Made CG state a class
Frank Dellaert
parent
43f9baf77a
commit
1f165a9f85
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@ -15,68 +15,111 @@ using namespace std;
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namespace gtsam {
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/* ************************************************************************* */
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/**
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* conjugate gradient method.
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* S: linear system, V: step vector, E: errors
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*/
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// state for CG method
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template<class S, class V, class E>
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V conjugateGradients(const S& Ab, V x, bool verbose, double epsilon, double epsilon_abs,
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size_t maxIterations, bool steepest = false) {
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if (maxIterations == 0) maxIterations = dim(x) * (steepest ? 10 : 1);
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size_t reset = (size_t)(sqrt(dim(x))+0.5); // when to reset
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struct CGState {
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// Start with g0 = A'*(A*x0-b), d0 = - g0
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// i.e., first step is in direction of negative gradient
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V g = Ab.gradient(x);
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V d = g; // instead of negating gradient, alpha will be negated
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double gamma0 = dot(g, g), gamma_old = gamma0;
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if (gamma0 < epsilon_abs) return x;
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double threshold = epsilon * epsilon * gamma0;
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bool steepest, verbose;
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double gamma, threshold;
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size_t k, maxIterations, reset;
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V g, d;
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E Ad;
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if (verbose) cout << "CG: epsilon = " << epsilon << ", maxIterations = "
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<< maxIterations << ", ||g0||^2 = " << gamma0 << ", threshold = "
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<< threshold << endl;
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/** constructor */
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CGState(const S& Ab, const V& x, bool verb, double epsilon,
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double epsilon_abs, size_t maxIt, bool steep) {
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k = 0;
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verbose = verb;
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steepest = steep;
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maxIterations == maxIt ? maxIt : dim(x) * (steepest ? 10 : 1);
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reset = (size_t) (sqrt(dim(x)) + 0.5); // when to reset
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// Allocate and calculate A*d for first iteration
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E Ad = Ab * d;
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// Start with g0 = A'*(A*x0-b), d0 = - g0
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// i.e., first step is in direction of negative gradient
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g = Ab.gradient(x);
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d = g; // instead of negating gradient, alpha will be negated
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// loop maxIterations times
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for (size_t k = 1;; k++) {
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// init gamma and calculate threshold
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gamma = dot(g, g);
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threshold = ::max(epsilon_abs, epsilon * epsilon * gamma);
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// calculate optimal step-size
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double alpha = - dot(d, g) / dot(Ad, Ad);
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// Allocate and calculate A*d for first iteration
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if (gamma > epsilon) Ad = Ab * d;
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}
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// do step in new search direction
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axpy(alpha, d, x); // x += alpha*d
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if (k==maxIterations) break;
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/** print */
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void print() {
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cout << "iteration = " << k << endl;
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cout << "dotg = " << gamma << endl;
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gtsam::print(g,"g");
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gtsam::print(d,"d");
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gtsam::print(Ad,"Ad");
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}
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/** step the solution */
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double takeOptimalStep(V& x) {
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double alpha = -dot(d, g) / dot(Ad, Ad); // calculate optimal step-size
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axpy(alpha, d, x); // // do step in new search direction, x += alpha*d
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return alpha;
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}
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/** take a step, return true if converged */
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bool step(const S& Ab, V& x) {
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k += 1; // increase iteration number
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double alpha = takeOptimalStep(x);
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if (k == maxIterations) return true; //---------------------------------->
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// update gradient (or re-calculate at reset time)
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if (k%reset==0)
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if (k % reset == 0)
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g = Ab.gradient(x);
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else
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// axpy(alpha, Ab ^ Ad, g); // g += alpha*(Ab^Ad)
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Ab.transposeMultiplyAdd(alpha, Ad, g);
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// check for convergence
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double gamma = dot(g, g);
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if (verbose) cout << "iteration " << k << ": alpha = " << alpha
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<< ", dotg = " << gamma << endl;
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if (gamma < threshold) break;
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double new_gamma = dot(g, g);
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if (verbose) cout << "iteration " << k << ": alpha = " << alpha << ", dotg = " << new_gamma << endl;
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// print();
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if (new_gamma < threshold) return true; //---------------------------------->
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// calculate new search direction
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if (steepest)
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d = g;
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else {
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double beta = gamma / gamma_old;
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gamma_old = gamma;
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double beta = new_gamma / gamma;
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gamma = new_gamma;
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// d = g + d*beta;
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scal(beta,d);
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scal(beta, d);
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axpy(1.0, g, d);
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}
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// In-place recalculation Ad <- A*d to avoid re-allocating Ad
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Ab.multiplyInPlace(d,Ad);
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Ab.multiplyInPlace(d, Ad);
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return false;
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}
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};
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/**
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* conjugate gradient method.
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* S: linear system, V: step vector, E: errors
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*/
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template<class S, class V, class E>
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V conjugateGradients(const S& Ab, V x, bool verbose, double epsilon,
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double epsilon_abs, size_t maxIterations, bool steepest = false) {
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CGState<S, V, E> state(Ab, x, verbose, epsilon, epsilon_abs, maxIterations, steepest);
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if (state.gamma < state.threshold) return x;
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if (verbose) cout << "CG: epsilon = " << epsilon << ", maxIterations = "
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<< maxIterations << ", ||g0||^2 = " << state.gamma
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<< ", threshold = " << state.threshold << endl;
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// loop maxIterations times
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while (!state.step(Ab, x))
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;
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return x;
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}
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@ -26,6 +26,8 @@ using namespace std;
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using namespace gtsam;
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using namespace example;
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static bool verbose = false;
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/* ************************************************************************* */
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TEST( Iterative, steepestDescent )
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{
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@ -38,7 +40,6 @@ TEST( Iterative, steepestDescent )
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// Do gradient descent
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GaussianFactorGraph fg2 = createGaussianFactorGraph();
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VectorConfig zero = createZeroDelta();
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bool verbose = false;
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VectorConfig actual = steepestDescent(fg2, zero, verbose);
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CHECK(assert_equal(expected,actual,1e-2));
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}
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@ -62,20 +63,20 @@ TEST( Iterative, conjugateGradientDescent )
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// Do conjugate gradient descent, System version
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System Ab(A, b);
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Vector actualX = conjugateGradientDescent(Ab, x0);
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Vector actualX = conjugateGradientDescent(Ab, x0, verbose);
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CHECK(assert_equal(expectedX,actualX,1e-9));
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// Do conjugate gradient descent, Matrix version
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Vector actualX2 = conjugateGradientDescent(A, b, x0);
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Vector actualX2 = conjugateGradientDescent(A, b, x0, verbose);
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CHECK(assert_equal(expectedX,actualX2,1e-9));
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// Do conjugate gradient descent on factor graph
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VectorConfig zero = createZeroDelta();
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VectorConfig actual = conjugateGradientDescent(fg2, zero);
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VectorConfig actual = conjugateGradientDescent(fg2, zero, verbose);
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CHECK(assert_equal(expected,actual,1e-2));
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// Test method
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VectorConfig actual2 = fg2.conjugateGradientDescent(zero);
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VectorConfig actual2 = fg2.conjugateGradientDescent(zero, verbose);
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CHECK(assert_equal(expected,actual2,1e-2));
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}
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@ -122,7 +123,7 @@ TEST( Iterative, conjugateGradientDescent_soft_constraint )
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zeros.insert("x2",zero(3));
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GaussianFactorGraph fg = graph.linearize(config);
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VectorConfig actual = conjugateGradientDescent(fg, zeros, false, 1e-3, 1e-5, 100);
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VectorConfig actual = conjugateGradientDescent(fg, zeros, verbose, 1e-3, 1e-5, 100);
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VectorConfig expected;
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expected.insert("x1", zero(3));
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@ -169,7 +170,7 @@ TEST( Iterative, subgraphPCG )
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// Solve the subgraph PCG
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VectorConfig ybar = conjugateGradients<SubgraphPreconditioner, VectorConfig,
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Errors> (system, zeros, false, 1e-5, 1e-5, 100);
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Errors> (system, zeros, verbose, 1e-5, 1e-5, 100);
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VectorConfig actual = system.x(ybar);
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VectorConfig expected;
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@ -210,7 +210,7 @@ TEST( SubgraphPreconditioner, conjugateGradients )
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// Compare with non preconditioned version:
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VectorConfig actual2 = conjugateGradientDescent(Ab, x1, verbose, epsilon,
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maxIterations);
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CHECK(assert_equal(xtrue,actual2,1e-5));
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CHECK(assert_equal(xtrue,actual2,1e-4));
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}
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/* ************************************************************************* */
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