Refactor LRSDP into the main class and a separate function (LRSDPFunction).
This is a patch from Abhishek Laddha for #318.
This commit is contained in:
Ryan Curtin
@@ -1,6 +1,8 @@
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set(SOURCES
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lrsdp.hpp
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lrsdp.cpp
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lrsdp_function.hpp
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lrsdp_function.cpp
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)
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set(DIR_SRCS)
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@@ -8,4 +10,4 @@ foreach(file ${SOURCES})
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set(DIR_SRCS ${DIR_SRCS} ${CMAKE_CURRENT_SOURCE_DIR}/${file})
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endforeach()
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set(MLPACK_SRCS ${MLPACK_SRCS} ${DIR_SRCS} PARENT_SCOPE)
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set(MLPACK_SRCS ${MLPACK_SRCS} ${DIR_SRCS} PARENT_SCOPE)
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@@ -13,23 +13,8 @@ using namespace std;
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LRSDP::LRSDP(const size_t numConstraints,
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const arma::mat& initialPoint) :
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a(numConstraints),
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b(numConstraints),
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aModes(numConstraints),
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initialPoint(initialPoint),
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augLagInternal(*this),
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augLag(augLagInternal)
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{ }
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LRSDP::LRSDP(const size_t numConstraints,
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const arma::mat& initialPoint,
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AugLagrangian<LRSDP>& augLag) :
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a(numConstraints),
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b(numConstraints),
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aModes(numConstraints),
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initialPoint(initialPoint),
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augLagInternal(*this),
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augLag(augLag)
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function(numConstraints, initialPoint),
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augLag(function)
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{ }
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double LRSDP::Optimize(arma::mat& coordinates)
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@@ -37,46 +22,7 @@ double LRSDP::Optimize(arma::mat& coordinates)
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augLag.Sigma() = 20;
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augLag.Optimize(coordinates, 1000);
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return Evaluate(coordinates);
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}
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double LRSDP::Evaluate(const arma::mat& coordinates) const
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{
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return -accu(coordinates * trans(coordinates));
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}
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void LRSDP::Gradient(const arma::mat& /*coordinates*/,
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arma::mat& /*gradient*/) const
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{
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Log::Fatal << "LRSDP::Gradient() called! Not implemented! Uh-oh..." << std::endl;
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}
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double LRSDP::EvaluateConstraint(const size_t index,
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const arma::mat& coordinates) const
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{
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arma::mat rrt = coordinates * trans(coordinates);
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if (aModes[index] == 0)
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return trace(a[index] * rrt) - b[index];
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else
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{
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double value = -b[index];
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for (size_t i = 0; i < a[index].n_cols; ++i)
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value += a[index](2, i) * rrt(a[index](0, i), a[index](1, i));
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return value;
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}
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}
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void LRSDP::GradientConstraint(const size_t /* index */,
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const arma::mat& /* coordinates */,
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arma::mat& /* gradient */) const
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{
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Log::Fatal << "LRSDP::GradientConstraint() called! Not implemented! Uh-oh..." << std::endl;
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}
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const arma::mat& LRSDP::GetInitialPoint()
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{
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return initialPoint;
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return augLag.Function().Evaluate(coordinates);
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}
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// Convert the object to a string.
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@@ -84,104 +30,9 @@ std::string LRSDP::ToString() const
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{
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std::ostringstream convert;
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convert << "LRSDP [" << this << "]" << std::endl;
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convert << " Matrix Size: " << c.n_rows << "x" << c.n_cols << std::endl;
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convert << " Initial point Size : " << initialPoint.n_rows << "x"
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<< initialPoint.n_cols << std::endl;
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convert << " Matrix Size: " << function.C().n_rows << "x"
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<< function.C().n_cols << std::endl;
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convert << " Initial point Size : " << function.GetInitialPoint().n_rows
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<< "x" << function.GetInitialPoint().n_cols << std::endl;
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return convert.str();
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}
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namespace mlpack {
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namespace optimization {
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// Custom specializations of the AugmentedLagrangianFunction for the LRSDP case.
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template<>
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double AugLagrangianFunction<LRSDP>::Evaluate(
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const arma::mat& coordinates) const
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{
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// We can calculate the entire objective in a smart way.
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// L(R, y, s) = Tr(C * (R R^T)) -
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// sum_{i = 1}^{m} (y_i (Tr(A_i * (R R^T)) - b_i)) +
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// (sigma / 2) * sum_{i = 1}^{m} (Tr(A_i * (R R^T)) - b_i)^2
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// Let's start with the objective: Tr(C * (R R^T)).
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// Simple, possibly slow solution.
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arma::mat rrt = coordinates * trans(coordinates);
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double objective = trace(function.C() * rrt);
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// Now each constraint.
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for (size_t i = 0; i < function.B().n_elem; ++i)
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{
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// Take the trace subtracted by the b_i.
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double constraint = -function.B()[i];
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if (function.AModes()[i] == 0)
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{
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constraint += trace(function.A()[i] * rrt);
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}
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else
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{
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for (size_t j = 0; j < function.A()[i].n_cols; ++j)
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{
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constraint += function.A()[i](2, j) *
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rrt(function.A()[i](0, j), function.A()[i](1, j));
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}
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}
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objective -= (lambda[i] * constraint);
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objective += (sigma / 2) * std::pow(constraint, 2.0);
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}
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return objective;
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}
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template<>
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void AugLagrangianFunction<LRSDP>::Gradient(
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const arma::mat& coordinates,
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arma::mat& gradient) const
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{
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// We can calculate the gradient in a smart way.
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// L'(R, y, s) = 2 * S' * R
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// with
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// S' = C - sum_{i = 1}^{m} y'_i A_i
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// y'_i = y_i - sigma * (Trace(A_i * (R R^T)) - b_i)
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arma::mat rrt = coordinates * trans(coordinates);
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arma::mat s = function.C();
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for (size_t i = 0; i < function.B().n_elem; ++i)
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{
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double constraint = -function.B()[i];
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if (function.AModes()[i] == 0)
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{
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constraint += trace(function.A()[i] * rrt);
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}
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else
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{
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for (size_t j = 0; j < function.A()[i].n_cols; ++j)
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{
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constraint += function.A()[i](2, j) *
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rrt(function.A()[i](0, j), function.A()[i](1, j));
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}
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}
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double y = lambda[i] - sigma * constraint;
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if (function.AModes()[i] == 0)
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{
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s -= (y * function.A()[i]);
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}
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else
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{
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// We only need to subtract the entries which could be modified.
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for (size_t j = 0; j < function.A()[i].n_cols; ++j)
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{
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s(function.A()[i](0, j), function.A()[i](1, j)) -= y;
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}
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}
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}
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gradient = 2 * s * coordinates;
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}
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}; // namespace optimization
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}; // namespace mlpack
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@@ -11,17 +11,15 @@
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#include <mlpack/core.hpp>
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#include <mlpack/core/optimizers/aug_lagrangian/aug_lagrangian.hpp>
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#include "lrsdp_function.hpp"
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namespace mlpack {
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namespace optimization {
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/**
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* An implementation of a low-rank semidefinite program solver, based on
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* Monteiro and Burer's formulation. The optimizer is the augmented Lagrangian
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* algorithm, and thus this class has Evaluate(), Gradient(),
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* EvaluateConstraint(), and GradientConstraint() functions for that purpose.
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* However, you should not call the Gradient() or GradientConstraint() functions
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* by hand, because they are only implemented as part of the augmented
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* Lagrangian optimizer.
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* LRSDP is the implementation of Monteiro and Burer's formulation of low-rank
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* semidefinite programs (LR-SDP). This solver uses the augmented Lagrangian
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* optimizer to solve low-rank semidefinite programs.
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*/
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class LRSDP
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{
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@@ -49,7 +47,7 @@ class LRSDP
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*/
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LRSDP(const size_t numConstraints,
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const arma::mat& initialPoint,
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AugLagrangian<LRSDP>& augLagrangian);
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AugLagrangian<LRSDPFunction>& augLagrangian);
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/**
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* Optimize the LRSDP and return the final objective value. The given
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@@ -59,87 +57,45 @@ class LRSDP
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*/
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double Optimize(arma::mat& coordinates);
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/**
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* Evaluate the objective function of the LRSDP (no constraints) at the given
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* coordinates. This is used by AugLagrangian<LRSDP>.
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*/
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double Evaluate(const arma::mat& coordinates) const;
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/**
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* Evaluate the gradient of the LRSDP (no constraints) at the given
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* coordinates. This is used by AugLagrangian<LRSDP>.
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*/
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void Gradient(const arma::mat& coordinates, arma::mat& gradient) const;
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/**
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* Evaluate a particular constraint of the LRSDP at the given coordinates.
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*/
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double EvaluateConstraint(const size_t index,
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const arma::mat& coordinates) const;
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/**
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* Evaluate the gradient of a particular constraint of the LRSDP at the given
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* coordinates.
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*/
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void GradientConstraint(const size_t index,
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const arma::mat& coordinates,
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arma::mat& gradient) const;
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//! Get the number of constraints in the LRSDP.
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size_t NumConstraints() const { return b.n_elem; }
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//! Get the initial point of the LRSDP.
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const arma::mat& GetInitialPoint();
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//! Return the objective function matrix (C).
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const arma::mat& C() const { return c; }
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const arma::mat& C() const { return function.C(); }
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//! Modify the objective function matrix (C).
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arma::mat& C() { return c; }
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arma::mat& C() { return function.C(); }
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//! Return the vector of A matrices (which correspond to the constraints).
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const std::vector<arma::mat>& A() const { return a; }
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const std::vector<arma::mat>& A() const { return function.A(); }
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//! Modify the veector of A matrices (which correspond to the constraints).
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std::vector<arma::mat>& A() { return a; }
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std::vector<arma::mat>& A() { return function.A(); }
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//! Return the vector of modes for the A matrices.
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const arma::uvec& AModes() const { return aModes; }
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const arma::uvec& AModes() const { return function.AModes(); }
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//! Modify the vector of modes for the A matrices.
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arma::uvec& AModes() { return aModes; }
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arma::uvec& AModes() { return function.AModes(); }
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//! Return the vector of B values.
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const arma::vec& B() const { return b; }
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const arma::vec& B() const { return function.B(); }
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//! Modify the vector of B values.
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arma::vec& B() { return b; }
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arma::vec& B() { return function.B(); }
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//! Return the function to be optimized.
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const LRSDPFunction& Function() const { return function; }
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//! Modify the function to be optimized.
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LRSDPFunction& Function() { return function; }
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//! Return the augmented Lagrangian object.
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const AugLagrangian<LRSDP>& AugLag() const { return augLag; }
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const AugLagrangian<LRSDPFunction>& AugLag() const { return augLag; }
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//! Modify the augmented Lagrangian object.
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AugLagrangian<LRSDP>& AugLag() { return augLag; }
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AugLagrangian<LRSDPFunction>& AugLag() { return augLag; }
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// convert the obkect into a string
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//! Return a string representation of the object.
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std::string ToString() const;
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private:
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// Should probably use sparse matrices for some of these.
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//! For objective function.
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arma::mat c;
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//! A_i for each constraint.
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std::vector<arma::mat> a;
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//! b_i for each constraint.
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arma::vec b;
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//! 1 if entries in matrix, 0 for normal.
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arma::uvec aModes;
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//! Initial point.
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arma::mat initialPoint;
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//! Internal AugLagrangian object, if one was not passed at construction time.
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AugLagrangian<LRSDP> augLagInternal;
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//! Function to optimize, which the AugLagrangian object holds.
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LRSDPFunction function;
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//! The AugLagrangian object which will be used for optimization.
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AugLagrangian<LRSDP>& augLag;
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AugLagrangian<LRSDPFunction> augLag;
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};
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}; // namespace optimization
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+58
-15
@@ -1,24 +1,67 @@
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/**
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* @file lrsdp_impl.hpp
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* @file lrsdp_function.cpp
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* @author Ryan Curtin
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* @author Abhishek Laddha
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*
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* An implementation of Monteiro and Burer's formulation of low-rank
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* semidefinite programs (LR-SDP).
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* Implementation of the LRSDPFunction class, and also template specializations
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* for faster execution with the AugLagrangian optimizer.
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*/
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#ifndef __MLPACK_CORE_OPTIMIZERS_LRSDP_LRSDP_IMPL_HPP
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#define __MLPACK_CORE_OPTIMIZERS_LRSDP_LRSDP_IMPL_HPP
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#include "lrsdp_function.hpp"
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// In case it hasn't already been included.
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#include "lrsdp.hpp"
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using namespace mlpack;
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using namespace mlpack::optimization;
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LRSDPFunction::LRSDPFunction(const size_t numConstraints,
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const arma::mat& initialPoint):
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a(numConstraints),
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b(numConstraints),
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initialPoint(initialPoint),
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aModes(numConstraints)
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{ }
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double LRSDPFunction::Evaluate(const arma::mat& coordinates) const
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{
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return -accu(coordinates * trans(coordinates));
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}
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void LRSDPFunction::Gradient(const arma::mat& /* coordinates */,
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arma::mat& /* gradient */) const
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{
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Log::Fatal << "LRSDP::Gradient() not implemented for arbitrary optimizers!"
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<< std::endl;
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}
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double LRSDPFunction::EvaluateConstraint(const size_t index,
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const arma::mat& coordinates) const
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{
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arma::mat rrt = coordinates * trans(coordinates);
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if (aModes[index] == 0)
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return trace(a[index] * rrt) - b[index];
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else
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{
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double value = -b[index];
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for (size_t i = 0; i < a[index].n_cols; ++i)
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value += a[index](2, i) * rrt(a[index](0, i), a[index](1, i));
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return value;
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}
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}
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void LRSDPFunction::GradientConstraint(const size_t /* index */,
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const arma::mat& /* coordinates */,
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arma::mat& /* gradient */) const
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{
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Log::Fatal << "LRSDP::GradientConstraint() not implemented for arbitrary "
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<< "optimizers!" << std::endl;
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}
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namespace mlpack {
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namespace optimization {
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// Custom specializations of the AugmentedLagrangianFunction for the LRSDP case.
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// Template specializations for function and gradient evaluation.
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template<>
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double AugLagrangianFunction<LRSDP>::Evaluate(const arma::mat& coordinates)
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const
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double AugLagrangianFunction<LRSDPFunction>::Evaluate(
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const arma::mat& coordinates) const
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{
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// We can calculate the entire objective in a smart way.
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// L(R, y, s) = Tr(C * (R R^T)) -
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@@ -56,9 +99,11 @@ double AugLagrangianFunction<LRSDP>::Evaluate(const arma::mat& coordinates)
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return objective;
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}
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template<>
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void AugLagrangianFunction<LRSDP>::Gradient(const arma::mat& coordinates,
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arma::mat& gradient) const
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void AugLagrangianFunction<LRSDPFunction>::Gradient(
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const arma::mat& coordinates,
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arma::mat& gradient) const
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{
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// We can calculate the gradient in a smart way.
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// L'(R, y, s) = 2 * S' * R
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@@ -107,5 +152,3 @@ void AugLagrangianFunction<LRSDP>::Gradient(const arma::mat& coordinates,
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}; // namespace optimization
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}; // namespace mlpack
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#endif
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@@ -0,0 +1,99 @@
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/**
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* @file lrsdp_function.hpp
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* @author Ryan Curtin
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* @author Abhishek Laddha
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*
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* A class that represents the objective function which LRSDP optimizes.
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*/
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#ifndef __MLPACK_CORE_OPTIMIZERS_LRSDP_LRSDP_FUNCTION_HPP
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#define __MLPACK_CORE_OPTIMIZERS_LRSDP_LRSDP_FUNCTION_HPP
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#include <mlpack/core.hpp>
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#include <mlpack/core/optimizers/aug_lagrangian/aug_lagrangian.hpp>
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namespace mlpack {
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namespace optimization {
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/**
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* The objective function that LRSDP is trying to optimize.
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*/
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class LRSDPFunction
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{
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public:
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/**
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* Construct the LRSDPFunction with the given initial point and number of
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* constraints. Set the A, B, and C matrices for each constraint using the
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* A(), B(), and C() functions.
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*/
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LRSDPFunction(const size_t numConstraints,
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const arma::mat& initialPoint);
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/**
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* Evaluate the objective function of the LRSDP (no constraints) at the given
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* coordinates.
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*/
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double Evaluate(const arma::mat& coordinates) const;
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||||
|
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/**
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* Evaluate the gradient of the LRSDP (no constraints) at the given
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* coordinates.
|
||||
*/
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void Gradient(const arma::mat& coordinates, arma::mat& gradient) const;
|
||||
|
||||
/**
|
||||
* Evaluate a particular constraint of the LRSDP at the given coordinates.
|
||||
*/
|
||||
double EvaluateConstraint(const size_t index,
|
||||
const arma::mat& coordinates) const;
|
||||
/**
|
||||
* Evaluate the gradient of a particular constraint of the LRSDP at the given
|
||||
* coordinates.
|
||||
*/
|
||||
void GradientConstraint(const size_t index,
|
||||
const arma::mat& coordinates,
|
||||
arma::mat& gradient) const;
|
||||
|
||||
//! Get the number of constraints in the LRSDP.
|
||||
size_t NumConstraints() const { return b.n_elem; }
|
||||
|
||||
//! Get the initial point of the LRSDP.
|
||||
const arma::mat& GetInitialPoint() const {return initialPoint; }
|
||||
|
||||
//! Return the objective function matrix (C).
|
||||
const arma::mat& C() const { return c; }
|
||||
//! Modify the objective function matrix (C).
|
||||
arma::mat& C() { return c; }
|
||||
|
||||
//! Return the vector of A matrices (which correspond to the constraints).
|
||||
const std::vector<arma::mat>& A() const { return a; }
|
||||
//! Modify the veector of A matrices (which correspond to the constraints).
|
||||
std::vector<arma::mat>& A() { return a; }
|
||||
|
||||
//! Return the vector of modes for the A matrices.
|
||||
const arma::uvec& AModes() const { return aModes; }
|
||||
//! Modify the vector of modes for the A matrices.
|
||||
arma::uvec& AModes() { return aModes; }
|
||||
|
||||
//! Return the vector of B values.
|
||||
const arma::vec& B() const { return b; }
|
||||
//! Modify the vector of B values.
|
||||
arma::vec& B() { return b; }
|
||||
|
||||
private:
|
||||
//! Objective function matrix c.
|
||||
arma::mat c;
|
||||
//! A_i for each constraint.
|
||||
std::vector<arma::mat> a;
|
||||
//! b_i for each constraint.
|
||||
arma::vec b;
|
||||
|
||||
//! Initial point.
|
||||
arma::mat initialPoint;
|
||||
//! 1 if entries in matrix, 0 for normal.
|
||||
arma::uvec aModes;
|
||||
};
|
||||
|
||||
};
|
||||
};
|
||||
|
||||
#endif // __MLPACK_CORE_OPTIMIZERS_LRSDP_LRSDP_FUNCTION_HPP
|
||||
Reference in New Issue
Block a user