B, D, T>::call(comm::CommunicatorGrid grid, Matrix<T, D>& mat_a,
+
1084  const SizeType band_size) {
+
1085  using namespace red2band::distributed;
1086 
-
1087  namespace ex = pika::execution::experimental;
-
1088 
-
1089  // Note:
-
1090  // This is a temporary workaround.
-
1091  // See issue https://github.com/eth-cscs/DLA-Future/issues/729
-
1092  pika::wait();
-
1093 
-
1094  common::Pipeline<comm::Communicator> mpi_col_chain_panel(grid.colCommunicator().clone());
-
1095  common::Pipeline<comm::Communicator> mpi_row_chain(grid.rowCommunicator().clone());
-
1096  common::Pipeline<comm::Communicator> mpi_col_chain(grid.colCommunicator().clone());
-
1097 
-
1098  const auto& dist = mat_a.distribution();
-
1099  const comm::Index2D rank = dist.rankIndex();
+
1087  using common::iterate_range2d;
+
1088  using factorization::internal::computeTFactor;
+
1089 
+
1090  namespace ex = pika::execution::experimental;
+
1091 
+
1092  // Note:
+
1093  // This is a temporary workaround.
+
1094  // See issue https://github.com/eth-cscs/DLA-Future/issues/729
+
1095  pika::wait();
+
1096 
+
1097  common::Pipeline<comm::Communicator> mpi_col_chain_panel(grid.colCommunicator().clone());
+
1098  common::Pipeline<comm::Communicator> mpi_row_chain(grid.rowCommunicator().clone());
+
1099  common::Pipeline<comm::Communicator> mpi_col_chain(grid.colCommunicator().clone());
1100 
-
1101  // Note:
-
1102  // Reflector of size = 1 is not considered whatever T is (i.e. neither real nor complex)
-
1103  const SizeType nrefls = std::max<SizeType>(0, dist.size().rows() - band_size - 1);
-
1104 
-
1105  // Row-vector that is distributed over columns, but exists locally on all rows of the grid
-
1106  DLAF_ASSERT(mat_a.blockSize().cols() % band_size == 0, mat_a.blockSize().cols(), band_size);
-
1107  Matrix<T, Device::CPU> mat_taus(matrix::Distribution(GlobalElementSize(nrefls, 1),
-
1108  TileElementSize(mat_a.blockSize().cols(), 1),
-
1109  comm::Size2D(mat_a.commGridSize().cols(), 1),
-
1110  comm::Index2D(mat_a.rankIndex().col(), 0),
-
1111  comm::Index2D(mat_a.sourceRankIndex().col(), 0)));
-
1112 
-
1113  if (nrefls == 0)
-
1114  return mat_taus;
+
1101  const auto& dist = mat_a.distribution();
+
1102  const comm::Index2D rank = dist.rankIndex();
+
1103 
+
1104  // Note:
+
1105  // Reflector of size = 1 is not considered whatever T is (i.e. neither real nor complex)
+
1106  const SizeType nrefls = std::max<SizeType>(0, dist.size().rows() - band_size - 1);
+
1107 
+
1108  // Row-vector that is distributed over columns, but exists locally on all rows of the grid
+
1109  DLAF_ASSERT(mat_a.blockSize().cols() % band_size == 0, mat_a.blockSize().cols(), band_size);
+
1110  Matrix<T, Device::CPU> mat_taus(matrix::Distribution(GlobalElementSize(nrefls, 1),
+
1111  TileElementSize(mat_a.blockSize().cols(), 1),
+
1112  comm::Size2D(mat_a.commGridSize().cols(), 1),
+
1113  comm::Index2D(mat_a.rankIndex().col(), 0),
+
1114  comm::Index2D(mat_a.sourceRankIndex().col(), 0)));
1115 
-
1116  Matrix<T, Device::CPU> mat_taus_retiled =
-
1117  mat_taus.retiledSubPipeline(LocalTileSize(mat_a.blockSize().cols() / band_size, 1));
+
1116  if (nrefls == 0)
+
1117  return mat_taus;
1118 
-
1119  const SizeType ntiles = (nrefls - 1) / band_size + 1;
-
1120  DLAF_ASSERT(ntiles == mat_taus_retiled.nrTiles().rows(), ntiles, mat_taus_retiled.nrTiles().rows());
+
1119  Matrix<T, Device::CPU> mat_taus_retiled =
+
1120  mat_taus.retiledSubPipeline(LocalTileSize(mat_a.blockSize().cols() / band_size, 1));
1121 
-
1122  const bool is_full_band = (band_size == dist.blockSize().cols());
-
1123 
-
1124  constexpr std::size_t n_workspaces = 2;
-
1125  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_v(n_workspaces, dist);
-
1126  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_vt(
-
1127  n_workspaces, dist);
-
1128 
-
1129  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_w(n_workspaces, dist);
-
1130  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_wt(
-
1131  n_workspaces, dist);
-
1132 
-
1133  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_x(n_workspaces, dist);
-
1134  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_xt(
-
1135  n_workspaces, dist);
-
1136 
-
1137  red2band::ComputePanelHelper<B, D, T> compute_panel_helper(n_workspaces, dist);
-
1138 
-
1139  ex::unique_any_sender<> trigger_panel{ex::just()};
-
1140  for (SizeType j_sub = 0; j_sub < ntiles; ++j_sub) {
-
1141  const SizeType i_sub = j_sub + 1;
-
1142 
-
1143  const GlobalElementIndex ij_offset(i_sub * band_size, j_sub * band_size);
-
1144  const GlobalElementIndex at_offset(i_sub * band_size, (j_sub + 1) * band_size);
+
1122  const SizeType ntiles = (nrefls - 1) / band_size + 1;
+
1123  DLAF_ASSERT(ntiles == mat_taus_retiled.nrTiles().rows(), ntiles, mat_taus_retiled.nrTiles().rows());
+
1124 
+
1125  const bool is_full_band = (band_size == dist.blockSize().cols());
+
1126 
+
1127  constexpr std::size_t n_workspaces = 2;
+
1128  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_v(n_workspaces, dist);
+
1129  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_vt(
+
1130  n_workspaces, dist);
+
1131 
+
1132  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_w(n_workspaces, dist);
+
1133  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_wt(
+
1134  n_workspaces, dist);
+
1135 
+
1136  common::RoundRobin<matrix::Panel<Coord::Col, T, D>> panels_x(n_workspaces, dist);
+
1137  common::RoundRobin<matrix::Panel<Coord::Row, T, D, matrix::StoreTransposed::Yes>> panels_xt(
+
1138  n_workspaces, dist);
+
1139 
+
1140  red2band::ComputePanelHelper<B, D, T> compute_panel_helper(n_workspaces, dist);
+
1141 
+
1142  ex::unique_any_sender<> trigger_panel{ex::just()};
+
1143  for (SizeType j_sub = 0; j_sub < ntiles; ++j_sub) {
+
1144  const SizeType i_sub = j_sub + 1;
1145 
-
1146  const comm::Index2D rank_v0{
-
1147  dist.template rankGlobalElement<Coord::Row>(ij_offset.row()),
-
1148  dist.template rankGlobalElement<Coord::Col>(ij_offset.col()),
-
1149  };
-
1150 
-
1151  const bool is_panel_rank_col = rank_v0.col() == rank.col();
-
1152 
-
1153  const SizeType nrefls_tile = mat_taus_retiled.tileSize(GlobalTileIndex(j_sub, 0)).rows();
-
1154 
-
1155  if (nrefls_tile == 0)
-
1156  break;
+
1146  const GlobalElementIndex ij_offset(i_sub * band_size, j_sub * band_size);
+
1147  const GlobalElementIndex at_offset(i_sub * band_size, (j_sub + 1) * band_size);
+
1148 
+
1149  const comm::Index2D rank_v0{
+
1150  dist.template rankGlobalElement<Coord::Row>(ij_offset.row()),
+
1151  dist.template rankGlobalElement<Coord::Col>(ij_offset.col()),
+
1152  };
+
1153 
+
1154  const bool is_panel_rank_col = rank_v0.col() == rank.col();
+
1155 
+
1156  const SizeType nrefls_tile = mat_taus_retiled.tileSize(GlobalTileIndex(j_sub, 0)).rows();
1157 
-
1158  auto& v = panels_v.nextResource();
-
1159  auto& vt = panels_vt.nextResource();
+
1158  if (nrefls_tile == 0)
+
1159  break;
1160 
-
1161  v.setRangeStart(at_offset);
-
1162  vt.setRangeStart(at_offset);
+
1161  auto& v = panels_v.nextResource();
+
1162  auto& vt = panels_vt.nextResource();
1163 
-
1164  v.setWidth(nrefls_tile);
-
1165  vt.setHeight(nrefls_tile);
+
1164  v.setRangeStart(at_offset);
+
1165  vt.setRangeStart(at_offset);
1166 
-
1167  const LocalTileIndex t_idx(0, 0);
-
1168  // TODO used just by the column, maybe we can re-use a panel tile?
-
1169  // TODO or we can keep just the sh_future and allocate just inside if (is_panel_rank_col)
-
1170  matrix::Matrix<T, D> t({nrefls_tile, nrefls_tile}, dist.blockSize());
-
1171 
-
1172  // PANEL
-
1173  const matrix::SubPanelView panel_view(dist, ij_offset, band_size);
+
1167  v.setWidth(nrefls_tile);
+
1168  vt.setHeight(nrefls_tile);
+
1169 
+
1170  const LocalTileIndex t_idx(0, 0);
+
1171  // TODO used just by the column, maybe we can re-use a panel tile?
+
1172  // TODO or we can keep just the sh_future and allocate just inside if (is_panel_rank_col)
+
1173  matrix::Matrix<T, D> t({nrefls_tile, nrefls_tile}, dist.blockSize());
1174 
-
1175  if (is_panel_rank_col) {
-
1176  compute_panel_helper.call(std::move(trigger_panel), rank_v0.row(), mpi_col_chain_panel(), mat_a,
-
1177  mat_taus_retiled, j_sub, panel_view);
-
1178 
-
1179  // Note:
-
1180  // - has_reflector_head tells if this rank owns the first tile of the panel
-
1181  // - if !is_full_band it has to force copy as a workaround, otherwise in update matrix it would
-
1182  // deadlock due to tile shared between panel and trailing matrix
-
1183  red2band::local::setupReflectorPanelV<B, D, T>(rank.row() == rank_v0.row(), panel_view,
-
1184  nrefls_tile, v, mat_a, !is_full_band);
-
1185  computeTFactor<B>(v, mat_taus_retiled.read(GlobalTileIndex(j_sub, 0)), t.readwrite(t_idx),
-
1186  mpi_col_chain);
-
1187  }
-
1188 
-
1189  // PREPARATION FOR TRAILING MATRIX UPDATE
-
1190 
-
1191  // Note: if there is no trailing matrix, algorithm has finised
-
1192  if (!at_offset.isIn(mat_a.size()))
-
1193  break;
-
1194 
-
1195  const matrix::SubMatrixView trailing_matrix_view(dist, at_offset);
-
1196 
-
1197  comm::broadcast(rank_v0.col(), v, vt, mpi_row_chain, mpi_col_chain);
-
1198 
-
1199  // W = V . T
-
1200  auto& w = panels_w.nextResource();
-
1201  auto& wt = panels_wt.nextResource();
-
1202 
-
1203  w.setRangeStart(at_offset);
-
1204  wt.setRangeStart(at_offset);
+
1175  // PANEL
+
1176  const matrix::SubPanelView panel_view(dist, ij_offset, band_size);
+
1177 
+
1178  if (is_panel_rank_col) {
+
1179  compute_panel_helper.call(std::move(trigger_panel), rank_v0.row(), mpi_col_chain_panel(), mat_a,
+
1180  mat_taus_retiled, j_sub, panel_view);
+
1181 
+
1182  // Note:
+
1183  // - has_reflector_head tells if this rank owns the first tile of the panel
+
1184  // - if !is_full_band it has to force copy as a workaround, otherwise in update matrix it would
+
1185  // deadlock due to tile shared between panel and trailing matrix
+
1186  red2band::local::setupReflectorPanelV<B, D, T>(rank.row() == rank_v0.row(), panel_view,
+
1187  nrefls_tile, v, mat_a, !is_full_band);
+
1188  computeTFactor<B>(v, mat_taus_retiled.read(GlobalTileIndex(j_sub, 0)), t.readwrite(t_idx),
+
1189  mpi_col_chain);
+
1190  }
+
1191 
+
1192  // PREPARATION FOR TRAILING MATRIX UPDATE
+
1193 
+
1194  // Note: if there is no trailing matrix, algorithm has finised
+
1195  if (!at_offset.isIn(mat_a.size()))
+
1196  break;
+
1197 
+
1198  const matrix::SubMatrixView trailing_matrix_view(dist, at_offset);
+
1199 
+
1200  comm::broadcast(rank_v0.col(), v, vt, mpi_row_chain, mpi_col_chain);
+
1201 
+
1202  // W = V . T
+
1203  auto& w = panels_w.nextResource();
+
1204  auto& wt = panels_wt.nextResource();
1205 
-
1206  w.setWidth(nrefls_tile);
-
1207  wt.setHeight(nrefls_tile);
+
1206  w.setRangeStart(at_offset);
+
1207  wt.setRangeStart(at_offset);
1208 
-
1209  if (is_panel_rank_col)
-
1210  red2band::local::trmmComputeW<B, D>(w, v, t.read(t_idx));
+
1209  w.setWidth(nrefls_tile);
+
1210  wt.setHeight(nrefls_tile);
1211 
-
1212  comm::broadcast(rank_v0.col(), w, wt, mpi_row_chain, mpi_col_chain);
-
1213 
-
1214  // X = At . W
-
1215  auto& x = panels_x.nextResource();
-
1216  auto& xt = panels_xt.nextResource();
-
1217 
-
1218  x.setRangeStart(at_offset);
-
1219  xt.setRangeStart(at_offset);
+
1212  if (is_panel_rank_col)
+
1213  red2band::local::trmmComputeW<B, D>(w, v, t.read(t_idx));
+
1214 
+
1215  comm::broadcast(rank_v0.col(), w, wt, mpi_row_chain, mpi_col_chain);
+
1216 
+
1217  // X = At . W
+
1218  auto& x = panels_x.nextResource();
+
1219  auto& xt = panels_xt.nextResource();
1220 
-
1221  x.setWidth(nrefls_tile);
-
1222  xt.setHeight(nrefls_tile);
+
1221  x.setRangeStart(at_offset);
+
1222  xt.setRangeStart(at_offset);
1223 
-
1224  // Note:
-
1225  // Since At is hermitian, just the lower part is referenced.
-
1226  // When the tile is not part of the main diagonal, the same tile has to be used for two computations
-
1227  // that will contribute to two different rows of X: the ones indexed with row and col.
-
1228  // This is achieved by storing the two results in two different workspaces: X and X_conj respectively.
-
1229  //
-
1230  // On exit, x will contain a valid result just on ranks belonging to the column panel.
-
1231  // For what concerns xt, it is just used as support and it contains junk data on all ranks.
-
1232  hemmComputeX<B, D>(rank_v0.col(), x, xt, trailing_matrix_view, mat_a, w, wt, mpi_row_chain,
-
1233  mpi_col_chain);
-
1234 
-
1235  // In the next section the next two operations are performed
-
1236  // A) W2 = W* . X
-
1237  // B) X -= 1/2 . V . W2
-
1238 
-
1239  // Note:
-
1240  // Now the intermediate result for X is available on the panel column ranks,
-
1241  // which have locally all the needed stuff for updating X and finalize the result
-
1242  if (is_panel_rank_col) {
-
1243  // Note:
-
1244  // T can be re-used because it is not needed anymore in this step and it has the same shape
-
1245  matrix::Matrix<T, D> w2 = std::move(t);
-
1246 
-
1247  red2band::local::gemmComputeW2<B, D>(w2, w, x);
-
1248  ex::start_detached(comm::scheduleAllReduceInPlace(mpi_col_chain(), MPI_SUM,
-
1249  w2.readwrite(LocalTileIndex(0, 0))));
-
1250 
-
1251  red2band::local::gemmUpdateX<B, D>(x, w2, v);
-
1252  }
+
1224  x.setWidth(nrefls_tile);
+
1225  xt.setHeight(nrefls_tile);
+
1226 
+
1227  // Note:
+
1228  // Since At is hermitian, just the lower part is referenced.
+
1229  // When the tile is not part of the main diagonal, the same tile has to be used for two computations
+
1230  // that will contribute to two different rows of X: the ones indexed with row and col.
+
1231  // This is achieved by storing the two results in two different workspaces: X and X_conj respectively.
+
1232  //
+
1233  // On exit, x will contain a valid result just on ranks belonging to the column panel.
+
1234  // For what concerns xt, it is just used as support and it contains junk data on all ranks.
+
1235  hemmComputeX<B, D>(rank_v0.col(), x, xt, trailing_matrix_view, mat_a, w, wt, mpi_row_chain,
+
1236  mpi_col_chain);
+
1237 
+
1238  // In the next section the next two operations are performed
+
1239  // A) W2 = W* . X
+
1240  // B) X -= 1/2 . V . W2
+
1241 
+
1242  // Note:
+
1243  // Now the intermediate result for X is available on the panel column ranks,
+
1244  // which have locally all the needed stuff for updating X and finalize the result
+
1245  if (is_panel_rank_col) {
+
1246  // Note:
+
1247  // T can be re-used because it is not needed anymore in this step and it has the same shape
+
1248  matrix::Matrix<T, D> w2 = std::move(t);
+
1249 
+
1250  red2band::local::gemmComputeW2<B, D>(w2, w, x);
+
1251  ex::start_detached(comm::scheduleAllReduceInPlace(mpi_col_chain(), MPI_SUM,
+
1252  w2.readwrite(LocalTileIndex(0, 0))));
1253 
-
1254  // Note:
-
1255  // xt has been used previously as workspace for hemmComputeX, so it has to be reset, because now it
-
1256  // will be used for accessing the broadcasted version of x
-
1257  xt.reset();
-
1258  xt.setRangeStart(at_offset);
-
1259  xt.setHeight(nrefls_tile);
-
1260 
-
1261  comm::broadcast(rank_v0.col(), x, xt, mpi_row_chain, mpi_col_chain);
-
1262 
-
1263  // TRAILING MATRIX UPDATE
-
1264 
-
1265  // Note:
-
1266  // This trigger mechanism allows to control when the next iteration of compute panel will start.
-
1267  //
-
1268  // * What?
-
1269  // Compute panel uses MPI blocking communication that might block the only computing thread
-
1270  // available (since blocking communication are scheduled on normal queues and not on the MPI
-
1271  // dedicated one).
-
1272  //
-
1273  // * How?
-
1274  // If pika runtime has only 2 threads, one is dedicated to MPI and there is just one for
-
1275  // computation, that might get blocked by blocking MPI communication, without the chance to do
-
1276  // anything else. (TODO this might happen even with more reductions happening in parallel)
-
1277  //
-
1278  // * Why?
-
1279  // Panel computation at step i is done on the first column of the trailing matrix computed
-
1280  // at step i-1.
-
1281  // The rank owning the top-left tile of the trailing matrix, can update it as soon as it
-
1282  // receives X[0], which due to the pivot position is also the Xt[0]. Once it can go to the next
-
1283  // iteration, it ends up stucked in an MPI blocking communication, waiting for the others joining
-
1284  // before being able to advance.
-
1285  //
-
1286  // But at the same time, other ranks in the same column (needed for the next panel update), cannot
-
1287  // complete the trailing matrix update. Indeed, they are waiting for the pivot rank to communicate
-
1288  // column-wise Xt[0] (during x -> xt panel transpose broadcast), but he is not going to schedule
-
1289  // anything because the only normal thread which can do that is stuck in an MPI blocking
-
1290  // communication that is not going to advance... and so it's a DEADLOCK!
-
1291  //
-
1292  // * Solution:
-
1293  // The idea is to make the next panel depending not only on tiles stored locally, but also to
-
1294  // ensure that others have received Xt[0], which is needed to advance the computation and let
-
1295  // others arrive at the next iteration where the pivot will wait for them to complete the MPI
-
1296  // blocking communication.
-
1297  //
-
1298  // * Why is it different between MC and GPU?
-
1299  // As said above, the problem is related to the communication. But the communication is not said
-
1300  // to be an atomic operation happening in a single task. It might have to create a copy to
-
1301  // a buffer more suitable for the communication (e.g. GPU -> CPU if RDMA is not available).
-
1302  //
-
1303  // And in order to not be blocked, it must be ensured that the actual communication task has
-
1304  // been scheduled.
-
1305  const SizeType j_tile_current = ij_offset.col() / dist.blockSize().cols();
-
1306  const SizeType j_tile_next = at_offset.col() / dist.blockSize().cols();
-
1307  const bool isNextColumnOnSameRank = (j_tile_current == j_tile_next);
-
1308  const comm::IndexT_MPI rank_next_col =
-
1309  isNextColumnOnSameRank ? rank_v0.col() : (rank_v0.col() + 1) % dist.commGridSize().cols();
-
1310 
-
1311  if (rank.col() == rank_next_col) {
-
1312  const LocalTileIndex at{
-
1313  dist.template nextLocalTileFromGlobalElement<Coord::Row>(at_offset.row()),
-
1314  dist.template nextLocalTileFromGlobalElement<Coord::Col>(at_offset.col()),
-
1315  };
-
1316 
-
1317  // Note:
-
1318  // This additional communication of the last tile is a workaround for supporting following trigger
-
1319  // when b < mb.
-
1320  // Indeed, if b < mb the last column have (at least) a panel to compute, but differently from
-
1321  // other columns, broadcast transposed doesn't communicate the last tile, which is an assumption
-
1322  // needed to make the following trigger work correctly.
-
1323  const SizeType at_tile_col =
-
1324  dist.template globalTileFromGlobalElement<Coord::Col>(at_offset.col());
-
1325 
-
1326  if (at_tile_col == dist.nrTiles().cols() - 1) {
-
1327  const comm::IndexT_MPI owner = rank_v0.row();
-
1328  if (rank.row() == owner) {
-
1329  xt.setTile(at, x.read(at));
-
1330 
-
1331  if (dist.commGridSize().rows() > 1)
-
1332  ex::start_detached(comm::scheduleSendBcast(mpi_col_chain(), xt.read(at)));
-
1333  }
-
1334  else {
-
1335  if (dist.commGridSize().rows() > 1)
-
1336  ex::start_detached(comm::scheduleRecvBcast(mpi_col_chain(), owner, xt.readwrite(at)));
-
1337  }
-
1338  }
-
1339 
-
1340  if constexpr (dlaf::comm::CommunicationDevice_v<D> == D) {
-
1341  // Note:
-
1342  // if there is no need for additional buffers, we can just wait that xt[0] is ready for
-
1343  // reading.
-
1344  if (rank.row() == rank_v0.row()) {
-
1345  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
-
1346  }
-
1347  else {
-
1348  // Note:
-
1349  // Conservatively ensure that xt[0] needed for updating the first column has been
-
1350  // received. Just wait for xt because communication of x happens over rows, while the
-
1351  // pivot rank can just block rank in the same column.
-
1352  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
-
1353  }
-
1354  }
-
1355  else {
-
1356  if (rank.row() == rank_v0.row()) {
-
1357  // Note:
-
1358  // on the pivot rank, i.e. the one that would quickly go to the next panel and block, from
-
1359  // implementation we know that xt[0] is set as an external tile pointing to x[0].
-
1360  // We cannot wait on xt readwrite (because it is an external tile in a panel, that constraints
-
1361  // it to be just readable), but we can wait on its source x[0]. This has a subtle implication,
-
1362  // since we will wait not just for the communication to be complete (which is already more
-
1363  // than what needed), but we will also wait till xt[0] will be released, so after all local
-
1364  // communication and computation on the first column of the trailing matrix will be completed.
-
1365  trigger_panel = x.readwrite(at) | ex::drop_value() | ex::ensure_started();
-
1366  }
-
1367  else {
-
1368  // Note:
-
1369  // Conservatively ensure that xt[0] needed for updating the first column has been
-
1370  // received. Just wait for xt because communication of x happens over rows, while the
-
1371  // pivot rank can just block rank in the same column.
-
1372  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
-
1373  }
-
1374  }
-
1375  }
-
1376 
-
1377  // At -= X . V* + V . X*
-
1378  her2kUpdateTrailingMatrix<B>(trailing_matrix_view, mat_a, x, vt, v, xt);
+
1254  red2band::local::gemmUpdateX<B, D>(x, w2, v);
+
1255  }
+
1256 
+
1257  // Note:
+
1258  // xt has been used previously as workspace for hemmComputeX, so it has to be reset, because now it
+
1259  // will be used for accessing the broadcasted version of x
+
1260  xt.reset();
+
1261  xt.setRangeStart(at_offset);
+
1262  xt.setHeight(nrefls_tile);
+
1263 
+
1264  comm::broadcast(rank_v0.col(), x, xt, mpi_row_chain, mpi_col_chain);
+
1265 
+
1266  // TRAILING MATRIX UPDATE
+
1267 
+
1268  // Note:
+
1269  // This trigger mechanism allows to control when the next iteration of compute panel will start.
+
1270  //
+
1271  // * What?
+
1272  // Compute panel uses MPI blocking communication that might block the only computing thread
+
1273  // available (since blocking communication are scheduled on normal queues and not on the MPI
+
1274  // dedicated one).
+
1275  //
+
1276  // * How?
+
1277  // If pika runtime has only 2 threads, one is dedicated to MPI and there is just one for
+
1278  // computation, that might get blocked by blocking MPI communication, without the chance to do
+
1279  // anything else. (TODO this might happen even with more reductions happening in parallel)
+
1280  //
+
1281  // * Why?
+
1282  // Panel computation at step i is done on the first column of the trailing matrix computed
+
1283  // at step i-1.
+
1284  // The rank owning the top-left tile of the trailing matrix, can update it as soon as it
+
1285  // receives X[0], which due to the pivot position is also the Xt[0]. Once it can go to the next
+
1286  // iteration, it ends up stucked in an MPI blocking communication, waiting for the others joining
+
1287  // before being able to advance.
+
1288  //
+
1289  // But at the same time, other ranks in the same column (needed for the next panel update), cannot
+
1290  // complete the trailing matrix update. Indeed, they are waiting for the pivot rank to communicate
+
1291  // column-wise Xt[0] (during x -> xt panel transpose broadcast), but he is not going to schedule
+
1292  // anything because the only normal thread which can do that is stuck in an MPI blocking
+
1293  // communication that is not going to advance... and so it's a DEADLOCK!
+
1294  //
+
1295  // * Solution:
+
1296  // The idea is to make the next panel depending not only on tiles stored locally, but also to
+
1297  // ensure that others have received Xt[0], which is needed to advance the computation and let
+
1298  // others arrive at the next iteration where the pivot will wait for them to complete the MPI
+
1299  // blocking communication.
+
1300  //
+
1301  // * Why is it different between MC and GPU?
+
1302  // As said above, the problem is related to the communication. But the communication is not said
+
1303  // to be an atomic operation happening in a single task. It might have to create a copy to
+
1304  // a buffer more suitable for the communication (e.g. GPU -> CPU if RDMA is not available).
+
1305  //
+
1306  // And in order to not be blocked, it must be ensured that the actual communication task has
+
1307  // been scheduled.
+
1308  const SizeType j_tile_current = ij_offset.col() / dist.blockSize().cols();
+
1309  const SizeType j_tile_next = at_offset.col() / dist.blockSize().cols();
+
1310  const bool isNextColumnOnSameRank = (j_tile_current == j_tile_next);
+
1311  const comm::IndexT_MPI rank_next_col =
+
1312  isNextColumnOnSameRank ? rank_v0.col() : (rank_v0.col() + 1) % dist.commGridSize().cols();
+
1313 
+
1314  if (rank.col() == rank_next_col) {
+
1315  const LocalTileIndex at{
+
1316  dist.template nextLocalTileFromGlobalElement<Coord::Row>(at_offset.row()),
+
1317  dist.template nextLocalTileFromGlobalElement<Coord::Col>(at_offset.col()),
+
1318  };
+
1319 
+
1320  // Note:
+
1321  // This additional communication of the last tile is a workaround for supporting following trigger
+
1322  // when b < mb.
+
1323  // Indeed, if b < mb the last column have (at least) a panel to compute, but differently from
+
1324  // other columns, broadcast transposed doesn't communicate the last tile, which is an assumption
+
1325  // needed to make the following trigger work correctly.
+
1326  const SizeType at_tile_col =
+
1327  dist.template globalTileFromGlobalElement<Coord::Col>(at_offset.col());
+
1328 
+
1329  if (at_tile_col == dist.nrTiles().cols() - 1) {
+
1330  const comm::IndexT_MPI owner = rank_v0.row();
+
1331  if (rank.row() == owner) {
+
1332  xt.setTile(at, x.read(at));
+
1333 
+
1334  if (dist.commGridSize().rows() > 1)
+
1335  ex::start_detached(comm::scheduleSendBcast(mpi_col_chain(), xt.read(at)));
+
1336  }
+
1337  else {
+
1338  if (dist.commGridSize().rows() > 1)
+
1339  ex::start_detached(comm::scheduleRecvBcast(mpi_col_chain(), owner, xt.readwrite(at)));
+
1340  }
+
1341  }
+
1342 
+
1343  if constexpr (dlaf::comm::CommunicationDevice_v<D> == D) {
+
1344  // Note:
+
1345  // if there is no need for additional buffers, we can just wait that xt[0] is ready for
+
1346  // reading.
+
1347  if (rank.row() == rank_v0.row()) {
+
1348  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
+
1349  }
+
1350  else {
+
1351  // Note:
+
1352  // Conservatively ensure that xt[0] needed for updating the first column has been
+
1353  // received. Just wait for xt because communication of x happens over rows, while the
+
1354  // pivot rank can just block rank in the same column.
+
1355  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
+
1356  }
+
1357  }
+
1358  else {
+
1359  if (rank.row() == rank_v0.row()) {
+
1360  // Note:
+
1361  // on the pivot rank, i.e. the one that would quickly go to the next panel and block, from
+
1362  // implementation we know that xt[0] is set as an external tile pointing to x[0].
+
1363  // We cannot wait on xt readwrite (because it is an external tile in a panel, that constraints
+
1364  // it to be just readable), but we can wait on its source x[0]. This has a subtle implication,
+
1365  // since we will wait not just for the communication to be complete (which is already more
+
1366  // than what needed), but we will also wait till xt[0] will be released, so after all local
+
1367  // communication and computation on the first column of the trailing matrix will be completed.
+
1368  trigger_panel = x.readwrite(at) | ex::drop_value() | ex::ensure_started();
+
1369  }
+
1370  else {
+
1371  // Note:
+
1372  // Conservatively ensure that xt[0] needed for updating the first column has been
+
1373  // received. Just wait for xt because communication of x happens over rows, while the
+
1374  // pivot rank can just block rank in the same column.
+
1375  trigger_panel = xt.read(at) | ex::drop_value() | ex::ensure_started();
+
1376  }
+
1377  }
+
1378  }
1379 
-
1380  xt.reset();
-
1381  x.reset();
-
1382  wt.reset();
-
1383  w.reset();
-
1384  vt.reset();
-
1385  v.reset();
-
1386  }
-
1387 
-
1388  return mat_taus;
-
1389 }
-
1390 }
+
1380  // At -= X . V* + V . X*
+
1381  her2kUpdateTrailingMatrix<B>(trailing_matrix_view, mat_a, x, vt, v, xt);
+
1382 
+
1383  xt.reset();
+
1384  x.reset();
+
1385  wt.reset();
+
1386  w.reset();
+
1387  vt.reset();
+
1388  v.reset();
+
1389  }
+
1390 
+
1391  return mat_taus;
+
1392 }
+
1393 }
tile.h
broadcast_panel.h
dlaf::common::Index2D< IndexT_MPI, TAG_MPI >
@@ -1493,7 +1496,7 @@
single_threaded_blas.h
dlaf::common::RoundRobin
Definition: round_robin.h:20
dlaf::eigensolver::internal::ReductionToBand
Definition: api.h:21
-
dlaf::eigensolver::internal::red2band::ComputePanelHelper
Definition: impl.h:826
+
dlaf::eigensolver::internal::red2band::ComputePanelHelper
Definition: impl.h:829
dlaf::matrix::Panel
Definition: panel.h:552
dlaf::matrix::Panel::readwrite
ReadWriteSenderType readwrite(LocalTileIndex index)
Definition: panel.h:570
dlaf::matrix::SubPanelView
Definition: views.h:132
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void dlaf::matrix::util::internal::set_diagonal_tile (const Tile< T, Device::CPU > &tile, internal::getter_random< T > &random_value, SizeType offset_value)   - + template<class T > -void dlaf::matrix::util::internal::set_lower_and_upper_tile (const Tile< T, Device::CPU > &tile, internal::getter_random< T > &random_value, TileElementSize full_tile_size, GlobalTileIndex tile_wrt_global) -  -template<class T > -void dlaf::matrix::util::internal::set_random_hermitian_with_offset (Matrix< T, Device::CPU > &matrix, const SizeType offset_value) -  +void dlaf::matrix::util::internal::set_lower_and_upper_tile (const Tile< T, Device::CPU > &tile, internal::getter_random< T > &random_value, TileElementSize full_tile_size, GlobalTileIndex tile_wrt_global, dlaf::matrix::Distribution dist, std::optional< SizeType > band_size=std::nullopt) +  +template<class T > +void dlaf::matrix::util::internal::set_random_hermitian_with_offset (Matrix< T, Device::CPU > &matrix, const SizeType offset_value, std::optional< SizeType > band_size=std::nullopt) +  template<class T > void dlaf::matrix::util::set_random_hermitian (Matrix< T, Device::CPU > &matrix)   +template<class T > +void dlaf::matrix::util::set_random_hermitian_banded (Matrix< T, Device::CPU > &matrix, const SizeType band_size) +  template<class T > void dlaf::matrix::util::set_random_hermitian_positive_definite (Matrix< T, Device::CPU > &matrix)   @@ -393,6 +396,56 @@

+

◆ set_random_hermitian_banded()

+ +
+
+
+template<class T >
+ + + + + + + + + + + + + + + + + + +
void dlaf::matrix::util::set_random_hermitian_banded (Matrix< T, Device::CPU > & matrix,
const SizeType band_size 
)
+
+

Set a banded matrix with random values assuring it will be hermitian

+

Values will be random numbers in:

    +
  • real: [-1, 1]
    • +
  • complex: a circle of radius 1 centered at origin
    • +
+

Each tile creates its own random generator engine with a unique seed which is computed as a function of the tile global index. This means that the elements of a specific tile, no matter how the matrix is distributed, will be set with the same set of values.

+
Precondition
+
Parameters
+ + +
matrixis a square matrix,
+
+
+
Precondition
+
Parameters
+ + +
matrixhas a square blocksize.
+
+
+
@@ -436,8 +489,8 @@

-

◆ set_random_hermitian_with_offset()

+ +

◆ set_random_hermitian_with_offset()

@@ -454,7 +507,13 @@

const SizeType  - offset_value  + offset_value, + + + + + std::optional< SizeType >  + band_size = std::nullopt  diff --git a/master/util__matrix_8h_source.html b/master/util__matrix_8h_source.html index d60f243f31..a84d588966 100644 --- a/master/util__matrix_8h_source.html +++ b/master/util__matrix_8h_source.html @@ -307,87 +307,110 @@
281 
282 template <class T>
283 void set_lower_and_upper_tile(const Tile<T, Device::CPU>& tile, internal::getter_random<T>& random_value,
-
284  TileElementSize full_tile_size, GlobalTileIndex tile_wrt_global) {
-
285  // LOWER or UPPER (except DIAGONAL)
-
286  // random values are requested in the same order for both original and transposed
-
287  for (SizeType j = 0; j < full_tile_size.cols(); ++j) {
-
288  for (SizeType i = 0; i < full_tile_size.rows(); ++i) {
-
289  auto value = random_value();
+
284  TileElementSize full_tile_size, GlobalTileIndex tile_wrt_global,
+
285  dlaf::matrix::Distribution dist,
+
286  std::optional<SizeType> band_size = std::nullopt) {
+
287  auto is_off_band = [](GlobalElementIndex ij, std::optional<SizeType> band_size) {
+
288  return band_size ? ij.col() < ij.row() - *band_size || ij.col() > ij.row() + *band_size : false;
+
289  };
290 
-
291  // but they are set row-wise in the original tile and col-wise in the
-
292  // transposed one
-
293  if (tile_wrt_global.row() > tile_wrt_global.col()) { // LOWER
-
294  TileElementIndex index{i, j};
-
295  if (index.isIn(tile.size()))
-
296  tile(index) = value;
-
297  }
-
298  else { // UPPER
-
299  TileElementIndex index{j, i};
-
300  if (index.isIn(tile.size()))
-
301  tile(index) = dlaf::conj(value);
-
302  }
-
303  }
-
304  }
-
305 }
-
306 
-
323 template <class T>
-
324 void set_random_hermitian_with_offset(Matrix<T, Device::CPU>& matrix, const SizeType offset_value) {
-
325  // note:
-
326  // By assuming square blocksizes, it is easier to locate elements. In fact:
-
327  // - Elements on the diagonal are stored in the diagonal of the diagonal tiles
-
328  // - Tiles under the diagonal store elements of the lower triangular matrix
-
329  // - Tiles over the diagonal store elements of the upper triangular matrix
-
330 
-
331  const Distribution& dist = matrix.distribution();
-
332 
-
333  DLAF_ASSERT(square_size(matrix), matrix);
-
334  DLAF_ASSERT(square_blocksize(matrix), matrix);
-
335 
-
336  auto full_tile_size = matrix.blockSize();
-
337 
-
338  for (auto tile_wrt_local : iterate_range2d(dist.localNrTiles())) {
-
339  GlobalTileIndex tile_wrt_global = dist.globalTileIndex(tile_wrt_local);
-
340 
-
341  auto tl_index = dist.globalElementIndex(tile_wrt_global, {0, 0});
-
342 
-
343  // compute the same seed for original and "transposed" tiles, so transposed ones will know the
-
344  // values of the original one without the need of accessing real values (nor communication in case
-
345  // of distributed matrices)
-
346  SizeType seed;
-
347  if (tile_wrt_global.row() >= tile_wrt_global.col()) // LOWER or DIAGONAL
-
348  seed = tl_index.col() + tl_index.row() * matrix.size().cols();
-
349  else
-
350  seed = tl_index.row() + tl_index.col() * matrix.size().rows();
-
351 
-
352  using TileType = typename std::decay_t<decltype(matrix)>::TileType;
-
353  auto set_hp_f = [=](const TileType& tile) {
-
354  internal::getter_random<T> random_value(seed);
-
355  if (tile_wrt_global.row() == tile_wrt_global.col())
-
356  internal::set_diagonal_tile(tile, random_value, offset_value);
-
357  else
-
358  internal::set_lower_and_upper_tile(tile, random_value, full_tile_size, tile_wrt_global);
-
359  };
-
360 
-
361  dlaf::internal::transformDetach(dlaf::internal::Policy<Backend::MC>(), std::move(set_hp_f),
-
362  matrix.readwrite(tile_wrt_local));
-
363  }
-
364 }
-
365 
-
366 }
-
367 
-
381 template <class T>
-
382 void set_random_hermitian(Matrix<T, Device::CPU>& matrix) {
-
383  internal::set_random_hermitian_with_offset(matrix, 0);
+
291  // LOWER or UPPER (except DIAGONAL)
+
292  // random values are requested in the same order for both original and transposed
+
293  for (SizeType j = 0; j < full_tile_size.cols(); ++j) {
+
294  for (SizeType i = 0; i < full_tile_size.rows(); ++i) {
+
295  auto value = random_value();
+
296 
+
297  // but they are set row-wise in the original tile and col-wise in the
+
298  // transposed one
+
299  if (tile_wrt_global.row() > tile_wrt_global.col()) { // LOWER
+
300  TileElementIndex index{i, j};
+
301  if (index.isIn(tile.size())) {
+
302  auto ij = dist.globalElementIndex(tile_wrt_global, index);
+
303  if (is_off_band(ij, band_size))
+
304  tile(index) = T(0);
+
305  else
+
306  tile(index) = value;
+
307  }
+
308  }
+
309  else { // UPPER
+
310  TileElementIndex index{j, i};
+
311  if (index.isIn(tile.size())) {
+
312  auto ij = dist.globalElementIndex(tile_wrt_global, index);
+
313  if (is_off_band(ij, band_size))
+
314  tile(index) = T(0);
+
315  else
+
316  tile(index) = dlaf::conj(value);
+
317  }
+
318  }
+
319  }
+
320  }
+
321 }
+
322 
+
339 template <class T>
+
340 void set_random_hermitian_with_offset(Matrix<T, Device::CPU>& matrix, const SizeType offset_value,
+
341  std::optional<SizeType> band_size = std::nullopt) {
+
342  // note:
+
343  // By assuming square blocksizes, it is easier to locate elements. In fact:
+
344  // - Elements on the diagonal are stored in the diagonal of the diagonal tiles
+
345  // - Tiles under the diagonal store elements of the lower triangular matrix
+
346  // - Tiles over the diagonal store elements of the upper triangular matrix
+
347 
+
348  const Distribution& dist = matrix.distribution();
+
349 
+
350  DLAF_ASSERT(square_size(matrix), matrix);
+
351  DLAF_ASSERT(square_blocksize(matrix), matrix);
+
352 
+
353  auto full_tile_size = matrix.blockSize();
+
354 
+
355  for (auto tile_wrt_local : iterate_range2d(dist.localNrTiles())) {
+
356  GlobalTileIndex tile_wrt_global = dist.globalTileIndex(tile_wrt_local);
+
357 
+
358  auto tl_index = dist.globalElementIndex(tile_wrt_global, {0, 0});
+
359 
+
360  // compute the same seed for original and "transposed" tiles, so transposed ones will know the
+
361  // values of the original one without the need of accessing real values (nor communication in case
+
362  // of distributed matrices)
+
363  SizeType seed;
+
364  if (tile_wrt_global.row() >= tile_wrt_global.col()) // LOWER or DIAGONAL
+
365  seed = tl_index.col() + tl_index.row() * matrix.size().cols();
+
366  else
+
367  seed = tl_index.row() + tl_index.col() * matrix.size().rows();
+
368 
+
369  using TileType = typename std::decay_t<decltype(matrix)>::TileType;
+
370  auto set_hp_f = [=](const TileType& tile) {
+
371  internal::getter_random<T> random_value(seed);
+
372  if (tile_wrt_global.row() == tile_wrt_global.col())
+
373  internal::set_diagonal_tile(tile, random_value, offset_value);
+
374  else
+
375  internal::set_lower_and_upper_tile(tile, random_value, full_tile_size, tile_wrt_global, dist,
+
376  band_size);
+
377  };
+
378 
+
379  dlaf::internal::transformDetach(dlaf::internal::Policy<Backend::MC>(), std::move(set_hp_f),
+
380  matrix.readwrite(tile_wrt_local));
+
381  }
+
382 }
+
383 
384 }
385 
-
402 template <class T>
-
403 void set_random_hermitian_positive_definite(Matrix<T, Device::CPU>& matrix) {
-
404  internal::set_random_hermitian_with_offset(matrix, 2 * matrix.size().rows());
-
405 }
-
406 
-
407 }
-
408 }
-
409 }
+
399 template <class T>
+
400 void set_random_hermitian(Matrix<T, Device::CPU>& matrix) {
+
401  internal::set_random_hermitian_with_offset(matrix, 0);
+
402 }
+
403 
+
417 template <class T>
+
418 void set_random_hermitian_banded(Matrix<T, Device::CPU>& matrix, const SizeType band_size) {
+
419  internal::set_random_hermitian_with_offset(matrix, 0, band_size);
+
420 }
+
421 
+
438 template <class T>
+
439 void set_random_hermitian_positive_definite(Matrix<T, Device::CPU>& matrix) {
+
440  internal::set_random_hermitian_with_offset(matrix, 2 * matrix.size().rows());
+
441 }
+
442 
+
443 }
+
444 }
+
445 }
enum_output.h
dlaf::comm::CommunicatorGrid
Definition: communicator_grid.h:42
@@ -414,10 +437,11 @@
dlaf::matrix::equal_blocksize
bool equal_blocksize(const Matrix< const T, D1 > &lhs, Matrix< const T, D2 > &rhs) noexcept
Returns true if matrices have equal blocksizes.
Definition: util_matrix.h:66
dlaf::matrix::multipliable
bool multipliable(const Matrix< const T, D > &a, const Matrix< const T, D > &b, const Matrix< const T, D > &c, const blas::Op opA, const blas::Op opB) noexcept
Returns true if matrices a, b and c have matrix multipliable sizes and block sizes.
Definition: util_matrix.h:102
dlaf::matrix::util::set
void set(Matrix< T, Device::CPU > &matrix, ElementGetter el_f)
Definition: util_matrix.h:184
-
dlaf::matrix::util::internal::set_random_hermitian_with_offset
void set_random_hermitian_with_offset(Matrix< T, Device::CPU > &matrix, const SizeType offset_value)
Definition: util_matrix.h:324
+
dlaf::matrix::util::set_random_hermitian_banded
void set_random_hermitian_banded(Matrix< T, Device::CPU > &matrix, const SizeType band_size)
Definition: util_matrix.h:418
dlaf::matrix::square_blocksize
bool square_blocksize(const MatrixLike &m) noexcept
Returns true if the matrix block size is square.
Definition: util_matrix.h:48
-
dlaf::matrix::util::set_random_hermitian
void set_random_hermitian(Matrix< T, Device::CPU > &matrix)
Definition: util_matrix.h:382
+
dlaf::matrix::util::set_random_hermitian
void set_random_hermitian(Matrix< T, Device::CPU > &matrix)
Definition: util_matrix.h:400
dlaf::matrix::single_tile_per_block
bool single_tile_per_block(const MatrixLike &m) noexcept
Returns true if the matrix has a single tile per block.
Definition: util_matrix.h:54
+
dlaf::matrix::util::internal::set_random_hermitian_with_offset
void set_random_hermitian_with_offset(Matrix< T, Device::CPU > &matrix, const SizeType offset_value, std::optional< SizeType > band_size=std::nullopt)
Definition: util_matrix.h:340
dlaf::matrix::equal_process_grid
bool equal_process_grid(const Matrix< const T, D > &m, const comm::CommunicatorGrid &g) noexcept
Returns true if the matrix is distributed on the communication grid.
Definition: util_matrix.h:78
dlaf::matrix::local_matrix
bool local_matrix(const Matrix< const T, D > &m) noexcept
Returns true if the matrix is local to a process.
Definition: util_matrix.h:72
dlaf::matrix::equal_distributions
bool equal_distributions(const Matrix< const T, D1 > &lhs, const Matrix< const T, D2 > &rhs) noexcept
Returns true if the matrices are distributed the same way.
Definition: util_matrix.h:84
@@ -425,7 +449,7 @@
dlaf::matrix::multipliable_sizes
bool multipliable_sizes(common::Size2D< IndexT, Tag > a, common::Size2D< IndexT, Tag > b, common::Size2D< IndexT, Tag > c, const blas::Op opA, const blas::Op opB) noexcept
Returns true if the sizes are compatible for matrix multiplication.
Definition: util_matrix.h:90
dlaf::matrix::square_size
bool square_size(const MatrixLike &m) noexcept
Returns true if the matrix is square.
Definition: util_matrix.h:42
dlaf::matrix::equal_size
bool equal_size(const MatrixLikeA &lhs, const MatrixLikeB &rhs) noexcept
Returns true if matrices have equal sizes.
Definition: util_matrix.h:60
-
dlaf::matrix::util::set_random_hermitian_positive_definite
void set_random_hermitian_positive_definite(Matrix< T, Device::CPU > &matrix)
Definition: util_matrix.h:403
+
dlaf::matrix::util::set_random_hermitian_positive_definite
void set_random_hermitian_positive_definite(Matrix< T, Device::CPU > &matrix)
Definition: util_matrix.h:439