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Added another code path inside solve_qp_box_constrained_blockdiag() that is 

much faster when the off-diagonal vectors are all simple multiples of the
ones_matrix().
This commit is contained in:
Davis King 2017-03-22 15:59:06 -04:00
parent dd16139a37
commit 83cfbf8adf
2 changed files with 182 additions and 7 deletions
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90
dlib/optimization/optimization_solve_qp_using_smo.h
View File

@ -550,6 +550,57 @@ namespace dlib
return iter+1;
}
// ----------------------------------------------------------------------------------------
// ----------------------------------------------------------------------------------------
namespace impl
{
// Check if each vector in Q_offdiag is actually a constant times the 1s vector.
template <
typename T, long NR, long NC, typename MM, typename L
>
bool has_uniform_offdiag_vectors(
const std::map<unordered_pair<size_t>, matrix<T,NR,NC,MM,L>>& Q_offdiag
)
{
for (auto& x : Q_offdiag)
{
auto ref = x.second(0);
for (auto& y : x.second)
if (ref != y)
return false;
}
return true;
}
template <
typename T, long NR, long NC, typename MM, typename L
>
matrix<T,0,0,MM,L> compact_offdiag(
const size_t& num_blocks,
const std::map<unordered_pair<size_t>, matrix<T,NR,NC,MM,L>>& Q_offdiag
)
{
matrix<T,0,0,MM,L> temp;
// we can only compact the offdiag information if they are uniform vectors
if (!has_uniform_offdiag_vectors(Q_offdiag))
return temp;
temp.set_size(num_blocks, num_blocks);
temp = 0;
for (auto& x : Q_offdiag)
{
long r = x.first.first;
long c = x.first.second;
temp(r,c) = x.second(0);
temp(c,r) = x.second(0);
}
return temp;
}
}
// ----------------------------------------------------------------------------------------
template <
@ -624,6 +675,8 @@ namespace dlib
#endif // ENABLE_ASSERTS
const auto offdiag_compact = impl::compact_offdiag(Q_blocks.size(), Q_offdiag);
matrix<T,0,0,MM,L> temp, alphas_compact;
// Compute f'(alpha) (i.e. the gradient of f(alpha)) for the current alpha.
std::vector<matrix<T,NR,NC,MM,L>> df;// = Q*alpha + b;
@ -632,18 +685,41 @@ namespace dlib
df.resize(Q_blocks.size());
for (size_t i = 0; i < df.size(); ++i)
df[i] = Q_blocks[i]*alphas[i] + bs[i];
// Don't forget to include the Q_offdiag terms in the computation
for (auto& p : Q_offdiag)
// Don't forget to include the Q_offdiag terms in the computation. Note that
// we have two options for how we can compute this part. If Q_offdiag is
// uniform and can be compacted into a simple matrix and there are a lot of off
// diagonal entries then it's faster to do it as a matrix multiply. Otherwise
// we do the more general computation.
if (offdiag_compact.size() != 0 && Q_offdiag.size() > Q_blocks.size()*5)
{
long r = p.first.first;
long c = p.first.second;
df[r] += pointwise_multiply(p.second, alphas[c]);
if (r != c)
df[c] += pointwise_multiply(p.second, alphas[r]);
// Do it as a matrix multiply (with a bit of data shuffling)
alphas_compact.set_size(alphas[0].size(), offdiag_compact.nr());
for (long c = 0; c < alphas_compact.nc(); ++c)
set_colm(alphas_compact,c) = alphas[c];
temp = alphas_compact*offdiag_compact;
for (size_t i = 0; i < df.size(); ++i)
df[i] += colm(temp,i);
}
else
{
// Do the fully general computation that allows for non-uniform values in
// the off diagonal vectors.
for (auto& p : Q_offdiag)
{
long r = p.first.first;
long c = p.first.second;
df[r] += pointwise_multiply(p.second, alphas[c]);
if (r != c)
df[c] += pointwise_multiply(p.second, alphas[r]);
}
}
};
compute_df();
std::vector<matrix<T,NR,NC,MM,L>> Q_diag, Q_ggd;
std::vector<matrix<T,NR,NC,MM,L>> QQ;// = reciprocal_max(diag(Q));
QQ.resize(Q_blocks.size());

99
dlib/test/opt_qp_solver.cpp
View File

@ -582,6 +582,96 @@ namespace
}
}
// ----------------------------------------------------------------------------------------
void test_solve_qp_box_constrained_blockdiag_compact(dlib::rand& rnd, double percent_off_diag_present)
{
print_spinner();
dlog << LINFO << "test_solve_qp_box_constrained_blockdiag_compact(), percent_off_diag_present==" << percent_off_diag_present;
std::map<unordered_pair<size_t>, matrix<double,0,1>> offdiag;
std::vector<matrix<double>> Q_blocks;
std::vector<matrix<double,0,1>> bs;
const long num_blocks = 20;
const long dims = 4;
const double lambda = 10;
for (long i = 0; i < num_blocks; ++i)
{
matrix<double> Q1;
matrix<double,0,1> b1;
Q1 = randm(dims,dims,rnd); Q1 = Q1*trans(Q1);
b1 = gaussian_randm(dims,1, i);
Q_blocks.push_back(Q1);
bs.push_back(b1);
// test with some graph regularization terms
for (long j = 0; j < num_blocks; ++j)
{
if (rnd.get_random_double() < percent_off_diag_present)
{
if (i==j)
offdiag[make_unordered_pair(i,j)] = (num_blocks-1)*lambda*rnd.get_random_double()*ones_matrix<double>(dims,1);
else
offdiag[make_unordered_pair(i,j)] = -lambda*rnd.get_random_double()*ones_matrix<double>(dims,1);
}
}
}
// build out the dense version of the QP so we can test it against the dense solver.
matrix<double> Q(num_blocks*dims, num_blocks*dims);
Q = 0;
matrix<double,0,1> b(num_blocks*dims);
for (long i = 0; i < num_blocks; ++i)
{
set_subm(Q,i*dims,i*dims,dims,dims) = Q_blocks[i];
set_subm(b,i*dims,0,dims,1) = bs[i];
}
for (auto& p : offdiag)
{
long r = p.first.first;
long c = p.first.second;
set_subm(Q, dims*r,dims*c, dims,dims) += diagm(p.second);
if (c != r)
set_subm(Q, dims*c,dims*r, dims,dims) += diagm(p.second);
}
matrix<double,0,1> alpha = zeros_matrix<double>(dims*num_blocks,1);
matrix<double,0,1> lower = -10000*ones_matrix<double>(dims*num_blocks,1);
matrix<double,0,1> upper = 10000*ones_matrix<double>(dims*num_blocks,1);
auto iters = solve_qp_box_constrained(Q, b, alpha, lower, upper, 1e-9, 20000);
dlog << LINFO << "iters: "<< iters;
matrix<double,0,1> init_alpha = zeros_matrix(bs[0]);
lower = -10000*ones_matrix(bs[0]);
upper = 10000*ones_matrix(bs[0]);
std::vector<matrix<double,0,1>> alphas(num_blocks, init_alpha);
std::vector<matrix<double,0,1>> lowers(num_blocks, lower);
std::vector<matrix<double,0,1>> uppers(num_blocks, upper);
auto iters2 = solve_qp_box_constrained_blockdiag(Q_blocks, bs, offdiag, alphas, lowers, uppers, 1e-9, 20000);
dlog << LINFO << "iters2: "<< iters2;
const matrix<double> refalpha = reshape(alpha, num_blocks, dims);
// now make sure the two solvers agree on the outputs.
for (long r = 0; r < num_blocks; ++r)
{
for (long c = 0; c < dims; ++c)
{
DLIB_TEST_MSG(std::abs(refalpha(r,c) - alphas[r](c)) < 1e-6, std::abs(refalpha(r,c) - alphas[r](c)));
}
}
}
// ----------------------------------------------------------------------------------------
class opt_qp_solver_tester : public tester
@ -642,6 +732,15 @@ namespace
test_find_gap_between_convex_hulls();
test_solve_qp_box_constrained_blockdiag();
// try a range of off diagonal sparseness. We do this to make sure we exercise both
// the compact and sparse code paths within the solver.
test_solve_qp_box_constrained_blockdiag_compact(rnd, 0.001);
test_solve_qp_box_constrained_blockdiag_compact(rnd, 0.01);
test_solve_qp_box_constrained_blockdiag_compact(rnd, 0.04);
test_solve_qp_box_constrained_blockdiag_compact(rnd, 0.10);
test_solve_qp_box_constrained_blockdiag_compact(rnd, 0.50);
test_solve_qp_box_constrained_blockdiag_compact(rnd, 1.00);
}
double do_the_test (