sharded_quadratic_program.cc

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// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
 
#include "ortools/pdlp/sharded_quadratic_program.h"
 
#include <cstdint>
#include <memory>
#include <utility>
 
#include "Eigen/Core"
#include "Eigen/SparseCore"
#include "absl/memory/memory.h"
#include "absl/strings/string_view.h"
#include "ortools/base/logging.h"
#include "ortools/base/threadpool.h"
#include "ortools/pdlp/quadratic_program.h"
#include "ortools/pdlp/sharder.h"
 
namespace operations_research::pdlp {
 
namespace {
 
// Logs a warning if the given matrix has more than density_limit non-zeros in
// a single column.
void WarnIfMatrixUnbalanced(
    const Eigen::SparseMatrix<double, Eigen::ColMajor, int64_t>& matrix,
    absl::string_view matrix_name, int64_t density_limit) {
  if (matrix.cols() == 0) return;
  int64_t worst_column = 0;
  for (int64_t col = 0; col < matrix.cols(); ++col) {
    if (matrix.col(col).nonZeros() > matrix.col(worst_column).nonZeros()) {
      worst_column = col;
    }
  }
  if (matrix.col(worst_column).nonZeros() > density_limit) {
    // TODO(user): fix this automatically in presolve instead of asking the
    // user to do it.
    LOG(WARNING)
        << "The " << matrix_name << " has "
        << matrix.col(worst_column).nonZeros() << " non-zeros in its "
        << worst_column
        << "th column. For best parallelization all rows and columns should "
           "have at most order "
        << density_limit
        << " non-zeros. Consider rewriting the QP to split the corresponding "
           "variable or constraint.";
  }
}
 
}  // namespace
 
ShardedQuadraticProgram::ShardedQuadraticProgram(QuadraticProgram qp,
                                                 const int num_threads,
                                                 const int num_shards)
    : qp_(std::move(qp)),
      transposed_constraint_matrix_(qp_.constraint_matrix.transpose()),
      thread_pool_(num_threads == 1
                       ? nullptr
                       : absl::make_unique<ThreadPool>("PDLP", num_threads)),
      constraint_matrix_sharder_(qp_.constraint_matrix, num_shards,
                                 thread_pool_.get()),
      transposed_constraint_matrix_sharder_(transposed_constraint_matrix_,
                                            num_shards, thread_pool_.get()),
      primal_sharder_(qp_.variable_lower_bounds.size(), num_shards,
                      thread_pool_.get()),
      dual_sharder_(qp_.constraint_lower_bounds.size(), num_shards,
                    thread_pool_.get()) {
  CHECK_GE(num_threads, 1);
  CHECK_GE(num_shards, num_threads);
  if (num_threads > 1) {
    thread_pool_->StartWorkers();
    const int64_t work_per_iteration = qp_.constraint_matrix.nonZeros() +
                                       qp_.variable_lower_bounds.size() +
                                       qp_.constraint_lower_bounds.size();
    const int64_t column_density_limit = work_per_iteration / num_threads;
    WarnIfMatrixUnbalanced(qp_.constraint_matrix, "constraint matrix",
                           column_density_limit);
    WarnIfMatrixUnbalanced(transposed_constraint_matrix_,
                           "transposed constraint matrix",
                           column_density_limit);
  }
}
 
namespace {
 
// Multiply each entry of the matrix by the corresponding element of
// row_scaling_vec and col_scaling_vec, i.e., matrix[i,j] *= row_scaling_vec[i]
// * col_scaling_vec[j].
void ScaleMatrix(
    const Eigen::VectorXd& col_scaling_vec,
    const Eigen::VectorXd& row_scaling_vec, const Sharder& sharder,
    Eigen::SparseMatrix<double, Eigen::ColMajor, int64_t>& matrix) {
  CHECK_EQ(matrix.cols(), col_scaling_vec.size());
  CHECK_EQ(matrix.rows(), row_scaling_vec.size());
  sharder.ParallelForEachShard([&](const Sharder::Shard& shard) {
    auto matrix_shard = shard(matrix);
    auto col_scaling_vec_shard = shard(col_scaling_vec);
    for (int64_t col_num = 0; col_num < shard(matrix).outerSize(); ++col_num) {
      for (decltype(matrix_shard)::InnerIterator it(matrix_shard, col_num); it;
           ++it) {
        it.valueRef() *=
            row_scaling_vec[it.row()] * col_scaling_vec_shard[it.col()];
      }
    }
  });
}
 
}  // namespace
 
void ShardedQuadraticProgram::RescaleQuadraticProgram(
    const Eigen::VectorXd& col_scaling_vec,
    const Eigen::VectorXd& row_scaling_vec) {
  CHECK_EQ(PrimalSize(), col_scaling_vec.size());
  CHECK_EQ(DualSize(), row_scaling_vec.size());
  primal_sharder_.ParallelForEachShard([&](const Sharder::Shard& shard) {
    CHECK((shard(col_scaling_vec).array() > 0.0).all());
    shard(qp_.objective_vector) =
        shard(qp_.objective_vector).cwiseProduct(shard(col_scaling_vec));
    shard(qp_.variable_lower_bounds) =
        shard(qp_.variable_lower_bounds).cwiseQuotient(shard(col_scaling_vec));
    shard(qp_.variable_upper_bounds) =
        shard(qp_.variable_upper_bounds).cwiseQuotient(shard(col_scaling_vec));
    if (!IsLinearProgram(qp_)) {
      shard(qp_.objective_matrix->diagonal()) =
          shard(qp_.objective_matrix->diagonal())
              .cwiseProduct(
                  shard(col_scaling_vec).cwiseProduct(shard(col_scaling_vec)));
    }
  });
  dual_sharder_.ParallelForEachShard([&](const Sharder::Shard& shard) {
    CHECK((shard(row_scaling_vec).array() > 0.0).all());
    shard(qp_.constraint_lower_bounds) =
        shard(qp_.constraint_lower_bounds).cwiseProduct(shard(row_scaling_vec));
    shard(qp_.constraint_upper_bounds) =
        shard(qp_.constraint_upper_bounds).cwiseProduct(shard(row_scaling_vec));
  });
 
  ScaleMatrix(col_scaling_vec, row_scaling_vec, constraint_matrix_sharder_,
              qp_.constraint_matrix);
  ScaleMatrix(row_scaling_vec, col_scaling_vec,
              transposed_constraint_matrix_sharder_,
              transposed_constraint_matrix_);
}
 
}  // namespace operations_research::pdlp