Parallelize block_jacobi_preconditioner

Use ParallelFor to parallelize both versions of the
block Jacobi preconditioner. Also add benchmarks for
varying number of threads.

Benchmark on M1 Mac Pro

Before:
-----------------------------------------------------------------------------------------
Benchmark                                               Time             CPU   Iterations
-----------------------------------------------------------------------------------------
BM_BlockSparseJacobiPreconditionerBA             44847927 ns     44788313 ns           16
BM_BlockCRSJacobiPreconditionerBA                48772330 ns     48723571 ns           14
BM_BlockSparseJacobiPreconditionerUnstructured   62385231 ns     62306818 ns           11
BM_BlockCRSJacobiPreconditionerUnstructured      60671473 ns     60577727 ns           11

After:
--------------------------------------------------------------------------------------------
Benchmark                                                  Time             CPU   Iterations
--------------------------------------------------------------------------------------------
BM_BlockSparseJacobiPreconditionerBA/1              53314862 ns     53302308 ns           13
BM_BlockSparseJacobiPreconditionerBA/2              33601214 ns     33295143 ns           21
BM_BlockSparseJacobiPreconditionerBA/4              28162794 ns     27224167 ns           30
BM_BlockSparseJacobiPreconditionerBA/8              31402448 ns     28038760 ns           25
BM_BlockSparseJacobiPreconditionerBA/16             30820813 ns     22625233 ns           30
BM_BlockCRSJacobiPreconditionerBA/1                 60348194 ns     60332167 ns           12
BM_BlockCRSJacobiPreconditionerBA/2                 35489954 ns     34782050 ns           20
BM_BlockCRSJacobiPreconditionerBA/4                 23636360 ns     22547032 ns           31
BM_BlockCRSJacobiPreconditionerBA/8                 31688798 ns     27857800 ns           25
BM_BlockCRSJacobiPreconditionerBA/16                30806695 ns     20562516 ns           31
BM_BlockSparseJacobiPreconditionerUnstructured/1    59793396 ns     59788583 ns           12
BM_BlockSparseJacobiPreconditionerUnstructured/2    35192900 ns     34968900 ns           20
BM_BlockSparseJacobiPreconditionerUnstructured/4    30171145 ns     28924480 ns           25
BM_BlockSparseJacobiPreconditionerUnstructured/8    24982583 ns     23193172 ns           29
BM_BlockSparseJacobiPreconditionerUnstructured/16   23370546 ns     18389694 ns           36
BM_BlockCRSJacobiPreconditionerUnstructured/1       63204538 ns     63204545 ns           11
BM_BlockCRSJacobiPreconditionerUnstructured/2       34466060 ns     34193429 ns           21
BM_BlockCRSJacobiPreconditionerUnstructured/4       22712230 ns     20491147 ns           34
BM_BlockCRSJacobiPreconditionerUnstructured/8       16701833 ns     16190395 ns           43
BM_BlockCRSJacobiPreconditionerUnstructured/16      16762565 ns     12857304 ns           56

Note that single threaded performance gets worse. Performance goes up for 2 and 4 threads
and then essentially stalls.

Change-Id: I96a5d2f719545e14c03d73e71c8c0564e8c1c729
This commit is contained in:
Sameer Agarwal
2022-08-29 20:40:30 -07:00
parent c0c4f93940
commit 739f2a25ae
5 changed files with 200 additions and 92 deletions
+101 -67
View File
@@ -39,12 +39,14 @@
#include "ceres/block_structure.h"
#include "ceres/casts.h"
#include "ceres/internal/eigen.h"
#include "ceres/parallel_for.h"
#include "ceres/small_blas.h"
namespace ceres::internal {
BlockSparseJacobiPreconditioner::BlockSparseJacobiPreconditioner(
const BlockSparseMatrix& A) {
Preconditioner::Options options, const BlockSparseMatrix& A)
: options_(std::move(options)) {
m_ = std::make_unique<BlockRandomAccessDiagonalMatrix>(
A.block_structure()->cols);
}
@@ -56,48 +58,63 @@ bool BlockSparseJacobiPreconditioner::UpdateImpl(const BlockSparseMatrix& A,
const CompressedRowBlockStructure* bs = A.block_structure();
const double* values = A.values();
m_->SetZero();
for (int i = 0; i < bs->rows.size(); ++i) {
const int row_block_size = bs->rows[i].block.size;
const std::vector<Cell>& cells = bs->rows[i].cells;
for (const auto& cell : cells) {
const int block_id = cell.block_id;
const int col_block_size = bs->cols[block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info =
m_->GetCell(block_id, block_id, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
ConstMatrixRef b(values + cell.position, row_block_size, col_block_size);
// clang-format off
MatrixTransposeMatrixMultiply<Eigen::Dynamic, Eigen::Dynamic,
Eigen::Dynamic,Eigen::Dynamic, 1>(
values + cell.position, row_block_size,col_block_size,
values + cell.position, row_block_size,col_block_size,
cell_info->values,r, c,row_stride,col_stride);
// clang-format on
}
}
ParallelFor(options_.context,
0,
bs->rows.size(),
options_.num_threads,
[this, bs, values](int i) {
const int row_block_size = bs->rows[i].block.size;
const std::vector<Cell>& cells = bs->rows[i].cells;
for (const auto& cell : cells) {
const int block_id = cell.block_id;
const int col_block_size = bs->cols[block_id].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = m_->GetCell(
block_id, block_id, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
ConstMatrixRef b(
values + cell.position, row_block_size, col_block_size);
std::lock_guard<std::mutex> l(cell_info->m);
// clang-format off
MatrixTransposeMatrixMultiply<Eigen::Dynamic, Eigen::Dynamic,
Eigen::Dynamic,Eigen::Dynamic, 1>(
values + cell.position, row_block_size,col_block_size,
values + cell.position, row_block_size,col_block_size,
cell_info->values,r, c,row_stride,col_stride);
// clang-format on
}
});
if (D != nullptr) {
// Add the diagonal.
int position = 0;
for (int i = 0; i < bs->cols.size(); ++i) {
const int block_size = bs->cols[i].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info = m_->GetCell(i, i, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
m.block(r, c, block_size, block_size).diagonal() +=
ConstVectorRef(D + position, block_size).array().square().matrix();
position += block_size;
}
ParallelFor(options_.context,
0,
bs->cols.size(),
options_.num_threads,
[this, bs, D](int i) {
const int block_size = bs->cols[i].size;
int r, c, row_stride, col_stride;
CellInfo* cell_info =
m_->GetCell(i, i, &r, &c, &row_stride, &col_stride);
MatrixRef m(cell_info->values, row_stride, col_stride);
m.block(r, c, block_size, block_size).diagonal() +=
ConstVectorRef(D + bs->cols[i].position, block_size)
.array()
.square()
.matrix();
});
}
// TODO(sameeragarwal): Once matrices are threaded, this call to invert should
// also be parallelized.
m_->Invert();
return true;
}
BlockCRSJacobiPreconditioner::BlockCRSJacobiPreconditioner(
const CompressedRowSparseMatrix& A) {
Preconditioner::Options options, const CompressedRowSparseMatrix& A)
: options_(std::move(options)), locks_(A.col_blocks().size()) {
auto& col_blocks = A.col_blocks();
// Compute the number of non-zeros in the preconditioner. This is needed so
@@ -126,6 +143,12 @@ BlockCRSJacobiPreconditioner::BlockCRSJacobiPreconditioner(
}
}
// In reality we only need num_col_blocks locks, however that would require
// that in UpdateImpl we are able to look up the column block from the it
// first column. To save ourselves this map we will instead spend a few extra
// lock objects.
std::vector<std::mutex> locks(A.num_cols());
locks_.swap(locks);
CHECK_EQ(m_rows[A.num_cols()], m_nnz);
}
@@ -141,49 +164,60 @@ bool BlockCRSJacobiPreconditioner::UpdateImpl(
const int* a_rows = A.rows();
const int* a_cols = A.cols();
const double* a_values = A.values();
m_->SetZero();
double* m_values = m_->mutable_values();
const int* m_rows = m_->rows();
for (int i = 0; i < num_row_blocks; ++i) {
const int row = row_blocks[i].position;
const int row_block_size = row_blocks[i].size;
const int row_nnz = a_rows[row + 1] - a_rows[row];
ConstMatrixRef row_block(a_values + a_rows[row], row_block_size, row_nnz);
int c = 0;
while (c < row_nnz) {
const int idx = a_rows[row] + c;
const int col = a_cols[idx];
const int col_block_size = m_rows[col + 1] - m_rows[col];
m_->SetZero();
// We make use of the fact that the entire diagonal block is stored
// contiguously in memory as a row-major matrix.
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
ParallelFor(
options_.context,
0,
num_row_blocks,
options_.num_threads,
[this, row_blocks, a_rows, a_cols, a_values, m_values, m_rows](int i) {
const int row = row_blocks[i].position;
const int row_block_size = row_blocks[i].size;
const int row_nnz = a_rows[row + 1] - a_rows[row];
ConstMatrixRef row_block(
a_values + a_rows[row], row_block_size, row_nnz);
int c = 0;
while (c < row_nnz) {
const int idx = a_rows[row] + c;
const int col = a_cols[idx];
const int col_block_size = m_rows[col + 1] - m_rows[col];
// We do not have a row_stride version of MatrixTransposeMatrixMultiply,
// otherwise we could use it here to further speed up the following
// expression.
auto b = row_block.middleCols(c, col_block_size);
m.noalias() += b.transpose() * b;
c += col_block_size;
}
}
// We make use of the fact that the entire diagonal block is
// stored contiguously in memory as a row-major matrix.
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
// We do not have a row_stride version of
// MatrixTransposeMatrixMultiply, otherwise we could use it
// here to further speed up the following expression.
auto b = row_block.middleCols(c, col_block_size);
std::lock_guard<std::mutex> l(locks_[col]);
m.noalias() += b.transpose() * b;
c += col_block_size;
}
});
for (int i = 0; i < num_col_blocks; ++i) {
const int col = col_blocks[i].position;
const int col_block_size = col_blocks[i].size;
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
ParallelFor(
options_.context,
0,
num_col_blocks,
options_.num_threads,
[col_blocks, m_rows, m_values, D](int i) {
const int col = col_blocks[i].position;
const int col_block_size = col_blocks[i].size;
MatrixRef m(m_values + m_rows[col], col_block_size, col_block_size);
if (D != nullptr) {
m.diagonal() +=
ConstVectorRef(D + col, col_block_size).array().square().matrix();
}
if (D != nullptr) {
m.diagonal() +=
ConstVectorRef(D + col, col_block_size).array().square().matrix();
}
// TODO(sameeragarwal): Deal with Cholesky inversion failure here and
// elsewhere.
m = m.llt().solve(Matrix::Identity(col_block_size, col_block_size));
}
// TODO(sameeragarwal): Deal with Cholesky inversion failure here and
// elsewhere.
m = m.llt().solve(Matrix::Identity(col_block_size, col_block_size));
});
return true;
}
+7 -2
View File
@@ -52,7 +52,8 @@ class CERES_NO_EXPORT BlockSparseJacobiPreconditioner
: public BlockSparseMatrixPreconditioner {
public:
// A must remain valid while the BlockJacobiPreconditioner is.
explicit BlockSparseJacobiPreconditioner(const BlockSparseMatrix& A);
explicit BlockSparseJacobiPreconditioner(Preconditioner::Options,
const BlockSparseMatrix& A);
~BlockSparseJacobiPreconditioner() override;
void RightMultiplyAndAccumulate(const double* x, double* y) const final {
return m_->RightMultiplyAndAccumulate(x, y);
@@ -64,6 +65,7 @@ class CERES_NO_EXPORT BlockSparseJacobiPreconditioner
private:
bool UpdateImpl(const BlockSparseMatrix& A, const double* D) final;
Preconditioner::Options options_;
std::unique_ptr<BlockRandomAccessDiagonalMatrix> m_;
};
@@ -73,7 +75,8 @@ class CERES_NO_EXPORT BlockCRSJacobiPreconditioner
: public CompressedRowSparseMatrixPreconditioner {
public:
// A must remain valid while the BlockJacobiPreconditioner is.
explicit BlockCRSJacobiPreconditioner(const CompressedRowSparseMatrix& A);
explicit BlockCRSJacobiPreconditioner(Preconditioner::Options options,
const CompressedRowSparseMatrix& A);
~BlockCRSJacobiPreconditioner() override;
void RightMultiplyAndAccumulate(const double* x, double* y) const final {
m_->RightMultiplyAndAccumulate(x, y);
@@ -85,6 +88,8 @@ class CERES_NO_EXPORT BlockCRSJacobiPreconditioner
private:
bool UpdateImpl(const CompressedRowSparseMatrix& A, const double* D) final;
Preconditioner::Options options_;
std::vector<std::mutex> locks_;
std::unique_ptr<CompressedRowSparseMatrix> m_;
};
@@ -59,14 +59,26 @@ static void BM_BlockSparseJacobiPreconditionerBA(benchmark::State& state) {
std::mt19937 prng;
auto jacobian = CreateFakeBundleAdjustmentJacobian(
kNumCameras, kNumPoints, kCameraSize, kPointSize, kVisibility, prng);
BlockSparseJacobiPreconditioner p(*jacobian);
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
preconditioner_options.num_threads = state.range(0);
context.EnsureMinimumThreads(preconditioner_options.num_threads);
BlockSparseJacobiPreconditioner p(preconditioner_options, *jacobian);
Vector d = Vector::Ones(jacobian->num_cols());
for (auto _ : state) {
p.Update(*jacobian, d.data());
}
}
BENCHMARK(BM_BlockSparseJacobiPreconditionerBA);
BENCHMARK(BM_BlockSparseJacobiPreconditionerBA)
->Arg(1)
->Arg(2)
->Arg(4)
->Arg(8)
->Arg(16);
static void BM_BlockCRSJacobiPreconditionerBA(benchmark::State& state) {
std::mt19937 prng;
@@ -76,14 +88,25 @@ static void BM_BlockCRSJacobiPreconditionerBA(benchmark::State& state) {
CompressedRowSparseMatrix jacobian_crs(
jacobian->num_rows(), jacobian->num_cols(), jacobian->num_nonzeros());
jacobian->ToCompressedRowSparseMatrix(&jacobian_crs);
BlockCRSJacobiPreconditioner p(jacobian_crs);
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
preconditioner_options.num_threads = state.range(0);
context.EnsureMinimumThreads(preconditioner_options.num_threads);
BlockCRSJacobiPreconditioner p(preconditioner_options, jacobian_crs);
Vector d = Vector::Ones(jacobian_crs.num_cols());
for (auto _ : state) {
p.Update(jacobian_crs, d.data());
}
}
BENCHMARK(BM_BlockCRSJacobiPreconditionerBA);
BENCHMARK(BM_BlockCRSJacobiPreconditionerBA)
->Arg(1)
->Arg(2)
->Arg(4)
->Arg(8)
->Arg(16);
static void BM_BlockSparseJacobiPreconditionerUnstructured(
benchmark::State& state) {
@@ -98,14 +121,25 @@ static void BM_BlockSparseJacobiPreconditionerUnstructured(
std::mt19937 prng;
auto jacobian = BlockSparseMatrix::CreateRandomMatrix(options, prng);
BlockSparseJacobiPreconditioner p(*jacobian);
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
preconditioner_options.num_threads = state.range(0);
context.EnsureMinimumThreads(preconditioner_options.num_threads);
BlockSparseJacobiPreconditioner p(preconditioner_options, *jacobian);
Vector d = Vector::Ones(jacobian->num_cols());
for (auto _ : state) {
p.Update(*jacobian, d.data());
}
}
BENCHMARK(BM_BlockSparseJacobiPreconditionerUnstructured);
BENCHMARK(BM_BlockSparseJacobiPreconditionerUnstructured)
->Arg(1)
->Arg(2)
->Arg(4)
->Arg(8)
->Arg(16);
static void BM_BlockCRSJacobiPreconditionerUnstructured(
benchmark::State& state) {
@@ -123,13 +157,24 @@ static void BM_BlockCRSJacobiPreconditionerUnstructured(
CompressedRowSparseMatrix jacobian_crs(
jacobian->num_rows(), jacobian->num_cols(), jacobian->num_nonzeros());
jacobian->ToCompressedRowSparseMatrix(&jacobian_crs);
BlockCRSJacobiPreconditioner p(jacobian_crs);
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
preconditioner_options.num_threads = state.range(0);
context.EnsureMinimumThreads(preconditioner_options.num_threads);
BlockCRSJacobiPreconditioner p(preconditioner_options, jacobian_crs);
Vector d = Vector::Ones(jacobian_crs.num_cols());
for (auto _ : state) {
p.Update(jacobian_crs, d.data());
}
}
BENCHMARK(BM_BlockCRSJacobiPreconditionerUnstructured);
BENCHMARK(BM_BlockCRSJacobiPreconditionerUnstructured)
->Arg(1)
->Arg(2)
->Arg(4)
->Arg(8)
->Arg(16);
} // namespace ceres::internal
@@ -55,6 +55,10 @@ TEST(BlockSparseJacobiPreconditioner, _) {
options.block_density = 0.25;
std::mt19937 prng;
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
for (int trial = 0; trial < kNumtrials; ++trial) {
auto jacobian = BlockSparseMatrix::CreateRandomMatrix(options, prng);
Vector diagonal = Vector::Ones(jacobian->num_cols());
@@ -63,7 +67,7 @@ TEST(BlockSparseJacobiPreconditioner, _) {
Matrix hessian = dense_jacobian.transpose() * dense_jacobian;
hessian.diagonal() += diagonal.array().square().matrix();
BlockSparseJacobiPreconditioner pre(*jacobian);
BlockSparseJacobiPreconditioner pre(preconditioner_options, *jacobian);
pre.Update(*jacobian, diagonal.data());
// The const_cast is needed to be able to call GetCell.
@@ -104,6 +108,10 @@ TEST(CompressedRowSparseJacobiPreconditioner, _) {
options.block_density = 0.25;
std::mt19937 prng;
Preconditioner::Options preconditioner_options;
ContextImpl context;
preconditioner_options.context = &context;
for (int trial = 0; trial < kNumtrials; ++trial) {
auto jacobian =
CompressedRowSparseMatrix::CreateRandomMatrix(options, prng);
@@ -114,7 +122,7 @@ TEST(CompressedRowSparseJacobiPreconditioner, _) {
Matrix hessian = dense_jacobian.transpose() * dense_jacobian;
hessian.diagonal() += diagonal.array().square().matrix();
BlockCRSJacobiPreconditioner pre(*jacobian);
BlockCRSJacobiPreconditioner pre(preconditioner_options, *jacobian);
pre.Update(*jacobian, diagonal.data());
auto& m = pre.matrix();
+29 -13
View File
@@ -135,18 +135,20 @@ LinearSolver::Summary CgnrSolver::SolveImpl(
double* x) {
EventLogger event_logger("CgnrSolver::Solve");
if (!preconditioner_) {
Preconditioner::Options preconditioner_options;
preconditioner_options.type = options_.preconditioner_type;
preconditioner_options.subset_preconditioner_start_row_block =
options_.subset_preconditioner_start_row_block;
preconditioner_options.sparse_linear_algebra_library_type =
options_.sparse_linear_algebra_library_type;
preconditioner_options.ordering_type = options_.ordering_type;
preconditioner_options.num_threads = options_.num_threads;
preconditioner_options.context = options_.context;
if (options_.preconditioner_type == JACOBI) {
preconditioner_ = std::make_unique<BlockSparseJacobiPreconditioner>(*A);
preconditioner_ = std::make_unique<BlockSparseJacobiPreconditioner>(
preconditioner_options, *A);
} else if (options_.preconditioner_type == SUBSET) {
Preconditioner::Options preconditioner_options;
preconditioner_options.type = SUBSET;
preconditioner_options.subset_preconditioner_start_row_block =
options_.subset_preconditioner_start_row_block;
preconditioner_options.sparse_linear_algebra_library_type =
options_.sparse_linear_algebra_library_type;
preconditioner_options.ordering_type = options_.ordering_type;
preconditioner_options.num_threads = options_.num_threads;
preconditioner_options.context = options_.context;
preconditioner_ =
std::make_unique<SubsetPreconditioner>(preconditioner_options, *A);
} else {
@@ -238,9 +240,11 @@ class CERES_NO_EXPORT CudaIdentityPreconditioner final
class CERES_NO_EXPORT CudaJacobiPreconditioner final
: public CudaPreconditioner {
public:
explicit CudaJacobiPreconditioner(ContextImpl* context,
explicit CudaJacobiPreconditioner(Preconditioner::Options options,
const CompressedRowSparseMatrix& A)
: cpu_preconditioner_(A), m_(context, cpu_preconditioner_.matrix()) {}
: options_(std::move(options)),
cpu_preconditioner_(options_, A),
m_(options_->context, cpu_preconditioner_.matrix()) {}
~CudaJacobiPreconditioner() = default;
void Update(const CompressedRowSparseMatrix& A, const double* D) final {
@@ -253,6 +257,7 @@ class CERES_NO_EXPORT CudaJacobiPreconditioner final
}
private:
Preconditioner::Options options_;
BlockCRSJacobiPreconditioner cpu_preconditioner_;
CudaSparseMatrix m_;
};
@@ -297,9 +302,20 @@ void CudaCgnrSolver::CpuToGpuTransfer(const CompressedRowSparseMatrix& A,
Atb_ = std::make_unique<CudaVector>(options_.context, A.num_cols());
Ax_ = std::make_unique<CudaVector>(options_.context, A.num_rows());
D_ = std::make_unique<CudaVector>(options_.context, A.num_cols());
Preconditioner::Options preconditioner_options;
preconditioner_options.type = options_.preconditioner_type;
preconditioner_options.subset_preconditioner_start_row_block =
options_.subset_preconditioner_start_row_block;
preconditioner_options.sparse_linear_algebra_library_type =
options_.sparse_linear_algebra_library_type;
preconditioner_options.ordering_type = options_.ordering_type;
preconditioner_options.num_threads = options_.num_threads;
preconditioner_options.context = options_.context;
if (options_.preconditioner_type == JACOBI) {
preconditioner_ =
std::make_unique<CudaJacobiPreconditioner>(options_.context, A);
std::make_unique<CudaJacobiPreconditioner>(preconditioner_options, A);
} else {
preconditioner_ = std::make_unique<CudaIdentityPreconditioner>();
}