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sharded_quadratic_program.cc
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sharded_quadratic_program.cc
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// Copyright 2010-2024 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 <limits>
#include <memory>
#include <optional>
#include <utility>
#include "Eigen/Core"
#include "Eigen/SparseCore"
#include "absl/log/check.h"
#include "absl/strings/string_view.h"
#include "ortools/base/logging.h"
#include "ortools/pdlp/quadratic_program.h"
#include "ortools/pdlp/scheduler.h"
#include "ortools/pdlp/sharder.h"
#include "ortools/pdlp/solvers.pb.h"
#include "ortools/util/logging.h"
namespace operations_research::pdlp {
namespace {
// Logs a warning if `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,
operations_research::SolverLogger* logger) {
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.
if (logger) {
SOLVER_LOG(
logger, "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.");
} else {
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,
SchedulerType scheduler_type, operations_research::SolverLogger* logger)
: qp_(std::move(qp)),
transposed_constraint_matrix_(qp_.constraint_matrix.transpose()),
scheduler_(num_threads == 1 ? nullptr
: MakeScheduler(scheduler_type, num_threads)),
constraint_matrix_sharder_(qp_.constraint_matrix, num_shards,
scheduler_.get()),
transposed_constraint_matrix_sharder_(transposed_constraint_matrix_,
num_shards, scheduler_.get()),
primal_sharder_(qp_.variable_lower_bounds.size(), num_shards,
scheduler_.get()),
dual_sharder_(qp_.constraint_lower_bounds.size(), num_shards,
scheduler_.get()) {
CHECK_GE(num_threads, 1);
CHECK_GE(num_shards, num_threads);
if (num_threads > 1) {
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, logger);
WarnIfMatrixUnbalanced(transposed_constraint_matrix_,
"transposed constraint matrix", column_density_limit,
logger);
}
}
namespace {
// Multiply each entry of `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()];
}
}
});
}
void ReplaceLargeValuesWithInfinity(const double threshold,
const Sharder& sharder,
Eigen::VectorXd& vector) {
constexpr double kInfinity = std::numeric_limits<double>::infinity();
sharder.ParallelForEachShard([&](const Sharder::Shard& shard) {
auto vector_shard = shard(vector);
for (int64_t i = 0; i < vector_shard.size(); ++i) {
if (vector_shard[i] <= -threshold) vector_shard[i] = -kInfinity;
if (vector_shard[i] >= threshold) vector_shard[i] = kInfinity;
}
});
}
} // 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_);
}
void ShardedQuadraticProgram::ReplaceLargeConstraintBoundsWithInfinity(
const double threshold) {
ReplaceLargeValuesWithInfinity(threshold, DualSharder(),
qp_.constraint_lower_bounds);
ReplaceLargeValuesWithInfinity(threshold, DualSharder(),
qp_.constraint_upper_bounds);
}
void ShardedQuadraticProgram::SetConstraintBounds(
int64_t constraint_index, std::optional<double> lower_bound,
std::optional<double> upper_bound) {
CHECK_LT(constraint_index, DualSize());
CHECK_GE(constraint_index, 0);
if (lower_bound.has_value()) {
qp_.constraint_lower_bounds[constraint_index] = *lower_bound;
}
if (upper_bound.has_value()) {
qp_.constraint_upper_bounds[constraint_index] = *upper_bound;
}
}
} // namespace operations_research::pdlp