From 2afbaaaf441c6825f4a0c50a79db70c727e7d5d2 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Sun, 13 Sep 2020 17:28:15 -0400 Subject: [PATCH 01/65] Add acc power method in Alg6 --- gtsam/sfm/PowerMethod.h | 166 ++++++++++++++++++++++++++++ gtsam/sfm/ShonanAveraging.cpp | 70 +++++++----- gtsam/sfm/tests/testPowerMethod.cpp | 38 +++++++ 3 files changed, 248 insertions(+), 26 deletions(-) create mode 100644 gtsam/sfm/PowerMethod.h create mode 100644 gtsam/sfm/tests/testPowerMethod.cpp diff --git a/gtsam/sfm/PowerMethod.h b/gtsam/sfm/PowerMethod.h new file mode 100644 index 000000000..f6620f162 --- /dev/null +++ b/gtsam/sfm/PowerMethod.h @@ -0,0 +1,166 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file PowerMethod.h + * @date Sept 2020 + * @author Jing Wu + * @brief accelerated power method for fast eigenvalue and eigenvector computation + */ + +#pragma once + +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include + +namespace gtsam { + /* ************************************************************************* */ +/// MINIMUM EIGENVALUE COMPUTATIONS + +/** This is a lightweight struct used in conjunction with Spectra to compute + * the minimum eigenvalue and eigenvector of a sparse matrix A; it has a single + * nontrivial function, perform_op(x,y), that computes and returns the product + * y = (A + sigma*I) x */ +struct MatrixProdFunctor { + // Const reference to an externally-held matrix whose minimum-eigenvalue we + // want to compute + const Sparse &A_; + + // Spectral shift + double sigma_; + + const int m_n_; + const int m_nev_; + const int m_ncv_; + Vector ritz_val_; + Matrix ritz_vectors_; + + // Constructor + explicit MatrixProdFunctor(const Sparse &A, int nev, int ncv, + double sigma = 0) + : A_(A), + m_n_(A.rows()), + m_nev_(nev), + m_ncv_(ncv > m_n_ ? m_n_ : ncv), + sigma_(sigma) {} + + int rows() const { return A_.rows(); } + int cols() const { return A_.cols(); } + + // Matrix-vector multiplication operation + void perform_op(const double *x, double *y) const { + // Wrap the raw arrays as Eigen Vector types + Eigen::Map X(x, rows()); + Eigen::Map Y(y, rows()); + + // Do the multiplication using wrapped Eigen vectors + Y = A_ * X + sigma_ * X; + } + + long next_long_rand(long seed) { + const unsigned int m_a = 16807; + const unsigned long m_max = 2147483647L; + long m_rand = m_n_ ? (m_n_ & m_max) : 1; + unsigned long lo, hi; + + lo = m_a * (long)(seed & 0xFFFF); + hi = m_a * (long)((unsigned long)seed >> 16); + lo += (hi & 0x7FFF) << 16; + if (lo > m_max) { + lo &= m_max; + ++lo; + } + lo += hi >> 15; + if (lo > m_max) { + lo &= m_max; + ++lo; + } + return (long)lo; + } + + Vector random_vec(const int len) { + Vector res(len); + const unsigned long m_max = 2147483647L; + for (int i = 0; i < len; i++) { + long m_rand = next_long_rand(m_rand); + res[i] = double(m_rand) / double(m_max) - double(0.5); + } + return res; + } + + void init(Vector data) { + ritz_val_.resize(m_ncv_); + ritz_val_.setZero(); + ritz_vectors_.resize(m_ncv_, m_nev_); + ritz_vectors_.setZero(); + Eigen::Map v0(init_resid.data(), m_n_); + } + + void init() { + Vector init_resid = random_vec(m_n_); + init(init_resid); + } + + bool converged(double tol, const Vector x) { + double theta = x.transpose() * A_ * x; + Vector diff = A_ * x - theta * x; + double error = diff.lpNorm<1>(); + return error < tol; + } + + int num_converged(double tol) { + int converge = 0; + for (int i=0; i= m_nev_) break; + + nev_adj = nev_adjusted(nconv); + restart(nev_adj); + } + // Sorting results + sort_ritzpair(sort_rule); + + m_niter += i + 1; + m_info = (nconv >= m_nev_) ? SUCCESSFUL : NOT_CONVERGING; + + return std::min(m_nev_, nconv); + } + + Vector eigenvalues() { + return ritz_val_; + } + + Matrix eigenvectors() { + return ritz_vectors_; + } + +}; + +} // namespace gtsam diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index df2d72c28..c2e2a528c 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -17,6 +17,7 @@ */ #include +#include #include #include #include @@ -470,38 +471,55 @@ Sparse ShonanAveraging::computeA(const Values &values) const { return Lambda - Q_; } -/* ************************************************************************* */ -/// MINIMUM EIGENVALUE COMPUTATIONS +// Alg.6 from paper Distributed Certifiably Correct Pose-Graph Optimization +static bool PowerMinimumEigenValue( + const Sparse &A, const Matrix &S, double *minEigenValue, + Vector *minEigenVector = 0, size_t *numIterations = 0, + size_t maxIterations = 1000, + double minEigenvalueNonnegativityTolerance = 10e-4, + Eigen::Index numLanczosVectors = 20) { -/** This is a lightweight struct used in conjunction with Spectra to compute - * the minimum eigenvalue and eigenvector of a sparse matrix A; it has a single - * nontrivial function, perform_op(x,y), that computes and returns the product - * y = (A + sigma*I) x */ -struct MatrixProdFunctor { - // Const reference to an externally-held matrix whose minimum-eigenvalue we - // want to compute - const Sparse &A_; + // a. Compute dominant eigenpair of S using power method + MatrixProdFunctor lmOperator(A, 1, std::min(numLanczosVectors, A.rows())); + lmOperator.init(); - // Spectral shift - double sigma_; + const int lmConverged = lmEigenValueSolver.compute( + maxIterations, 1e-4); - // Constructor - explicit MatrixProdFunctor(const Sparse &A, double sigma = 0) - : A_(A), sigma_(sigma) {} + // Check convergence and bail out if necessary + if (lmConverged != 1) return false; - int rows() const { return A_.rows(); } - int cols() const { return A_.cols(); } + const double lmEigenValue = lmEigenValueSolver.eigenvalues()(0); - // Matrix-vector multiplication operation - void perform_op(const double *x, double *y) const { - // Wrap the raw arrays as Eigen Vector types - Eigen::Map X(x, rows()); - Eigen::Map Y(y, rows()); - - // Do the multiplication using wrapped Eigen vectors - Y = A_ * X + sigma_ * X; + if (lmEigenValue < 0) { + // The largest-magnitude eigenvalue is negative, and therefore also the + // minimum eigenvalue, so just return this solution + *minEigenValue = lmEigenValue; + if (minEigenVector) { + *minEigenVector = lmEigenValueSolver.eigenvectors().col(0); + minEigenVector->normalize(); // Ensure that this is a unit vector + } + return true; } -}; + + Matrix C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; + MatrixProdFunctor minShiftedOperator( + C, 1, std::min(numLanczosVectors, A.rows())); + minShiftedOperator.init(); + + const int minConverged = minShiftedOperator.compute( + maxIterations, minEigenvalueNonnegativityTolerance / lmEigenValue); + + if (minConverged != 1) return false; + + *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalues()(0); + if (minEigenVector) { + *minEigenVector = minShiftedOperator.eigenvectors().col(0); + minEigenVector->normalize(); // Ensure that this is a unit vector + } + if (numIterations) *numIterations = minShiftedOperator.num_iterations(); + return true; +} /// Function to compute the minimum eigenvalue of A using Lanczos in Spectra. /// This does 2 things: diff --git a/gtsam/sfm/tests/testPowerMethod.cpp b/gtsam/sfm/tests/testPowerMethod.cpp new file mode 100644 index 000000000..f67fad458 --- /dev/null +++ b/gtsam/sfm/tests/testPowerMethod.cpp @@ -0,0 +1,38 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * testPowerMethod.cpp + * + * @file testPowerMethod.cpp + * @date Sept 2020 + * @author Jing Wu + * @brief Check eigenvalue and eigenvector computed by power method + */ + +#include +#include + +using namespace std; +using namespace gtsam; + +/* ************************************************************************* */ +TEST(PowerMethod, initialize) { + gtsam::Sparse A; + MatrixProdFunctor(A, 1, A.rows()); +} + +/* ************************************************************************* */ +int main() { + TestResult tr; + return TestRegistry::runAllTests(tr); +} +/* ************************************************************************* */ From e02633c74582c0bfa3674af78691c506e780ab43 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 14 Sep 2020 01:58:44 -0400 Subject: [PATCH 02/65] Completed and tested power method with unittest --- gtsam/sfm/PowerMethod.h | 157 +++++++++++++++++++++------- gtsam/sfm/tests/testPowerMethod.cpp | 35 ++++++- 2 files changed, 149 insertions(+), 43 deletions(-) diff --git a/gtsam/sfm/PowerMethod.h b/gtsam/sfm/PowerMethod.h index f6620f162..3b83fb8a4 100644 --- a/gtsam/sfm/PowerMethod.h +++ b/gtsam/sfm/PowerMethod.h @@ -24,14 +24,17 @@ #include #include -#include #include #include #include #include #include +#include namespace gtsam { + +using Sparse = Eigen::SparseMatrix; + /* ************************************************************************* */ /// MINIMUM EIGENVALUE COMPUTATIONS @@ -39,46 +42,63 @@ namespace gtsam { * the minimum eigenvalue and eigenvector of a sparse matrix A; it has a single * nontrivial function, perform_op(x,y), that computes and returns the product * y = (A + sigma*I) x */ -struct MatrixProdFunctor { +struct PowerFunctor { // Const reference to an externally-held matrix whose minimum-eigenvalue we // want to compute const Sparse &A_; - // Spectral shift - double sigma_; + const int m_n_; // dimension of Matrix A + const int m_nev_; // number of eigenvalues required - const int m_n_; - const int m_nev_; - const int m_ncv_; - Vector ritz_val_; - Matrix ritz_vectors_; + // a Polyak momentum term + double beta_; + // const int m_ncv_; // dimention of orthonormal basis subspace + size_t m_niter_; // number of iterations + +private: + Vector ritz_val_; // all ritz eigenvalues + Matrix ritz_vectors_; // all ritz eigenvectors + Vector ritz_conv_; // store whether the ritz eigenpair converged + Vector sorted_ritz_val_; // sorted converged eigenvalue + Matrix sorted_ritz_vectors_; // sorted converged eigenvectors + +public: // Constructor - explicit MatrixProdFunctor(const Sparse &A, int nev, int ncv, - double sigma = 0) + explicit PowerFunctor(const Sparse &A, int nev, int ncv, + double beta = 0) : A_(A), m_n_(A.rows()), m_nev_(nev), - m_ncv_(ncv > m_n_ ? m_n_ : ncv), - sigma_(sigma) {} + // m_ncv_(ncv > m_n_ ? m_n_ : ncv), + beta_(beta), + m_niter_(0) + {} int rows() const { return A_.rows(); } int cols() const { return A_.cols(); } // Matrix-vector multiplication operation - void perform_op(const double *x, double *y) const { - // Wrap the raw arrays as Eigen Vector types - Eigen::Map X(x, rows()); - Eigen::Map Y(y, rows()); + Vector perform_op(const Vector& x1, const Vector& x0) const { // Do the multiplication using wrapped Eigen vectors - Y = A_ * X + sigma_ * X; + Vector x2 = A_ * x1 - beta_ * x0; + x2.normalize(); + return x2; + } + + Vector perform_op(int i) const { + + // Do the multiplication using wrapped Eigen vectors + Vector x1 = ritz_vectors_.col(i-1); + Vector x2 = ritz_vectors_.col(i-2); + return perform_op(x1, x2); } long next_long_rand(long seed) { const unsigned int m_a = 16807; const unsigned long m_max = 2147483647L; - long m_rand = m_n_ ? (m_n_ & m_max) : 1; + // long m_rand = m_n_ ? (m_n_ & m_max) : 1; unsigned long lo, hi; lo = m_a * (long)(seed & 0xFFFF); @@ -103,62 +123,119 @@ struct MatrixProdFunctor { long m_rand = next_long_rand(m_rand); res[i] = double(m_rand) / double(m_max) - double(0.5); } + res.normalize(); return res; } - void init(Vector data) { - ritz_val_.resize(m_ncv_); + void init(const Vector x0, const Vector x00) { + // initialzie ritz eigen values + ritz_val_.resize(m_n_); ritz_val_.setZero(); - ritz_vectors_.resize(m_ncv_, m_nev_); + + // initialzie the ritz converged vector + ritz_conv_.resize(m_n_); + ritz_conv_.setZero(); + + // initialzie ritz eigen vectors + ritz_vectors_.resize(m_n_, m_n_); ritz_vectors_.setZero(); - Eigen::Map v0(init_resid.data(), m_n_); + ritz_vectors_.col(0) = perform_op(x0, x00); + ritz_vectors_.col(1) = perform_op(ritz_vectors_.col(0), x0); + + // setting beta + Vector init_resid = ritz_vectors_.col(0); + const double up = init_resid.transpose() * A_ * init_resid; + const double down = init_resid.transpose().dot(init_resid); + const double mu = up/down; + beta_ = mu*mu/4; + } void init() { - Vector init_resid = random_vec(m_n_); - init(init_resid); + Vector x0 = random_vec(m_n_); + Vector x00 = random_vec(m_n_); + init(x0, x00); } - bool converged(double tol, const Vector x) { + bool converged(double tol, int i) { + Vector x = ritz_vectors_.col(i); double theta = x.transpose() * A_ * x; + + // store the ritz eigen value + ritz_val_(i) = theta; + + // update beta + beta_ = std::max(beta_, theta * theta / 4); + Vector diff = A_ * x - theta * x; double error = diff.lpNorm<1>(); + if (error < tol) ritz_conv_(i) = 1; return error < tol; } int num_converged(double tol) { - int converge = 0; + int num_converge = 0; for (int i=0; i0 && i> pairs; + for(int i=0; i& left, const std::pair& right) { + return left.first < right.first; + }); + + // initialzie sorted ritz eigenvalues and eigenvectors + size_t num_converged = pairs.size(); + sorted_ritz_val_.resize(num_converged); + sorted_ritz_val_.setZero(); + sorted_ritz_vectors_.resize(m_n_, num_converged); + sorted_ritz_vectors_.setZero(); + + // fill sorted ritz eigenvalues and eigenvectors with sorted index + for(size_t j=0; j= m_nev_) break; - - nev_adj = nev_adjusted(nconv); - restart(nev_adj); } - // Sorting results - sort_ritzpair(sort_rule); - m_niter += i + 1; - m_info = (nconv >= m_nev_) ? SUCCESSFUL : NOT_CONVERGING; + // sort the result + sort_eigenpair(); return std::min(m_nev_, nconv); } Vector eigenvalues() { - return ritz_val_; + return sorted_ritz_val_; } Matrix eigenvectors() { - return ritz_vectors_; + return sorted_ritz_vectors_; } }; diff --git a/gtsam/sfm/tests/testPowerMethod.cpp b/gtsam/sfm/tests/testPowerMethod.cpp index f67fad458..2e9c17345 100644 --- a/gtsam/sfm/tests/testPowerMethod.cpp +++ b/gtsam/sfm/tests/testPowerMethod.cpp @@ -18,16 +18,45 @@ * @brief Check eigenvalue and eigenvector computed by power method */ +#include +#include + #include -#include + +#include +#include +#include +#include using namespace std; using namespace gtsam; +ShonanAveraging3 fromExampleName( + const std::string &name, + ShonanAveraging3::Parameters parameters = ShonanAveraging3::Parameters()) { + string g2oFile = findExampleDataFile(name); + return ShonanAveraging3(g2oFile, parameters); +} + +static const ShonanAveraging3 kShonan = fromExampleName("toyExample.g2o"); + /* ************************************************************************* */ TEST(PowerMethod, initialize) { - gtsam::Sparse A; - MatrixProdFunctor(A, 1, A.rows()); + gtsam::Sparse A(6, 6); + A.coeffRef(0, 0) = 6; + PowerFunctor pf(A, 1, A.rows()); + pf.init(); + pf.compute(20, 1e-4); + EXPECT_LONGS_EQUAL(6, pf.eigenvectors().cols()); + EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); + + const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); + Vector6 actual = pf.eigenvectors().col(0); + actual(0) = abs(actual(0)); + EXPECT(assert_equal(x1, actual)); + + const double ev1 = 6.0; + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues()(0), 1e-5); } /* ************************************************************************* */ From fc112a4dc7a3fb62bf2ba951e2b3ea650f55bc70 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 14 Sep 2020 01:59:31 -0400 Subject: [PATCH 03/65] Added PowerMinimumEigenValue method and unittest. --- gtsam/sfm/ShonanAveraging.cpp | 62 +++++++++++++++++++++---- gtsam/sfm/ShonanAveraging.h | 8 ++++ gtsam/sfm/tests/testShonanAveraging.cpp | 5 ++ 3 files changed, 67 insertions(+), 8 deletions(-) diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index c2e2a528c..786c91890 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -480,31 +480,30 @@ static bool PowerMinimumEigenValue( Eigen::Index numLanczosVectors = 20) { // a. Compute dominant eigenpair of S using power method - MatrixProdFunctor lmOperator(A, 1, std::min(numLanczosVectors, A.rows())); + PowerFunctor lmOperator(A, 1, std::min(numLanczosVectors, A.rows())); lmOperator.init(); - const int lmConverged = lmEigenValueSolver.compute( - maxIterations, 1e-4); + const int lmConverged = lmOperator.compute( + maxIterations, 1e-5); // Check convergence and bail out if necessary if (lmConverged != 1) return false; - const double lmEigenValue = lmEigenValueSolver.eigenvalues()(0); + const double lmEigenValue = lmOperator.eigenvalues()(0); if (lmEigenValue < 0) { // The largest-magnitude eigenvalue is negative, and therefore also the // minimum eigenvalue, so just return this solution *minEigenValue = lmEigenValue; if (minEigenVector) { - *minEigenVector = lmEigenValueSolver.eigenvectors().col(0); + *minEigenVector = lmOperator.eigenvectors().col(0); minEigenVector->normalize(); // Ensure that this is a unit vector } return true; } - Matrix C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; - MatrixProdFunctor minShiftedOperator( - C, 1, std::min(numLanczosVectors, A.rows())); + Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; + PowerFunctor minShiftedOperator(C, 1, std::min(numLanczosVectors, C.rows())); minShiftedOperator.init(); const int minConverged = minShiftedOperator.compute( @@ -521,6 +520,36 @@ static bool PowerMinimumEigenValue( return true; } +/** This is a lightweight struct used in conjunction with Spectra to compute + * the minimum eigenvalue and eigenvector of a sparse matrix A; it has a single + * nontrivial function, perform_op(x,y), that computes and returns the product + * y = (A + sigma*I) x */ +struct MatrixProdFunctor { + // Const reference to an externally-held matrix whose minimum-eigenvalue we + // want to compute + const Sparse &A_; + + // Spectral shift + double sigma_; + + // Constructor + explicit MatrixProdFunctor(const Sparse &A, double sigma = 0) + : A_(A), sigma_(sigma) {} + + int rows() const { return A_.rows(); } + int cols() const { return A_.cols(); } + + // Matrix-vector multiplication operation + void perform_op(const double *x, double *y) const { + // Wrap the raw arrays as Eigen Vector types + Eigen::Map X(x, rows()); + Eigen::Map Y(y, rows()); + + // Do the multiplication using wrapped Eigen vectors + Y = A_ * X + sigma_ * X; + } +}; + /// Function to compute the minimum eigenvalue of A using Lanczos in Spectra. /// This does 2 things: /// @@ -659,6 +688,23 @@ double ShonanAveraging::computeMinEigenValue(const Values &values, return minEigenValue; } +/* ************************************************************************* */ +template +double ShonanAveraging::computeMinEigenValueAP(const Values &values, + Vector *minEigenVector) const { + assert(values.size() == nrUnknowns()); + const Matrix S = StiefelElementMatrix(values); + auto A = computeA(S); + + double minEigenValue; + bool success = PowerMinimumEigenValue(A, S, &minEigenValue, minEigenVector); + if (!success) { + throw std::runtime_error( + "PowerMinimumEigenValue failed to compute minimum eigenvalue."); + } + return minEigenValue; +} + /* ************************************************************************* */ template std::pair ShonanAveraging::computeMinEigenVector( diff --git a/gtsam/sfm/ShonanAveraging.h b/gtsam/sfm/ShonanAveraging.h index edd9f33a2..9d117a266 100644 --- a/gtsam/sfm/ShonanAveraging.h +++ b/gtsam/sfm/ShonanAveraging.h @@ -26,6 +26,7 @@ #include #include #include +#include #include #include @@ -202,6 +203,13 @@ class GTSAM_EXPORT ShonanAveraging { double computeMinEigenValue(const Values &values, Vector *minEigenVector = nullptr) const; + /** + * Compute minimum eigenvalue with accelerated power method. + * @param values: should be of type SOn + */ + double computeMinEigenValueAP(const Values &values, + Vector *minEigenVector = nullptr) const; + /// Project pxdN Stiefel manifold matrix S to Rot3^N Values roundSolutionS(const Matrix &S) const; diff --git a/gtsam/sfm/tests/testShonanAveraging.cpp b/gtsam/sfm/tests/testShonanAveraging.cpp index 1200c8ebb..4434043e8 100644 --- a/gtsam/sfm/tests/testShonanAveraging.cpp +++ b/gtsam/sfm/tests/testShonanAveraging.cpp @@ -166,9 +166,14 @@ TEST(ShonanAveraging3, CheckWithEigen) { for (int i = 1; i < lambdas.size(); i++) minEigenValue = min(lambdas(i), minEigenValue); + // Compute Eigenvalue with Accelerated Power method + double lambdaAP = kShonan.computeMinEigenValueAP(Qstar3); + // Actual check EXPECT_DOUBLES_EQUAL(0, lambda, 1e-11); EXPECT_DOUBLES_EQUAL(0, minEigenValue, 1e-11); + EXPECT_DOUBLES_EQUAL(0, lambdaAP, 1e-11); + // Construct test descent direction (as minEigenVector is not predictable // across platforms, being one from a basically flat 3d- subspace) From d6e2546cf546d9863a5c2d1c1ffa48036f2459ff Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Sat, 19 Sep 2020 23:28:43 -0400 Subject: [PATCH 04/65] feat: Add Best Heavy Ball alg to set beta --- gtsam/sfm/PowerMethod.h | 202 ++++++++++++++++++++++------ gtsam/sfm/ShonanAveraging.cpp | 4 +- gtsam/sfm/tests/testPowerMethod.cpp | 34 +++-- 3 files changed, 190 insertions(+), 50 deletions(-) diff --git a/gtsam/sfm/PowerMethod.h b/gtsam/sfm/PowerMethod.h index 3b83fb8a4..b8471e8e2 100644 --- a/gtsam/sfm/PowerMethod.h +++ b/gtsam/sfm/PowerMethod.h @@ -30,26 +30,47 @@ #include #include #include +#include +#include +#include namespace gtsam { using Sparse = Eigen::SparseMatrix; - /* ************************************************************************* */ +/* ************************************************************************* */ /// MINIMUM EIGENVALUE COMPUTATIONS -/** This is a lightweight struct used in conjunction with Spectra to compute - * the minimum eigenvalue and eigenvector of a sparse matrix A; it has a single - * nontrivial function, perform_op(x,y), that computes and returns the product - * y = (A + sigma*I) x */ struct PowerFunctor { + /** + * \brief Computer i-th Eigenpair with power method + * + * References : + * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * enhancements for certifiably correct SLAM. In Proceedings of the + * International Conference on Intelligent Robots and Systems. + * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv + * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. 58–67 + * + * It performs the following iteration: \f$ x_{k+1} = A * x_k + \beta * + * x_{k-1} \f$ where A is the certificate matrix, x is the ritz vector + * + */ + // Const reference to an externally-held matrix whose minimum-eigenvalue we // want to compute const Sparse &A_; + const Matrix &S_; + const int m_n_; // dimension of Matrix A const int m_nev_; // number of eigenvalues required + // flag for running power method or accelerated power method. If false, the former, vice versa. + bool accelerated_; + // a Polyak momentum term double beta_; @@ -64,41 +85,55 @@ private: Matrix sorted_ritz_vectors_; // sorted converged eigenvectors public: - // Constructor - explicit PowerFunctor(const Sparse &A, int nev, int ncv, - double beta = 0) - : A_(A), - m_n_(A.rows()), - m_nev_(nev), - // m_ncv_(ncv > m_n_ ? m_n_ : ncv), - beta_(beta), - m_niter_(0) - {} + // Constructor + explicit PowerFunctor(const Sparse& A, const Matrix& S, int nev, int ncv, + bool accelerated = false, double beta = 0) + : A_(A), + S_(S), + m_n_(A.rows()), + m_nev_(nev), + // m_ncv_(ncv > m_n_ ? m_n_ : ncv), + accelerated_(accelerated), + beta_(beta), + m_niter_(0) { + // Do nothing + } - int rows() const { return A_.rows(); } - int cols() const { return A_.cols(); } + int rows() const { return A_.rows(); } + int cols() const { return A_.cols(); } - // Matrix-vector multiplication operation - Vector perform_op(const Vector& x1, const Vector& x0) const { + // Matrix-vector multiplication operation + Vector perform_op(const Vector& x1, const Vector& x0) const { + // Do the multiplication + Vector x2 = A_ * x1 - beta_ * x0; + x2.normalize(); + return x2; + } - // Do the multiplication using wrapped Eigen vectors - Vector x2 = A_ * x1 - beta_ * x0; + Vector perform_op(const Vector& x1, const Vector& x0, const double beta) const { + Vector x2 = A_ * x1 - beta * x0; + x2.normalize(); + return x2; + } + + Vector perform_op(const Vector& x1) const { + Vector x2 = A_ * x1; x2.normalize(); return x2; } Vector perform_op(int i) const { - - // Do the multiplication using wrapped Eigen vectors - Vector x1 = ritz_vectors_.col(i-1); - Vector x2 = ritz_vectors_.col(i-2); - return perform_op(x1, x2); + if (accelerated_) { + Vector x1 = ritz_vectors_.col(i-1); + Vector x2 = ritz_vectors_.col(i-2); + return perform_op(x1, x2); + } else + return perform_op(ritz_vectors_.col(i-1)); } long next_long_rand(long seed) { const unsigned int m_a = 16807; const unsigned long m_max = 2147483647L; - // long m_rand = m_n_ ? (m_n_ & m_max) : 1; unsigned long lo, hi; lo = m_a * (long)(seed & 0xFFFF); @@ -127,6 +162,68 @@ public: return res; } + /// Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) + void setBeta() { + if (m_n_ < 10) return; + double maxBeta = beta_; + size_t maxIndex; + std::vector betas = {2/3*maxBeta, 0.99*maxBeta, maxBeta, 1.01*maxBeta, 1.5*maxBeta}; + + Matrix tmp_ritz_vectors; + tmp_ritz_vectors.resize(m_n_, 10); + tmp_ritz_vectors.setZero(); + for (size_t i = 0; i < 10; i++) { + for (size_t k = 0; k < betas.size(); ++k) { + for (size_t j = 1; j < 10; j++) { + // double rayleighQuotient; + if (j <2 ) { + Vector x0 = random_vec(m_n_); + Vector x00 = random_vec(m_n_); + tmp_ritz_vectors.col(0) = perform_op(x0, x00, betas[k]); + tmp_ritz_vectors.col(1) = + perform_op(tmp_ritz_vectors.col(0), x0, betas[k]); + } + else { + tmp_ritz_vectors.col(j) = + perform_op(tmp_ritz_vectors.col(j - 1), + tmp_ritz_vectors.col(j - 2), betas[k]); + } + const Vector x = tmp_ritz_vectors.col(j); + const double up = x.transpose() * A_ * x; + const double down = x.transpose().dot(x); + const double mu = up / down; + if (mu * mu / 4 > maxBeta) { + maxIndex = k; + maxBeta = mu * mu / 4; + break; + } + } + } + } + + beta_ = betas[maxIndex]; + } + + void perturb(int i) { + // generate a 0.03*||x_0||_2 as stated in David's paper + unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + std::mt19937 generator (seed); + std::uniform_real_distribution uniform01(0.0, 1.0); + + int n = m_n_; + Vector disturb; + disturb.resize(n); + disturb.setZero(); + for (int i =0; i(); @@ -179,7 +291,9 @@ public: if (converged(tol, i)) { num_converge += 1; } - if (i>0 && i0 && i= m_nev_) break; + else reset(); } // sort the result diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 786c91890..f287437d4 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -480,7 +480,7 @@ static bool PowerMinimumEigenValue( Eigen::Index numLanczosVectors = 20) { // a. Compute dominant eigenpair of S using power method - PowerFunctor lmOperator(A, 1, std::min(numLanczosVectors, A.rows())); + PowerFunctor lmOperator(A, S, 1, A.rows()); lmOperator.init(); const int lmConverged = lmOperator.compute( @@ -503,7 +503,7 @@ static bool PowerMinimumEigenValue( } Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; - PowerFunctor minShiftedOperator(C, 1, std::min(numLanczosVectors, C.rows())); + PowerFunctor minShiftedOperator(C, S, 1, C.rows(), true); minShiftedOperator.init(); const int minConverged = minShiftedOperator.compute( diff --git a/gtsam/sfm/tests/testPowerMethod.cpp b/gtsam/sfm/tests/testPowerMethod.cpp index 2e9c17345..4547c91b9 100644 --- a/gtsam/sfm/tests/testPowerMethod.cpp +++ b/gtsam/sfm/tests/testPowerMethod.cpp @@ -41,21 +41,37 @@ ShonanAveraging3 fromExampleName( static const ShonanAveraging3 kShonan = fromExampleName("toyExample.g2o"); /* ************************************************************************* */ -TEST(PowerMethod, initialize) { +TEST(PowerMethod, powerIteration) { + // test power accelerated iteration gtsam::Sparse A(6, 6); A.coeffRef(0, 0) = 6; - PowerFunctor pf(A, 1, A.rows()); - pf.init(); - pf.compute(20, 1e-4); - EXPECT_LONGS_EQUAL(6, pf.eigenvectors().cols()); - EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); + Matrix S = Matrix66::Zero(); + PowerFunctor apf(A, S, 1, A.rows(), true); + apf.init(); + apf.compute(20, 1e-4); + EXPECT_LONGS_EQUAL(6, apf.eigenvectors().cols()); + EXPECT_LONGS_EQUAL(6, apf.eigenvectors().rows()); const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); - Vector6 actual = pf.eigenvectors().col(0); - actual(0) = abs(actual(0)); - EXPECT(assert_equal(x1, actual)); + Vector6 actual0 = apf.eigenvectors().col(0); + actual0(0) = abs(actual0(0)); + EXPECT(assert_equal(x1, actual0)); const double ev1 = 6.0; + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues()(0), 1e-5); + + // test power iteration, beta is set to 0 + PowerFunctor pf(A, S, 1, A.rows()); + pf.init(); + pf.compute(20, 1e-4); + // for power method, only 5 ritz vectors converge with 20 iteration + EXPECT_LONGS_EQUAL(5, pf.eigenvectors().cols()); + EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); + + Vector6 actual1 = apf.eigenvectors().col(0); + actual1(0) = abs(actual1(0)); + EXPECT(assert_equal(x1, actual1)); + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues()(0), 1e-5); } From 758c4b061d695fabe931e0df8aa5c6c1a6ec082e Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Wed, 30 Sep 2020 11:55:18 -0400 Subject: [PATCH 05/65] Refactor power and accelerated method --- gtsam/sfm/PowerMethod.h | 420 ++++++++++------------------ gtsam/sfm/ShonanAveraging.cpp | 16 +- gtsam/sfm/tests/testPowerMethod.cpp | 71 +++-- 3 files changed, 206 insertions(+), 301 deletions(-) diff --git a/gtsam/sfm/PowerMethod.h b/gtsam/sfm/PowerMethod.h index b8471e8e2..5fa355aaa 100644 --- a/gtsam/sfm/PowerMethod.h +++ b/gtsam/sfm/PowerMethod.h @@ -13,7 +13,8 @@ * @file PowerMethod.h * @date Sept 2020 * @author Jing Wu - * @brief accelerated power method for fast eigenvalue and eigenvector computation + * @brief accelerated power method for fast eigenvalue and eigenvector + * computation */ #pragma once @@ -24,15 +25,15 @@ #include #include +#include +#include +#include #include +#include #include #include #include #include -#include -#include -#include -#include namespace gtsam { @@ -41,9 +42,11 @@ using Sparse = Eigen::SparseMatrix; /* ************************************************************************* */ /// MINIMUM EIGENVALUE COMPUTATIONS -struct PowerFunctor { +// Template argument Operator just needs multiplication operator +template +class PowerMethod { /** - * \brief Computer i-th Eigenpair with power method + * \brief Compute maximum Eigenpair with power method * * References : * 1) Rosen, D. and Carlone, L., 2017, September. Computational @@ -52,144 +55,180 @@ struct PowerFunctor { * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated - * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. 58–67 + * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. + * 58–67 * * It performs the following iteration: \f$ x_{k+1} = A * x_k + \beta * - * x_{k-1} \f$ where A is the certificate matrix, x is the ritz vector + * x_{k-1} \f$ where A is the certificate matrix, x is the Ritz vector * */ - + public: // Const reference to an externally-held matrix whose minimum-eigenvalue we // want to compute - const Sparse &A_; + const Operator &A_; - const Matrix &S_; + const int dim_; // dimension of Matrix A - const int m_n_; // dimension of Matrix A - const int m_nev_; // number of eigenvalues required + size_t nrIterations_; // number of iterations - // flag for running power method or accelerated power method. If false, the former, vice versa. - bool accelerated_; + private: + double ritzValues_; // all Ritz eigenvalues + Vector ritzVectors_; // all Ritz eigenvectors - // a Polyak momentum term - double beta_; + public: + // Constructor + explicit PowerMethod(const Operator &A, const Vector &initial) + : A_(A), dim_(A.rows()), nrIterations_(0) { + Vector x0; + x0 = initial.isZero(0) ? Vector::Random(dim_) : initial; + x0.normalize(); - // const int m_ncv_; // dimention of orthonormal basis subspace - size_t m_niter_; // number of iterations + // initialize Ritz eigen values + ritzValues_ = 0.0; -private: - Vector ritz_val_; // all ritz eigenvalues - Matrix ritz_vectors_; // all ritz eigenvectors - Vector ritz_conv_; // store whether the ritz eigenpair converged - Vector sorted_ritz_val_; // sorted converged eigenvalue - Matrix sorted_ritz_vectors_; // sorted converged eigenvectors + // initialize Ritz eigen vectors + ritzVectors_.resize(dim_, 1); + ritzVectors_.setZero(); -public: - // Constructor - explicit PowerFunctor(const Sparse& A, const Matrix& S, int nev, int ncv, - bool accelerated = false, double beta = 0) - : A_(A), - S_(S), - m_n_(A.rows()), - m_nev_(nev), - // m_ncv_(ncv > m_n_ ? m_n_ : ncv), - accelerated_(accelerated), - beta_(beta), - m_niter_(0) { - // Do nothing - } - - int rows() const { return A_.rows(); } - int cols() const { return A_.cols(); } - - // Matrix-vector multiplication operation - Vector perform_op(const Vector& x1, const Vector& x0) const { - // Do the multiplication - Vector x2 = A_ * x1 - beta_ * x0; - x2.normalize(); - return x2; + ritzVectors_.col(0) = update(x0); + perturb(); } - Vector perform_op(const Vector& x1, const Vector& x0, const double beta) const { - Vector x2 = A_ * x1 - beta * x0; - x2.normalize(); - return x2; + Vector update(const Vector &x) const { + Vector y = A_ * x; + y.normalize(); + return y; } - Vector perform_op(const Vector& x1) const { - Vector x2 = A_ * x1; - x2.normalize(); - return x2; - } + Vector update() const { return update(ritzVectors_); } - Vector perform_op(int i) const { - if (accelerated_) { - Vector x1 = ritz_vectors_.col(i-1); - Vector x2 = ritz_vectors_.col(i-2); - return perform_op(x1, x2); - } else - return perform_op(ritz_vectors_.col(i-1)); - } + void updateRitz(const Vector &ritz) { ritzVectors_ = ritz; } - long next_long_rand(long seed) { - const unsigned int m_a = 16807; - const unsigned long m_max = 2147483647L; - unsigned long lo, hi; + Vector getRitz() { return ritzVectors_; } - lo = m_a * (long)(seed & 0xFFFF); - hi = m_a * (long)((unsigned long)seed >> 16); - lo += (hi & 0x7FFF) << 16; - if (lo > m_max) { - lo &= m_max; - ++lo; + void perturb() { + // generate a 0.03*||x_0||_2 as stated in David's paper + unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + std::mt19937 generator(seed); + std::uniform_real_distribution uniform01(0.0, 1.0); + + int n = dim_; + Vector disturb; + disturb.resize(n); + disturb.setZero(); + for (int i = 0; i < n; ++i) { + disturb(i) = uniform01(generator); } - lo += hi >> 15; - if (lo > m_max) { - lo &= m_max; - ++lo; - } - return (long)lo; + disturb.normalize(); + + Vector x0 = ritzVectors_; + double magnitude = x0.norm(); + ritzVectors_ = x0 + 0.03 * magnitude * disturb; } - Vector random_vec(const int len) { - Vector res(len); - const unsigned long m_max = 2147483647L; - for (int i = 0; i < len; i++) { - long m_rand = next_long_rand(m_rand); - res[i] = double(m_rand) / double(m_max) - double(0.5); + // Perform power iteration on a single Ritz value + // Updates ritzValues_ + bool iterateOne(double tol) { + const Vector x = ritzVectors_; + double theta = x.transpose() * A_ * x; + + // store the Ritz eigen value + ritzValues_ = theta; + + const Vector diff = A_ * x - theta * x; + double error = diff.norm(); + return error < tol; + } + + size_t nrIterations() { return nrIterations_; } + + int compute(int maxit, double tol) { + // Starting + int nrConverged = 0; + + for (int i = 0; i < maxit; i++) { + nrIterations_ += 1; + ritzVectors_ = update(); + nrConverged = iterateOne(tol); + if (nrConverged) break; } - res.normalize(); - return res; + + return std::min(1, nrConverged); + } + + double eigenvalues() { return ritzValues_; } + + Vector eigenvectors() { return ritzVectors_; } +}; + +template +class AcceleratedPowerMethod : public PowerMethod { + double beta_ = 0; // a Polyak momentum term + + Vector previousVector_; // store previous vector + + public: + // Constructor + explicit AcceleratedPowerMethod(const Operator &A, const Vector &initial) + : PowerMethod(A, initial) { + Vector x0 = initial; + // initialize ritz vector + x0 = x0.isZero(0) ? Vector::Random(PowerMethod::dim_) : x0; + Vector x00 = Vector::Random(PowerMethod::dim_); + x0.normalize(); + x00.normalize(); + + // initialize Ritz eigen vector and previous vector + previousVector_ = update(x0, x00, beta_); + this->updateRitz(update(previousVector_, x0, beta_)); + this->perturb(); + + // set beta + Vector init_resid = this->getRitz(); + const double up = init_resid.transpose() * this->A_ * init_resid; + const double down = init_resid.transpose().dot(init_resid); + const double mu = up / down; + beta_ = mu * mu / 4; + setBeta(); + } + + Vector update(const Vector &x1, const Vector &x0, const double beta) const { + Vector y = this->A_ * x1 - beta * x0; + y.normalize(); + return y; + } + + Vector update() const { + Vector y = update(this->ritzVectors_, previousVector_, beta_); + previousVector_ = this->ritzVectors_; + return y; } /// Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) void setBeta() { - if (m_n_ < 10) return; + if (PowerMethod::dim_ < 10) return; double maxBeta = beta_; size_t maxIndex; - std::vector betas = {2/3*maxBeta, 0.99*maxBeta, maxBeta, 1.01*maxBeta, 1.5*maxBeta}; + std::vector betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, + 1.01 * maxBeta, 1.5 * maxBeta}; - Matrix tmp_ritz_vectors; - tmp_ritz_vectors.resize(m_n_, 10); - tmp_ritz_vectors.setZero(); + Matrix tmpRitzVectors; + tmpRitzVectors.resize(PowerMethod::dim_, 10); + tmpRitzVectors.setZero(); for (size_t i = 0; i < 10; i++) { for (size_t k = 0; k < betas.size(); ++k) { for (size_t j = 1; j < 10; j++) { - // double rayleighQuotient; - if (j <2 ) { - Vector x0 = random_vec(m_n_); - Vector x00 = random_vec(m_n_); - tmp_ritz_vectors.col(0) = perform_op(x0, x00, betas[k]); - tmp_ritz_vectors.col(1) = - perform_op(tmp_ritz_vectors.col(0), x0, betas[k]); + if (j < 2) { + Vector x0 = Vector::Random(PowerMethod::dim_); + Vector x00 = Vector::Random(PowerMethod::dim_); + tmpRitzVectors.col(0) = update(x0, x00, betas[k]); + tmpRitzVectors.col(1) = update(tmpRitzVectors.col(0), x0, betas[k]); + } else { + tmpRitzVectors.col(j) = update(tmpRitzVectors.col(j - 1), + tmpRitzVectors.col(j - 2), betas[k]); } - else { - tmp_ritz_vectors.col(j) = - perform_op(tmp_ritz_vectors.col(j - 1), - tmp_ritz_vectors.col(j - 2), betas[k]); - } - const Vector x = tmp_ritz_vectors.col(j); - const double up = x.transpose() * A_ * x; + const Vector x = tmpRitzVectors.col(j); + const double up = x.transpose() * this->A_ * x; const double down = x.transpose().dot(x); const double mu = up / down; if (mu * mu / 4 > maxBeta) { @@ -203,165 +242,6 @@ public: beta_ = betas[maxIndex]; } - - void perturb(int i) { - // generate a 0.03*||x_0||_2 as stated in David's paper - unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); - std::mt19937 generator (seed); - std::uniform_real_distribution uniform01(0.0, 1.0); - - int n = m_n_; - Vector disturb; - disturb.resize(n); - disturb.setZero(); - for (int i =0; i(); - if (error < tol) ritz_conv_(i) = 1; - return error < tol; - } - - int num_converged(double tol) { - int num_converge = 0; - for (int i=0; i0 && i> pairs; - for(int i=0; i& left, const std::pair& right) { - return left.first < right.first; - }); - - // initialzie sorted ritz eigenvalues and eigenvectors - size_t num_converged = pairs.size(); - sorted_ritz_val_.resize(num_converged); - sorted_ritz_val_.setZero(); - sorted_ritz_vectors_.resize(m_n_, num_converged); - sorted_ritz_vectors_.setZero(); - - // fill sorted ritz eigenvalues and eigenvectors with sorted index - for(size_t j=0; j= m_nev_) break; - else reset(); - } - - // sort the result - sort_eigenpair(); - - return std::min(m_nev_, nconv); - } - - Vector eigenvalues() { - return sorted_ritz_val_; - } - - Matrix eigenvectors() { - return sorted_ritz_vectors_; - } - }; -} // namespace gtsam +} // namespace gtsam diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index f287437d4..9ebee4f9f 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -480,8 +480,7 @@ static bool PowerMinimumEigenValue( Eigen::Index numLanczosVectors = 20) { // a. Compute dominant eigenpair of S using power method - PowerFunctor lmOperator(A, S, 1, A.rows()); - lmOperator.init(); + PowerMethod lmOperator(A, S.row(0)); const int lmConverged = lmOperator.compute( maxIterations, 1e-5); @@ -489,34 +488,33 @@ static bool PowerMinimumEigenValue( // Check convergence and bail out if necessary if (lmConverged != 1) return false; - const double lmEigenValue = lmOperator.eigenvalues()(0); + const double lmEigenValue = lmOperator.eigenvalues(); if (lmEigenValue < 0) { // The largest-magnitude eigenvalue is negative, and therefore also the // minimum eigenvalue, so just return this solution *minEigenValue = lmEigenValue; if (minEigenVector) { - *minEigenVector = lmOperator.eigenvectors().col(0); + *minEigenVector = lmOperator.eigenvectors(); minEigenVector->normalize(); // Ensure that this is a unit vector } return true; } Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; - PowerFunctor minShiftedOperator(C, S, 1, C.rows(), true); - minShiftedOperator.init(); + AcceleratedPowerMethod minShiftedOperator(C, S.row(0)); const int minConverged = minShiftedOperator.compute( maxIterations, minEigenvalueNonnegativityTolerance / lmEigenValue); if (minConverged != 1) return false; - *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalues()(0); + *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalues(); if (minEigenVector) { - *minEigenVector = minShiftedOperator.eigenvectors().col(0); + *minEigenVector = minShiftedOperator.eigenvectors(); minEigenVector->normalize(); // Ensure that this is a unit vector } - if (numIterations) *numIterations = minShiftedOperator.num_iterations(); + if (numIterations) *numIterations = minShiftedOperator.nrIterations(); return true; } diff --git a/gtsam/sfm/tests/testPowerMethod.cpp b/gtsam/sfm/tests/testPowerMethod.cpp index 4547c91b9..d02906980 100644 --- a/gtsam/sfm/tests/testPowerMethod.cpp +++ b/gtsam/sfm/tests/testPowerMethod.cpp @@ -18,38 +18,34 @@ * @brief Check eigenvalue and eigenvector computed by power method */ +#include +#include +#include +#include #include -#include #include #include #include +#include + #include #include using namespace std; using namespace gtsam; - -ShonanAveraging3 fromExampleName( - const std::string &name, - ShonanAveraging3::Parameters parameters = ShonanAveraging3::Parameters()) { - string g2oFile = findExampleDataFile(name); - return ShonanAveraging3(g2oFile, parameters); -} - -static const ShonanAveraging3 kShonan = fromExampleName("toyExample.g2o"); +using symbol_shorthand::X; /* ************************************************************************* */ TEST(PowerMethod, powerIteration) { - // test power accelerated iteration - gtsam::Sparse A(6, 6); + // test power iteration, beta is set to 0 + Sparse A(6, 6); A.coeffRef(0, 0) = 6; Matrix S = Matrix66::Zero(); - PowerFunctor apf(A, S, 1, A.rows(), true); - apf.init(); + PowerMethod apf(A, S.row(0)); apf.compute(20, 1e-4); - EXPECT_LONGS_EQUAL(6, apf.eigenvectors().cols()); + EXPECT_LONGS_EQUAL(1, apf.eigenvectors().cols()); EXPECT_LONGS_EQUAL(6, apf.eigenvectors().rows()); const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); @@ -58,21 +54,52 @@ TEST(PowerMethod, powerIteration) { EXPECT(assert_equal(x1, actual0)); const double ev1 = 6.0; - EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues()(0), 1e-5); + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-5); - // test power iteration, beta is set to 0 - PowerFunctor pf(A, S, 1, A.rows()); - pf.init(); + // test power accelerated iteration + AcceleratedPowerMethod pf(A, S.row(0)); pf.compute(20, 1e-4); - // for power method, only 5 ritz vectors converge with 20 iteration - EXPECT_LONGS_EQUAL(5, pf.eigenvectors().cols()); + // for power method, only 5 ritz vectors converge with 20 iterations + EXPECT_LONGS_EQUAL(1, pf.eigenvectors().cols()); EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); Vector6 actual1 = apf.eigenvectors().col(0); actual1(0) = abs(actual1(0)); EXPECT(assert_equal(x1, actual1)); - EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues()(0), 1e-5); + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues(), 1e-5); +} + +/* ************************************************************************* */ +TEST(PowerMethod, useFactorGraph) { + // Let's make a scalar synchronization graph with 4 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + for (size_t j = 0; j < 3; j++) { + fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); + } + fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + + // Get eigenvalues and eigenvectors with Eigen + auto L = fg.hessian(); + cout << L.first << endl; + Eigen::EigenSolver solver(L.first); + cout << solver.eigenvalues() << endl; + cout << solver.eigenvectors() << endl; + + // Check that we get zero eigenvalue and "constant" eigenvector + EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); + auto v0 = solver.eigenvectors().col(0); + for (size_t j = 0; j < 3; j++) + EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + + // test power iteration, beta is set to 0 + Matrix S = Matrix44::Zero(); + // PowerMethod pf(L.first, S.row(0)); + AcceleratedPowerMethod pf(L.first, S.row(0)); + pf.compute(20, 1e-4); + cout << pf.eigenvalues() << endl; + cout << pf.eigenvectors() << endl; } /* ************************************************************************* */ From b7f29a051a4b8f77c6bdd1e65490c579db0c1272 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Tue, 13 Oct 2020 02:34:24 -0400 Subject: [PATCH 06/65] Reformat code. --- gtsam/linear/AcceleratedPowerMethod.h | 135 ++++++++++ gtsam/linear/PowerMethod.h | 140 ++++++++++ .../tests/testAcceleratedPowerMethod.cpp | 107 ++++++++ .../{sfm => linear}/tests/testPowerMethod.cpp | 55 ++-- gtsam/sfm/PowerMethod.h | 247 ------------------ gtsam/sfm/ShonanAveraging.cpp | 19 +- gtsam/sfm/ShonanAveraging.h | 3 +- 7 files changed, 422 insertions(+), 284 deletions(-) create mode 100644 gtsam/linear/AcceleratedPowerMethod.h create mode 100644 gtsam/linear/PowerMethod.h create mode 100644 gtsam/linear/tests/testAcceleratedPowerMethod.cpp rename gtsam/{sfm => linear}/tests/testPowerMethod.cpp (70%) delete mode 100644 gtsam/sfm/PowerMethod.h diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h new file mode 100644 index 000000000..2cbcaf67e --- /dev/null +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -0,0 +1,135 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file AcceleratedPowerMethod.h + * @date Sept 2020 + * @author Jing Wu + * @brief accelerated power method for fast eigenvalue and eigenvector + * computation + */ + +#pragma once + +// #include +// #include +#include + +namespace gtsam { + +using Sparse = Eigen::SparseMatrix; + +/* ************************************************************************* */ +/// MINIMUM EIGENVALUE COMPUTATIONS + +// Template argument Operator just needs multiplication operator +template +class AcceleratedPowerMethod : public PowerMethod { + /** + * \brief Compute maximum Eigenpair with power method + * + * References : + * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * enhancements for certifiably correct SLAM. In Proceedings of the + * International Conference on Intelligent Robots and Systems. + * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv + * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. + * 58–67 + * + * It performs the following iteration: \f$ x_{k+1} = A * x_k + \beta * + * x_{k-1} \f$ where A is the certificate matrix, x is the Ritz vector + * + */ + + double beta_ = 0; // a Polyak momentum term + + Vector previousVector_; // store previous vector + + public: + // Constructor from aim matrix A (given as Matrix or Sparse), optional intial + // vector as ritzVector + explicit AcceleratedPowerMethod( + const Operator &A, const boost::optional initial = boost::none) + : PowerMethod(A, initial) { + Vector x0; + // initialize ritz vector + x0 = initial ? Vector::Random(this->dim_) : initial.get(); + Vector x00 = Vector::Random(this->dim_); + x0.normalize(); + x00.normalize(); + + // initialize Ritz eigen vector and previous vector + previousVector_ = update(x0, x00, beta_); + this->updateRitz(update(previousVector_, x0, beta_)); + this->ritzVector_ = update(previousVector_, x0, beta_); + // this->updateRitz(update(previousVector_, x0, beta_)); + this->perturb(); + + // set beta + Vector init_resid = this->ritzVector_; + const double up = init_resid.transpose() * this->A_ * init_resid; + const double down = init_resid.transpose().dot(init_resid); + const double mu = up / down; + beta_ = mu * mu / 4; + setBeta(); + } + + // Update the ritzVector with beta and previous two ritzVector + Vector update(const Vector &x1, const Vector &x0, const double beta) const { + Vector y = this->A_ * x1 - beta * x0; + y.normalize(); + return y; + } + + // Update the ritzVector with beta and previous two ritzVector + Vector update() const { + Vector y = update(this->ritzVector_, previousVector_, beta_); + previousVector_ = this->ritzVector_; + return y; + } + + // Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) + void setBeta() { + double maxBeta = beta_; + size_t maxIndex; + std::vector betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, + 1.01 * maxBeta, 1.5 * maxBeta}; + + Matrix R = Matrix::Zero(this->dim_, 10); + for (size_t i = 0; i < 10; i++) { + for (size_t k = 0; k < betas.size(); ++k) { + for (size_t j = 1; j < 10; j++) { + if (j < 2) { + Vector x0 = this->ritzVector_; + Vector x00 = previousVector_; + R.col(0) = update(x0, x00, betas[k]); + R.col(1) = update(R.col(0), x0, betas[k]); + } else { + R.col(j) = update(R.col(j - 1), R.col(j - 2), betas[k]); + } + } + const Vector x = R.col(9); + const double up = x.transpose() * this->A_ * x; + const double down = x.transpose().dot(x); + const double mu = up / down; + if (mu * mu / 4 > maxBeta) { + maxIndex = k; + maxBeta = mu * mu / 4; + } + } + } + beta_ = betas[maxIndex]; + } +}; + +} // namespace gtsam diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h new file mode 100644 index 000000000..fe9aabb46 --- /dev/null +++ b/gtsam/linear/PowerMethod.h @@ -0,0 +1,140 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file PowerMethod.h + * @date Sept 2020 + * @author Jing Wu + * @brief Power method for fast eigenvalue and eigenvector + * computation + */ + +#pragma once + +#include +#include + +#include +#include +#include +#include + +namespace gtsam { + +using Sparse = Eigen::SparseMatrix; + +/* ************************************************************************* */ +/// MINIMUM EIGENVALUE COMPUTATIONS + +// Template argument Operator just needs multiplication operator +template +class PowerMethod { + protected: + // Const reference to an externally-held matrix whose minimum-eigenvalue we + // want to compute + const Operator &A_; + + const int dim_; // dimension of Matrix A + + size_t nrIterations_; // number of iterations + + double ritzValue_; // all Ritz eigenvalues + Vector ritzVector_; // all Ritz eigenvectors + + public: + // Constructor + explicit PowerMethod(const Operator &A, + const boost::optional initial = boost::none) + : A_(A), dim_(A.rows()), nrIterations_(0) { + Vector x0; + x0 = initial ? Vector::Random(dim_) : initial.get(); + x0.normalize(); + + // initialize Ritz eigen values + ritzValue_ = 0.0; + + // initialize Ritz eigen vectors + ritzVector_ = Vector::Zero(dim_); + + ritzVector_.col(0) = update(x0); + perturb(); + } + + // Update the vector by dot product with A_ + Vector update(const Vector &x) const { + Vector y = A_ * x; + y.normalize(); + return y; + } + + Vector update() const { return update(ritzVector_); } + + // Update the ritzVector_ + void updateRitz(const Vector &ritz) { ritzVector_ = ritz; } + + // Perturb the initial ritzvector + void perturb() { + // generate a 0.03*||x_0||_2 as stated in David's paper + std::mt19937 rng(42); + std::uniform_real_distribution uniform01(0.0, 1.0); + + int n = dim_; + Vector disturb(n); + for (int i = 0; i < n; ++i) { + disturb(i) = uniform01(rng); + } + disturb.normalize(); + + Vector x0 = ritzVector_; + double magnitude = x0.norm(); + ritzVector_ = x0 + 0.03 * magnitude * disturb; + } + + // Perform power iteration on a single Ritz value + // Updates ritzValue_ + bool iterateOne(double tol) { + const Vector x = ritzVector_; + double theta = x.transpose() * A_ * x; + + // store the Ritz eigen value + ritzValue_ = theta; + + const Vector diff = A_ * x - theta * x; + double error = diff.norm(); + return error < tol; + } + + // Return the number of iterations + size_t nrIterations() const { return nrIterations_; } + + // Start the iteration until the ritz error converge + int compute(int maxIterations, double tol) { + // Starting + int nrConverged = 0; + + for (int i = 0; i < maxIterations; i++) { + nrIterations_ += 1; + ritzVector_ = update(); + nrConverged = iterateOne(tol); + if (nrConverged) break; + } + + return std::min(1, nrConverged); + } + + // Return the eigenvalue + double eigenvalues() const { return ritzValue_; } + + // Return the eigenvector + const Vector eigenvectors() const { return ritzVector_; } +}; + +} // namespace gtsam diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp new file mode 100644 index 000000000..2a117d53b --- /dev/null +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -0,0 +1,107 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * testPowerMethod.cpp + * + * @file testAcceleratedPowerMethod.cpp + * @date Sept 2020 + * @author Jing Wu + * @brief Check eigenvalue and eigenvector computed by accelerated power method + */ + +#include +#include +#include +#include +#include + +#include + +#include +#include +#include + +#include +#include + +using namespace std; +using namespace gtsam; +using symbol_shorthand::X; + +/* ************************************************************************* */ +TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { + // test power iteration, beta is set to 0 + Sparse A(6, 6); + A.coeffRef(0, 0) = 6; + A.coeffRef(0, 0) = 5; + A.coeffRef(0, 0) = 4; + A.coeffRef(0, 0) = 3; + A.coeffRef(0, 0) = 2; + A.coeffRef(0, 0) = 1; + Vector initial = Vector6::Zero(); + const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); + const double ev1 = 1.0; + + // test accelerated power iteration + AcceleratedPowerMethod apf(A, initial); + apf.compute(20, 1e-4); + EXPECT_LONGS_EQUAL(1, apf.eigenvectors().cols()); + EXPECT_LONGS_EQUAL(6, apf.eigenvectors().rows()); + + Vector6 actual1 = apf.eigenvectors(); + // actual1(0) = abs (actual1(0)); + EXPECT(assert_equal(x1, actual1)); + + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-5); +} + +/* ************************************************************************* */ +TEST(AcceleratedPowerMethod, useFactorGraph) { + // Let's make a scalar synchronization graph with 4 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + for (size_t j = 0; j < 3; j++) { + fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); + } + fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + + // Get eigenvalues and eigenvectors with Eigen + auto L = fg.hessian(); + Eigen::EigenSolver solver(L.first); + + // Check that we get zero eigenvalue and "constant" eigenvector + EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); + auto v0 = solver.eigenvectors().col(0); + for (size_t j = 0; j < 3; j++) + EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + + size_t maxIdx = 0; + for (auto i =0; i= solver.eigenvalues()(maxIdx).real()) maxIdx = i; + } + // Store the max eigenvalue and its according eigenvector + const auto ev1 = solver.eigenvalues()(maxIdx).real(); + auto ev2 = solver.eigenvectors().col(maxIdx).real(); + + Vector initial = Vector4::Zero(); + AcceleratedPowerMethod apf(L.first, initial); + apf.compute(20, 1e-4); + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-8); + EXPECT(assert_equal(ev2, apf.eigenvectors(), 3e-5)); +} + +/* ************************************************************************* */ +int main() { + TestResult tr; + return TestRegistry::runAllTests(tr); +} +/* ************************************************************************* */ diff --git a/gtsam/sfm/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp similarity index 70% rename from gtsam/sfm/tests/testPowerMethod.cpp rename to gtsam/linear/tests/testPowerMethod.cpp index d02906980..621286c85 100644 --- a/gtsam/sfm/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -22,7 +22,7 @@ #include #include #include -#include +#include #include @@ -42,31 +42,22 @@ TEST(PowerMethod, powerIteration) { // test power iteration, beta is set to 0 Sparse A(6, 6); A.coeffRef(0, 0) = 6; - Matrix S = Matrix66::Zero(); - PowerMethod apf(A, S.row(0)); - apf.compute(20, 1e-4); - EXPECT_LONGS_EQUAL(1, apf.eigenvectors().cols()); - EXPECT_LONGS_EQUAL(6, apf.eigenvectors().rows()); - - const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); - Vector6 actual0 = apf.eigenvectors().col(0); - actual0(0) = abs(actual0(0)); - EXPECT(assert_equal(x1, actual0)); - - const double ev1 = 6.0; - EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-5); - - // test power accelerated iteration - AcceleratedPowerMethod pf(A, S.row(0)); + A.coeffRef(0, 0) = 5; + A.coeffRef(0, 0) = 4; + A.coeffRef(0, 0) = 3; + A.coeffRef(0, 0) = 2; + A.coeffRef(0, 0) = 1; + Vector initial = Vector6::Zero(); + PowerMethod pf(A, initial); pf.compute(20, 1e-4); - // for power method, only 5 ritz vectors converge with 20 iterations EXPECT_LONGS_EQUAL(1, pf.eigenvectors().cols()); EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); - Vector6 actual1 = apf.eigenvectors().col(0); - actual1(0) = abs(actual1(0)); - EXPECT(assert_equal(x1, actual1)); + const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); + Vector6 actual0 = pf.eigenvectors(); + EXPECT(assert_equal(x1, actual0)); + const double ev1 = 1.0; EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues(), 1e-5); } @@ -82,10 +73,7 @@ TEST(PowerMethod, useFactorGraph) { // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); - cout << L.first << endl; Eigen::EigenSolver solver(L.first); - cout << solver.eigenvalues() << endl; - cout << solver.eigenvectors() << endl; // Check that we get zero eigenvalue and "constant" eigenvector EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); @@ -93,13 +81,20 @@ TEST(PowerMethod, useFactorGraph) { for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); - // test power iteration, beta is set to 0 - Matrix S = Matrix44::Zero(); - // PowerMethod pf(L.first, S.row(0)); - AcceleratedPowerMethod pf(L.first, S.row(0)); + size_t maxIdx = 0; + for (auto i =0; i= solver.eigenvalues()(maxIdx).real()) maxIdx = i; + } + // Store the max eigenvalue and its according eigenvector + const auto ev1 = solver.eigenvalues()(maxIdx).real(); + auto ev2 = solver.eigenvectors().col(maxIdx).real(); + + Vector initial = Vector4::Zero(); + PowerMethod pf(L.first, initial); pf.compute(20, 1e-4); - cout << pf.eigenvalues() << endl; - cout << pf.eigenvectors() << endl; + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues(), 1e-8); + // auto actual2 = pf.eigenvectors(); + // EXPECT(assert_equal(ev2, actual2, 3e-5)); } /* ************************************************************************* */ diff --git a/gtsam/sfm/PowerMethod.h b/gtsam/sfm/PowerMethod.h deleted file mode 100644 index 5fa355aaa..000000000 --- a/gtsam/sfm/PowerMethod.h +++ /dev/null @@ -1,247 +0,0 @@ -/* ---------------------------------------------------------------------------- - - * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, - * Atlanta, Georgia 30332-0415 - * All Rights Reserved - * Authors: Frank Dellaert, et al. (see THANKS for the full author list) - - * See LICENSE for the license information - - * -------------------------------------------------------------------------- */ - -/** - * @file PowerMethod.h - * @date Sept 2020 - * @author Jing Wu - * @brief accelerated power method for fast eigenvalue and eigenvector - * computation - */ - -#pragma once - -#include -#include -#include - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - -namespace gtsam { - -using Sparse = Eigen::SparseMatrix; - -/* ************************************************************************* */ -/// MINIMUM EIGENVALUE COMPUTATIONS - -// Template argument Operator just needs multiplication operator -template -class PowerMethod { - /** - * \brief Compute maximum Eigenpair with power method - * - * References : - * 1) Rosen, D. and Carlone, L., 2017, September. Computational - * enhancements for certifiably correct SLAM. In Proceedings of the - * International Conference on Intelligent Robots and Systems. - * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, - * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv - * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated - * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. - * 58–67 - * - * It performs the following iteration: \f$ x_{k+1} = A * x_k + \beta * - * x_{k-1} \f$ where A is the certificate matrix, x is the Ritz vector - * - */ - public: - // Const reference to an externally-held matrix whose minimum-eigenvalue we - // want to compute - const Operator &A_; - - const int dim_; // dimension of Matrix A - - size_t nrIterations_; // number of iterations - - private: - double ritzValues_; // all Ritz eigenvalues - Vector ritzVectors_; // all Ritz eigenvectors - - public: - // Constructor - explicit PowerMethod(const Operator &A, const Vector &initial) - : A_(A), dim_(A.rows()), nrIterations_(0) { - Vector x0; - x0 = initial.isZero(0) ? Vector::Random(dim_) : initial; - x0.normalize(); - - // initialize Ritz eigen values - ritzValues_ = 0.0; - - // initialize Ritz eigen vectors - ritzVectors_.resize(dim_, 1); - ritzVectors_.setZero(); - - ritzVectors_.col(0) = update(x0); - perturb(); - } - - Vector update(const Vector &x) const { - Vector y = A_ * x; - y.normalize(); - return y; - } - - Vector update() const { return update(ritzVectors_); } - - void updateRitz(const Vector &ritz) { ritzVectors_ = ritz; } - - Vector getRitz() { return ritzVectors_; } - - void perturb() { - // generate a 0.03*||x_0||_2 as stated in David's paper - unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); - std::mt19937 generator(seed); - std::uniform_real_distribution uniform01(0.0, 1.0); - - int n = dim_; - Vector disturb; - disturb.resize(n); - disturb.setZero(); - for (int i = 0; i < n; ++i) { - disturb(i) = uniform01(generator); - } - disturb.normalize(); - - Vector x0 = ritzVectors_; - double magnitude = x0.norm(); - ritzVectors_ = x0 + 0.03 * magnitude * disturb; - } - - // Perform power iteration on a single Ritz value - // Updates ritzValues_ - bool iterateOne(double tol) { - const Vector x = ritzVectors_; - double theta = x.transpose() * A_ * x; - - // store the Ritz eigen value - ritzValues_ = theta; - - const Vector diff = A_ * x - theta * x; - double error = diff.norm(); - return error < tol; - } - - size_t nrIterations() { return nrIterations_; } - - int compute(int maxit, double tol) { - // Starting - int nrConverged = 0; - - for (int i = 0; i < maxit; i++) { - nrIterations_ += 1; - ritzVectors_ = update(); - nrConverged = iterateOne(tol); - if (nrConverged) break; - } - - return std::min(1, nrConverged); - } - - double eigenvalues() { return ritzValues_; } - - Vector eigenvectors() { return ritzVectors_; } -}; - -template -class AcceleratedPowerMethod : public PowerMethod { - double beta_ = 0; // a Polyak momentum term - - Vector previousVector_; // store previous vector - - public: - // Constructor - explicit AcceleratedPowerMethod(const Operator &A, const Vector &initial) - : PowerMethod(A, initial) { - Vector x0 = initial; - // initialize ritz vector - x0 = x0.isZero(0) ? Vector::Random(PowerMethod::dim_) : x0; - Vector x00 = Vector::Random(PowerMethod::dim_); - x0.normalize(); - x00.normalize(); - - // initialize Ritz eigen vector and previous vector - previousVector_ = update(x0, x00, beta_); - this->updateRitz(update(previousVector_, x0, beta_)); - this->perturb(); - - // set beta - Vector init_resid = this->getRitz(); - const double up = init_resid.transpose() * this->A_ * init_resid; - const double down = init_resid.transpose().dot(init_resid); - const double mu = up / down; - beta_ = mu * mu / 4; - setBeta(); - } - - Vector update(const Vector &x1, const Vector &x0, const double beta) const { - Vector y = this->A_ * x1 - beta * x0; - y.normalize(); - return y; - } - - Vector update() const { - Vector y = update(this->ritzVectors_, previousVector_, beta_); - previousVector_ = this->ritzVectors_; - return y; - } - - /// Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) - void setBeta() { - if (PowerMethod::dim_ < 10) return; - double maxBeta = beta_; - size_t maxIndex; - std::vector betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, - 1.01 * maxBeta, 1.5 * maxBeta}; - - Matrix tmpRitzVectors; - tmpRitzVectors.resize(PowerMethod::dim_, 10); - tmpRitzVectors.setZero(); - for (size_t i = 0; i < 10; i++) { - for (size_t k = 0; k < betas.size(); ++k) { - for (size_t j = 1; j < 10; j++) { - if (j < 2) { - Vector x0 = Vector::Random(PowerMethod::dim_); - Vector x00 = Vector::Random(PowerMethod::dim_); - tmpRitzVectors.col(0) = update(x0, x00, betas[k]); - tmpRitzVectors.col(1) = update(tmpRitzVectors.col(0), x0, betas[k]); - } else { - tmpRitzVectors.col(j) = update(tmpRitzVectors.col(j - 1), - tmpRitzVectors.col(j - 2), betas[k]); - } - const Vector x = tmpRitzVectors.col(j); - const double up = x.transpose() * this->A_ * x; - const double down = x.transpose().dot(x); - const double mu = up / down; - if (mu * mu / 4 > maxBeta) { - maxIndex = k; - maxBeta = mu * mu / 4; - break; - } - } - } - } - - beta_ = betas[maxIndex]; - } -}; - -} // namespace gtsam diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 9ebee4f9f..5f509c91e 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -471,16 +471,23 @@ Sparse ShonanAveraging::computeA(const Values &values) const { return Lambda - Q_; } -// Alg.6 from paper Distributed Certifiably Correct Pose-Graph Optimization +/* ************************************************************************* */ +/// MINIMUM EIGENVALUE COMPUTATIONS +// Alg.6 from paper Distributed Certifiably Correct Pose-Graph Optimization, +// it takes in the certificate matrix A as input, the maxIterations and the +// minEigenvalueNonnegativityTolerance is set to 1000 and 10e-4 ad default, +// there are two parts +// in this algorithm: +// (1) static bool PowerMinimumEigenValue( const Sparse &A, const Matrix &S, double *minEigenValue, Vector *minEigenVector = 0, size_t *numIterations = 0, size_t maxIterations = 1000, - double minEigenvalueNonnegativityTolerance = 10e-4, - Eigen::Index numLanczosVectors = 20) { + double minEigenvalueNonnegativityTolerance = 10e-4) { // a. Compute dominant eigenpair of S using power method - PowerMethod lmOperator(A, S.row(0)); + const boost::optional initial(S.row(0)); + PowerMethod lmOperator(A, initial); const int lmConverged = lmOperator.compute( maxIterations, 1e-5); @@ -501,8 +508,8 @@ static bool PowerMinimumEigenValue( return true; } - Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; - AcceleratedPowerMethod minShiftedOperator(C, S.row(0)); + const Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; + AcceleratedPowerMethod minShiftedOperator(C, initial); const int minConverged = minShiftedOperator.compute( maxIterations, minEigenvalueNonnegativityTolerance / lmEigenValue); diff --git a/gtsam/sfm/ShonanAveraging.h b/gtsam/sfm/ShonanAveraging.h index 9d117a266..49659386f 100644 --- a/gtsam/sfm/ShonanAveraging.h +++ b/gtsam/sfm/ShonanAveraging.h @@ -26,7 +26,8 @@ #include #include #include -#include +#include +#include #include #include From fbebd3ed6954fed7766c31a172e8761cc0c56ef7 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Tue, 13 Oct 2020 12:00:25 -0400 Subject: [PATCH 07/65] Small fix --- gtsam/linear/AcceleratedPowerMethod.h | 2 -- gtsam/linear/PowerMethod.h | 13 ++++++------- gtsam/linear/tests/testAcceleratedPowerMethod.cpp | 3 +++ 3 files changed, 9 insertions(+), 9 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 2cbcaf67e..0e47c6a53 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -70,9 +70,7 @@ class AcceleratedPowerMethod : public PowerMethod { // initialize Ritz eigen vector and previous vector previousVector_ = update(x0, x00, beta_); - this->updateRitz(update(previousVector_, x0, beta_)); this->ritzVector_ = update(previousVector_, x0, beta_); - // this->updateRitz(update(previousVector_, x0, beta_)); this->perturb(); // set beta diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index fe9aabb46..4807e0e6a 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -75,11 +75,9 @@ class PowerMethod { return y; } + // Update the vector by dot product with A_ Vector update() const { return update(ritzVector_); } - // Update the ritzVector_ - void updateRitz(const Vector &ritz) { ritzVector_ = ritz; } - // Perturb the initial ritzvector void perturb() { // generate a 0.03*||x_0||_2 as stated in David's paper @@ -87,10 +85,11 @@ class PowerMethod { std::uniform_real_distribution uniform01(0.0, 1.0); int n = dim_; - Vector disturb(n); - for (int i = 0; i < n; ++i) { - disturb(i) = uniform01(rng); - } + // Vector disturb(n); + // for (int i = 0; i < n; ++i) { + // disturb(i) = uniform01(rng); + // } + Vector disturb = Vector::Random(n); disturb.normalize(); Vector x0 = ritzVector_; diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index 2a117d53b..a84a31a0f 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -76,7 +76,10 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); + cout << L.first << endl; Eigen::EigenSolver solver(L.first); + cout << solver.eigenvalues() << endl; + cout << solver.eigenvectors() << endl; // Check that we get zero eigenvalue and "constant" eigenvector EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); From 5f50e740b746573e6b85e1c300e6f50c9c593828 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Thu, 22 Oct 2020 14:19:05 -0400 Subject: [PATCH 08/65] Revise according to Frank and David's comments --- gtsam/linear/AcceleratedPowerMethod.h | 53 +++++++++++--------- gtsam/linear/PowerMethod.h | 72 +++++++++------------------ gtsam/sfm/ShonanAveraging.cpp | 61 +++++++++++++++-------- 3 files changed, 94 insertions(+), 92 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 0e47c6a53..0ad87626b 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -34,7 +34,7 @@ using Sparse = Eigen::SparseMatrix; template class AcceleratedPowerMethod : public PowerMethod { /** - * \brief Compute maximum Eigenpair with power method + * \brief Compute maximum Eigenpair with accelerated power method * * References : * 1) Rosen, D. and Carlone, L., 2017, September. Computational @@ -46,8 +46,9 @@ class AcceleratedPowerMethod : public PowerMethod { * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. * 58–67 * - * It performs the following iteration: \f$ x_{k+1} = A * x_k + \beta * - * x_{k-1} \f$ where A is the certificate matrix, x is the Ritz vector + * It performs the following iteration: \f$ x_{k+1} = A * x_k - \beta * + * x_{k-1} \f$ where A is the aim matrix we want to get eigenpair of, x is the + * Ritz vector * */ @@ -59,46 +60,52 @@ class AcceleratedPowerMethod : public PowerMethod { // Constructor from aim matrix A (given as Matrix or Sparse), optional intial // vector as ritzVector explicit AcceleratedPowerMethod( - const Operator &A, const boost::optional initial = boost::none) + const Operator &A, const boost::optional initial = boost::none, + const double initialBeta = 0.0) : PowerMethod(A, initial) { Vector x0; // initialize ritz vector - x0 = initial ? Vector::Random(this->dim_) : initial.get(); + x0 = initial ? initial.get() : Vector::Random(this->dim_); Vector x00 = Vector::Random(this->dim_); x0.normalize(); x00.normalize(); // initialize Ritz eigen vector and previous vector - previousVector_ = update(x0, x00, beta_); - this->ritzVector_ = update(previousVector_, x0, beta_); - this->perturb(); + previousVector_ = powerIteration(x0, x00, beta_); + this->ritzVector_ = powerIteration(previousVector_, x0, beta_); - // set beta - Vector init_resid = this->ritzVector_; - const double up = init_resid.transpose() * this->A_ * init_resid; - const double down = init_resid.transpose().dot(init_resid); - const double mu = up / down; - beta_ = mu * mu / 4; - setBeta(); + // initialize beta_ + if (!initialBeta) { + estimateBeta(); + } else { + beta_ = initialBeta; + } + } // Update the ritzVector with beta and previous two ritzVector - Vector update(const Vector &x1, const Vector &x0, const double beta) const { + Vector powerIteration(const Vector &x1, const Vector &x0, + const double beta) const { Vector y = this->A_ * x1 - beta * x0; y.normalize(); return y; } // Update the ritzVector with beta and previous two ritzVector - Vector update() const { - Vector y = update(this->ritzVector_, previousVector_, beta_); + Vector powerIteration() const { + Vector y = powerIteration(this->ritzVector_, previousVector_, beta_); previousVector_ = this->ritzVector_; return y; } // Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) - void setBeta() { - double maxBeta = beta_; + void estimateBeta() { + // set beta + Vector init_resid = this->ritzVector_; + const double up = init_resid.transpose() * this->A_ * init_resid; + const double down = init_resid.transpose().dot(init_resid); + const double mu = up / down; + double maxBeta = mu * mu / 4; size_t maxIndex; std::vector betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, 1.01 * maxBeta, 1.5 * maxBeta}; @@ -110,10 +117,10 @@ class AcceleratedPowerMethod : public PowerMethod { if (j < 2) { Vector x0 = this->ritzVector_; Vector x00 = previousVector_; - R.col(0) = update(x0, x00, betas[k]); - R.col(1) = update(R.col(0), x0, betas[k]); + R.col(0) = powerIteration(x0, x00, betas[k]); + R.col(1) = powerIteration(R.col(0), x0, betas[k]); } else { - R.col(j) = update(R.col(j - 1), R.col(j - 2), betas[k]); + R.col(j) = powerIteration(R.col(j - 1), R.col(j - 2), betas[k]); } } const Vector x = R.col(9); diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index 4807e0e6a..ee7a04429 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -46,8 +46,8 @@ class PowerMethod { size_t nrIterations_; // number of iterations - double ritzValue_; // all Ritz eigenvalues - Vector ritzVector_; // all Ritz eigenvectors + double ritzValue_; // Ritz eigenvalue + Vector ritzVector_; // Ritz eigenvector public: // Constructor @@ -55,85 +55,61 @@ class PowerMethod { const boost::optional initial = boost::none) : A_(A), dim_(A.rows()), nrIterations_(0) { Vector x0; - x0 = initial ? Vector::Random(dim_) : initial.get(); + x0 = initial ? initial.get() : Vector::Random(dim_); x0.normalize(); - // initialize Ritz eigen values + // initialize Ritz eigen value ritzValue_ = 0.0; // initialize Ritz eigen vectors ritzVector_ = Vector::Zero(dim_); - - ritzVector_.col(0) = update(x0); - perturb(); + ritzVector_ = powerIteration(x0); } // Update the vector by dot product with A_ - Vector update(const Vector &x) const { + Vector powerIteration(const Vector &x) const { Vector y = A_ * x; y.normalize(); return y; } // Update the vector by dot product with A_ - Vector update() const { return update(ritzVector_); } + Vector powerIteration() const { return powerIteration(ritzVector_); } - // Perturb the initial ritzvector - void perturb() { - // generate a 0.03*||x_0||_2 as stated in David's paper - std::mt19937 rng(42); - std::uniform_real_distribution uniform01(0.0, 1.0); - - int n = dim_; - // Vector disturb(n); - // for (int i = 0; i < n; ++i) { - // disturb(i) = uniform01(rng); - // } - Vector disturb = Vector::Random(n); - disturb.normalize(); - - Vector x0 = ritzVector_; - double magnitude = x0.norm(); - ritzVector_ = x0 + 0.03 * magnitude * disturb; - } - - // Perform power iteration on a single Ritz value - // Updates ritzValue_ - bool iterateOne(double tol) { + // After Perform power iteration on a single Ritz value, if the error is less + // than the tol then return true else false + bool converged(double tol) { const Vector x = ritzVector_; - double theta = x.transpose() * A_ * x; - // store the Ritz eigen value - ritzValue_ = theta; - - const Vector diff = A_ * x - theta * x; - double error = diff.norm(); + ritzValue_ = x.dot(A_ * x); + double error = (A_ * x - ritzValue_ * x).norm(); return error < tol; } // Return the number of iterations size_t nrIterations() const { return nrIterations_; } - // Start the iteration until the ritz error converge - int compute(int maxIterations, double tol) { + // Start the power/accelerated iteration, after updated the ritz vector, + // calculate the ritz error, repeat this operation until the ritz error converge + int compute(size_t maxIterations, double tol) { // Starting - int nrConverged = 0; + bool isConverged = false; - for (int i = 0; i < maxIterations; i++) { - nrIterations_ += 1; - ritzVector_ = update(); - nrConverged = iterateOne(tol); - if (nrConverged) break; + for (size_t i = 0; i < maxIterations; i++) { + ++nrIterations_ ; + ritzVector_ = powerIteration(); + isConverged = converged(tol); + if (isConverged) return isConverged; } - return std::min(1, nrConverged); + return isConverged; } // Return the eigenvalue - double eigenvalues() const { return ritzValue_; } + double eigenvalue() const { return ritzValue_; } // Return the eigenvector - const Vector eigenvectors() const { return ritzVector_; } + Vector eigenvector() const { return ritzVector_; } }; } // namespace gtsam diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 5f509c91e..60233fc6e 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -471,14 +471,40 @@ Sparse ShonanAveraging::computeA(const Values &values) const { return Lambda - Q_; } +/* ************************************************************************* */ +template +Sparse ShonanAveraging::computeA(const Matrix &S) const { + auto Lambda = computeLambda(S); + return Lambda - Q_; +} + +/* ************************************************************************* */ +// Perturb the initial initialVector by adding a spherically-uniformly +// distributed random vector with 0.03*||initialVector||_2 magnitude to +// initialVector +Vector perturb(const Vector &initialVector) { + // generate a 0.03*||x_0||_2 as stated in David's paper + int n = initialVector.rows(); + Vector disturb = Vector::Random(n); + disturb.normalize(); + + double magnitude = initialVector.norm(); + Vector perturbedVector = initialVector + 0.03 * magnitude * disturb; + perturbedVector.normalize(); + return perturbedVector; +} + /* ************************************************************************* */ /// MINIMUM EIGENVALUE COMPUTATIONS -// Alg.6 from paper Distributed Certifiably Correct Pose-Graph Optimization, -// it takes in the certificate matrix A as input, the maxIterations and the -// minEigenvalueNonnegativityTolerance is set to 1000 and 10e-4 ad default, +// Alg.6 from paper Distributed Certifiably Correct Pose-Graph Optimization, +// it takes in the certificate matrix A as input, the maxIterations and the +// minEigenvalueNonnegativityTolerance is set to 1000 and 10e-4 ad default, // there are two parts // in this algorithm: -// (1) +// (1) compute the maximum eigenpair (\lamda_dom, \vect{v}_dom) of A by power +// method. if \lamda_dom is less than zero, then return the eigenpair. (2) +// compute the maximum eigenpair (\theta, \vect{v}) of C = \lamda_dom * I - A by +// accelerated power method. Then return (\lamda_dom - \theta, \vect{v}). static bool PowerMinimumEigenValue( const Sparse &A, const Matrix &S, double *minEigenValue, Vector *minEigenVector = 0, size_t *numIterations = 0, @@ -486,39 +512,39 @@ static bool PowerMinimumEigenValue( double minEigenvalueNonnegativityTolerance = 10e-4) { // a. Compute dominant eigenpair of S using power method - const boost::optional initial(S.row(0)); - PowerMethod lmOperator(A, initial); + PowerMethod lmOperator(A); - const int lmConverged = lmOperator.compute( + const bool lmConverged = lmOperator.compute( maxIterations, 1e-5); // Check convergence and bail out if necessary - if (lmConverged != 1) return false; + if (!lmConverged) return false; - const double lmEigenValue = lmOperator.eigenvalues(); + const double lmEigenValue = lmOperator.eigenvalue(); if (lmEigenValue < 0) { // The largest-magnitude eigenvalue is negative, and therefore also the // minimum eigenvalue, so just return this solution *minEigenValue = lmEigenValue; if (minEigenVector) { - *minEigenVector = lmOperator.eigenvectors(); + *minEigenVector = lmOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector } return true; } const Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; + const boost::optional initial = perturb(S.row(0)); AcceleratedPowerMethod minShiftedOperator(C, initial); - const int minConverged = minShiftedOperator.compute( + const bool minConverged = minShiftedOperator.compute( maxIterations, minEigenvalueNonnegativityTolerance / lmEigenValue); - if (minConverged != 1) return false; + if (!minConverged) return false; - *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalues(); + *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalue(); if (minEigenVector) { - *minEigenVector = minShiftedOperator.eigenvectors(); + *minEigenVector = minShiftedOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector } if (numIterations) *numIterations = minShiftedOperator.nrIterations(); @@ -669,13 +695,6 @@ static bool SparseMinimumEigenValue( return true; } -/* ************************************************************************* */ -template -Sparse ShonanAveraging::computeA(const Matrix &S) const { - auto Lambda = computeLambda(S); - return Lambda - Q_; -} - /* ************************************************************************* */ template double ShonanAveraging::computeMinEigenValue(const Values &values, From f86ad955827efd5397b4f392a596d1e975f2d2a4 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Thu, 22 Oct 2020 14:19:23 -0400 Subject: [PATCH 09/65] Correct unittest input error --- .../tests/testAcceleratedPowerMethod.cpp | 37 ++++++++----------- gtsam/linear/tests/testPowerMethod.cpp | 35 +++++++++--------- 2 files changed, 33 insertions(+), 39 deletions(-) diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index a84a31a0f..474492475 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -42,26 +42,24 @@ TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { // test power iteration, beta is set to 0 Sparse A(6, 6); A.coeffRef(0, 0) = 6; - A.coeffRef(0, 0) = 5; - A.coeffRef(0, 0) = 4; - A.coeffRef(0, 0) = 3; - A.coeffRef(0, 0) = 2; - A.coeffRef(0, 0) = 1; - Vector initial = Vector6::Zero(); + A.coeffRef(1, 1) = 5; + A.coeffRef(2, 2) = 4; + A.coeffRef(3, 3) = 3; + A.coeffRef(4, 4) = 2; + A.coeffRef(5, 5) = 1; + Vector initial = Vector6::Random(); const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); - const double ev1 = 1.0; + const double ev1 = 6.0; // test accelerated power iteration AcceleratedPowerMethod apf(A, initial); - apf.compute(20, 1e-4); - EXPECT_LONGS_EQUAL(1, apf.eigenvectors().cols()); - EXPECT_LONGS_EQUAL(6, apf.eigenvectors().rows()); + apf.compute(50, 1e-4); + EXPECT_LONGS_EQUAL(6, apf.eigenvector().rows()); - Vector6 actual1 = apf.eigenvectors(); - // actual1(0) = abs (actual1(0)); - EXPECT(assert_equal(x1, actual1)); + Vector6 actual1 = apf.eigenvector(); + EXPECT(assert_equal(x1, actual1, 1e-4)); - EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-5); + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-5); } /* ************************************************************************* */ @@ -76,10 +74,7 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); - cout << L.first << endl; Eigen::EigenSolver solver(L.first); - cout << solver.eigenvalues() << endl; - cout << solver.eigenvectors() << endl; // Check that we get zero eigenvalue and "constant" eigenvector EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); @@ -95,11 +90,11 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { const auto ev1 = solver.eigenvalues()(maxIdx).real(); auto ev2 = solver.eigenvectors().col(maxIdx).real(); - Vector initial = Vector4::Zero(); + Vector initial = Vector4::Random(); AcceleratedPowerMethod apf(L.first, initial); - apf.compute(20, 1e-4); - EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalues(), 1e-8); - EXPECT(assert_equal(ev2, apf.eigenvectors(), 3e-5)); + apf.compute(50, 1e-4); + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-8); + EXPECT(assert_equal(-ev2, apf.eigenvector(), 3e-5)); } /* ************************************************************************* */ diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 621286c85..58d1ca0cc 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -42,23 +42,22 @@ TEST(PowerMethod, powerIteration) { // test power iteration, beta is set to 0 Sparse A(6, 6); A.coeffRef(0, 0) = 6; - A.coeffRef(0, 0) = 5; - A.coeffRef(0, 0) = 4; - A.coeffRef(0, 0) = 3; - A.coeffRef(0, 0) = 2; - A.coeffRef(0, 0) = 1; - Vector initial = Vector6::Zero(); + A.coeffRef(1, 1) = 5; + A.coeffRef(2, 2) = 4; + A.coeffRef(3, 3) = 3; + A.coeffRef(4, 4) = 2; + A.coeffRef(5, 5) = 1; + Vector initial = Vector6::Random(); PowerMethod pf(A, initial); - pf.compute(20, 1e-4); - EXPECT_LONGS_EQUAL(1, pf.eigenvectors().cols()); - EXPECT_LONGS_EQUAL(6, pf.eigenvectors().rows()); + pf.compute(50, 1e-4); + EXPECT_LONGS_EQUAL(6, pf.eigenvector().rows()); const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); - Vector6 actual0 = pf.eigenvectors(); - EXPECT(assert_equal(x1, actual0)); + Vector6 actual0 = pf.eigenvector(); + EXPECT(assert_equal(x1, actual0, 1e-4)); - const double ev1 = 1.0; - EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues(), 1e-5); + const double ev1 = 6.0; + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-5); } /* ************************************************************************* */ @@ -89,12 +88,12 @@ TEST(PowerMethod, useFactorGraph) { const auto ev1 = solver.eigenvalues()(maxIdx).real(); auto ev2 = solver.eigenvectors().col(maxIdx).real(); - Vector initial = Vector4::Zero(); + Vector initial = Vector4::Random(); PowerMethod pf(L.first, initial); - pf.compute(20, 1e-4); - EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalues(), 1e-8); - // auto actual2 = pf.eigenvectors(); - // EXPECT(assert_equal(ev2, actual2, 3e-5)); + pf.compute(50, 1e-4); + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-8); + auto actual2 = pf.eigenvector(); + EXPECT(assert_equal(-ev2, actual2, 3e-5)); } /* ************************************************************************* */ From 32bf81efeacd6057f9aa06ee401bc8176e8a0d3f Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Thu, 22 Oct 2020 15:51:36 -0400 Subject: [PATCH 10/65] Added more detailed documentation --- gtsam/linear/AcceleratedPowerMethod.h | 3 +-- gtsam/linear/PowerMethod.h | 10 ++++---- .../tests/testAcceleratedPowerMethod.cpp | 24 ++++++++++--------- gtsam/linear/tests/testPowerMethod.cpp | 16 ++++++------- gtsam/sfm/ShonanAveraging.cpp | 3 +++ 5 files changed, 30 insertions(+), 26 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 0ad87626b..2e54775d9 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -80,8 +80,7 @@ class AcceleratedPowerMethod : public PowerMethod { } else { beta_ = initialBeta; } - - } + } // Update the ritzVector with beta and previous two ritzVector Vector powerIteration(const Vector &x1, const Vector &x0, diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index ee7a04429..acb583296 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -89,14 +89,16 @@ class PowerMethod { // Return the number of iterations size_t nrIterations() const { return nrIterations_; } - // Start the power/accelerated iteration, after updated the ritz vector, - // calculate the ritz error, repeat this operation until the ritz error converge - int compute(size_t maxIterations, double tol) { + // Start the power/accelerated iteration, after performing the + // power/accelerated power iteration, calculate the ritz error, repeat this + // operation until the ritz error converge. If converged return true, else + // false. + bool compute(size_t maxIterations, double tol) { // Starting bool isConverged = false; for (size_t i = 0; i < maxIterations; i++) { - ++nrIterations_ ; + ++nrIterations_; ritzVector_ = powerIteration(); isConverged = converged(tol); if (isConverged) return isConverged; diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index 474492475..b72556e0a 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -18,18 +18,16 @@ * @brief Check eigenvalue and eigenvector computed by accelerated power method */ +#include #include #include #include -#include #include - -#include +#include #include #include #include - #include #include @@ -70,7 +68,7 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { for (size_t j = 0; j < 3; j++) { fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); } - fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); @@ -79,22 +77,26 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { // Check that we get zero eigenvalue and "constant" eigenvector EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); auto v0 = solver.eigenvectors().col(0); - for (size_t j = 0; j < 3; j++) - EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); size_t maxIdx = 0; - for (auto i =0; i= solver.eigenvalues()(maxIdx).real()) maxIdx = i; + for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { + if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) + maxIdx = i; } // Store the max eigenvalue and its according eigenvector const auto ev1 = solver.eigenvalues()(maxIdx).real(); auto ev2 = solver.eigenvectors().col(maxIdx).real(); - Vector initial = Vector4::Random(); + Vector disturb = Vector4::Random(); + disturb.normalize(); + Vector initial = L.first.row(0); + double magnitude = initial.norm(); + initial += 0.03 * magnitude * disturb; AcceleratedPowerMethod apf(L.first, initial); apf.compute(50, 1e-4); EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-8); - EXPECT(assert_equal(-ev2, apf.eigenvector(), 3e-5)); + EXPECT(assert_equal(ev2, apf.eigenvector(), 3e-5)); } /* ************************************************************************* */ diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 58d1ca0cc..7f6d1efa7 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -18,18 +18,16 @@ * @brief Check eigenvalue and eigenvector computed by power method */ +#include #include #include #include #include #include -#include - #include #include #include - #include #include @@ -68,7 +66,7 @@ TEST(PowerMethod, useFactorGraph) { for (size_t j = 0; j < 3; j++) { fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); } - fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); @@ -77,12 +75,12 @@ TEST(PowerMethod, useFactorGraph) { // Check that we get zero eigenvalue and "constant" eigenvector EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); auto v0 = solver.eigenvectors().col(0); - for (size_t j = 0; j < 3; j++) - EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); size_t maxIdx = 0; - for (auto i =0; i= solver.eigenvalues()(maxIdx).real()) maxIdx = i; + for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { + if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) + maxIdx = i; } // Store the max eigenvalue and its according eigenvector const auto ev1 = solver.eigenvalues()(maxIdx).real(); @@ -92,7 +90,7 @@ TEST(PowerMethod, useFactorGraph) { PowerMethod pf(L.first, initial); pf.compute(50, 1e-4); EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-8); - auto actual2 = pf.eigenvector(); + auto actual2 = pf.eigenvector(); EXPECT(assert_equal(-ev2, actual2, 3e-5)); } diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 60233fc6e..50b38f75b 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -482,6 +482,9 @@ Sparse ShonanAveraging::computeA(const Matrix &S) const { // Perturb the initial initialVector by adding a spherically-uniformly // distributed random vector with 0.03*||initialVector||_2 magnitude to // initialVector +// ref : Part III. C, Rosen, D. and Carlone, L., 2017, September. Computational +// enhancements for certifiably correct SLAM. In Proceedings of the +// International Conference on Intelligent Robots and Systems. Vector perturb(const Vector &initialVector) { // generate a 0.03*||x_0||_2 as stated in David's paper int n = initialVector.rows(); From 56300ca23c292f2e1142600fd3de8c0b7dbedc8d Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Thu, 22 Oct 2020 18:05:09 -0400 Subject: [PATCH 11/65] Fixed not solve errors and detailed documentation --- gtsam/linear/AcceleratedPowerMethod.h | 33 +++++++++---------- gtsam/linear/PowerMethod.h | 6 ++-- .../tests/testAcceleratedPowerMethod.cpp | 2 +- gtsam/sfm/ShonanAveraging.cpp | 28 ++++++++-------- 4 files changed, 33 insertions(+), 36 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 2e54775d9..a5148e1d4 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -63,16 +63,10 @@ class AcceleratedPowerMethod : public PowerMethod { const Operator &A, const boost::optional initial = boost::none, const double initialBeta = 0.0) : PowerMethod(A, initial) { - Vector x0; - // initialize ritz vector - x0 = initial ? initial.get() : Vector::Random(this->dim_); - Vector x00 = Vector::Random(this->dim_); - x0.normalize(); - x00.normalize(); - // initialize Ritz eigen vector and previous vector - previousVector_ = powerIteration(x0, x00, beta_); - this->ritzVector_ = powerIteration(previousVector_, x0, beta_); + this->ritzVector_ = initial ? initial.get() : Vector::Random(this->dim_); + this->ritzVector_.normalize(); + previousVector_ = Vector::Zero(this->dim_); // initialize beta_ if (!initialBeta) { @@ -80,9 +74,10 @@ class AcceleratedPowerMethod : public PowerMethod { } else { beta_ = initialBeta; } - } + } - // Update the ritzVector with beta and previous two ritzVector + // Update the ritzVector with beta and previous two ritzVector, and return + // x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - \beta * x_{k-1} || Vector powerIteration(const Vector &x1, const Vector &x0, const double beta) const { Vector y = this->A_ * x1 - beta * x0; @@ -90,7 +85,8 @@ class AcceleratedPowerMethod : public PowerMethod { return y; } - // Update the ritzVector with beta and previous two ritzVector + // Update the ritzVector with beta and previous two ritzVector, and return + // x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - \beta * x_{k-1} || Vector powerIteration() const { Vector y = powerIteration(this->ritzVector_, previousVector_, beta_); previousVector_ = this->ritzVector_; @@ -101,8 +97,8 @@ class AcceleratedPowerMethod : public PowerMethod { void estimateBeta() { // set beta Vector init_resid = this->ritzVector_; - const double up = init_resid.transpose() * this->A_ * init_resid; - const double down = init_resid.transpose().dot(init_resid); + const double up = init_resid.dot( this->A_ * init_resid ); + const double down = init_resid.dot(init_resid); const double mu = up / down; double maxBeta = mu * mu / 4; size_t maxIndex; @@ -111,11 +107,12 @@ class AcceleratedPowerMethod : public PowerMethod { Matrix R = Matrix::Zero(this->dim_, 10); for (size_t i = 0; i < 10; i++) { + Vector x0 = Vector::Random(this->dim_); + x0.normalize(); + Vector x00 = Vector::Zero(this->dim_); for (size_t k = 0; k < betas.size(); ++k) { for (size_t j = 1; j < 10; j++) { if (j < 2) { - Vector x0 = this->ritzVector_; - Vector x00 = previousVector_; R.col(0) = powerIteration(x0, x00, betas[k]); R.col(1) = powerIteration(R.col(0), x0, betas[k]); } else { @@ -123,8 +120,8 @@ class AcceleratedPowerMethod : public PowerMethod { } } const Vector x = R.col(9); - const double up = x.transpose() * this->A_ * x; - const double down = x.transpose().dot(x); + const double up = x.dot(this->A_ * x); + const double down = x.dot(x); const double mu = up / down; if (mu * mu / 4 > maxBeta) { maxIndex = k; diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index acb583296..8a577aa92 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -61,19 +61,19 @@ class PowerMethod { // initialize Ritz eigen value ritzValue_ = 0.0; - // initialize Ritz eigen vectors + // initialize Ritz eigen vector ritzVector_ = Vector::Zero(dim_); ritzVector_ = powerIteration(x0); } - // Update the vector by dot product with A_ + // Update the vector by dot product with A_, and return A * x / || A * x || Vector powerIteration(const Vector &x) const { Vector y = A_ * x; y.normalize(); return y; } - // Update the vector by dot product with A_ + // Update the vector by dot product with A_, and return A * x / || A * x || Vector powerIteration() const { return powerIteration(ritzVector_); } // After Perform power iteration on a single Ritz value, if the error is less diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index b72556e0a..6179d6ca6 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -96,7 +96,7 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { AcceleratedPowerMethod apf(L.first, initial); apf.compute(50, 1e-4); EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-8); - EXPECT(assert_equal(ev2, apf.eigenvector(), 3e-5)); + EXPECT(assert_equal(ev2, apf.eigenvector(), 4e-5)); } /* ************************************************************************* */ diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 50b38f75b..8d2bf4653 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -515,42 +515,42 @@ static bool PowerMinimumEigenValue( double minEigenvalueNonnegativityTolerance = 10e-4) { // a. Compute dominant eigenpair of S using power method - PowerMethod lmOperator(A); + PowerMethod pmOperator(A); - const bool lmConverged = lmOperator.compute( + const bool pmConverged = pmOperator.compute( maxIterations, 1e-5); // Check convergence and bail out if necessary - if (!lmConverged) return false; + if (!pmConverged) return false; - const double lmEigenValue = lmOperator.eigenvalue(); + const double pmEigenValue = pmOperator.eigenvalue(); - if (lmEigenValue < 0) { + if (pmEigenValue < 0) { // The largest-magnitude eigenvalue is negative, and therefore also the // minimum eigenvalue, so just return this solution - *minEigenValue = lmEigenValue; + *minEigenValue = pmEigenValue; if (minEigenVector) { - *minEigenVector = lmOperator.eigenvector(); + *minEigenVector = pmOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector } return true; } - const Sparse C = lmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; + const Sparse C = pmEigenValue * Matrix::Identity(A.rows(), A.cols()) - A; const boost::optional initial = perturb(S.row(0)); - AcceleratedPowerMethod minShiftedOperator(C, initial); + AcceleratedPowerMethod apmShiftedOperator(C, initial); - const bool minConverged = minShiftedOperator.compute( - maxIterations, minEigenvalueNonnegativityTolerance / lmEigenValue); + const bool minConverged = apmShiftedOperator.compute( + maxIterations, minEigenvalueNonnegativityTolerance / pmEigenValue); if (!minConverged) return false; - *minEigenValue = lmEigenValue - minShiftedOperator.eigenvalue(); + *minEigenValue = pmEigenValue - apmShiftedOperator.eigenvalue(); if (minEigenVector) { - *minEigenVector = minShiftedOperator.eigenvector(); + *minEigenVector = apmShiftedOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector } - if (numIterations) *numIterations = minShiftedOperator.nrIterations(); + if (numIterations) *numIterations = apmShiftedOperator.nrIterations(); return true; } From cf813c5a64b213ffd46a7ae7a6add1a2f342b80c Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 26 Oct 2020 15:40:49 -0400 Subject: [PATCH 12/65] Revised as David's second review --- gtsam/linear/AcceleratedPowerMethod.h | 78 +++++++++++++++++++-------- gtsam/linear/PowerMethod.h | 23 ++++---- gtsam/sfm/ShonanAveraging.cpp | 10 ++-- 3 files changed, 75 insertions(+), 36 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index a5148e1d4..eea007353 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -61,7 +61,7 @@ class AcceleratedPowerMethod : public PowerMethod { // vector as ritzVector explicit AcceleratedPowerMethod( const Operator &A, const boost::optional initial = boost::none, - const double initialBeta = 0.0) + double initialBeta = 0.0) : PowerMethod(A, initial) { // initialize Ritz eigen vector and previous vector this->ritzVector_ = initial ? initial.get() : Vector::Random(this->dim_); @@ -76,61 +76,97 @@ class AcceleratedPowerMethod : public PowerMethod { } } - // Update the ritzVector with beta and previous two ritzVector, and return - // x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - \beta * x_{k-1} || - Vector powerIteration(const Vector &x1, const Vector &x0, + // Run accelerated power iteration on the ritzVector with beta and previous + // two ritzVector, and return x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k + // - \beta * x_{k-1} || + Vector acceleratedPowerIteration (const Vector &x1, const Vector &x0, const double beta) const { Vector y = this->A_ * x1 - beta * x0; y.normalize(); return y; } - // Update the ritzVector with beta and previous two ritzVector, and return - // x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - \beta * x_{k-1} || - Vector powerIteration() const { - Vector y = powerIteration(this->ritzVector_, previousVector_, beta_); - previousVector_ = this->ritzVector_; + // Run accelerated power iteration on the ritzVector with beta and previous + // two ritzVector, and return x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k + // - \beta * x_{k-1} || + Vector acceleratedPowerIteration () const { + Vector y = acceleratedPowerIteration(this->ritzVector_, previousVector_, beta_); return y; } // Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) void estimateBeta() { // set beta - Vector init_resid = this->ritzVector_; - const double up = init_resid.dot( this->A_ * init_resid ); - const double down = init_resid.dot(init_resid); + Vector initVector = this->ritzVector_; + const double up = initVector.dot( this->A_ * initVector ); + const double down = initVector.dot(initVector); const double mu = up / down; double maxBeta = mu * mu / 4; size_t maxIndex; - std::vector betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, - 1.01 * maxBeta, 1.5 * maxBeta}; + std::vector betas; Matrix R = Matrix::Zero(this->dim_, 10); - for (size_t i = 0; i < 10; i++) { - Vector x0 = Vector::Random(this->dim_); - x0.normalize(); - Vector x00 = Vector::Zero(this->dim_); + size_t T = 10; + // run T times of iteration to find the beta that has the largest Rayleigh quotient + for (size_t t = 0; t < T; t++) { + // after each t iteration, reset the betas with the current maxBeta + betas = {2 / 3 * maxBeta, 0.99 * maxBeta, maxBeta, 1.01 * maxBeta, + 1.5 * maxBeta}; + // iterate through every beta value for (size_t k = 0; k < betas.size(); ++k) { + // initialize x0 and x00 in each iteration of each beta + Vector x0 = initVector; + Vector x00 = Vector::Zero(this->dim_); + // run 10 steps of accelerated power iteration with this beta for (size_t j = 1; j < 10; j++) { if (j < 2) { - R.col(0) = powerIteration(x0, x00, betas[k]); - R.col(1) = powerIteration(R.col(0), x0, betas[k]); + R.col(0) = acceleratedPowerIteration(x0, x00, betas[k]); + R.col(1) = acceleratedPowerIteration(R.col(0), x0, betas[k]); } else { - R.col(j) = powerIteration(R.col(j - 1), R.col(j - 2), betas[k]); + R.col(j) = acceleratedPowerIteration(R.col(j - 1), R.col(j - 2), betas[k]); } } + // compute the Rayleigh quotient for the randomly sampled vector after + // 10 steps of power accelerated iteration const Vector x = R.col(9); const double up = x.dot(this->A_ * x); const double down = x.dot(x); const double mu = up / down; + // store the momentum with largest Rayleigh quotient and its according index of beta_ if (mu * mu / 4 > maxBeta) { + // save the max beta index maxIndex = k; maxBeta = mu * mu / 4; } } } + // set beta_ to momentum with largest Rayleigh quotient beta_ = betas[maxIndex]; } + + // Start the accelerated iteration, after performing the + // accelerated iteration, calculate the ritz error, repeat this + // operation until the ritz error converge. If converged return true, else + // false. + bool compute(size_t maxIterations, double tol) { + // Starting + bool isConverged = false; + + for (size_t i = 0; i < maxIterations; i++) { + ++(this->nrIterations_); + Vector tmp = this->ritzVector_; + // update the ritzVector after accelerated power iteration + this->ritzVector_ = acceleratedPowerIteration(); + // update the previousVector with ritzVector + previousVector_ = tmp; + // update the ritzValue + this->ritzValue_ = this->ritzVector_.dot(this->A_ * this->ritzVector_); + isConverged = this->converged(tol); + if (isConverged) return isConverged; + } + + return isConverged; + } }; } // namespace gtsam diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index 8a577aa92..ae1d97cc7 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -66,23 +66,24 @@ class PowerMethod { ritzVector_ = powerIteration(x0); } - // Update the vector by dot product with A_, and return A * x / || A * x || + // Run power iteration on the vector, and return A * x / || A * x || Vector powerIteration(const Vector &x) const { Vector y = A_ * x; y.normalize(); return y; } - // Update the vector by dot product with A_, and return A * x / || A * x || + // Run power iteration on the vector, and return A * x / || A * x || Vector powerIteration() const { return powerIteration(ritzVector_); } - // After Perform power iteration on a single Ritz value, if the error is less - // than the tol then return true else false - bool converged(double tol) { + // After Perform power iteration on a single Ritz value, check if the Ritz + // residual for the current Ritz pair is less than the required convergence + // tol, return true if yes, else false + bool converged(double tol) const { const Vector x = ritzVector_; // store the Ritz eigen value - ritzValue_ = x.dot(A_ * x); - double error = (A_ * x - ritzValue_ * x).norm(); + const double ritzValue = x.dot(A_ * x); + const double error = (A_ * x - ritzValue * x).norm(); return error < tol; } @@ -90,18 +91,20 @@ class PowerMethod { size_t nrIterations() const { return nrIterations_; } // Start the power/accelerated iteration, after performing the - // power/accelerated power iteration, calculate the ritz error, repeat this + // power/accelerated iteration, calculate the ritz error, repeat this // operation until the ritz error converge. If converged return true, else // false. bool compute(size_t maxIterations, double tol) { // Starting bool isConverged = false; - for (size_t i = 0; i < maxIterations; i++) { + for (size_t i = 0; i < maxIterations && !isConverged; i++) { ++nrIterations_; + // update the ritzVector after power iteration ritzVector_ = powerIteration(); + // update the ritzValue + ritzValue_ = ritzVector_.dot(A_ * ritzVector_); isConverged = converged(tol); - if (isConverged) return isConverged; } return isConverged; diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index 8d2bf4653..fab57c828 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -509,7 +509,7 @@ Vector perturb(const Vector &initialVector) { // compute the maximum eigenpair (\theta, \vect{v}) of C = \lamda_dom * I - A by // accelerated power method. Then return (\lamda_dom - \theta, \vect{v}). static bool PowerMinimumEigenValue( - const Sparse &A, const Matrix &S, double *minEigenValue, + const Sparse &A, const Matrix &S, double &minEigenValue, Vector *minEigenVector = 0, size_t *numIterations = 0, size_t maxIterations = 1000, double minEigenvalueNonnegativityTolerance = 10e-4) { @@ -528,7 +528,7 @@ static bool PowerMinimumEigenValue( if (pmEigenValue < 0) { // The largest-magnitude eigenvalue is negative, and therefore also the // minimum eigenvalue, so just return this solution - *minEigenValue = pmEigenValue; + minEigenValue = pmEigenValue; if (minEigenVector) { *minEigenVector = pmOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector @@ -545,7 +545,7 @@ static bool PowerMinimumEigenValue( if (!minConverged) return false; - *minEigenValue = pmEigenValue - apmShiftedOperator.eigenvalue(); + minEigenValue = pmEigenValue - apmShiftedOperator.eigenvalue(); if (minEigenVector) { *minEigenVector = apmShiftedOperator.eigenvector(); minEigenVector->normalize(); // Ensure that this is a unit vector @@ -723,8 +723,8 @@ double ShonanAveraging::computeMinEigenValueAP(const Values &values, const Matrix S = StiefelElementMatrix(values); auto A = computeA(S); - double minEigenValue; - bool success = PowerMinimumEigenValue(A, S, &minEigenValue, minEigenVector); + double minEigenValue = 0; + bool success = PowerMinimumEigenValue(A, S, minEigenValue, minEigenVector); if (!success) { throw std::runtime_error( "PowerMinimumEigenValue failed to compute minimum eigenvalue."); From 4ee4014d7a345fc410461c1d2855ef296b8820ba Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 26 Oct 2020 15:41:01 -0400 Subject: [PATCH 13/65] Refined unittest --- .../tests/testAcceleratedPowerMethod.cpp | 23 +++++++++++++------ gtsam/linear/tests/testPowerMethod.cpp | 15 +++++++----- 2 files changed, 25 insertions(+), 13 deletions(-) diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index 6179d6ca6..228ce157c 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -45,17 +45,19 @@ TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { A.coeffRef(3, 3) = 3; A.coeffRef(4, 4) = 2; A.coeffRef(5, 5) = 1; - Vector initial = Vector6::Random(); - const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); + Vector initial = (Vector(6) << 0.24434602, 0.22829942, 0.70094486, 0.15463092, 0.55871359, + 0.2465342).finished(); const double ev1 = 6.0; // test accelerated power iteration AcceleratedPowerMethod apf(A, initial); - apf.compute(50, 1e-4); + apf.compute(100, 1e-5); EXPECT_LONGS_EQUAL(6, apf.eigenvector().rows()); Vector6 actual1 = apf.eigenvector(); - EXPECT(assert_equal(x1, actual1, 1e-4)); + const double ritzValue = actual1.dot(A * actual1); + const double ritzResidual = (A * actual1 - ritzValue * actual1).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-5); } @@ -79,6 +81,7 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { auto v0 = solver.eigenvectors().col(0); for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + // find the index of the max eigenvalue size_t maxIdx = 0; for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) @@ -86,7 +89,6 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { } // Store the max eigenvalue and its according eigenvector const auto ev1 = solver.eigenvalues()(maxIdx).real(); - auto ev2 = solver.eigenvectors().col(maxIdx).real(); Vector disturb = Vector4::Random(); disturb.normalize(); @@ -94,9 +96,16 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { double magnitude = initial.norm(); initial += 0.03 * magnitude * disturb; AcceleratedPowerMethod apf(L.first, initial); - apf.compute(50, 1e-4); + apf.compute(100, 1e-5); + // Check if the eigenvalue is the maximum eigen value EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-8); - EXPECT(assert_equal(ev2, apf.eigenvector(), 4e-5)); + + // Check if the according ritz residual converged to the threshold + Vector actual1 = apf.eigenvector(); + const double ritzValue = actual1.dot(L.first * actual1); + const double ritzResidual = (L.first * actual1 - ritzValue * actual1).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); + // Check } /* ************************************************************************* */ diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 7f6d1efa7..4c96c5bca 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -45,14 +45,16 @@ TEST(PowerMethod, powerIteration) { A.coeffRef(3, 3) = 3; A.coeffRef(4, 4) = 2; A.coeffRef(5, 5) = 1; - Vector initial = Vector6::Random(); + Vector initial = (Vector(6) << 0.24434602, 0.22829942, 0.70094486, 0.15463092, 0.55871359, + 0.2465342).finished(); PowerMethod pf(A, initial); - pf.compute(50, 1e-4); + pf.compute(100, 1e-5); EXPECT_LONGS_EQUAL(6, pf.eigenvector().rows()); - const Vector6 x1 = (Vector(6) << 1.0, 0.0, 0.0, 0.0, 0.0, 0.0).finished(); - Vector6 actual0 = pf.eigenvector(); - EXPECT(assert_equal(x1, actual0, 1e-4)); + Vector6 actual1 = pf.eigenvector(); + const double ritzValue = actual1.dot(A * actual1); + const double ritzResidual = (A * actual1 - ritzValue * actual1).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); const double ev1 = 6.0; EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-5); @@ -77,6 +79,7 @@ TEST(PowerMethod, useFactorGraph) { auto v0 = solver.eigenvectors().col(0); for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); + // find the index of the max eigenvalue size_t maxIdx = 0; for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) @@ -91,7 +94,7 @@ TEST(PowerMethod, useFactorGraph) { pf.compute(50, 1e-4); EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-8); auto actual2 = pf.eigenvector(); - EXPECT(assert_equal(-ev2, actual2, 3e-5)); + EXPECT(assert_equal(ev2, actual2, 3e-5)); } /* ************************************************************************* */ From f604a9784de84a3c9699be737f295e77976b9a5b Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Sun, 1 Nov 2020 20:45:59 -0500 Subject: [PATCH 14/65] Delete forcing compare eigenvector in unittest --- gtsam/linear/tests/testAcceleratedPowerMethod.cpp | 6 ------ gtsam/linear/tests/testPowerMethod.cpp | 5 ----- 2 files changed, 11 deletions(-) diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index 228ce157c..dd593e7d3 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -76,11 +76,6 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { auto L = fg.hessian(); Eigen::EigenSolver solver(L.first); - // Check that we get zero eigenvalue and "constant" eigenvector - EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); - auto v0 = solver.eigenvectors().col(0); - for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); - // find the index of the max eigenvalue size_t maxIdx = 0; for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { @@ -105,7 +100,6 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { const double ritzValue = actual1.dot(L.first * actual1); const double ritzResidual = (L.first * actual1 - ritzValue * actual1).norm(); EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); - // Check } /* ************************************************************************* */ diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 4c96c5bca..ccac4556c 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -74,11 +74,6 @@ TEST(PowerMethod, useFactorGraph) { auto L = fg.hessian(); Eigen::EigenSolver solver(L.first); - // Check that we get zero eigenvalue and "constant" eigenvector - EXPECT_DOUBLES_EQUAL(0.0, solver.eigenvalues()[0].real(), 1e-9); - auto v0 = solver.eigenvectors().col(0); - for (size_t j = 0; j < 3; j++) EXPECT_DOUBLES_EQUAL(-0.5, v0[j].real(), 1e-9); - // find the index of the max eigenvalue size_t maxIdx = 0; for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { From 70cecb3a61d14f1b1f960f888b1a93f42a43eed6 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Sun, 1 Nov 2020 20:46:42 -0500 Subject: [PATCH 15/65] Revised documentation --- gtsam/linear/AcceleratedPowerMethod.h | 13 ++++++------- 1 file changed, 6 insertions(+), 7 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index eea007353..0c544f05c 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -77,8 +77,8 @@ class AcceleratedPowerMethod : public PowerMethod { } // Run accelerated power iteration on the ritzVector with beta and previous - // two ritzVector, and return x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - // - \beta * x_{k-1} || + // two ritzVector, and return y = (A * x0 - \beta * x00) / || A * x0 + // - \beta * x00 || Vector acceleratedPowerIteration (const Vector &x1, const Vector &x0, const double beta) const { Vector y = this->A_ * x1 - beta * x0; @@ -87,8 +87,8 @@ class AcceleratedPowerMethod : public PowerMethod { } // Run accelerated power iteration on the ritzVector with beta and previous - // two ritzVector, and return x_{k+1} = A * x_k - \beta * x_{k-1} / || A * x_k - // - \beta * x_{k-1} || + // two ritzVector, and return y = (A * x0 - \beta * x00) / || A * x0 + // - \beta * x00 || Vector acceleratedPowerIteration () const { Vector y = acceleratedPowerIteration(this->ritzVector_, previousVector_, beta_); return y; @@ -96,7 +96,7 @@ class AcceleratedPowerMethod : public PowerMethod { // Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) void estimateBeta() { - // set beta + // set initial estimation of maxBeta Vector initVector = this->ritzVector_; const double up = initVector.dot( this->A_ * initVector ); const double down = initVector.dot(initVector); @@ -152,7 +152,7 @@ class AcceleratedPowerMethod : public PowerMethod { // Starting bool isConverged = false; - for (size_t i = 0; i < maxIterations; i++) { + for (size_t i = 0; i < maxIterations && !isConverged; i++) { ++(this->nrIterations_); Vector tmp = this->ritzVector_; // update the ritzVector after accelerated power iteration @@ -162,7 +162,6 @@ class AcceleratedPowerMethod : public PowerMethod { // update the ritzValue this->ritzValue_ = this->ritzVector_.dot(this->A_ * this->ritzVector_); isConverged = this->converged(tol); - if (isConverged) return isConverged; } return isConverged; From abfc98e13d738c4ac4e97147e52a2cacecd7347c Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 2 Nov 2020 15:39:39 -0500 Subject: [PATCH 16/65] Fixed forcing comparing eigenvector. --- gtsam/linear/tests/testPowerMethod.cpp | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index ccac4556c..2e0f2152b 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -82,14 +82,15 @@ TEST(PowerMethod, useFactorGraph) { } // Store the max eigenvalue and its according eigenvector const auto ev1 = solver.eigenvalues()(maxIdx).real(); - auto ev2 = solver.eigenvectors().col(maxIdx).real(); Vector initial = Vector4::Random(); PowerMethod pf(L.first, initial); - pf.compute(50, 1e-4); + pf.compute(100, 1e-5); EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-8); auto actual2 = pf.eigenvector(); - EXPECT(assert_equal(ev2, actual2, 3e-5)); + const double ritzValue = actual2.dot(L.first * actual2); + const double ritzResidual = (L.first * actual2 - ritzValue * actual2).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); } /* ************************************************************************* */ From 6d9f95d32eff60b4635bc665e94fab081f4c66db Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Sun, 15 Nov 2020 22:49:36 -0500 Subject: [PATCH 17/65] Fixed doxygen --- gtsam/linear/AcceleratedPowerMethod.h | 89 ++++++++++++++------------- gtsam/linear/PowerMethod.h | 70 +++++++++++++++------ 2 files changed, 96 insertions(+), 63 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 0c544f05c..0699f237e 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -19,46 +19,44 @@ #pragma once -// #include -// #include #include namespace gtsam { using Sparse = Eigen::SparseMatrix; -/* ************************************************************************* */ -/// MINIMUM EIGENVALUE COMPUTATIONS - -// Template argument Operator just needs multiplication operator +/** + * \brief Compute maximum Eigenpair with accelerated power method + * + * References : + * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * enhancements for certifiably correct SLAM. In Proceedings of the + * International Conference on Intelligent Robots and Systems. + * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv + * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. + * 58–67 + * + * It performs the following iteration: \f$ x_{k+1} = A * x_k - \beta * + * x_{k-1} \f$ where A is the aim matrix we want to get eigenpair of, x is the + * Ritz vector + * + * Template argument Operator just needs multiplication operator + * + */ template class AcceleratedPowerMethod : public PowerMethod { - /** - * \brief Compute maximum Eigenpair with accelerated power method - * - * References : - * 1) Rosen, D. and Carlone, L., 2017, September. Computational - * enhancements for certifiably correct SLAM. In Proceedings of the - * International Conference on Intelligent Robots and Systems. - * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, - * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv - * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated - * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. - * 58–67 - * - * It performs the following iteration: \f$ x_{k+1} = A * x_k - \beta * - * x_{k-1} \f$ where A is the aim matrix we want to get eigenpair of, x is the - * Ritz vector - * - */ double beta_ = 0; // a Polyak momentum term Vector previousVector_; // store previous vector public: - // Constructor from aim matrix A (given as Matrix or Sparse), optional intial - // vector as ritzVector + /** + * Constructor from aim matrix A (given as Matrix or Sparse), optional intial + * vector as ritzVector + */ explicit AcceleratedPowerMethod( const Operator &A, const boost::optional initial = boost::none, double initialBeta = 0.0) @@ -70,15 +68,16 @@ class AcceleratedPowerMethod : public PowerMethod { // initialize beta_ if (!initialBeta) { - estimateBeta(); - } else { + beta_ = estimateBeta(); + } else beta_ = initialBeta; - } } - // Run accelerated power iteration on the ritzVector with beta and previous - // two ritzVector, and return y = (A * x0 - \beta * x00) / || A * x0 - // - \beta * x00 || + /** + * Run accelerated power iteration to get ritzVector with beta and previous + * two ritzVector x0 and x00, and return y = (A * x0 - \beta * x00) / || A * x0 + * - \beta * x00 || + */ Vector acceleratedPowerIteration (const Vector &x1, const Vector &x0, const double beta) const { Vector y = this->A_ * x1 - beta * x0; @@ -86,16 +85,18 @@ class AcceleratedPowerMethod : public PowerMethod { return y; } - // Run accelerated power iteration on the ritzVector with beta and previous - // two ritzVector, and return y = (A * x0 - \beta * x00) / || A * x0 - // - \beta * x00 || + /** + * Run accelerated power iteration to get ritzVector with beta and previous + * two ritzVector x0 and x00, and return y = (A * x0 - \beta * x00) / || A * x0 + * - \beta * x00 || + */ Vector acceleratedPowerIteration () const { Vector y = acceleratedPowerIteration(this->ritzVector_, previousVector_, beta_); return y; } - // Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) - void estimateBeta() { + /// Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) + double estimateBeta() const { // set initial estimation of maxBeta Vector initVector = this->ritzVector_; const double up = initVector.dot( this->A_ * initVector ); @@ -106,7 +107,7 @@ class AcceleratedPowerMethod : public PowerMethod { std::vector betas; Matrix R = Matrix::Zero(this->dim_, 10); - size_t T = 10; + const size_t T = 10; // run T times of iteration to find the beta that has the largest Rayleigh quotient for (size_t t = 0; t < T; t++) { // after each t iteration, reset the betas with the current maxBeta @@ -141,13 +142,15 @@ class AcceleratedPowerMethod : public PowerMethod { } } // set beta_ to momentum with largest Rayleigh quotient - beta_ = betas[maxIndex]; + return betas[maxIndex]; } - // Start the accelerated iteration, after performing the - // accelerated iteration, calculate the ritz error, repeat this - // operation until the ritz error converge. If converged return true, else - // false. + /** + * Start the accelerated iteration, after performing the + * accelerated iteration, calculate the ritz error, repeat this + * operation until the ritz error converge. If converged return true, else + * false. + */ bool compute(size_t maxIterations, double tol) { // Starting bool isConverged = false; diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index ae1d97cc7..a209c5779 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -31,15 +31,33 @@ namespace gtsam { using Sparse = Eigen::SparseMatrix; -/* ************************************************************************* */ -/// MINIMUM EIGENVALUE COMPUTATIONS - -// Template argument Operator just needs multiplication operator +/** + * \brief Compute maximum Eigenpair with power method + * + * References : + * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * enhancements for certifiably correct SLAM. In Proceedings of the + * International Conference on Intelligent Robots and Systems. + * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv + * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. + * 58–67 + * + * It performs the following iteration: \f$ x_{k+1} = A * x_k \f$ + * where A is the aim matrix we want to get eigenpair of, x is the + * Ritz vector + * + * Template argument Operator just needs multiplication operator + * + */ template class PowerMethod { protected: - // Const reference to an externally-held matrix whose minimum-eigenvalue we - // want to compute + /** + * Const reference to an externally-held matrix whose minimum-eigenvalue we + * want to compute + */ const Operator &A_; const int dim_; // dimension of Matrix A @@ -50,7 +68,10 @@ class PowerMethod { Vector ritzVector_; // Ritz eigenvector public: - // Constructor + /// @name Standard Constructors + /// @{ + + /// Construct from the aim matrix and intial ritz vector explicit PowerMethod(const Operator &A, const boost::optional initial = boost::none) : A_(A), dim_(A.rows()), nrIterations_(0) { @@ -62,23 +83,30 @@ class PowerMethod { ritzValue_ = 0.0; // initialize Ritz eigen vector - ritzVector_ = Vector::Zero(dim_); ritzVector_ = powerIteration(x0); } - // Run power iteration on the vector, and return A * x / || A * x || + /** + * Run power iteration to get ritzVector with previous ritzVector x, and + * return A * x / || A * x || + */ Vector powerIteration(const Vector &x) const { Vector y = A_ * x; y.normalize(); return y; } - // Run power iteration on the vector, and return A * x / || A * x || + /** + * Run power iteration to get ritzVector with previous ritzVector x, and + * return A * x / || A * x || + */ Vector powerIteration() const { return powerIteration(ritzVector_); } - // After Perform power iteration on a single Ritz value, check if the Ritz - // residual for the current Ritz pair is less than the required convergence - // tol, return true if yes, else false + /** + * After Perform power iteration on a single Ritz value, check if the Ritz + * residual for the current Ritz pair is less than the required convergence + * tol, return true if yes, else false + */ bool converged(double tol) const { const Vector x = ritzVector_; // store the Ritz eigen value @@ -87,13 +115,15 @@ class PowerMethod { return error < tol; } - // Return the number of iterations + /// Return the number of iterations size_t nrIterations() const { return nrIterations_; } - // Start the power/accelerated iteration, after performing the - // power/accelerated iteration, calculate the ritz error, repeat this - // operation until the ritz error converge. If converged return true, else - // false. + /** + * Start the power/accelerated iteration, after performing the + * power/accelerated iteration, calculate the ritz error, repeat this + * operation until the ritz error converge. If converged return true, else + * false. + */ bool compute(size_t maxIterations, double tol) { // Starting bool isConverged = false; @@ -110,10 +140,10 @@ class PowerMethod { return isConverged; } - // Return the eigenvalue + /// Return the eigenvalue double eigenvalue() const { return ritzValue_; } - // Return the eigenvector + /// Return the eigenvector Vector eigenvector() const { return ritzVector_; } }; From 844cbead2b4d6e429af9004c1e13262a0ea8faa2 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Mon, 30 Nov 2020 18:52:33 -0500 Subject: [PATCH 18/65] Added dense matrix test case in power/acc --- .../tests/testAcceleratedPowerMethod.cpp | 50 ++++++++++++++++++- gtsam/linear/tests/testPowerMethod.cpp | 43 +++++++++++++++- 2 files changed, 91 insertions(+), 2 deletions(-) diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index dd593e7d3..c7c8e8a55 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -63,7 +63,7 @@ TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { } /* ************************************************************************* */ -TEST(AcceleratedPowerMethod, useFactorGraph) { +TEST(AcceleratedPowerMethod, useFactorGraphSparse) { // Let's make a scalar synchronization graph with 4 nodes GaussianFactorGraph fg; auto model = noiseModel::Unit::Create(1); @@ -102,6 +102,54 @@ TEST(AcceleratedPowerMethod, useFactorGraph) { EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); } +/* ************************************************************************* */ +TEST(AcceleratedPowerMethod, useFactorGraphDense) { + // Let's make a scalar synchronization graph with 10 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + // Each node has an edge with all the others + for (size_t j = 0; j < 10; j++) { + fg.add(X(j), -I_1x1, X((j + 1)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 2)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 3)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 4)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 5)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 6)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 7)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 8)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 9)%10 ), I_1x1, Vector1::Zero(), model); + } + + // Get eigenvalues and eigenvectors with Eigen + auto L = fg.hessian(); + Eigen::EigenSolver solver(L.first); + + // find the index of the max eigenvalue + size_t maxIdx = 0; + for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { + if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) + maxIdx = i; + } + // Store the max eigenvalue and its according eigenvector + const auto ev1 = solver.eigenvalues()(maxIdx).real(); + + Vector disturb = Vector10::Random(); + disturb.normalize(); + Vector initial = L.first.row(0); + double magnitude = initial.norm(); + initial += 0.03 * magnitude * disturb; + AcceleratedPowerMethod apf(L.first, initial); + apf.compute(100, 1e-5); + // Check if the eigenvalue is the maximum eigen value + EXPECT_DOUBLES_EQUAL(ev1, apf.eigenvalue(), 1e-8); + + // Check if the according ritz residual converged to the threshold + Vector actual1 = apf.eigenvector(); + const double ritzValue = actual1.dot(L.first * actual1); + const double ritzResidual = (L.first * actual1 - ritzValue * actual1).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); +} + /* ************************************************************************* */ int main() { TestResult tr; diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 2e0f2152b..7adfd0aa5 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -61,7 +61,7 @@ TEST(PowerMethod, powerIteration) { } /* ************************************************************************* */ -TEST(PowerMethod, useFactorGraph) { +TEST(PowerMethod, useFactorGraphSparse) { // Let's make a scalar synchronization graph with 4 nodes GaussianFactorGraph fg; auto model = noiseModel::Unit::Create(1); @@ -93,6 +93,47 @@ TEST(PowerMethod, useFactorGraph) { EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); } +/* ************************************************************************* */ +TEST(PowerMethod, useFactorGraphDense) { + // Let's make a scalar synchronization graph with 10 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + // Each node has an edge with all the others + for (size_t j = 0; j < 10; j++) { + fg.add(X(j), -I_1x1, X((j + 1)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 2)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 3)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 4)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 5)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 6)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 7)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 8)%10 ), I_1x1, Vector1::Zero(), model); + fg.add(X(j), -I_1x1, X((j + 9)%10 ), I_1x1, Vector1::Zero(), model); + } + + // Get eigenvalues and eigenvectors with Eigen + auto L = fg.hessian(); + Eigen::EigenSolver solver(L.first); + + // find the index of the max eigenvalue + size_t maxIdx = 0; + for (auto i = 0; i < solver.eigenvalues().rows(); ++i) { + if (solver.eigenvalues()(i).real() >= solver.eigenvalues()(maxIdx).real()) + maxIdx = i; + } + // Store the max eigenvalue and its according eigenvector + const auto ev1 = solver.eigenvalues()(maxIdx).real(); + + Vector initial = Vector10::Random(); + PowerMethod pf(L.first, initial); + pf.compute(100, 1e-5); + EXPECT_DOUBLES_EQUAL(ev1, pf.eigenvalue(), 1e-8); + auto actual2 = pf.eigenvector(); + const double ritzValue = actual2.dot(L.first * actual2); + const double ritzResidual = (L.first * actual2 - ritzValue * actual2).norm(); + EXPECT_DOUBLES_EQUAL(0, ritzResidual, 1e-5); +} + /* ************************************************************************* */ int main() { TestResult tr; From 720ac412081602732933004af2263b13974199c5 Mon Sep 17 00:00:00 2001 From: Russell Buchanan Date: Tue, 8 Dec 2020 15:22:01 +0000 Subject: [PATCH 19/65] Adds unit test for imu preintegration of a single step --- tests/ImuMeasurement.h | 23 +++++ tests/Measurement.h | 23 +++++ tests/testImuPreintegration.cpp | 155 ++++++++++++++++++++++++++++++++ 3 files changed, 201 insertions(+) create mode 100644 tests/ImuMeasurement.h create mode 100644 tests/Measurement.h create mode 100644 tests/testImuPreintegration.cpp diff --git a/tests/ImuMeasurement.h b/tests/ImuMeasurement.h new file mode 100644 index 000000000..5ac3d54be --- /dev/null +++ b/tests/ImuMeasurement.h @@ -0,0 +1,23 @@ +#pragma once + +#include + +namespace drs { + +/// +/// \brief Contains data from the IMU mesaurements. +/// +class ImuMeasurement : public Measurement { + public: + enum Name { BODY = 0, RF_FOOT = 1, RH_FOOT = 2 }; + + Name name; ///< Unique string identifier + Eigen::Vector3d I_a_WI; ///< Raw acceleration from the IMU (m/s/s) + Eigen::Vector3d I_w_WI; ///< Raw angular velocity from the IMU (rad/s) + + virtual ~ImuMeasurement() override {} + ImuMeasurement(); + friend std::ostream& operator<<(std::ostream& stream, const ImuMeasurement& meas); +}; + +} // namespace drs diff --git a/tests/Measurement.h b/tests/Measurement.h new file mode 100644 index 000000000..e26c5d918 --- /dev/null +++ b/tests/Measurement.h @@ -0,0 +1,23 @@ +#pragma once + +#include +#include + +namespace drs { + +/// +/// \brief This is the base class for all measurement types. +/// +class Measurement { +public: + EIGEN_MAKE_ALIGNED_OPERATOR_NEW + uint64_t dt; ///< Time since the last message of this type (nanoseconds). + uint64_t time; ///< ROS time message recieved (nanoseconds). + std::string type; ///< The type of message (to enable dynamic/static casting). + + virtual ~Measurement() {} + Measurement(); + Measurement(std::string _type); +}; + +} // namespace drs diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp new file mode 100644 index 000000000..6e3b6396d --- /dev/null +++ b/tests/testImuPreintegration.cpp @@ -0,0 +1,155 @@ +/** + * @file testImuPreintegration.cpp + * @brief Unit tests for IMU Preintegration + * @author Russell Buchanan + **/ + +#include + +#include +#include + +#include +#include +#include +#include + +namespace drs { + +Measurement::Measurement() : dt(0), time(0), type("UNDEFINED") {} + +Measurement::Measurement(std::string _type) : dt(0), time(0), type(_type) {} + +ImuMeasurement::ImuMeasurement() : I_a_WI{0, 0, 0}, I_w_WI{0, 0, 0} { type = "ImuMeasurement"; } + +std::ostream& operator<<(std::ostream& stream, const ImuMeasurement& meas) { + stream << "IMU Measurement at time = " << meas.time << " : \n" + << "dt : " << meas.dt << "\n" + << "I_a_WI: " << meas.I_a_WI.transpose() << "\n" + << "I_w_WI: " << meas.I_w_WI.transpose() << "\n"; + return stream; +} + +} // namespace drs + +using namespace gtsam; + +/* ************************************************************************* */ +/// \brief Uses the GTSAM library to perform IMU preintegration on an acceleration input. +/// +TEST(GtsamLibraryTests, LoadedSimulationData) { + Eigen::Vector3d finalPos; + + std::vector imuMeasurements; + + double accNoiseSigma = 0.001249; + double accBiasRwSigma = 0.000106; + double gyrNoiseSigma = 0.000208; + double gyrBiasRwSigma = 0.000004; + double integrationCovariance = 1e-8; + double biasAccOmegaInt = 1e-5; + + double gravity = 9.81; + double rate = 400.0; // Hz + + /// @todo Update directory to correct location + std::string inFileString = "/home/russell/imu_data.csv"; + std::ofstream outputFile; + outputFile.open("/home/russell/gtsam_output.csv", std::ofstream::out); + std::ifstream inputFile(inFileString); + std::string line; + while (std::getline(inputFile, line)) { + std::stringstream ss(line); + std::string str; + std::vector results; + while (getline(ss, str, ',')) { + results.push_back(std::atof(str.c_str())); + } + drs::ImuMeasurement measurement; + measurement.dt = static_cast(1e9 * (1 / rate)); + measurement.time = results[2]; + measurement.I_a_WI = {results[29], results[30], results[31]}; + measurement.I_w_WI = {results[17], results[18], results[19]}; + imuMeasurements.push_back(measurement); + + // std::cout << "IMU measurement " << measurement << std::endl; + } + + // Assume a Z-up navigation (assuming we are performing optimization in the IMU frame). + boost::shared_ptr imuPreintegratedParams = + gtsam::PreintegratedCombinedMeasurements::Params::MakeSharedU(gravity); + imuPreintegratedParams->accelerometerCovariance = I_3x3 * pow(accNoiseSigma, 2); + imuPreintegratedParams->biasAccCovariance = I_3x3 * pow(accBiasRwSigma, 2); + imuPreintegratedParams->gyroscopeCovariance = I_3x3 * pow(gyrNoiseSigma, 2); + imuPreintegratedParams->biasOmegaCovariance = I_3x3 * pow(gyrBiasRwSigma, 2); + imuPreintegratedParams->integrationCovariance = I_3x3 * integrationCovariance; + imuPreintegratedParams->biasAccOmegaInt = I_6x6 * biasAccOmegaInt; + + // Initial state + gtsam::Pose3 priorPose; + gtsam::Vector3 priorVelocity; + gtsam::imuBias::ConstantBias priorImuBias; + gtsam::PreintegratedCombinedMeasurements imuPreintegrated; + Eigen::Vector3d position; + Eigen::Vector3d velocity; + gtsam::NavState propState; + + gtsam::NavState initialNavState(priorPose, priorVelocity); + + // Bias estimated by my Algorithm + priorImuBias = + gtsam::imuBias::ConstantBias(Eigen::Vector3d(-0.0314648, 0.0219921, 6.95945e-05), + Eigen::Vector3d(4.88581e-08, -1.04971e-09, -0.000122868)); + + // zero bias + // priorImuBias = gtsam::imuBias::ConstantBias(Eigen::Vector3d(0,0,0), + // Eigen::Vector3d(0,0,0)); + + imuPreintegrated = gtsam::PreintegratedCombinedMeasurements(imuPreintegratedParams, priorImuBias); + + // Put header row in output csv + outputFile << "X Position," + << "Y Position," + << "Z Position," + << "X Velocity," + << "Y Velocity," + << "Z Velocity," + << "\n"; + + for (int n = 1; n < imuMeasurements.size(); n++) { //start at 1 to skip header + // integrate + imuPreintegrated.integrateMeasurement(imuMeasurements[n].I_a_WI, imuMeasurements[n].I_w_WI, + 1 / rate); + // predict + propState = imuPreintegrated.predict(initialNavState, priorImuBias); + position = propState.pose().translation(); + velocity = propState.velocity(); + // std::cout << "IMU Position " << position.transpose() << std::endl; + // std::cout << "IMU Velocity " << velocity.transpose() << std::endl; + + // Write to csv + outputFile << std::to_string(position.x()) << "," << std::to_string(position.y()) << "," + << std::to_string(position.z()) << "," << std::to_string(velocity.x()) << "," + << std::to_string(velocity.y()) << "," << std::to_string(velocity.z()) << "," + << "\n"; + } + + outputFile.close(); + + gtsam::Vector3 rotation = propState.pose().rotation().rpy(); + + // Dont have ground truth for x and y position yet + // DOUBLES_EQUAL(0.1, position[0], 1e-2); + // DOUBLES_EQUAL(0.1, position[1], 1e-2); + DOUBLES_EQUAL(0.0, position[2], 1e-2); + + DOUBLES_EQUAL(0.0, rotation[0], 1e-2); + DOUBLES_EQUAL(0.0, rotation[1], 1e-2); + DOUBLES_EQUAL(0.0, rotation[2], 1e-2); +} +/* ************************************************************************* */ +int main() { + TestResult tr; + return TestRegistry::runAllTests(tr); +} +/* ************************************************************************* */ From afb6ebb933308f755f6f4c9384925ed9c6bfc128 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Fri, 11 Dec 2020 01:01:27 -0500 Subject: [PATCH 20/65] Added the example graph in powerMethodExample.h --- gtsam/linear/tests/powerMethodExample.h | 67 +++++++++++++++++++ .../tests/testAcceleratedPowerMethod.cpp | 24 +------ gtsam/linear/tests/testPowerMethod.cpp | 24 +------ 3 files changed, 73 insertions(+), 42 deletions(-) create mode 100644 gtsam/linear/tests/powerMethodExample.h diff --git a/gtsam/linear/tests/powerMethodExample.h b/gtsam/linear/tests/powerMethodExample.h new file mode 100644 index 000000000..f80299386 --- /dev/null +++ b/gtsam/linear/tests/powerMethodExample.h @@ -0,0 +1,67 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * powerMethodExample.h + * + * @file powerMethodExample.h + * @date Nov 2020 + * @author Jing Wu + * @brief Create sparse and dense factor graph for + * PowerMethod/AcceleratedPowerMethod + */ + +#include + +#include + + +namespace gtsam { +namespace linear { +namespace test { +namespace example { + +/* ************************************************************************* */ +inline GaussianFactorGraph createSparseGraph() { + using symbol_shorthand::X; + // Let's make a scalar synchronization graph with 4 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + for (size_t j = 0; j < 3; j++) { + fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); + } + fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + + return fg; +} + +/* ************************************************************************* */ +inline GaussianFactorGraph createDenseGraph() { + using symbol_shorthand::X; + // Let's make a scalar synchronization graph with 10 nodes + GaussianFactorGraph fg; + auto model = noiseModel::Unit::Create(1); + // Iterate over nodes + for (size_t j = 0; j < 10; j++) { + // Each node has an edge with all the others + for (size_t i = 1; i < 10; i++) + fg.add(X(j), -I_1x1, X((j + i) % 10), I_1x1, Vector1::Zero(), model); + } + + return fg; +} + +/* ************************************************************************* */ + +} // namespace example +} // namespace test +} // namespace linear +} // namespace gtsam diff --git a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp index c7c8e8a55..7c4a90936 100644 --- a/gtsam/linear/tests/testAcceleratedPowerMethod.cpp +++ b/gtsam/linear/tests/testAcceleratedPowerMethod.cpp @@ -24,6 +24,7 @@ #include #include #include +#include #include #include @@ -33,7 +34,6 @@ using namespace std; using namespace gtsam; -using symbol_shorthand::X; /* ************************************************************************* */ TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { @@ -65,12 +65,7 @@ TEST(AcceleratedPowerMethod, acceleratedPowerIteration) { /* ************************************************************************* */ TEST(AcceleratedPowerMethod, useFactorGraphSparse) { // Let's make a scalar synchronization graph with 4 nodes - GaussianFactorGraph fg; - auto model = noiseModel::Unit::Create(1); - for (size_t j = 0; j < 3; j++) { - fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); - } - fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + GaussianFactorGraph fg = gtsam::linear::test::example::createSparseGraph(); // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); @@ -105,20 +100,7 @@ TEST(AcceleratedPowerMethod, useFactorGraphSparse) { /* ************************************************************************* */ TEST(AcceleratedPowerMethod, useFactorGraphDense) { // Let's make a scalar synchronization graph with 10 nodes - GaussianFactorGraph fg; - auto model = noiseModel::Unit::Create(1); - // Each node has an edge with all the others - for (size_t j = 0; j < 10; j++) { - fg.add(X(j), -I_1x1, X((j + 1)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 2)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 3)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 4)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 5)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 6)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 7)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 8)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 9)%10 ), I_1x1, Vector1::Zero(), model); - } + GaussianFactorGraph fg = gtsam::linear::test::example::createDenseGraph(); // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); diff --git a/gtsam/linear/tests/testPowerMethod.cpp b/gtsam/linear/tests/testPowerMethod.cpp index 7adfd0aa5..54d4c720d 100644 --- a/gtsam/linear/tests/testPowerMethod.cpp +++ b/gtsam/linear/tests/testPowerMethod.cpp @@ -24,6 +24,7 @@ #include #include #include +#include #include #include @@ -33,7 +34,6 @@ using namespace std; using namespace gtsam; -using symbol_shorthand::X; /* ************************************************************************* */ TEST(PowerMethod, powerIteration) { @@ -63,12 +63,7 @@ TEST(PowerMethod, powerIteration) { /* ************************************************************************* */ TEST(PowerMethod, useFactorGraphSparse) { // Let's make a scalar synchronization graph with 4 nodes - GaussianFactorGraph fg; - auto model = noiseModel::Unit::Create(1); - for (size_t j = 0; j < 3; j++) { - fg.add(X(j), -I_1x1, X(j + 1), I_1x1, Vector1::Zero(), model); - } - fg.add(X(3), -I_1x1, X(0), I_1x1, Vector1::Zero(), model); // extra row + GaussianFactorGraph fg = gtsam::linear::test::example::createSparseGraph(); // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); @@ -96,20 +91,7 @@ TEST(PowerMethod, useFactorGraphSparse) { /* ************************************************************************* */ TEST(PowerMethod, useFactorGraphDense) { // Let's make a scalar synchronization graph with 10 nodes - GaussianFactorGraph fg; - auto model = noiseModel::Unit::Create(1); - // Each node has an edge with all the others - for (size_t j = 0; j < 10; j++) { - fg.add(X(j), -I_1x1, X((j + 1)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 2)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 3)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 4)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 5)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 6)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 7)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 8)%10 ), I_1x1, Vector1::Zero(), model); - fg.add(X(j), -I_1x1, X((j + 9)%10 ), I_1x1, Vector1::Zero(), model); - } + GaussianFactorGraph fg = gtsam::linear::test::example::createDenseGraph(); // Get eigenvalues and eigenvectors with Eigen auto L = fg.hessian(); From 55ad1f16a630f23a1f15ddeeb70f995b36ffa3ec Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Fri, 11 Dec 2020 01:01:40 -0500 Subject: [PATCH 21/65] Refined reference documentation --- gtsam/linear/AcceleratedPowerMethod.h | 10 ++++++---- gtsam/linear/PowerMethod.h | 12 +++++++----- 2 files changed, 13 insertions(+), 9 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 0699f237e..4cb25daf7 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -29,19 +29,21 @@ using Sparse = Eigen::SparseMatrix; * \brief Compute maximum Eigenpair with accelerated power method * * References : - * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * 1) G. Golub and C. V. Loan, Matrix Computations, 3rd ed. Baltimore, Johns + * Hopkins University Press, 1996, pp.405-411 + * 2) Rosen, D. and Carlone, L., 2017, September. Computational * enhancements for certifiably correct SLAM. In Proceedings of the * International Conference on Intelligent Robots and Systems. - * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 3) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv - * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * 4) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. * 58–67 * * It performs the following iteration: \f$ x_{k+1} = A * x_k - \beta * * x_{k-1} \f$ where A is the aim matrix we want to get eigenpair of, x is the * Ritz vector - * + * * Template argument Operator just needs multiplication operator * */ diff --git a/gtsam/linear/PowerMethod.h b/gtsam/linear/PowerMethod.h index a209c5779..8834777cc 100644 --- a/gtsam/linear/PowerMethod.h +++ b/gtsam/linear/PowerMethod.h @@ -35,19 +35,21 @@ using Sparse = Eigen::SparseMatrix; * \brief Compute maximum Eigenpair with power method * * References : - * 1) Rosen, D. and Carlone, L., 2017, September. Computational + * 1) G. Golub and C. V. Loan, Matrix Computations, 3rd ed. Baltimore, Johns + * Hopkins University Press, 1996, pp.405-411 + * 2) Rosen, D. and Carlone, L., 2017, September. Computational * enhancements for certifiably correct SLAM. In Proceedings of the * International Conference on Intelligent Robots and Systems. - * 2) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, + * 3) Yulun Tian and Kasra Khosoussi and David M. Rosen and Jonathan P. How, * 2020, Aug, Distributed Certifiably Correct Pose-Graph Optimization, Arxiv - * 3) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated + * 4) C. de Sa, B. He, I. Mitliagkas, C. Ré, and P. Xu, “Accelerated * stochastic power iteration,” in Proc. Mach. Learn. Res., no. 84, 2018, pp. * 58–67 * - * It performs the following iteration: \f$ x_{k+1} = A * x_k \f$ + * It performs the following iteration: \f$ x_{k+1} = A * x_k \f$ * where A is the aim matrix we want to get eigenpair of, x is the * Ritz vector - * + * * Template argument Operator just needs multiplication operator * */ From 525dbb6058a0c4ba5cb7fcf7d9811dc6af43d110 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Fri, 11 Dec 2020 01:21:14 -0500 Subject: [PATCH 22/65] Make purturb static --- gtsam/sfm/ShonanAveraging.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/sfm/ShonanAveraging.cpp b/gtsam/sfm/ShonanAveraging.cpp index fab57c828..dfab2bf52 100644 --- a/gtsam/sfm/ShonanAveraging.cpp +++ b/gtsam/sfm/ShonanAveraging.cpp @@ -485,7 +485,7 @@ Sparse ShonanAveraging::computeA(const Matrix &S) const { // ref : Part III. C, Rosen, D. and Carlone, L., 2017, September. Computational // enhancements for certifiably correct SLAM. In Proceedings of the // International Conference on Intelligent Robots and Systems. -Vector perturb(const Vector &initialVector) { +static Vector perturb(const Vector &initialVector) { // generate a 0.03*||x_0||_2 as stated in David's paper int n = initialVector.rows(); Vector disturb = Vector::Random(n); From 8b9f917f4327c0d36e73b06c80fb444bdf0d3739 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Mon, 14 Dec 2020 14:32:04 -0500 Subject: [PATCH 23/65] refactored code for ImuMeasurements --- tests/ImuMeasurement.h | 26 +++++++++++++++++++------- tests/Measurement.h | 24 +++++++++++++----------- 2 files changed, 32 insertions(+), 18 deletions(-) diff --git a/tests/ImuMeasurement.h b/tests/ImuMeasurement.h index 5ac3d54be..d49759545 100644 --- a/tests/ImuMeasurement.h +++ b/tests/ImuMeasurement.h @@ -2,11 +2,11 @@ #include -namespace drs { +namespace gtsam { -/// -/// \brief Contains data from the IMU mesaurements. -/// +/** + *\brief Contains data from the IMU mesaurements. + */ class ImuMeasurement : public Measurement { public: enum Name { BODY = 0, RF_FOOT = 1, RH_FOOT = 2 }; @@ -15,9 +15,21 @@ class ImuMeasurement : public Measurement { Eigen::Vector3d I_a_WI; ///< Raw acceleration from the IMU (m/s/s) Eigen::Vector3d I_w_WI; ///< Raw angular velocity from the IMU (rad/s) + ImuMeasurement() + : Measurement("ImuMeasurement"), I_a_WI{0, 0, 0}, I_w_WI{0, 0, 0} {} + virtual ~ImuMeasurement() override {} - ImuMeasurement(); - friend std::ostream& operator<<(std::ostream& stream, const ImuMeasurement& meas); + + friend std::ostream& operator<<(std::ostream& stream, + const ImuMeasurement& meas); }; -} // namespace drs +std::ostream& operator<<(std::ostream& stream, const ImuMeasurement& meas) { + stream << "IMU Measurement at time = " << meas.time << " : \n" + << "dt : " << meas.dt << "\n" + << "I_a_WI: " << meas.I_a_WI.transpose() << "\n" + << "I_w_WI: " << meas.I_w_WI.transpose() << "\n"; + return stream; +} + +} // namespace gtsam diff --git a/tests/Measurement.h b/tests/Measurement.h index e26c5d918..be38ac4f3 100644 --- a/tests/Measurement.h +++ b/tests/Measurement.h @@ -3,21 +3,23 @@ #include #include -namespace drs { +namespace gtsam { -/// -/// \brief This is the base class for all measurement types. -/// +/** + * \brief This is the base class for all measurement types. + */ class Measurement { -public: + public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW - uint64_t dt; ///< Time since the last message of this type (nanoseconds). - uint64_t time; ///< ROS time message recieved (nanoseconds). - std::string type; ///< The type of message (to enable dynamic/static casting). + size_t dt; ///< Time since the last message of this type (nanoseconds). + size_t time; ///< ROS time message recieved (nanoseconds). + ///< The type of message (to enable dynamic/static casting). + std::string type; + + Measurement() : dt(0), time(0), type("UNDEFINED") {} + Measurement(std::string _type) : dt(0), time(0), type(_type) {} virtual ~Measurement() {} - Measurement(); - Measurement(std::string _type); }; -} // namespace drs +} // namespace gtsam From 7f975d194adff9043c81d1cba6d0b0fe03db0c42 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Mon, 14 Dec 2020 14:32:24 -0500 Subject: [PATCH 24/65] refactored code for testing ImuPreintegration with impact --- tests/testImuPreintegration.cpp | 133 ++++++++++++++++---------------- 1 file changed, 68 insertions(+), 65 deletions(-) diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp index 6e3b6396d..43b3461ee 100644 --- a/tests/testImuPreintegration.cpp +++ b/tests/testImuPreintegration.cpp @@ -1,46 +1,42 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + /** * @file testImuPreintegration.cpp * @brief Unit tests for IMU Preintegration * @author Russell Buchanan **/ +#include +#include +#include +#include +#include #include #include #include -#include -#include -#include -#include - -namespace drs { - -Measurement::Measurement() : dt(0), time(0), type("UNDEFINED") {} - -Measurement::Measurement(std::string _type) : dt(0), time(0), type(_type) {} - -ImuMeasurement::ImuMeasurement() : I_a_WI{0, 0, 0}, I_w_WI{0, 0, 0} { type = "ImuMeasurement"; } - -std::ostream& operator<<(std::ostream& stream, const ImuMeasurement& meas) { - stream << "IMU Measurement at time = " << meas.time << " : \n" - << "dt : " << meas.dt << "\n" - << "I_a_WI: " << meas.I_a_WI.transpose() << "\n" - << "I_w_WI: " << meas.I_w_WI.transpose() << "\n"; - return stream; -} - -} // namespace drs - +using namespace std; using namespace gtsam; /* ************************************************************************* */ -/// \brief Uses the GTSAM library to perform IMU preintegration on an acceleration input. -/// -TEST(GtsamLibraryTests, LoadedSimulationData) { +/** + * \brief Uses the GTSAM library to perform IMU preintegration on an + * acceleration input. + */ +TEST(TestImuPreintegration, LoadedSimulationData) { Eigen::Vector3d finalPos; - std::vector imuMeasurements; + vector imuMeasurements; double accNoiseSigma = 0.001249; double accBiasRwSigma = 0.000106; @@ -52,33 +48,36 @@ TEST(GtsamLibraryTests, LoadedSimulationData) { double gravity = 9.81; double rate = 400.0; // Hz - /// @todo Update directory to correct location - std::string inFileString = "/home/russell/imu_data.csv"; - std::ofstream outputFile; - outputFile.open("/home/russell/gtsam_output.csv", std::ofstream::out); - std::ifstream inputFile(inFileString); - std::string line; - while (std::getline(inputFile, line)) { - std::stringstream ss(line); - std::string str; - std::vector results; + string inFileString = findExampleDataFile("quadraped_imu_data.csv"); + ofstream outputFile; + outputFile.open("imu_preint_output.csv", ios::out); + ifstream inputFile(inFileString); + string line; + while (getline(inputFile, line)) { + stringstream ss(line); + string str; + vector results; while (getline(ss, str, ',')) { - results.push_back(std::atof(str.c_str())); + results.push_back(atof(str.c_str())); } - drs::ImuMeasurement measurement; - measurement.dt = static_cast(1e9 * (1 / rate)); + ImuMeasurement measurement; + measurement.dt = static_cast(1e9 * (1 / rate)); measurement.time = results[2]; measurement.I_a_WI = {results[29], results[30], results[31]}; measurement.I_w_WI = {results[17], results[18], results[19]}; imuMeasurements.push_back(measurement); - // std::cout << "IMU measurement " << measurement << std::endl; + // cout << "IMU measurement " << measurement << endl; } - // Assume a Z-up navigation (assuming we are performing optimization in the IMU frame). - boost::shared_ptr imuPreintegratedParams = - gtsam::PreintegratedCombinedMeasurements::Params::MakeSharedU(gravity); - imuPreintegratedParams->accelerometerCovariance = I_3x3 * pow(accNoiseSigma, 2); + // Assume a Z-up navigation (assuming we are performing optimization in the + // IMU frame). + boost::shared_ptr + imuPreintegratedParams = + PreintegratedCombinedMeasurements::Params::MakeSharedU( + gravity); + imuPreintegratedParams->accelerometerCovariance = + I_3x3 * pow(accNoiseSigma, 2); imuPreintegratedParams->biasAccCovariance = I_3x3 * pow(accBiasRwSigma, 2); imuPreintegratedParams->gyroscopeCovariance = I_3x3 * pow(gyrNoiseSigma, 2); imuPreintegratedParams->biasOmegaCovariance = I_3x3 * pow(gyrBiasRwSigma, 2); @@ -86,26 +85,27 @@ TEST(GtsamLibraryTests, LoadedSimulationData) { imuPreintegratedParams->biasAccOmegaInt = I_6x6 * biasAccOmegaInt; // Initial state - gtsam::Pose3 priorPose; - gtsam::Vector3 priorVelocity; - gtsam::imuBias::ConstantBias priorImuBias; - gtsam::PreintegratedCombinedMeasurements imuPreintegrated; + Pose3 priorPose; + Vector3 priorVelocity; + imuBias::ConstantBias priorImuBias; + PreintegratedCombinedMeasurements imuPreintegrated; Eigen::Vector3d position; Eigen::Vector3d velocity; - gtsam::NavState propState; + NavState propState; - gtsam::NavState initialNavState(priorPose, priorVelocity); + NavState initialNavState(priorPose, priorVelocity); // Bias estimated by my Algorithm - priorImuBias = - gtsam::imuBias::ConstantBias(Eigen::Vector3d(-0.0314648, 0.0219921, 6.95945e-05), - Eigen::Vector3d(4.88581e-08, -1.04971e-09, -0.000122868)); + priorImuBias = imuBias::ConstantBias( + Eigen::Vector3d(-0.0314648, 0.0219921, 6.95945e-05), + Eigen::Vector3d(4.88581e-08, -1.04971e-09, -0.000122868)); // zero bias - // priorImuBias = gtsam::imuBias::ConstantBias(Eigen::Vector3d(0,0,0), + // priorImuBias = imuBias::ConstantBias(Eigen::Vector3d(0,0,0), // Eigen::Vector3d(0,0,0)); - imuPreintegrated = gtsam::PreintegratedCombinedMeasurements(imuPreintegratedParams, priorImuBias); + imuPreintegrated = PreintegratedCombinedMeasurements( + imuPreintegratedParams, priorImuBias); // Put header row in output csv outputFile << "X Position," @@ -116,27 +116,29 @@ TEST(GtsamLibraryTests, LoadedSimulationData) { << "Z Velocity," << "\n"; - for (int n = 1; n < imuMeasurements.size(); n++) { //start at 1 to skip header + // start at 1 to skip header + for (size_t n = 1; n < imuMeasurements.size(); n++) { // integrate - imuPreintegrated.integrateMeasurement(imuMeasurements[n].I_a_WI, imuMeasurements[n].I_w_WI, - 1 / rate); + imuPreintegrated.integrateMeasurement(imuMeasurements[n].I_a_WI, + imuMeasurements[n].I_w_WI, 1 / rate); // predict propState = imuPreintegrated.predict(initialNavState, priorImuBias); position = propState.pose().translation(); velocity = propState.velocity(); - // std::cout << "IMU Position " << position.transpose() << std::endl; - // std::cout << "IMU Velocity " << velocity.transpose() << std::endl; + // cout << "IMU Position " << position.transpose() << endl; + // cout << "IMU Velocity " << velocity.transpose() << endl; // Write to csv - outputFile << std::to_string(position.x()) << "," << std::to_string(position.y()) << "," - << std::to_string(position.z()) << "," << std::to_string(velocity.x()) << "," - << std::to_string(velocity.y()) << "," << std::to_string(velocity.z()) << "," + outputFile << to_string(position.x()) << "," << to_string(position.y()) + << "," << to_string(position.z()) << "," + << to_string(velocity.x()) << "," << to_string(velocity.y()) + << "," << to_string(velocity.z()) << "," << "\n"; } outputFile.close(); - gtsam::Vector3 rotation = propState.pose().rotation().rpy(); + Vector3 rotation = propState.pose().rotation().rpy(); // Dont have ground truth for x and y position yet // DOUBLES_EQUAL(0.1, position[0], 1e-2); @@ -147,6 +149,7 @@ TEST(GtsamLibraryTests, LoadedSimulationData) { DOUBLES_EQUAL(0.0, rotation[1], 1e-2); DOUBLES_EQUAL(0.0, rotation[2], 1e-2); } + /* ************************************************************************* */ int main() { TestResult tr; From e54ef580f7356203ce22f65e8eeef20529eba24f Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Mon, 14 Dec 2020 14:32:36 -0500 Subject: [PATCH 25/65] add simulation data --- examples/Data/quadraped_imu_data.csv | 2636 ++++++++++++++++++++++++++ 1 file changed, 2636 insertions(+) create mode 100644 examples/Data/quadraped_imu_data.csv diff --git a/examples/Data/quadraped_imu_data.csv b/examples/Data/quadraped_imu_data.csv new file mode 100644 index 000000000..d324066d8 --- /dev/null +++ b/examples/Data/quadraped_imu_data.csv @@ -0,0 +1,2636 @@ +%time,field.header.seq,field.header.stamp,field.header.frame_id,field.orientation.x,field.orientation.y,field.orientation.z,field.orientation.w,field.orientation_covariance0,field.orientation_covariance1,field.orientation_covariance2,field.orientation_covariance3,field.orientation_covariance4,field.orientation_covariance5,field.orientation_covariance6,field.orientation_covariance7,field.orientation_covariance8,field.angular_velocity.x,field.angular_velocity.y,field.angular_velocity.z,field.angular_velocity_covariance0,field.angular_velocity_covariance1,field.angular_velocity_covariance2,field.angular_velocity_covariance3,field.angular_velocity_covariance4,field.angular_velocity_covariance5,field.angular_velocity_covariance6,field.angular_velocity_covariance7,field.angular_velocity_covariance8,field.linear_acceleration.x,field.linear_acceleration.y,field.linear_acceleration.z,field.linear_acceleration_covariance0,field.linear_acceleration_covariance1,field.linear_acceleration_covariance2,field.linear_acceleration_covariance3,field.linear_acceleration_covariance4,field.linear_acceleration_covariance5,field.linear_acceleration_covariance6,field.linear_acceleration_covariance7,field.linear_acceleration_covariance8 +117735250000,11048,117735250000,RH_EXTIMU,2.2932715788e-06,1.53196171221e-05,-0.703285780478,0.71090724482,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.19800998937e-07,-8.13380203893e-09,-7.22038459104e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245457587107,-0.000181612558247,9.8100077031,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117737750000,11049,117737750000,RH_EXTIMU,2.29313402886e-06,1.53196621872e-05,-0.70328584464,0.710907181346,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.0268029415e-07,-5.10996651005e-08,-7.22029453453e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246233372419,-0.00017714749759,9.81001157075,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117737750000,11050,117740250000,RH_EXTIMU,2.29307998339e-06,1.53197209386e-05,-0.703285908801,0.710907117872,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.28894961166e-08,3.66612768662e-09,-7.22022488535e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244992819707,-0.000178649476366,9.80999936342,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117742750000,11051,117742750000,RH_EXTIMU,2.29322015822e-06,1.531966497e-05,-0.703285972962,0.710907054399,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.12113343221e-07,4.76958204019e-08,-7.22016100777e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244525990158,-0.000181660653484,9.80999679571,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117745250000,11052,117745250000,RH_EXTIMU,2.293183196e-06,1.53196615055e-05,-0.703286037122,0.710906990927,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.81693540833e-08,-2.21061727875e-08,-7.22009336014e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246087327017,-0.000178542674556,9.80998704598,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117747750000,11053,117747750000,RH_EXTIMU,2.29329139507e-06,1.53195613238e-05,-0.703286101282,0.710906927455,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.18803441961e-07,4.56022684731e-09,-7.22002706405e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244808220716,-0.000181947765531,9.81000178509,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117750250000,11054,117750250000,RH_EXTIMU,2.29320463572e-06,1.53195684906e-05,-0.703286165441,0.710906863984,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-5.24717115333e-08,-4.40772440141e-08,-7.21995169286e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246213828915,-0.000178047842864,9.80999242585,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117750250000,11055,117752750000,RH_EXTIMU,2.2932913045e-06,1.53195007692e-05,-0.703286229599,0.710906800514,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,8.82954801468e-08,1.09076674284e-08,-7.21985776802e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.00024522225298,-0.000180891416039,9.81003509629,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117755250000,11056,117755250000,RH_EXTIMU,2.29309344794e-06,1.53196727566e-05,-0.703286293756,0.710906737044,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-2.08388404483e-07,-1.28460937909e-08,-7.21977440579e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245213461921,-0.000175906863484,9.81000608935,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117757750000,11057,117757750000,RH_EXTIMU,2.29316299034e-06,1.53196814379e-05,-0.703286357913,0.710906673575,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.55688884737e-08,4.47240318075e-08,-7.21971848869e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244776732528,-0.000180521462445,9.80998867347,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117762750000,11058,117760250000,RH_EXTIMU,2.29329336854e-06,1.53195824688e-05,-0.703286422069,0.710906610106,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.30734970339e-07,1.77285196194e-08,-7.21965870892e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244880811467,-0.00018178797353,9.80998622901,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117762750000,11059,117762750000,RH_EXTIMU,2.29346102476e-06,1.53194455635e-05,-0.703286486225,0.710906546638,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.73279948265e-07,1.71269066204e-08,-7.21959389915e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245332844923,-0.000182313647277,9.80999880236,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117765250000,11060,117765250000,RH_EXTIMU,2.29328861395e-06,1.53194931639e-05,-0.70328655038,0.710906483171,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.23933033463e-07,-6.92717073101e-08,-7.21950602553e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246438505825,-0.000176454593377,9.81000353275,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117767750000,11061,117767750000,RH_EXTIMU,2.2932347149e-06,1.53195711494e-05,-0.703286614534,0.710906419704,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-7.36279925846e-08,1.46872759233e-08,-7.21944124447e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244868756476,-0.000178376840913,9.80999213137,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117770250000,11062,117770250000,RH_EXTIMU,2.29324288354e-06,1.53194222205e-05,-0.703286678688,0.710906356238,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,8.93401640611e-08,-7.94435817158e-08,-7.21937101628e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246818966152,-0.000181203011244,9.80999464601,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117772750000,11063,117772750000,RH_EXTIMU,2.29334011956e-06,1.53193373544e-05,-0.703286742841,0.710906292773,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.03951387808e-07,7.10245973005e-09,-7.21930125849e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244546602605,-0.000181295434791,9.81000279832,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117775250000,11064,117775250000,RH_EXTIMU,2.29339758781e-06,1.53193252454e-05,-0.703286806993,0.710906229308,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,4.03991495598e-08,2.61067521579e-08,-7.21921821507e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.00024530078765,-0.000179816386255,9.81001520402,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117777750000,11065,117777750000,RH_EXTIMU,2.29321328605e-06,1.53194107569e-05,-0.703286871145,0.710906165844,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-1.52025648402e-07,-5.44010003828e-08,-7.21914868296e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246114543589,-0.000176779202578,9.80998767173,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117780250000,11066,117780250000,RH_EXTIMU,2.29346682906e-06,1.53193439089e-05,-0.703286935296,0.71090610238,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.82709551224e-07,1.05292710498e-07,-7.21908096192e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000243455110003,-0.000182903971445,9.81001128283,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117782750000,11067,117782750000,RH_EXTIMU,2.29346689621e-06,1.53194037111e-05,-0.703286999447,0.710906038917,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-3.2705656399e-08,3.47088488136e-08,-7.21901204274e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244904453409,-0.000178694839104,9.80999319876,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117785250000,11068,117785250000,RH_EXTIMU,2.29354782256e-06,1.53193775937e-05,-0.703287063597,0.710905975455,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,6.16218465478e-08,3.1338040657e-08,-7.21894458253e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244950317669,-0.000180523918674,9.80999732479,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117787750000,11069,117787750000,RH_EXTIMU,2.29347003814e-06,1.53193682817e-05,-0.703287127746,0.710905911993,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-3.80961105574e-08,-4.83997246667e-08,-7.21887250549e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000246498335555,-0.000178285597786,9.80999058003,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117790250000,11070,117790250000,RH_EXTIMU,2.29348046574e-06,1.53192806352e-05,-0.703287191895,0.710905848532,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,5.6145567215e-08,-4.3319799211e-08,-7.21880606691e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245644492047,-0.000180658336284,9.80999408856,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117792750000,11071,117792750000,RH_EXTIMU,2.29357044321e-06,1.53191846988e-05,-0.703287256043,0.710905785072,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.06051697715e-07,-3.27738287266e-09,-7.21873195951e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245212177494,-0.000181344617064,9.81000696248,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117795250000,11072,117795250000,RH_EXTIMU,2.29356910901e-06,1.53191888447e-05,-0.70328732019,0.710905721612,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-2.18879634395e-09,2.2672175202e-09,-7.21864858755e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245192142085,-0.000179227576991,9.8100126012,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117797750000,11073,117797750000,RH_EXTIMU,2.293528312e-06,1.53192850058e-05,-0.703287384336,0.710905658153,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-7.64028065804e-08,3.2395600678e-08,-7.21857442193e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000244845794011,-0.00017800513415,9.81000374321,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 +117800250000,11074,117800250000,RH_EXTIMU,2.2934606798e-06,1.531933274e-05,-0.703287448482,0.710905594694,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-6.44181789099e-08,-1.02443096786e-08,-7.21850481782e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.000245794011011,-0.000178191663677,9.80999156635,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 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+124320250000,13682,124320250000,RH_EXTIMU,1.54441756041e-05,3.33331097357e-05,-0.702979677557,0.711209934964,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-0.00398784999429,0.00900697382457,-7.46660532534e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.154699949727,0.0598659055842,9.97228429688,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 From fd43d817df34b7809e11080c126e0715f7d00448 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 15 Dec 2020 10:50:28 -0500 Subject: [PATCH 26/65] save time in CSV, formatting --- tests/testImuPreintegration.cpp | 40 ++++++++++++++++----------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp index 43b3461ee..9c55960f8 100644 --- a/tests/testImuPreintegration.cpp +++ b/tests/testImuPreintegration.cpp @@ -34,7 +34,7 @@ using namespace gtsam; * acceleration input. */ TEST(TestImuPreintegration, LoadedSimulationData) { - Eigen::Vector3d finalPos; + Vector3 finalPos(0, 0, 0); vector imuMeasurements; @@ -72,10 +72,8 @@ TEST(TestImuPreintegration, LoadedSimulationData) { // Assume a Z-up navigation (assuming we are performing optimization in the // IMU frame). - boost::shared_ptr - imuPreintegratedParams = - PreintegratedCombinedMeasurements::Params::MakeSharedU( - gravity); + auto imuPreintegratedParams = + PreintegratedCombinedMeasurements::Params::MakeSharedU(gravity); imuPreintegratedParams->accelerometerCovariance = I_3x3 * pow(accNoiseSigma, 2); imuPreintegratedParams->biasAccCovariance = I_3x3 * pow(accBiasRwSigma, 2); @@ -86,29 +84,29 @@ TEST(TestImuPreintegration, LoadedSimulationData) { // Initial state Pose3 priorPose; - Vector3 priorVelocity; + Vector3 priorVelocity(0, 0, 0); imuBias::ConstantBias priorImuBias; PreintegratedCombinedMeasurements imuPreintegrated; - Eigen::Vector3d position; - Eigen::Vector3d velocity; + Vector3 position(0, 0, 0); + Vector3 velocity(0, 0, 0); NavState propState; NavState initialNavState(priorPose, priorVelocity); // Bias estimated by my Algorithm - priorImuBias = imuBias::ConstantBias( - Eigen::Vector3d(-0.0314648, 0.0219921, 6.95945e-05), - Eigen::Vector3d(4.88581e-08, -1.04971e-09, -0.000122868)); + priorImuBias = + imuBias::ConstantBias(Vector3(-0.0314648, 0.0219921, 6.95945e-05), + Vector3(4.88581e-08, -1.04971e-09, -0.000122868)); // zero bias - // priorImuBias = imuBias::ConstantBias(Eigen::Vector3d(0,0,0), - // Eigen::Vector3d(0,0,0)); + // priorImuBias = imuBias::ConstantBias(Vector3(0, 0, 0), Vector3(0, 0, 0)); - imuPreintegrated = PreintegratedCombinedMeasurements( - imuPreintegratedParams, priorImuBias); + imuPreintegrated = + PreintegratedCombinedMeasurements(imuPreintegratedParams, priorImuBias); // Put header row in output csv - outputFile << "X Position," + outputFile << "Time [s]," + << "X Position," << "Y Position," << "Z Position," << "X Velocity," @@ -128,11 +126,13 @@ TEST(TestImuPreintegration, LoadedSimulationData) { // cout << "IMU Position " << position.transpose() << endl; // cout << "IMU Velocity " << velocity.transpose() << endl; + size_t time = imuMeasurements[n].time - imuMeasurements[0].time; + // Write to csv - outputFile << to_string(position.x()) << "," << to_string(position.y()) - << "," << to_string(position.z()) << "," - << to_string(velocity.x()) << "," << to_string(velocity.y()) - << "," << to_string(velocity.z()) << "," + outputFile << time << "," << to_string(position.x()) << "," + << to_string(position.y()) << "," << to_string(position.z()) + << "," << to_string(velocity.x()) << "," + << to_string(velocity.y()) << "," << to_string(velocity.z()) << "\n"; } From 56e9b3ac9ffa2edac339ce54af4cafeac0467b26 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Mon, 18 Jan 2021 21:10:52 -0500 Subject: [PATCH 27/65] Mandy+Fan's original code for converting sparse matrices to Eigen format --- gtsam/linear/SparseEigenSolver.cpp | 231 +++++++++++++++++++++++++++++ gtsam/linear/SparseEigenSolver.h | 62 ++++++++ 2 files changed, 293 insertions(+) create mode 100644 gtsam/linear/SparseEigenSolver.cpp create mode 100644 gtsam/linear/SparseEigenSolver.h diff --git a/gtsam/linear/SparseEigenSolver.cpp b/gtsam/linear/SparseEigenSolver.cpp new file mode 100644 index 000000000..f0dfd83f3 --- /dev/null +++ b/gtsam/linear/SparseEigenSolver.cpp @@ -0,0 +1,231 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file SparseEigenSolver.cpp + * + * @brief Eigen SparseSolver based linear solver backend for GTSAM + * + * @date Aug 2019 + * @author Mandy Xie + * @author Fan Jiang + * @author Frank Dellaert + */ + +#include +#include +#include + +#include + +using namespace std; + +namespace gtsam { + + using SpMat = Eigen::SparseMatrix; + + Eigen::SparseMatrix + SparseEigenSolver::sparseJacobianEigen( + const GaussianFactorGraph &gfg, + const Ordering &ordering) { + // First find dimensions of each variable + std::map dims; + for (const boost::shared_ptr &factor : gfg) { + if (!static_cast(factor)) + continue; + + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); + } + } + + // Compute first scalar column of each variable + size_t currentColIndex = 0; + std::map columnIndices; + for (const auto key : ordering) { + columnIndices[key] = currentColIndex; + currentColIndex += dims[key]; + } + + // Iterate over all factors, adding sparse scalar entries + vector> entries; + entries.reserve(60 * gfg.size()); + + size_t row = 0; + for (const boost::shared_ptr &factor : gfg) { + if (!static_cast(factor)) continue; + + // Convert to JacobianFactor if necessary + JacobianFactor::shared_ptr jacobianFactor( + boost::dynamic_pointer_cast(factor)); + if (!jacobianFactor) { + HessianFactor::shared_ptr hessian( + boost::dynamic_pointer_cast(factor)); + if (hessian) + jacobianFactor.reset(new JacobianFactor(*hessian)); + else + throw invalid_argument( + "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor."); + } + + // Whiten the factor and add entries for it + // iterate over all variables in the factor + const JacobianFactor whitened(jacobianFactor->whiten()); + for (JacobianFactor::const_iterator key = whitened.begin(); + key < whitened.end(); ++key) { + JacobianFactor::constABlock whitenedA = whitened.getA(key); + // find first column index for this key + size_t column_start = columnIndices[*key]; + for (size_t i = 0; i < (size_t) whitenedA.rows(); i++) + for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { + double s = whitenedA(i, j); + if (std::abs(s) > 1e-12) + entries.emplace_back(row + i, column_start + j, s); + } + } + + JacobianFactor::constBVector whitenedb(whitened.getb()); + size_t bcolumn = currentColIndex; + for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { + double s = whitenedb(i); + if (std::abs(s) > 1e-12) + entries.emplace_back(row + i, bcolumn, s); + } + + // Increment row index + row += jacobianFactor->rows(); + } + + // ...and make a sparse matrix with it. + Eigen::SparseMatrix Ab(row + 1, currentColIndex + 1); + Ab.setFromTriplets(entries.begin(), entries.end()); + return Ab; + } + + + /// obtain sparse matrix for eigen sparse solver + std::pair obtainSparseMatrix( + const GaussianFactorGraph &gfg, + const Ordering &ordering) { + + gttic_(EigenOptimizer_obtainSparseMatrix); + + // Get sparse entries of Jacobian [A|b] augmented with RHS b. + auto entries = gfg.sparseJacobian(ordering); + + gttic_(EigenOptimizer_convertSparse); + // Convert boost tuples to Eigen triplets + vector> triplets; + triplets.reserve(entries.size()); + size_t rows = 0, cols = 0; + for (const auto &e : entries) { + size_t temp_rows = e.get<0>(), temp_cols = e.get<1>(); + triplets.emplace_back(temp_rows, temp_cols, e.get<2>()); + rows = std::max(rows, temp_rows); + cols = std::max(cols, temp_cols); + } + + // ...and make a sparse matrix with it. + SpMat Ab(rows + 1, cols + 1); + Ab.setFromTriplets(triplets.begin(), triplets.end()); + Ab.makeCompressed(); + gttoc_(EigenOptimizer_convertSparse); + + gttoc_(EigenOptimizer_obtainSparseMatrix); + + return make_pair(Ab.block(0, 0, rows + 1, cols), + Ab.col(cols)); + } + + bool SparseEigenSolver::isIterative() { + return false; + } + + bool SparseEigenSolver::isSequential() { + return false; + } + + VectorValues SparseEigenSolver::solve(const GaussianFactorGraph &gfg) { + if (solverType == QR) { + gttic_(EigenOptimizer_optimizeEigenQR); + auto Ab_pair = obtainSparseMatrix(gfg, ordering); + + // Solve A*x = b using sparse QR from Eigen + gttic_(EigenOptimizer_optimizeEigenQR_create_solver); + Eigen::SparseQR> solver(Ab_pair.first); + gttoc_(EigenOptimizer_optimizeEigenQR_create_solver); + + gttic_(EigenOptimizer_optimizeEigenQR_solve); + Eigen::VectorXd x = solver.solve(Ab_pair.second); + gttoc_(EigenOptimizer_optimizeEigenQR_solve); + + return VectorValues(x, gfg.getKeyDimMap()); + } else if (solverType == CHOLESKY) { + gttic_(EigenOptimizer_optimizeEigenCholesky); + SpMat Ab = sparseJacobianEigen(gfg, ordering); + auto rows = Ab.rows(), cols = Ab.cols(); + auto A = Ab.block(0, 0, rows, cols - 1); + auto At = A.transpose(); + auto b = Ab.col(cols - 1); + + SpMat AtA(A.cols(), A.cols()); + AtA.selfadjointView().rankUpdate(At); + + gttic_(EigenOptimizer_optimizeEigenCholesky_create_solver); + // Solve A*x = b using sparse Cholesky from Eigen + Eigen::SimplicialLDLT> + solver(AtA); + + gttoc_(EigenOptimizer_optimizeEigenCholesky_create_solver); + + gttic_(EigenOptimizer_optimizeEigenCholesky_solve); + Eigen::VectorXd x = solver.solve(At * b); + gttoc_(EigenOptimizer_optimizeEigenCholesky_solve); + + // NOTE: b is reordered now, so we need to transform back the order. + // First find dimensions of each variable + std::map dims; + for (const boost::shared_ptr &factor : gfg) { + if (!static_cast(factor)) + continue; + + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); + } + } + + VectorValues vv; + + std::map columnIndices; + + { + size_t currentColIndex = 0; + for (const auto key : ordering) { + columnIndices[key] = currentColIndex; + currentColIndex += dims[key]; + } + } + + for (const pair keyDim : dims) { + vv.insert(keyDim.first, x.segment(columnIndices[keyDim.first], keyDim.second)); + } + + return vv; + } + + throw std::exception(); + } + + SparseEigenSolver::SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering) { + solverType = type; + this->ordering = ordering; + } +} // namespace gtsam \ No newline at end of file diff --git a/gtsam/linear/SparseEigenSolver.h b/gtsam/linear/SparseEigenSolver.h new file mode 100644 index 000000000..d71365864 --- /dev/null +++ b/gtsam/linear/SparseEigenSolver.h @@ -0,0 +1,62 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file SparseEigenSolver.h + * + * @brief Eigen SparseSolver based linear solver backend for GTSAM + * + * @date Aug 2019 + * @author Mandy Xie + * @author Fan Jiang + * @author Frank Dellaert + */ + +#pragma once + +#include +#include +#include +#include +#include + +namespace gtsam { + + /** + * Eigen SparseSolver based Backend class + */ + class GTSAM_EXPORT SparseEigenSolver : public LinearSolver { + public: + + typedef enum { + QR, + CHOLESKY + } SparseEigenSolverType; + + + explicit SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering); + + bool isIterative() override; + + bool isSequential() override; + + VectorValues solve(const GaussianFactorGraph &gfg) override; + + static Eigen::SparseMatrix + sparseJacobianEigen(const GaussianFactorGraph &gfg, const Ordering &ordering); + + protected: + + SparseEigenSolverType solverType = QR; + + Ordering ordering; + }; +} // namespace gtsam From a477ec681170ee7f5c4d9eadac460b595eeee972 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Mon, 18 Jan 2021 20:20:05 -0500 Subject: [PATCH 28/65] merge Mandy + Fan's sparseJacobian unit test additions --- .../linear/tests/testGaussianFactorGraph.cpp | 80 ++++++++++++------- 1 file changed, 50 insertions(+), 30 deletions(-) diff --git a/gtsam/linear/tests/testGaussianFactorGraph.cpp b/gtsam/linear/tests/testGaussianFactorGraph.cpp index 45f652d05..57a663e8c 100644 --- a/gtsam/linear/tests/testGaussianFactorGraph.cpp +++ b/gtsam/linear/tests/testGaussianFactorGraph.cpp @@ -36,9 +36,18 @@ using namespace boost::assign; using namespace std; using namespace gtsam; -// static SharedDiagonal -// sigma0_1 = noiseModel::Isotropic::Sigma(2,0.1), sigma_02 = noiseModel::Isotropic::Sigma(2,0.2), -// constraintModel = noiseModel::Constrained::All(2); +typedef boost::tuple BoostTriplet; +bool triplet_equal(BoostTriplet a, BoostTriplet b) { + if (a.get<0>() == b.get<0>() && a.get<1>() == b.get<1>() && + a.get<2>() == b.get<2>()) return true; + + cout << "not equal:" << endl; + cout << "\texpected: " + "(" << a.get<0>() << ", " << a.get<1>() << ") = " << a.get<2>() << endl; + cout << "\tactual: " + "(" << b.get<0>() << ", " << b.get<1>() << ") = " << b.get<2>() << endl; + return false; +} /* ************************************************************************* */ TEST(GaussianFactorGraph, initialization) { @@ -73,37 +82,48 @@ TEST(GaussianFactorGraph, sparseJacobian) { // 5 6 7 0 0 8 // 9 10 0 11 12 13 // 0 0 0 14 15 16 - - // Expected - NOTE that we transpose this! - Matrix expectedT = (Matrix(16, 3) << - 1., 1., 2., - 1., 2., 4., - 1., 3., 6., - 2., 1.,10., - 2., 2.,12., - 2., 3.,14., - 1., 6., 8., - 2., 6.,16., - 3., 1.,18., - 3., 2.,20., - 3., 4.,22., - 3., 5.,24., - 4., 4.,28., - 4., 5.,30., - 3., 6.,26., - 4., 6.,32.).finished(); - - Matrix expected = expectedT.transpose(); - GaussianFactorGraph gfg; SharedDiagonal model = noiseModel::Isotropic::Sigma(2, 0.5); - gfg.add(0, (Matrix(2, 3) << 1., 2., 3., 5., 6., 7.).finished(), Vector2(4., 8.), model); - gfg.add(0, (Matrix(2, 3) << 9., 10., 0., 0., 0., 0.).finished(), 1, - (Matrix(2, 2) << 11., 12., 14., 15.).finished(), Vector2(13., 16.), model); + const Key x123 = 0, x45 = 1; + gfg.add(x123, (Matrix(2, 3) << 1, 2, 3, 5, 6, 7).finished(), + Vector2(4, 8), model); + gfg.add(x123, (Matrix(2, 3) << 9, 10, 0, 0, 0, 0).finished(), + x45, (Matrix(2, 2) << 11, 12, 14, 15.).finished(), + Vector2(13, 16), model); - Matrix actual = gfg.sparseJacobian_(); + // Check version for MATLAB - NOTE that we transpose this! + Matrix expectedT = (Matrix(16, 3) << + 1, 1, 2., + 1, 2, 4., + 1, 3, 6., + 2, 1, 10., + 2, 2, 12., + 2, 3, 14., + 1, 6, 8., + 2, 6, 16., + 3, 1, 18., + 3, 2, 20., + 3, 4, 22., + 3, 5, 24., + 4, 4, 28., + 4, 5, 30., + 3, 6, 26., + 4, 6, 32.).finished(); - EXPECT(assert_equal(expected, actual)); + // matrix form (matlab) + Matrix expectedMatlab = expectedT.transpose(); + EXPECT(assert_equal(expectedMatlab, gfg.sparseJacobian_())); + + // BoostTriplets + auto boostActual = gfg.sparseJacobian(); + // check the triplets size... + EXPECT_LONGS_EQUAL(16, boostActual.size()); + // check content + for (int i = 0; i < 16; i++) { + EXPECT(triplet_equal( + BoostTriplet(expectedT(i, 0) - 1, expectedT(i, 1) - 1, expectedT(i, 2)), + boostActual.at(i))); + } } /* ************************************************************************* */ From 44c232a128c4fac074079f11d91db0601edff127 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Mon, 18 Jan 2021 20:39:34 -0500 Subject: [PATCH 29/65] organize/isolate sparseEigen functionality --- gtsam/linear/SparseEigen.h | 146 ++++++++++++++++ gtsam/linear/SparseEigenSolver.cpp | 231 ------------------------- gtsam/linear/SparseEigenSolver.h | 62 ------- gtsam/linear/tests/testSparseEigen.cpp | 72 ++++++++ 4 files changed, 218 insertions(+), 293 deletions(-) create mode 100644 gtsam/linear/SparseEigen.h delete mode 100644 gtsam/linear/SparseEigenSolver.cpp delete mode 100644 gtsam/linear/SparseEigenSolver.h create mode 100644 gtsam/linear/tests/testSparseEigen.cpp diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h new file mode 100644 index 000000000..a157be2b1 --- /dev/null +++ b/gtsam/linear/SparseEigen.h @@ -0,0 +1,146 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file SparseEigen.h + * + * @brief Utilities for converting to Eigen's sparse matrix representations + * + * @date Aug 2019 + * @author Mandy Xie + * @author Fan Jiang + * @author Gerry Chen + * @author Frank Dellaert + */ + +#pragma once + +#include +#include + +#include + +namespace gtsam { + +typedef Eigen::SparseMatrix SpMat; + +SpMat sparseJacobianEigen( + const GaussianFactorGraph &gfg, const Ordering &ordering) { + // First find dimensions of each variable + std::map dims; + for (const boost::shared_ptr &factor : gfg) { + if (!static_cast(factor)) continue; + + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); + } + } + + // Compute first scalar column of each variable + size_t currentColIndex = 0; + std::map columnIndices; + for (const auto key : ordering) { + columnIndices[key] = currentColIndex; + currentColIndex += dims[key]; + } + + // Iterate over all factors, adding sparse scalar entries + std::vector> entries; + entries.reserve(60 * gfg.size()); + + size_t row = 0; + for (const boost::shared_ptr &factor : gfg) { + if (!static_cast(factor)) continue; + + // Convert to JacobianFactor if necessary + JacobianFactor::shared_ptr jacobianFactor( + boost::dynamic_pointer_cast(factor)); + if (!jacobianFactor) { + HessianFactor::shared_ptr hessian( + boost::dynamic_pointer_cast(factor)); + if (hessian) + jacobianFactor.reset(new JacobianFactor(*hessian)); + else + throw std::invalid_argument( + "GaussianFactorGraph contains a factor that is neither a " + "JacobianFactor nor a HessianFactor."); + } + + // Whiten the factor and add entries for it + // iterate over all variables in the factor + const JacobianFactor whitened(jacobianFactor->whiten()); + for (JacobianFactor::const_iterator key = whitened.begin(); + key < whitened.end(); ++key) { + JacobianFactor::constABlock whitenedA = whitened.getA(key); + // find first column index for this key + size_t column_start = columnIndices[*key]; + for (size_t i = 0; i < (size_t)whitenedA.rows(); i++) + for (size_t j = 0; j < (size_t)whitenedA.cols(); j++) { + double s = whitenedA(i, j); + if (std::abs(s) > 1e-12) + entries.emplace_back(row + i, column_start + j, s); + } + } + + JacobianFactor::constBVector whitenedb(whitened.getb()); + size_t bcolumn = currentColIndex; + for (size_t i = 0; i < (size_t)whitenedb.size(); i++) { + double s = whitenedb(i); + if (std::abs(s) > 1e-12) entries.emplace_back(row + i, bcolumn, s); + } + + // Increment row index + row += jacobianFactor->rows(); + } + + // ...and make a sparse matrix with it. + SpMat Ab(row + 1, currentColIndex + 1); + Ab.setFromTriplets(entries.begin(), entries.end()); + return Ab; +} + +SpMat sparseJacobianEigen(const GaussianFactorGraph &gfg) { + return sparseJacobianEigen(gfg, Ordering(gfg.keys())); +} + +// /// obtain sparse matrix for eigen sparse solver +// std::pair obtainSparseMatrix( +// const GaussianFactorGraph &gfg, const Ordering &ordering) { +// gttic_(EigenOptimizer_obtainSparseMatrix); + +// // Get sparse entries of Jacobian [A|b] augmented with RHS b. +// auto entries = gfg.sparseJacobian(ordering); + +// gttic_(EigenOptimizer_convertSparse); +// // Convert boost tuples to Eigen triplets +// vector> triplets; +// triplets.reserve(entries.size()); +// size_t rows = 0, cols = 0; +// for (const auto &e : entries) { +// size_t temp_rows = e.get<0>(), temp_cols = e.get<1>(); +// triplets.emplace_back(temp_rows, temp_cols, e.get<2>()); +// rows = std::max(rows, temp_rows); +// cols = std::max(cols, temp_cols); +// } + +// // ...and make a sparse matrix with it. +// SpMat Ab(rows + 1, cols + 1); +// Ab.setFromTriplets(triplets.begin(), triplets.end()); +// Ab.makeCompressed(); +// gttoc_(EigenOptimizer_convertSparse); + +// gttoc_(EigenOptimizer_obtainSparseMatrix); + +// return make_pair(Ab.block(0, 0, rows + 1, cols), +// Ab.col(cols)); +// } + +} // namespace gtsam diff --git a/gtsam/linear/SparseEigenSolver.cpp b/gtsam/linear/SparseEigenSolver.cpp deleted file mode 100644 index f0dfd83f3..000000000 --- a/gtsam/linear/SparseEigenSolver.cpp +++ /dev/null @@ -1,231 +0,0 @@ -/* ---------------------------------------------------------------------------- - - * GTSAM Copyright 2010, Georgia Tech Research Corporation, - * Atlanta, Georgia 30332-0415 - * All Rights Reserved - * Authors: Frank Dellaert, et al. (see THANKS for the full author list) - - * See LICENSE for the license information - - * -------------------------------------------------------------------------- */ - -/** - * @file SparseEigenSolver.cpp - * - * @brief Eigen SparseSolver based linear solver backend for GTSAM - * - * @date Aug 2019 - * @author Mandy Xie - * @author Fan Jiang - * @author Frank Dellaert - */ - -#include -#include -#include - -#include - -using namespace std; - -namespace gtsam { - - using SpMat = Eigen::SparseMatrix; - - Eigen::SparseMatrix - SparseEigenSolver::sparseJacobianEigen( - const GaussianFactorGraph &gfg, - const Ordering &ordering) { - // First find dimensions of each variable - std::map dims; - for (const boost::shared_ptr &factor : gfg) { - if (!static_cast(factor)) - continue; - - for (auto it = factor->begin(); it != factor->end(); ++it) { - dims[*it] = factor->getDim(it); - } - } - - // Compute first scalar column of each variable - size_t currentColIndex = 0; - std::map columnIndices; - for (const auto key : ordering) { - columnIndices[key] = currentColIndex; - currentColIndex += dims[key]; - } - - // Iterate over all factors, adding sparse scalar entries - vector> entries; - entries.reserve(60 * gfg.size()); - - size_t row = 0; - for (const boost::shared_ptr &factor : gfg) { - if (!static_cast(factor)) continue; - - // Convert to JacobianFactor if necessary - JacobianFactor::shared_ptr jacobianFactor( - boost::dynamic_pointer_cast(factor)); - if (!jacobianFactor) { - HessianFactor::shared_ptr hessian( - boost::dynamic_pointer_cast(factor)); - if (hessian) - jacobianFactor.reset(new JacobianFactor(*hessian)); - else - throw invalid_argument( - "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor."); - } - - // Whiten the factor and add entries for it - // iterate over all variables in the factor - const JacobianFactor whitened(jacobianFactor->whiten()); - for (JacobianFactor::const_iterator key = whitened.begin(); - key < whitened.end(); ++key) { - JacobianFactor::constABlock whitenedA = whitened.getA(key); - // find first column index for this key - size_t column_start = columnIndices[*key]; - for (size_t i = 0; i < (size_t) whitenedA.rows(); i++) - for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { - double s = whitenedA(i, j); - if (std::abs(s) > 1e-12) - entries.emplace_back(row + i, column_start + j, s); - } - } - - JacobianFactor::constBVector whitenedb(whitened.getb()); - size_t bcolumn = currentColIndex; - for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { - double s = whitenedb(i); - if (std::abs(s) > 1e-12) - entries.emplace_back(row + i, bcolumn, s); - } - - // Increment row index - row += jacobianFactor->rows(); - } - - // ...and make a sparse matrix with it. - Eigen::SparseMatrix Ab(row + 1, currentColIndex + 1); - Ab.setFromTriplets(entries.begin(), entries.end()); - return Ab; - } - - - /// obtain sparse matrix for eigen sparse solver - std::pair obtainSparseMatrix( - const GaussianFactorGraph &gfg, - const Ordering &ordering) { - - gttic_(EigenOptimizer_obtainSparseMatrix); - - // Get sparse entries of Jacobian [A|b] augmented with RHS b. - auto entries = gfg.sparseJacobian(ordering); - - gttic_(EigenOptimizer_convertSparse); - // Convert boost tuples to Eigen triplets - vector> triplets; - triplets.reserve(entries.size()); - size_t rows = 0, cols = 0; - for (const auto &e : entries) { - size_t temp_rows = e.get<0>(), temp_cols = e.get<1>(); - triplets.emplace_back(temp_rows, temp_cols, e.get<2>()); - rows = std::max(rows, temp_rows); - cols = std::max(cols, temp_cols); - } - - // ...and make a sparse matrix with it. - SpMat Ab(rows + 1, cols + 1); - Ab.setFromTriplets(triplets.begin(), triplets.end()); - Ab.makeCompressed(); - gttoc_(EigenOptimizer_convertSparse); - - gttoc_(EigenOptimizer_obtainSparseMatrix); - - return make_pair(Ab.block(0, 0, rows + 1, cols), - Ab.col(cols)); - } - - bool SparseEigenSolver::isIterative() { - return false; - } - - bool SparseEigenSolver::isSequential() { - return false; - } - - VectorValues SparseEigenSolver::solve(const GaussianFactorGraph &gfg) { - if (solverType == QR) { - gttic_(EigenOptimizer_optimizeEigenQR); - auto Ab_pair = obtainSparseMatrix(gfg, ordering); - - // Solve A*x = b using sparse QR from Eigen - gttic_(EigenOptimizer_optimizeEigenQR_create_solver); - Eigen::SparseQR> solver(Ab_pair.first); - gttoc_(EigenOptimizer_optimizeEigenQR_create_solver); - - gttic_(EigenOptimizer_optimizeEigenQR_solve); - Eigen::VectorXd x = solver.solve(Ab_pair.second); - gttoc_(EigenOptimizer_optimizeEigenQR_solve); - - return VectorValues(x, gfg.getKeyDimMap()); - } else if (solverType == CHOLESKY) { - gttic_(EigenOptimizer_optimizeEigenCholesky); - SpMat Ab = sparseJacobianEigen(gfg, ordering); - auto rows = Ab.rows(), cols = Ab.cols(); - auto A = Ab.block(0, 0, rows, cols - 1); - auto At = A.transpose(); - auto b = Ab.col(cols - 1); - - SpMat AtA(A.cols(), A.cols()); - AtA.selfadjointView().rankUpdate(At); - - gttic_(EigenOptimizer_optimizeEigenCholesky_create_solver); - // Solve A*x = b using sparse Cholesky from Eigen - Eigen::SimplicialLDLT> - solver(AtA); - - gttoc_(EigenOptimizer_optimizeEigenCholesky_create_solver); - - gttic_(EigenOptimizer_optimizeEigenCholesky_solve); - Eigen::VectorXd x = solver.solve(At * b); - gttoc_(EigenOptimizer_optimizeEigenCholesky_solve); - - // NOTE: b is reordered now, so we need to transform back the order. - // First find dimensions of each variable - std::map dims; - for (const boost::shared_ptr &factor : gfg) { - if (!static_cast(factor)) - continue; - - for (auto it = factor->begin(); it != factor->end(); ++it) { - dims[*it] = factor->getDim(it); - } - } - - VectorValues vv; - - std::map columnIndices; - - { - size_t currentColIndex = 0; - for (const auto key : ordering) { - columnIndices[key] = currentColIndex; - currentColIndex += dims[key]; - } - } - - for (const pair keyDim : dims) { - vv.insert(keyDim.first, x.segment(columnIndices[keyDim.first], keyDim.second)); - } - - return vv; - } - - throw std::exception(); - } - - SparseEigenSolver::SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering) { - solverType = type; - this->ordering = ordering; - } -} // namespace gtsam \ No newline at end of file diff --git a/gtsam/linear/SparseEigenSolver.h b/gtsam/linear/SparseEigenSolver.h deleted file mode 100644 index d71365864..000000000 --- a/gtsam/linear/SparseEigenSolver.h +++ /dev/null @@ -1,62 +0,0 @@ -/* ---------------------------------------------------------------------------- - - * GTSAM Copyright 2010, Georgia Tech Research Corporation, - * Atlanta, Georgia 30332-0415 - * All Rights Reserved - * Authors: Frank Dellaert, et al. (see THANKS for the full author list) - - * See LICENSE for the license information - - * -------------------------------------------------------------------------- */ - -/** - * @file SparseEigenSolver.h - * - * @brief Eigen SparseSolver based linear solver backend for GTSAM - * - * @date Aug 2019 - * @author Mandy Xie - * @author Fan Jiang - * @author Frank Dellaert - */ - -#pragma once - -#include -#include -#include -#include -#include - -namespace gtsam { - - /** - * Eigen SparseSolver based Backend class - */ - class GTSAM_EXPORT SparseEigenSolver : public LinearSolver { - public: - - typedef enum { - QR, - CHOLESKY - } SparseEigenSolverType; - - - explicit SparseEigenSolver(SparseEigenSolver::SparseEigenSolverType type, const Ordering &ordering); - - bool isIterative() override; - - bool isSequential() override; - - VectorValues solve(const GaussianFactorGraph &gfg) override; - - static Eigen::SparseMatrix - sparseJacobianEigen(const GaussianFactorGraph &gfg, const Ordering &ordering); - - protected: - - SparseEigenSolverType solverType = QR; - - Ordering ordering; - }; -} // namespace gtsam diff --git a/gtsam/linear/tests/testSparseEigen.cpp b/gtsam/linear/tests/testSparseEigen.cpp new file mode 100644 index 000000000..225e1dab2 --- /dev/null +++ b/gtsam/linear/tests/testSparseEigen.cpp @@ -0,0 +1,72 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file testSparseMatrix.cpp + * @author Mandy Xie + * @author Fan Jiang + * @author Gerry Chen + * @author Frank Dellaert + * @date Jan, 2021 + */ + +#include +#include + +#include +using boost::assign::list_of; + +#include +#include + +using namespace std; +using namespace gtsam; + +/* ************************************************************************* */ +TEST(SparseEigen, sparseJacobianEigen) { + GaussianFactorGraph gfg; + SharedDiagonal model = noiseModel::Isotropic::Sigma(2, 0.5); + const Key x123 = 0, x45 = 1; + gfg.add(x123, (Matrix(2, 3) << 1, 2, 3, 5, 6, 7).finished(), + Vector2(4, 8), model); + gfg.add(x123, (Matrix(2, 3) << 9, 10, 0, 0, 0, 0).finished(), + x45, (Matrix(2, 2) << 11, 12, 14, 15.).finished(), + Vector2(13, 16), model); + + // Sparse Matrix + auto sparseResult = sparseJacobianEigen(gfg); + EXPECT_LONGS_EQUAL(16, sparseResult.nonZeros()); + EXPECT(assert_equal(4, sparseResult.rows())); + EXPECT(assert_equal(6, sparseResult.cols())); + EXPECT(assert_equal(gfg.augmentedJacobian(), Matrix(sparseResult))); + + // Call sparseJacobian with optional ordering... + auto ordering = Ordering(list_of(x45)(x123)); + + // Eigen Sparse with optional ordering + EXPECT(assert_equal(gfg.augmentedJacobian(ordering), + Matrix(sparseJacobianEigen(gfg, ordering)))); + + // Check matrix dimensions when zero rows / cols + gfg.add(x123, Matrix23::Zero(), Vector2::Zero(), model); // zero row + gfg.add(2, Matrix21::Zero(), Vector2::Zero(), model); // zero col + sparseResult = sparseJacobianEigen(gfg); + EXPECT_LONGS_EQUAL(16, sparseResult.nonZeros()); + EXPECT(assert_equal(8, sparseResult.rows())); + EXPECT(assert_equal(7, sparseResult.cols())); +} + +/* ************************************************************************* */ +int main() { + TestResult tr; + return TestRegistry::runAllTests(tr); +} +/* ************************************************************************* */ From ee5701dcda6a3aeb05d30991bfd7aefd3bf7a443 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Mon, 18 Jan 2021 20:39:53 -0500 Subject: [PATCH 30/65] fix off-by-one bug --- gtsam/linear/SparseEigen.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index a157be2b1..35062c4fe 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -102,7 +102,7 @@ SpMat sparseJacobianEigen( } // ...and make a sparse matrix with it. - SpMat Ab(row + 1, currentColIndex + 1); + SpMat Ab(row, currentColIndex + 1); Ab.setFromTriplets(entries.begin(), entries.end()); return Ab; } From d9c03aa827f3b8e30180c41dd94249515ad376c0 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Mon, 18 Jan 2021 20:56:44 -0500 Subject: [PATCH 31/65] cleanup --- gtsam/linear/SparseEigen.h | 37 +++++-------------------------------- 1 file changed, 5 insertions(+), 32 deletions(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 35062c4fe..5ee67f6d9 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -32,8 +32,13 @@ namespace gtsam { typedef Eigen::SparseMatrix SpMat; +/// Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph SpMat sparseJacobianEigen( const GaussianFactorGraph &gfg, const Ordering &ordering) { + // TODO(gerry): eliminate copy/pasta by making GaussianFactorGraph version + // more general, or by creating an Eigen::Triplet compatible wrapper for + // boost::tuple return type + // First find dimensions of each variable std::map dims; for (const boost::shared_ptr &factor : gfg) { @@ -111,36 +116,4 @@ SpMat sparseJacobianEigen(const GaussianFactorGraph &gfg) { return sparseJacobianEigen(gfg, Ordering(gfg.keys())); } -// /// obtain sparse matrix for eigen sparse solver -// std::pair obtainSparseMatrix( -// const GaussianFactorGraph &gfg, const Ordering &ordering) { -// gttic_(EigenOptimizer_obtainSparseMatrix); - -// // Get sparse entries of Jacobian [A|b] augmented with RHS b. -// auto entries = gfg.sparseJacobian(ordering); - -// gttic_(EigenOptimizer_convertSparse); -// // Convert boost tuples to Eigen triplets -// vector> triplets; -// triplets.reserve(entries.size()); -// size_t rows = 0, cols = 0; -// for (const auto &e : entries) { -// size_t temp_rows = e.get<0>(), temp_cols = e.get<1>(); -// triplets.emplace_back(temp_rows, temp_cols, e.get<2>()); -// rows = std::max(rows, temp_rows); -// cols = std::max(cols, temp_cols); -// } - -// // ...and make a sparse matrix with it. -// SpMat Ab(rows + 1, cols + 1); -// Ab.setFromTriplets(triplets.begin(), triplets.end()); -// Ab.makeCompressed(); -// gttoc_(EigenOptimizer_convertSparse); - -// gttoc_(EigenOptimizer_obtainSparseMatrix); - -// return make_pair(Ab.block(0, 0, rows + 1, cols), -// Ab.col(cols)); -// } - } // namespace gtsam From 9c781b605ff81533fdf9a4c145004a2ce27433a4 Mon Sep 17 00:00:00 2001 From: jingwuOUO Date: Tue, 19 Jan 2021 00:07:21 -0500 Subject: [PATCH 32/65] Set estimateBeta() as optional --- gtsam/linear/AcceleratedPowerMethod.h | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/gtsam/linear/AcceleratedPowerMethod.h b/gtsam/linear/AcceleratedPowerMethod.h index 4cb25daf7..6653d43c9 100644 --- a/gtsam/linear/AcceleratedPowerMethod.h +++ b/gtsam/linear/AcceleratedPowerMethod.h @@ -69,10 +69,7 @@ class AcceleratedPowerMethod : public PowerMethod { previousVector_ = Vector::Zero(this->dim_); // initialize beta_ - if (!initialBeta) { - beta_ = estimateBeta(); - } else - beta_ = initialBeta; + beta_ = initialBeta; } /** @@ -97,8 +94,11 @@ class AcceleratedPowerMethod : public PowerMethod { return y; } - /// Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3) - double estimateBeta() const { + /** + * Tuning the momentum beta using the Best Heavy Ball algorithm in Ref(3), T + * is the iteration time to find beta with largest Rayleigh quotient + */ + double estimateBeta(const size_t T = 10) const { // set initial estimation of maxBeta Vector initVector = this->ritzVector_; const double up = initVector.dot( this->A_ * initVector ); @@ -109,7 +109,6 @@ class AcceleratedPowerMethod : public PowerMethod { std::vector betas; Matrix R = Matrix::Zero(this->dim_, 10); - const size_t T = 10; // run T times of iteration to find the beta that has the largest Rayleigh quotient for (size_t t = 0; t < T; t++) { // after each t iteration, reset the betas with the current maxBeta @@ -120,13 +119,14 @@ class AcceleratedPowerMethod : public PowerMethod { // initialize x0 and x00 in each iteration of each beta Vector x0 = initVector; Vector x00 = Vector::Zero(this->dim_); - // run 10 steps of accelerated power iteration with this beta + // run 10 steps of accelerated power iteration with this beta for (size_t j = 1; j < 10; j++) { if (j < 2) { R.col(0) = acceleratedPowerIteration(x0, x00, betas[k]); R.col(1) = acceleratedPowerIteration(R.col(0), x0, betas[k]); } else { - R.col(j) = acceleratedPowerIteration(R.col(j - 1), R.col(j - 2), betas[k]); + R.col(j) = acceleratedPowerIteration(R.col(j - 1), R.col(j - 2), + betas[k]); } } // compute the Rayleigh quotient for the randomly sampled vector after From bb662f0cb439205b6b3fb05ee87c21b274a7b0b2 Mon Sep 17 00:00:00 2001 From: Russell Buchanan Date: Tue, 19 Jan 2021 10:49:42 +0000 Subject: [PATCH 33/65] clean up --- tests/testImuPreintegration.cpp | 31 +++---------------------------- 1 file changed, 3 insertions(+), 28 deletions(-) diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp index 43b3461ee..7975ff794 100644 --- a/tests/testImuPreintegration.cpp +++ b/tests/testImuPreintegration.cpp @@ -49,8 +49,6 @@ TEST(TestImuPreintegration, LoadedSimulationData) { double rate = 400.0; // Hz string inFileString = findExampleDataFile("quadraped_imu_data.csv"); - ofstream outputFile; - outputFile.open("imu_preint_output.csv", ios::out); ifstream inputFile(inFileString); string line; while (getline(inputFile, line)) { @@ -95,27 +93,13 @@ TEST(TestImuPreintegration, LoadedSimulationData) { NavState initialNavState(priorPose, priorVelocity); - // Bias estimated by my Algorithm - priorImuBias = imuBias::ConstantBias( - Eigen::Vector3d(-0.0314648, 0.0219921, 6.95945e-05), - Eigen::Vector3d(4.88581e-08, -1.04971e-09, -0.000122868)); - - // zero bias - // priorImuBias = imuBias::ConstantBias(Eigen::Vector3d(0,0,0), - // Eigen::Vector3d(0,0,0)); + // Assume zero bias for simulated data + priorImuBias = imuBias::ConstantBias(Eigen::Vector3d(0,0,0), + Eigen::Vector3d(0,0,0)); imuPreintegrated = PreintegratedCombinedMeasurements( imuPreintegratedParams, priorImuBias); - // Put header row in output csv - outputFile << "X Position," - << "Y Position," - << "Z Position," - << "X Velocity," - << "Y Velocity," - << "Z Velocity," - << "\n"; - // start at 1 to skip header for (size_t n = 1; n < imuMeasurements.size(); n++) { // integrate @@ -127,17 +111,8 @@ TEST(TestImuPreintegration, LoadedSimulationData) { velocity = propState.velocity(); // cout << "IMU Position " << position.transpose() << endl; // cout << "IMU Velocity " << velocity.transpose() << endl; - - // Write to csv - outputFile << to_string(position.x()) << "," << to_string(position.y()) - << "," << to_string(position.z()) << "," - << to_string(velocity.x()) << "," << to_string(velocity.y()) - << "," << to_string(velocity.z()) << "," - << "\n"; } - outputFile.close(); - Vector3 rotation = propState.pose().rotation().rpy(); // Dont have ground truth for x and y position yet From d8491b27fb010e5d0061c8926730b11512433578 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 10:53:22 -0500 Subject: [PATCH 34/65] rename matrix type from `SpMat` to `SparseEigen` --- gtsam/linear/SparseEigen.h | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 5ee67f6d9..ee2a26330 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -30,10 +30,10 @@ namespace gtsam { -typedef Eigen::SparseMatrix SpMat; +typedef Eigen::SparseMatrix SparseEigen; /// Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph -SpMat sparseJacobianEigen( +SparseEigen sparseJacobianEigen( const GaussianFactorGraph &gfg, const Ordering &ordering) { // TODO(gerry): eliminate copy/pasta by making GaussianFactorGraph version // more general, or by creating an Eigen::Triplet compatible wrapper for @@ -107,12 +107,12 @@ SpMat sparseJacobianEigen( } // ...and make a sparse matrix with it. - SpMat Ab(row, currentColIndex + 1); + SparseEigen Ab(row, currentColIndex + 1); Ab.setFromTriplets(entries.begin(), entries.end()); return Ab; } -SpMat sparseJacobianEigen(const GaussianFactorGraph &gfg) { +SparseEigen sparseJacobianEigen(const GaussianFactorGraph &gfg) { return sparseJacobianEigen(gfg, Ordering(gfg.keys())); } From 25e3b5609e64999c8a42b6416cf5c4634693663c Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 11:01:25 -0500 Subject: [PATCH 35/65] roll back some cosmetic changes to minimize the diff --- .../linear/tests/testGaussianFactorGraph.cpp | 48 ++++++++++--------- 1 file changed, 26 insertions(+), 22 deletions(-) diff --git a/gtsam/linear/tests/testGaussianFactorGraph.cpp b/gtsam/linear/tests/testGaussianFactorGraph.cpp index 57a663e8c..0ae500824 100644 --- a/gtsam/linear/tests/testGaussianFactorGraph.cpp +++ b/gtsam/linear/tests/testGaussianFactorGraph.cpp @@ -82,6 +82,29 @@ TEST(GaussianFactorGraph, sparseJacobian) { // 5 6 7 0 0 8 // 9 10 0 11 12 13 // 0 0 0 14 15 16 + + // Expected + Matrix expected = (Matrix(16, 3) << + 1., 1., 2., + 1., 2., 4., + 1., 3., 6., + 2., 1.,10., + 2., 2.,12., + 2., 3.,14., + 1., 6., 8., + 2., 6.,16., + 3., 1.,18., + 3., 2.,20., + 3., 4.,22., + 3., 5.,24., + 4., 4.,28., + 4., 5.,30., + 3., 6.,26., + 4., 6.,32.).finished(); + + // expected: in matlab format - NOTE the transpose!) + Matrix expectedMatlab = expected.transpose(); + GaussianFactorGraph gfg; SharedDiagonal model = noiseModel::Isotropic::Sigma(2, 0.5); const Key x123 = 0, x45 = 1; @@ -91,28 +114,9 @@ TEST(GaussianFactorGraph, sparseJacobian) { x45, (Matrix(2, 2) << 11, 12, 14, 15.).finished(), Vector2(13, 16), model); - // Check version for MATLAB - NOTE that we transpose this! - Matrix expectedT = (Matrix(16, 3) << - 1, 1, 2., - 1, 2, 4., - 1, 3, 6., - 2, 1, 10., - 2, 2, 12., - 2, 3, 14., - 1, 6, 8., - 2, 6, 16., - 3, 1, 18., - 3, 2, 20., - 3, 4, 22., - 3, 5, 24., - 4, 4, 28., - 4, 5, 30., - 3, 6, 26., - 4, 6, 32.).finished(); + Matrix actual = gfg.sparseJacobian_(); - // matrix form (matlab) - Matrix expectedMatlab = expectedT.transpose(); - EXPECT(assert_equal(expectedMatlab, gfg.sparseJacobian_())); + EXPECT(assert_equal(expected, actual)); // BoostTriplets auto boostActual = gfg.sparseJacobian(); @@ -121,7 +125,7 @@ TEST(GaussianFactorGraph, sparseJacobian) { // check content for (int i = 0; i < 16; i++) { EXPECT(triplet_equal( - BoostTriplet(expectedT(i, 0) - 1, expectedT(i, 1) - 1, expectedT(i, 2)), + BoostTriplet(expected(i, 0) - 1, expected(i, 1) - 1, expected(i, 2)), boostActual.at(i))); } } From e2f5be4e4700e26758f100881375627ae0368c64 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 11:04:26 -0500 Subject: [PATCH 36/65] SparseEigen docstring --- gtsam/linear/SparseEigen.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index ee2a26330..7963d3ef5 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -12,7 +12,7 @@ /** * @file SparseEigen.h * - * @brief Utilities for converting to Eigen's sparse matrix representations + * @brief Utilities for creating Eigen sparse matrices (gtsam::SparseEigen) * * @date Aug 2019 * @author Mandy Xie From b76993b171a44c902fcc6cbb45794bc245808042 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 11:47:44 -0500 Subject: [PATCH 37/65] typo: `expected` changed to `expectedMatlab` --- gtsam/linear/tests/testGaussianFactorGraph.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/linear/tests/testGaussianFactorGraph.cpp b/gtsam/linear/tests/testGaussianFactorGraph.cpp index 0ae500824..8b9ce94a9 100644 --- a/gtsam/linear/tests/testGaussianFactorGraph.cpp +++ b/gtsam/linear/tests/testGaussianFactorGraph.cpp @@ -116,7 +116,7 @@ TEST(GaussianFactorGraph, sparseJacobian) { Matrix actual = gfg.sparseJacobian_(); - EXPECT(assert_equal(expected, actual)); + EXPECT(assert_equal(expectedMatlab, actual)); // BoostTriplets auto boostActual = gfg.sparseJacobian(); From 77c65f81763e9cd6d95a24c2fa31af6e8ebce851 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 14:03:14 -0500 Subject: [PATCH 38/65] timing sparse eigen --- gtsam/linear/SparseEigen.h | 2 ++ 1 file changed, 2 insertions(+) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 7963d3ef5..9df74f9fc 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -38,6 +38,7 @@ SparseEigen sparseJacobianEigen( // TODO(gerry): eliminate copy/pasta by making GaussianFactorGraph version // more general, or by creating an Eigen::Triplet compatible wrapper for // boost::tuple return type + gttic_(SparseEigen_sparseJacobianEigen); // First find dimensions of each variable std::map dims; @@ -113,6 +114,7 @@ SparseEigen sparseJacobianEigen( } SparseEigen sparseJacobianEigen(const GaussianFactorGraph &gfg) { + gttic_(SparseEigen_sparseJacobianEigen_defaultOrdering); return sparseJacobianEigen(gfg, Ordering(gfg.keys())); } From ada83d92dc8c939cb44b917c31e690d130b7d9f0 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 14:38:10 -0500 Subject: [PATCH 39/65] minor efficiency modifications --- gtsam/linear/GaussianFactorGraph.cpp | 2 +- gtsam/linear/SparseEigen.h | 4 +++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 69890c32d..9a22d6111 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -154,7 +154,7 @@ namespace gtsam { for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { double s = whitenedA(i, j); if (std::abs(s) > 1e-12) - entries.push_back(boost::make_tuple(row + i, column_start + j, s)); + entries.emplace_back(row + i, column_start + j, s); } } diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 9df74f9fc..eac4178aa 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -30,7 +30,9 @@ namespace gtsam { -typedef Eigen::SparseMatrix SparseEigen; +/// Eigen-format sparse matrix. Note: ColMajor is ~20% faster since +/// InnerIndices must be sorted +typedef Eigen::SparseMatrix SparseEigen; /// Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph SparseEigen sparseJacobianEigen( From 6f6588457b7330799e261c66c5514fd963ff8623 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:22:41 -0500 Subject: [PATCH 40/65] use streams instead of printf --- gtsam/base/Testable.h | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/gtsam/base/Testable.h b/gtsam/base/Testable.h index 92c464940..2145360df 100644 --- a/gtsam/base/Testable.h +++ b/gtsam/base/Testable.h @@ -33,9 +33,9 @@ #pragma once -#include #include -#include +#include +#include #include #define GTSAM_PRINT(x)((x).print(#x)) @@ -72,10 +72,10 @@ namespace gtsam { }; // \ Testable inline void print(float v, const std::string& s = "") { - printf("%s%f\n",s.c_str(),v); + std::cout << (s == "" ? s : s + " ") << v << std::endl; } inline void print(double v, const std::string& s = "") { - printf("%s%lf\n",s.c_str(),v); + std::cout << (s == "" ? s : s + " ") << v << std::endl; } /** Call equal on the object */ From 56eb1bb808483bcbb1a369034ca5e73fe06e4640 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:23:14 -0500 Subject: [PATCH 41/65] use of passed in stream for print capture --- gtsam/base/Matrix.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/gtsam/base/Matrix.cpp b/gtsam/base/Matrix.cpp index 551bdac10..41a80629b 100644 --- a/gtsam/base/Matrix.cpp +++ b/gtsam/base/Matrix.cpp @@ -153,7 +153,7 @@ const Eigen::IOFormat& matlabFormat() { /* ************************************************************************* */ //3 argument call void print(const Matrix& A, const string &s, ostream& stream) { - cout << s << A.format(matlabFormat()) << endl; + stream << s << A.format(matlabFormat()) << endl; } /* ************************************************************************* */ From 2168cd4a04da47478eb1985d1268b157c03c1fc5 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:39:37 -0500 Subject: [PATCH 42/65] stream printing for Pose2 --- gtsam/geometry/Pose2.cpp | 8 +++++++- gtsam/geometry/Pose2.h | 4 ++++ 2 files changed, 11 insertions(+), 1 deletion(-) diff --git a/gtsam/geometry/Pose2.cpp b/gtsam/geometry/Pose2.cpp index 71df0f753..bebe53dfa 100644 --- a/gtsam/geometry/Pose2.cpp +++ b/gtsam/geometry/Pose2.cpp @@ -48,7 +48,13 @@ Matrix3 Pose2::matrix() const { /* ************************************************************************* */ void Pose2::print(const string& s) const { - cout << s << "(" << t_.x() << ", " << t_.y() << ", " << r_.theta() << ")" << endl; + cout << s << this << endl; +} + +/* ************************************************************************* */ +std::ostream &operator<<(std::ostream &os, const Pose2& pose) { + os << "(" << pose.x() << ", " << pose.y() << ", " << pose.theta() << ")"; + return os; } /* ************************************************************************* */ diff --git a/gtsam/geometry/Pose2.h b/gtsam/geometry/Pose2.h index 6372779c3..a54951728 100644 --- a/gtsam/geometry/Pose2.h +++ b/gtsam/geometry/Pose2.h @@ -287,6 +287,10 @@ public: */ static std::pair rotationInterval() { return std::make_pair(2, 2); } + /// Output stream operator + GTSAM_EXPORT + friend std::ostream &operator<<(std::ostream &os, const Pose2& p); + /// @} private: From afb28e91b67f16679c6f779d6da1385044a30301 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:40:21 -0500 Subject: [PATCH 43/65] add BearingRange measured to wrapper --- gtsam/gtsam.i | 2 ++ 1 file changed, 2 insertions(+) diff --git a/gtsam/gtsam.i b/gtsam/gtsam.i index abba7437d..22c2cc17d 100644 --- a/gtsam/gtsam.i +++ b/gtsam/gtsam.i @@ -2623,6 +2623,8 @@ virtual class BearingRangeFactor : gtsam::NoiseModelFactor { const BEARING& measuredBearing, const RANGE& measuredRange, const gtsam::noiseModel::Base* noiseModel); + BearingRange measured() const; + // enabling serialization functionality void serialize() const; }; From f831bfd62ec56373677c52ea5e035f2816451de0 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:40:37 -0500 Subject: [PATCH 44/65] add override and formatting --- gtsam_unstable/slam/SmartStereoProjectionPoseFactor.h | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/gtsam_unstable/slam/SmartStereoProjectionPoseFactor.h b/gtsam_unstable/slam/SmartStereoProjectionPoseFactor.h index 93a83ab30..2ecd7b75c 100644 --- a/gtsam_unstable/slam/SmartStereoProjectionPoseFactor.h +++ b/gtsam_unstable/slam/SmartStereoProjectionPoseFactor.h @@ -113,12 +113,13 @@ class SmartStereoProjectionPoseFactor : public SmartStereoProjectionFactor { * print * @param s optional string naming the factor * @param keyFormatter optional formatter useful for printing Symbols - */ void print( - const std::string& s = "", - const KeyFormatter& keyFormatter = DefaultKeyFormatter) const override; + */ + void print(const std::string& s = "", const KeyFormatter& keyFormatter = + DefaultKeyFormatter) const override; /// equals - virtual bool equals(const NonlinearFactor& p, double tol = 1e-9) const; + virtual bool equals(const NonlinearFactor& p, + double tol = 1e-9) const override; /** * error calculates the error of the factor. @@ -155,4 +156,4 @@ template <> struct traits : public Testable {}; -} // \ namespace gtsam +} // namespace gtsam From 7eeed6dc14c61f7eeeda35a642bafb1df5888aad Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 15:47:15 -0500 Subject: [PATCH 45/65] remove cout statements from testImuPreintegration tests --- tests/testImuPreintegration.cpp | 8 ++------ 1 file changed, 2 insertions(+), 6 deletions(-) diff --git a/tests/testImuPreintegration.cpp b/tests/testImuPreintegration.cpp index 2a2553697..1f584be0e 100644 --- a/tests/testImuPreintegration.cpp +++ b/tests/testImuPreintegration.cpp @@ -64,8 +64,6 @@ TEST(TestImuPreintegration, LoadedSimulationData) { measurement.I_a_WI = {results[29], results[30], results[31]}; measurement.I_w_WI = {results[17], results[18], results[19]}; imuMeasurements.push_back(measurement); - - // cout << "IMU measurement " << measurement << endl; } // Assume a Z-up navigation (assuming we are performing optimization in the @@ -92,8 +90,8 @@ TEST(TestImuPreintegration, LoadedSimulationData) { NavState initialNavState(priorPose, priorVelocity); // Assume zero bias for simulated data - priorImuBias = imuBias::ConstantBias(Eigen::Vector3d(0,0,0), - Eigen::Vector3d(0,0,0)); + priorImuBias = + imuBias::ConstantBias(Eigen::Vector3d(0, 0, 0), Eigen::Vector3d(0, 0, 0)); imuPreintegrated = PreintegratedCombinedMeasurements(imuPreintegratedParams, priorImuBias); @@ -107,8 +105,6 @@ TEST(TestImuPreintegration, LoadedSimulationData) { propState = imuPreintegrated.predict(initialNavState, priorImuBias); position = propState.pose().translation(); velocity = propState.velocity(); - // cout << "IMU Position " << position.transpose() << endl; - // cout << "IMU Velocity " << velocity.transpose() << endl; } Vector3 rotation = propState.pose().rotation().rpy(); From 7a6f632f4cbb898da3c79f1a1697d22b71d3ee13 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 16:59:12 -0500 Subject: [PATCH 46/65] add generic optional parameters to sparseJacobian Also, the unit test changed due to a 0 entry that was previously wrongly included in the b-column of the sparse representation. --- gtsam/base/Matrix.h | 8 ++ gtsam/linear/GaussianFactorGraph.cpp | 107 ++++++++++++------ gtsam/linear/GaussianFactorGraph.h | 46 +++++++- .../linear/tests/testGaussianFactorGraph.cpp | 9 +- 4 files changed, 128 insertions(+), 42 deletions(-) diff --git a/gtsam/base/Matrix.h b/gtsam/base/Matrix.h index a3a14c6c3..11058ef40 100644 --- a/gtsam/base/Matrix.h +++ b/gtsam/base/Matrix.h @@ -33,6 +33,8 @@ #include #include +#include + /** * Matrix is a typedef in the gtsam namespace * TODO: make a version to work with matlab wrapping @@ -73,6 +75,12 @@ GTSAM_MAKE_MATRIX_DEFS(9); typedef Eigen::Block SubMatrix; typedef Eigen::Block ConstSubMatrix; +/// Sparse matrix representation as vector of tuples. +/// See SparseMatrix.h for additional representations SparseMatrixEigenTriplets +/// and SparseMatrixEigen +typedef std::vector> + SparseMatrixBoostTriplets; + // Matrix formatting arguments when printing. // Akin to Matlab style. const Eigen::IOFormat& matlabFormat(); diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 9a22d6111..7790b5328 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -100,7 +100,9 @@ namespace gtsam { } /* ************************************************************************* */ - vector > GaussianFactorGraph::sparseJacobian() const { + SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + const Ordering& ordering, size_t& nrows, size_t& ncols) const { + gttic_(GaussianFactorGraph_sparseJacobian); // First find dimensions of each variable typedef std::map KeySizeMap; KeySizeMap dims; @@ -108,24 +110,24 @@ namespace gtsam { if (!static_cast(factor)) continue; - for (GaussianFactor::const_iterator key = factor->begin(); - key != factor->end(); ++key) { - dims[*key] = factor->getDim(key); + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); } } // Compute first scalar column of each variable - size_t currentColIndex = 0; + ncols = 0; KeySizeMap columnIndices = dims; - for (const KeySizeMap::value_type& col : dims) { - columnIndices[col.first] = currentColIndex; - currentColIndex += dims[col.first]; + for (const auto key : ordering) { + columnIndices[key] = ncols; + ncols += dims[key]; } // Iterate over all factors, adding sparse scalar entries - typedef boost::tuple triplet; - vector entries; - size_t row = 0; + SparseMatrixBoostTriplets entries; + entries.reserve(60 * size()); + + nrows = 0; for (const sharedFactor& factor : *this) { if (!static_cast(factor)) continue; @@ -154,38 +156,79 @@ namespace gtsam { for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { double s = whitenedA(i, j); if (std::abs(s) > 1e-12) - entries.emplace_back(row + i, column_start + j, s); + entries.emplace_back(nrows + i, column_start + j, s); } } JacobianFactor::constBVector whitenedb(whitened.getb()); - size_t bcolumn = currentColIndex; - for (size_t i = 0; i < (size_t) whitenedb.size(); i++) - entries.push_back(boost::make_tuple(row + i, bcolumn, whitenedb(i))); + for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { + double s = whitenedb(i); + if (std::abs(s) > 1e-12) entries.emplace_back(nrows + i, ncols, s); + } // Increment row index - row += jacobianFactor->rows(); + nrows += jacobianFactor->rows(); } - return vector(entries.begin(), entries.end()); + + ncols++; // +1 for b-column + return entries; + } + + /* ************************************************************************* */ + SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + const Ordering& ordering) const { + size_t dummy1, dummy2; + return sparseJacobian(ordering, dummy1, dummy2); + } + + /* ************************************************************************* */ + SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + size_t& nrows, size_t& ncols) const { + return sparseJacobian(Ordering(this->keys()), nrows, ncols); + } + + /* ************************************************************************* */ + SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian() const { + size_t dummy1, dummy2; + return sparseJacobian(dummy1, dummy2); + } + + /* ************************************************************************* */ + Matrix GaussianFactorGraph::sparseJacobian_( + const Ordering& ordering, size_t& nrows, size_t& ncols) const { + gttic_(GaussianFactorGraph_sparseJacobian_matrix); + // call sparseJacobian + auto result = sparseJacobian(ordering, nrows, ncols); + + // translate to base 1 matrix + size_t nzmax = result.size(); + Matrix IJS(3, nzmax); + for (size_t k = 0; k < result.size(); k++) { + const auto& entry = result[k]; + IJS(0, k) = double(entry.get<0>() + 1); + IJS(1, k) = double(entry.get<1>() + 1); + IJS(2, k) = entry.get<2>(); + } + return IJS; + } + + /* ************************************************************************* */ + Matrix GaussianFactorGraph::sparseJacobian_( + const Ordering& ordering) const { + size_t dummy1, dummy2; + return sparseJacobian_(ordering, dummy1, dummy2); + } + + /* ************************************************************************* */ + Matrix GaussianFactorGraph::sparseJacobian_( + size_t& nrows, size_t& ncols) const { + return sparseJacobian_(Ordering(this->keys()), nrows, ncols); } /* ************************************************************************* */ Matrix GaussianFactorGraph::sparseJacobian_() const { - - // call sparseJacobian - typedef boost::tuple triplet; - vector result = sparseJacobian(); - - // translate to base 1 matrix - size_t nzmax = result.size(); - Matrix IJS(3,nzmax); - for (size_t k = 0; k < result.size(); k++) { - const triplet& entry = result[k]; - IJS(0,k) = double(entry.get<0>() + 1); - IJS(1,k) = double(entry.get<1>() + 1); - IJS(2,k) = entry.get<2>(); - } - return IJS; + size_t dummy1, dummy2; + return sparseJacobian_(dummy1, dummy2); } /* ************************************************************************* */ diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 2b9e8e675..5eb47ca48 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -181,17 +181,51 @@ namespace gtsam { ///@{ /** - * Return vector of i, j, and s to generate an m-by-n sparse Jacobian matrix, - * where i(k) and j(k) are the base 0 row and column indices, s(k) a double. - * The standard deviations are baked into A and b + * Return vector of i, j, and s to generate an m-by-n sparse augmented + * Jacobian matrix, where i(k) and j(k) are the base 0 row and column + * indices, s(k) a double. The standard deviations are baked into A and b + * @param ordering the column ordering + * @param[out] nrows The number of rows in the Jacobian + * @param[out] ncols The number of columns in the Jacobian + * @return the sparse matrix in one of the 4 forms above */ - std::vector > sparseJacobian() const; + SparseMatrixBoostTriplets sparseJacobian(const Ordering& ordering, + size_t& nrows, + size_t& ncols) const; + + /// Returns a sparse augmented Jacobian without outputting its dimensions + SparseMatrixBoostTriplets sparseJacobian( + const Ordering& ordering) const; + + /// Returns a sparse augmented Jacobian with default Ordering + SparseMatrixBoostTriplets sparseJacobian(size_t& nrows, + size_t& ncols) const; + + /// Returns a sparse augmented Jacobian without with default ordering and + /// outputting its dimensions + SparseMatrixBoostTriplets sparseJacobian() const; /** - * Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] entries - * such that S(i(k),j(k)) = s(k), which can be given to MATLAB's sparse. + * Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] + * entries such that S(i(k),j(k)) = s(k), which can be given to MATLAB's + * sparse. Note: i, j are 1-indexed. * The standard deviations are baked into A and b */ + Matrix sparseJacobian_(const Ordering& ordering, + size_t& nrows, + size_t& ncols) const; + + /// Returns a matrix-form sparse augmented Jacobian without outputting its + /// dimensions + Matrix sparseJacobian_( + const Ordering& ordering) const; + + /// Returns a matrix-form sparse augmented Jacobian with default Ordering + Matrix sparseJacobian_(size_t& nrows, + size_t& ncols) const; + + /// Returns a matrix-form sparse augmented Jacobian with default ordering + /// and without outputting its dimensions Matrix sparseJacobian_() const; /** diff --git a/gtsam/linear/tests/testGaussianFactorGraph.cpp b/gtsam/linear/tests/testGaussianFactorGraph.cpp index 8b9ce94a9..493e7667c 100644 --- a/gtsam/linear/tests/testGaussianFactorGraph.cpp +++ b/gtsam/linear/tests/testGaussianFactorGraph.cpp @@ -66,10 +66,11 @@ TEST(GaussianFactorGraph, initialization) { // Test sparse, which takes a vector and returns a matrix, used in MATLAB // Note that this the augmented vector and the RHS is in column 7 Matrix expectedIJS = - (Matrix(3, 22) << 1., 2., 1., 2., 3., 4., 3., 4., 3., 4., 5., 6., 5., 6., 5., 6., 7., 8., 7., - 8., 7., 8., 1., 2., 7., 7., 1., 2., 3., 4., 7., 7., 1., 2., 5., 6., 7., 7., 3., 4., 5., 6., - 7., 7., 10., 10., -1., -1., -10., -10., 10., 10., 2., -1., -5., -5., 5., 5., 0., 1., -5., - -5., 5., 5., -1., 1.5).finished(); + (Matrix(3, 21) << + 1., 2., 1., 2., 3., 4., 3., 4., 3., 4., 5., 6., 5., 6., 6., 7., 8., 7., 8., 7., 8., + 1., 2., 7., 7., 1., 2., 3., 4., 7., 7., 1., 2., 5., 6., 7., 3., 4., 5., 6., 7., 7., + 10., 10., -1., -1., -10., -10., 10., 10., 2., -1., -5., -5., 5., 5., + 1., -5., -5., 5., 5., -1., 1.5).finished(); Matrix actualIJS = fg.sparseJacobian_(); EQUALITY(expectedIJS, actualIJS); } From e3dd22925a2507805aff8c21d4e6b56e4f94a1c9 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 20:25:57 -0500 Subject: [PATCH 47/65] more generic sparseJacobianInPlace function --- gtsam/linear/GaussianFactorGraph-impl.h | 100 ++++++++++++++++++++++++ gtsam/linear/GaussianFactorGraph.cpp | 68 +--------------- gtsam/linear/GaussianFactorGraph.h | 21 ++++- 3 files changed, 121 insertions(+), 68 deletions(-) create mode 100644 gtsam/linear/GaussianFactorGraph-impl.h diff --git a/gtsam/linear/GaussianFactorGraph-impl.h b/gtsam/linear/GaussianFactorGraph-impl.h new file mode 100644 index 000000000..e3e6125c6 --- /dev/null +++ b/gtsam/linear/GaussianFactorGraph-impl.h @@ -0,0 +1,100 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file GaussianFactorGraph.cpp + * @brief Linear Factor Graph where all factors are Gaussians + * @author Kai Ni + * @author Christian Potthast + * @author Richard Roberts + * @author Gerry Chen + * @author Frank Dellaert + */ + +#include // for autocomplete/intellisense + +namespace gtsam { + +/* ************************************************************************* */ +template +void GaussianFactorGraph::sparseJacobianInPlace(T& entries, + const Ordering& ordering, + size_t& nrows, + size_t& ncols) const { + gttic_(GaussianFactorGraph_sparseJacobianInPlace); + // First find dimensions of each variable + typedef std::map KeySizeMap; + KeySizeMap dims; + for (const sharedFactor& factor : *this) { + if (!static_cast(factor)) + continue; + + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); + } + } + + // Compute first scalar column of each variable + ncols = 0; + KeySizeMap columnIndices = dims; + for (const auto key : ordering) { + columnIndices[key] = ncols; + ncols += dims[key]; + } + + // Iterate over all factors, adding sparse scalar entries + nrows = 0; + for (const sharedFactor& factor : *this) { + if (!static_cast(factor)) continue; + + // Convert to JacobianFactor if necessary + JacobianFactor::shared_ptr jacobianFactor( + boost::dynamic_pointer_cast(factor)); + if (!jacobianFactor) { + HessianFactor::shared_ptr hessian( + boost::dynamic_pointer_cast(factor)); + if (hessian) + jacobianFactor.reset(new JacobianFactor(*hessian)); + else + throw std::invalid_argument( + "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor."); + } + + // Whiten the factor and add entries for it + // iterate over all variables in the factor + const JacobianFactor whitened(jacobianFactor->whiten()); + for (JacobianFactor::const_iterator key = whitened.begin(); + key < whitened.end(); ++key) { + JacobianFactor::constABlock whitenedA = whitened.getA(key); + // find first column index for this key + size_t column_start = columnIndices[*key]; + for (size_t i = 0; i < (size_t) whitenedA.rows(); i++) + for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { + double s = whitenedA(i, j); + if (std::abs(s) > 1e-12) + entries.emplace_back(nrows + i, column_start + j, s); + } + } + + JacobianFactor::constBVector whitenedb(whitened.getb()); + for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { + double s = whitenedb(i); + if (std::abs(s) > 1e-12) entries.emplace_back(nrows + i, ncols, s); + } + + // Increment row index + nrows += jacobianFactor->rows(); + } + + ncols++; // +1 for b-column +} + +} // namespace gtsam diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 7790b5328..c4e4ed109 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -102,75 +102,9 @@ namespace gtsam { /* ************************************************************************* */ SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( const Ordering& ordering, size_t& nrows, size_t& ncols) const { - gttic_(GaussianFactorGraph_sparseJacobian); - // First find dimensions of each variable - typedef std::map KeySizeMap; - KeySizeMap dims; - for (const sharedFactor& factor : *this) { - if (!static_cast(factor)) - continue; - - for (auto it = factor->begin(); it != factor->end(); ++it) { - dims[*it] = factor->getDim(it); - } - } - - // Compute first scalar column of each variable - ncols = 0; - KeySizeMap columnIndices = dims; - for (const auto key : ordering) { - columnIndices[key] = ncols; - ncols += dims[key]; - } - - // Iterate over all factors, adding sparse scalar entries SparseMatrixBoostTriplets entries; entries.reserve(60 * size()); - - nrows = 0; - for (const sharedFactor& factor : *this) { - if (!static_cast(factor)) continue; - - // Convert to JacobianFactor if necessary - JacobianFactor::shared_ptr jacobianFactor( - boost::dynamic_pointer_cast(factor)); - if (!jacobianFactor) { - HessianFactor::shared_ptr hessian( - boost::dynamic_pointer_cast(factor)); - if (hessian) - jacobianFactor.reset(new JacobianFactor(*hessian)); - else - throw invalid_argument( - "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor."); - } - - // Whiten the factor and add entries for it - // iterate over all variables in the factor - const JacobianFactor whitened(jacobianFactor->whiten()); - for (JacobianFactor::const_iterator key = whitened.begin(); - key < whitened.end(); ++key) { - JacobianFactor::constABlock whitenedA = whitened.getA(key); - // find first column index for this key - size_t column_start = columnIndices[*key]; - for (size_t i = 0; i < (size_t) whitenedA.rows(); i++) - for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { - double s = whitenedA(i, j); - if (std::abs(s) > 1e-12) - entries.emplace_back(nrows + i, column_start + j, s); - } - } - - JacobianFactor::constBVector whitenedb(whitened.getb()); - for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { - double s = whitenedb(i); - if (std::abs(s) > 1e-12) entries.emplace_back(nrows + i, ncols, s); - } - - // Increment row index - nrows += jacobianFactor->rows(); - } - - ncols++; // +1 for b-column + sparseJacobianInPlace(entries, ordering, nrows, ncols); return entries; } diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 5eb47ca48..2f21d9619 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -180,10 +180,27 @@ namespace gtsam { ///@name Linear Algebra ///@{ + /** + * Populates a container of triplets: (i, j, s) to generate an m-by-n sparse + * augmented Jacobian matrix, where i(k) and j(k) are the base 0 row and + * column indices, s(k) a double. + * The standard deviations are baked into A and b + * @param entries a container of triplets (i, j, s) which supports + * `emplace_back(size_t, size_t, double)` + * @param ordering the column ordering + * @param[out] nrows The number of rows in the Jacobian + * @param[out] ncols The number of columns in the Jacobian + * @return the sparse matrix in one of the 4 forms above + */ + template + void sparseJacobianInPlace(T& entries, const Ordering& ordering, + size_t& nrows, size_t& ncols) const; + /** * Return vector of i, j, and s to generate an m-by-n sparse augmented * Jacobian matrix, where i(k) and j(k) are the base 0 row and column - * indices, s(k) a double. The standard deviations are baked into A and b + * indices, s(k) a double. + * The standard deviations are baked into A and b * @param ordering the column ordering * @param[out] nrows The number of rows in the Jacobian * @param[out] ncols The number of columns in the Jacobian @@ -435,3 +452,5 @@ struct traits : public Testable { }; } // \ namespace gtsam + +#include From 9584860da0e91fecfe04ce60c569233b5a6fbb98 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 20:27:30 -0500 Subject: [PATCH 48/65] eliminate copy/pasta from SparseEigen with generic version of sparseJacobian --- gtsam/linear/SparseEigen.h | 77 +++----------------------------------- 1 file changed, 6 insertions(+), 71 deletions(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index eac4178aa..5773099d5 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -37,80 +37,15 @@ typedef Eigen::SparseMatrix SparseEigen; /// Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph SparseEigen sparseJacobianEigen( const GaussianFactorGraph &gfg, const Ordering &ordering) { - // TODO(gerry): eliminate copy/pasta by making GaussianFactorGraph version - // more general, or by creating an Eigen::Triplet compatible wrapper for - // boost::tuple return type gttic_(SparseEigen_sparseJacobianEigen); - - // First find dimensions of each variable - std::map dims; - for (const boost::shared_ptr &factor : gfg) { - if (!static_cast(factor)) continue; - - for (auto it = factor->begin(); it != factor->end(); ++it) { - dims[*it] = factor->getDim(it); - } - } - - // Compute first scalar column of each variable - size_t currentColIndex = 0; - std::map columnIndices; - for (const auto key : ordering) { - columnIndices[key] = currentColIndex; - currentColIndex += dims[key]; - } - - // Iterate over all factors, adding sparse scalar entries + // intermediate `entries` vector is kind of unavoidable due to how expensive + // factor->rows() is, which prevents us from populating SparseEigen directly std::vector> entries; entries.reserve(60 * gfg.size()); - - size_t row = 0; - for (const boost::shared_ptr &factor : gfg) { - if (!static_cast(factor)) continue; - - // Convert to JacobianFactor if necessary - JacobianFactor::shared_ptr jacobianFactor( - boost::dynamic_pointer_cast(factor)); - if (!jacobianFactor) { - HessianFactor::shared_ptr hessian( - boost::dynamic_pointer_cast(factor)); - if (hessian) - jacobianFactor.reset(new JacobianFactor(*hessian)); - else - throw std::invalid_argument( - "GaussianFactorGraph contains a factor that is neither a " - "JacobianFactor nor a HessianFactor."); - } - - // Whiten the factor and add entries for it - // iterate over all variables in the factor - const JacobianFactor whitened(jacobianFactor->whiten()); - for (JacobianFactor::const_iterator key = whitened.begin(); - key < whitened.end(); ++key) { - JacobianFactor::constABlock whitenedA = whitened.getA(key); - // find first column index for this key - size_t column_start = columnIndices[*key]; - for (size_t i = 0; i < (size_t)whitenedA.rows(); i++) - for (size_t j = 0; j < (size_t)whitenedA.cols(); j++) { - double s = whitenedA(i, j); - if (std::abs(s) > 1e-12) - entries.emplace_back(row + i, column_start + j, s); - } - } - - JacobianFactor::constBVector whitenedb(whitened.getb()); - size_t bcolumn = currentColIndex; - for (size_t i = 0; i < (size_t)whitenedb.size(); i++) { - double s = whitenedb(i); - if (std::abs(s) > 1e-12) entries.emplace_back(row + i, bcolumn, s); - } - - // Increment row index - row += jacobianFactor->rows(); - } - - // ...and make a sparse matrix with it. - SparseEigen Ab(row, currentColIndex + 1); + size_t nrows, ncols; + gfg.sparseJacobianInPlace(entries, ordering, nrows, ncols); + // create sparse matrix + SparseEigen Ab(nrows, ncols); Ab.setFromTriplets(entries.begin(), entries.end()); return Ab; } From b5951d033e8fe4ba80bccc653ab5c76d4acb8e6a Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Tue, 19 Jan 2021 20:56:18 -0500 Subject: [PATCH 49/65] populate sparse matrix with `insert` rather than `setFromTriplets` About 5% speed improvement. --- gtsam/linear/SparseEigen.h | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 5773099d5..72e77a021 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -39,14 +39,22 @@ SparseEigen sparseJacobianEigen( const GaussianFactorGraph &gfg, const Ordering &ordering) { gttic_(SparseEigen_sparseJacobianEigen); // intermediate `entries` vector is kind of unavoidable due to how expensive - // factor->rows() is, which prevents us from populating SparseEigen directly + // factor->rows() is, which prevents us from populating SparseEigen directly. + // Triplet is about 11% faster than boost tuple. std::vector> entries; entries.reserve(60 * gfg.size()); size_t nrows, ncols; gfg.sparseJacobianInPlace(entries, ordering, nrows, ncols); - // create sparse matrix + // declare sparse matrix SparseEigen Ab(nrows, ncols); - Ab.setFromTriplets(entries.begin(), entries.end()); + // See Eigen::set_from_triplets. This is about 5% faster. + // pass 1: count the nnz per inner-vector + std::vector nnz(ncols, 0); + for (const auto &entry : entries) nnz[entry.col()]++; + // pass 2: insert the elements + Ab.reserve(nnz); + for (const auto &entry : entries) + Ab.insert(entry.row(), entry.col()) = entry.value(); return Ab; } From e8d71735bac0d788fb3d19f6dd83d820f39c4f97 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 21:09:20 -0500 Subject: [PATCH 50/65] upgrade minimum required Boost version to 1.67. --- INSTALL.md | 2 +- README.md | 2 +- cmake/HandleBoost.cmake | 4 ++-- cmake/HandleCPack.cmake | 2 +- 4 files changed, 5 insertions(+), 5 deletions(-) diff --git a/INSTALL.md b/INSTALL.md index 1fddf4df0..44051815a 100644 --- a/INSTALL.md +++ b/INSTALL.md @@ -13,7 +13,7 @@ $ make install ## Important Installation Notes 1. GTSAM requires the following libraries to be installed on your system: - - BOOST version 1.58 or greater (install through Linux repositories or MacPorts) + - BOOST version 1.67 or greater (install through Linux repositories or MacPorts) - Cmake version 3.0 or higher - Support for XCode 4.3 command line tools on Mac requires CMake 2.8.8 or higher diff --git a/README.md b/README.md index 60eff197a..82a17a8fa 100644 --- a/README.md +++ b/README.md @@ -40,7 +40,7 @@ $ make install Prerequisites: -- [Boost](http://www.boost.org/users/download/) >= 1.58 (Ubuntu: `sudo apt-get install libboost-all-dev`) +- [Boost](http://www.boost.org/users/download/) >= 1.67 (Ubuntu: `sudo apt-get install libboost-all-dev`) - [CMake](http://www.cmake.org/cmake/resources/software.html) >= 3.0 (Ubuntu: `sudo apt-get install cmake`) - A modern compiler, i.e., at least gcc 4.7.3 on Linux. diff --git a/cmake/HandleBoost.cmake b/cmake/HandleBoost.cmake index e73c2237d..a02afba57 100644 --- a/cmake/HandleBoost.cmake +++ b/cmake/HandleBoost.cmake @@ -22,7 +22,7 @@ endif() # Store these in variables so they are automatically replicated in GTSAMConfig.cmake and such. -set(BOOST_FIND_MINIMUM_VERSION 1.58) +set(BOOST_FIND_MINIMUM_VERSION 1.67) set(BOOST_FIND_MINIMUM_COMPONENTS serialization system filesystem thread program_options date_time timer chrono regex) find_package(Boost ${BOOST_FIND_MINIMUM_VERSION} COMPONENTS ${BOOST_FIND_MINIMUM_COMPONENTS}) @@ -30,7 +30,7 @@ find_package(Boost ${BOOST_FIND_MINIMUM_VERSION} COMPONENTS ${BOOST_FIND_MINIMUM # Required components if(NOT Boost_SERIALIZATION_LIBRARY OR NOT Boost_SYSTEM_LIBRARY OR NOT Boost_FILESYSTEM_LIBRARY OR NOT Boost_THREAD_LIBRARY OR NOT Boost_DATE_TIME_LIBRARY) - message(FATAL_ERROR "Missing required Boost components >= v1.58, please install/upgrade Boost or configure your search paths.") + message(FATAL_ERROR "Missing required Boost components >= v1.67, please install/upgrade Boost or configure your search paths.") endif() option(GTSAM_DISABLE_NEW_TIMERS "Disables using Boost.chrono for timing" OFF) diff --git a/cmake/HandleCPack.cmake b/cmake/HandleCPack.cmake index 1c32433a4..eff36c42d 100644 --- a/cmake/HandleCPack.cmake +++ b/cmake/HandleCPack.cmake @@ -25,4 +25,4 @@ set(CPACK_SOURCE_PACKAGE_FILE_NAME "gtsam-${GTSAM_VERSION_MAJOR}.${GTSAM_VERSION # Deb-package specific cpack set(CPACK_DEBIAN_PACKAGE_NAME "libgtsam-dev") -set(CPACK_DEBIAN_PACKAGE_DEPENDS "libboost-dev (>= 1.58)") #Example: "libc6 (>= 2.3.1-6), libgcc1 (>= 1:3.4.2-12)") +set(CPACK_DEBIAN_PACKAGE_DEPENDS "libboost-dev (>= 1.67)") #Example: "libc6 (>= 2.3.1-6), libgcc1 (>= 1:3.4.2-12)") From 3e8973e8a87b1ad93cf1a26f87cf86664c6738bc Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 23:39:02 -0500 Subject: [PATCH 51/65] Revert "upgrade minimum required Boost version to 1.67." This reverts commit e8d71735bac0d788fb3d19f6dd83d820f39c4f97. --- INSTALL.md | 2 +- README.md | 2 +- cmake/HandleBoost.cmake | 4 ++-- cmake/HandleCPack.cmake | 2 +- 4 files changed, 5 insertions(+), 5 deletions(-) diff --git a/INSTALL.md b/INSTALL.md index 44051815a..1fddf4df0 100644 --- a/INSTALL.md +++ b/INSTALL.md @@ -13,7 +13,7 @@ $ make install ## Important Installation Notes 1. GTSAM requires the following libraries to be installed on your system: - - BOOST version 1.67 or greater (install through Linux repositories or MacPorts) + - BOOST version 1.58 or greater (install through Linux repositories or MacPorts) - Cmake version 3.0 or higher - Support for XCode 4.3 command line tools on Mac requires CMake 2.8.8 or higher diff --git a/README.md b/README.md index 82a17a8fa..60eff197a 100644 --- a/README.md +++ b/README.md @@ -40,7 +40,7 @@ $ make install Prerequisites: -- [Boost](http://www.boost.org/users/download/) >= 1.67 (Ubuntu: `sudo apt-get install libboost-all-dev`) +- [Boost](http://www.boost.org/users/download/) >= 1.58 (Ubuntu: `sudo apt-get install libboost-all-dev`) - [CMake](http://www.cmake.org/cmake/resources/software.html) >= 3.0 (Ubuntu: `sudo apt-get install cmake`) - A modern compiler, i.e., at least gcc 4.7.3 on Linux. diff --git a/cmake/HandleBoost.cmake b/cmake/HandleBoost.cmake index a02afba57..e73c2237d 100644 --- a/cmake/HandleBoost.cmake +++ b/cmake/HandleBoost.cmake @@ -22,7 +22,7 @@ endif() # Store these in variables so they are automatically replicated in GTSAMConfig.cmake and such. -set(BOOST_FIND_MINIMUM_VERSION 1.67) +set(BOOST_FIND_MINIMUM_VERSION 1.58) set(BOOST_FIND_MINIMUM_COMPONENTS serialization system filesystem thread program_options date_time timer chrono regex) find_package(Boost ${BOOST_FIND_MINIMUM_VERSION} COMPONENTS ${BOOST_FIND_MINIMUM_COMPONENTS}) @@ -30,7 +30,7 @@ find_package(Boost ${BOOST_FIND_MINIMUM_VERSION} COMPONENTS ${BOOST_FIND_MINIMUM # Required components if(NOT Boost_SERIALIZATION_LIBRARY OR NOT Boost_SYSTEM_LIBRARY OR NOT Boost_FILESYSTEM_LIBRARY OR NOT Boost_THREAD_LIBRARY OR NOT Boost_DATE_TIME_LIBRARY) - message(FATAL_ERROR "Missing required Boost components >= v1.67, please install/upgrade Boost or configure your search paths.") + message(FATAL_ERROR "Missing required Boost components >= v1.58, please install/upgrade Boost or configure your search paths.") endif() option(GTSAM_DISABLE_NEW_TIMERS "Disables using Boost.chrono for timing" OFF) diff --git a/cmake/HandleCPack.cmake b/cmake/HandleCPack.cmake index eff36c42d..1c32433a4 100644 --- a/cmake/HandleCPack.cmake +++ b/cmake/HandleCPack.cmake @@ -25,4 +25,4 @@ set(CPACK_SOURCE_PACKAGE_FILE_NAME "gtsam-${GTSAM_VERSION_MAJOR}.${GTSAM_VERSION # Deb-package specific cpack set(CPACK_DEBIAN_PACKAGE_NAME "libgtsam-dev") -set(CPACK_DEBIAN_PACKAGE_DEPENDS "libboost-dev (>= 1.67)") #Example: "libc6 (>= 2.3.1-6), libgcc1 (>= 1:3.4.2-12)") +set(CPACK_DEBIAN_PACKAGE_DEPENDS "libboost-dev (>= 1.58)") #Example: "libc6 (>= 2.3.1-6), libgcc1 (>= 1:3.4.2-12)") From 0bb6d25baca592b6ebc99bcf6bfe8deb8a250af7 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 19 Jan 2021 23:53:54 -0500 Subject: [PATCH 52/65] add known issues section with info about march=native --- INSTALL.md | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/INSTALL.md b/INSTALL.md index 1fddf4df0..520bddf3c 100644 --- a/INSTALL.md +++ b/INSTALL.md @@ -41,11 +41,6 @@ $ make install - MacOS 10.6 - 10.14 - Windows 7, 8, 8.1, 10 - Known issues: - - - MSVC 2013 is not yet supported because it cannot build the serialization module - of Boost 1.55 (or earlier). - 2. GTSAM makes extensive use of debug assertions, and we highly recommend you work in Debug mode while developing (enabled by default). Likewise, it is imperative that you switch to release mode when running finished code and for timing. GTSAM @@ -70,6 +65,13 @@ execute commands as follows for an out-of-source build: This will build the library and unit tests, run all of the unit tests, and then install the library itself. +## Known Issues + +- When using `GTSAM_BUILD_WITH_MARCH_NATIVE=ON`, you may encounter issues in running tests which we are still investigating: + - Use of a version of GCC < 7.5 results in an "Indeterminant Linear System" error for `testSmartProjectionFactor`. + - Use of Boost version < 1.67 with clang will give a segfault for mulitple test cases. +- MSVC 2013 is not yet supported because it cannot build the serialization module of Boost 1.55 (or earlier). + # Windows Installation This section details how to build a GTSAM `.sln` file using Visual Studio. From 286898a8471584310c81ae020afae1b8c553f6eb Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 20 Jan 2021 12:25:20 -0500 Subject: [PATCH 53/65] move SparseMatrixBoostTriplets typedef to gfg --- gtsam/base/Matrix.h | 6 ------ gtsam/linear/GaussianFactorGraph.cpp | 11 ++++++----- gtsam/linear/GaussianFactorGraph.h | 3 +++ 3 files changed, 9 insertions(+), 11 deletions(-) diff --git a/gtsam/base/Matrix.h b/gtsam/base/Matrix.h index 11058ef40..b4ecf6f6a 100644 --- a/gtsam/base/Matrix.h +++ b/gtsam/base/Matrix.h @@ -75,12 +75,6 @@ GTSAM_MAKE_MATRIX_DEFS(9); typedef Eigen::Block SubMatrix; typedef Eigen::Block ConstSubMatrix; -/// Sparse matrix representation as vector of tuples. -/// See SparseMatrix.h for additional representations SparseMatrixEigenTriplets -/// and SparseMatrixEigen -typedef std::vector> - SparseMatrixBoostTriplets; - // Matrix formatting arguments when printing. // Akin to Matlab style. const Eigen::IOFormat& matlabFormat(); diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index c4e4ed109..825c6c5d2 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -99,30 +99,31 @@ namespace gtsam { return result; } + using BoostTriplets = GaussianFactorGraph::SparseMatrixBoostTriplets; /* ************************************************************************* */ - SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + BoostTriplets GaussianFactorGraph::sparseJacobian( const Ordering& ordering, size_t& nrows, size_t& ncols) const { - SparseMatrixBoostTriplets entries; + BoostTriplets entries; entries.reserve(60 * size()); sparseJacobianInPlace(entries, ordering, nrows, ncols); return entries; } /* ************************************************************************* */ - SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + BoostTriplets GaussianFactorGraph::sparseJacobian( const Ordering& ordering) const { size_t dummy1, dummy2; return sparseJacobian(ordering, dummy1, dummy2); } /* ************************************************************************* */ - SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian( + BoostTriplets GaussianFactorGraph::sparseJacobian( size_t& nrows, size_t& ncols) const { return sparseJacobian(Ordering(this->keys()), nrows, ncols); } /* ************************************************************************* */ - SparseMatrixBoostTriplets GaussianFactorGraph::sparseJacobian() const { + BoostTriplets GaussianFactorGraph::sparseJacobian() const { size_t dummy1, dummy2; return sparseJacobian(dummy1, dummy2); } diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 2f21d9619..f2ca3bd60 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -180,6 +180,9 @@ namespace gtsam { ///@name Linear Algebra ///@{ + typedef std::vector> + SparseMatrixBoostTriplets; ///< Sparse matrix representation as vector of tuples. + /** * Populates a container of triplets: (i, j, s) to generate an m-by-n sparse * augmented Jacobian matrix, where i(k) and j(k) are the base 0 row and From fd2d8a236a1fadbf2c67df981ff1355f7891be13 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 20 Jan 2021 17:01:15 -0500 Subject: [PATCH 54/65] remove templating while maintaining efficiency Templating still used in cpp file for generic-ness, but not exposed anymore std::tuple has the same performance as Eigen::Triplet, but boost::tuple is slower. Sparse matrix indices are int instead of size_t for efficiency (e.g. A(i, j) = s -> i/j are int's instead of size_t's) --- gtsam/linear/GaussianFactorGraph-impl.h | 100 ---------------------- gtsam/linear/GaussianFactorGraph.cpp | 105 +++++++++++++++++++++++- gtsam/linear/GaussianFactorGraph.h | 84 +++++++++++-------- gtsam/linear/SparseEigen.h | 13 ++- 4 files changed, 158 insertions(+), 144 deletions(-) delete mode 100644 gtsam/linear/GaussianFactorGraph-impl.h diff --git a/gtsam/linear/GaussianFactorGraph-impl.h b/gtsam/linear/GaussianFactorGraph-impl.h deleted file mode 100644 index e3e6125c6..000000000 --- a/gtsam/linear/GaussianFactorGraph-impl.h +++ /dev/null @@ -1,100 +0,0 @@ -/* ---------------------------------------------------------------------------- - - * GTSAM Copyright 2010, Georgia Tech Research Corporation, - * Atlanta, Georgia 30332-0415 - * All Rights Reserved - * Authors: Frank Dellaert, et al. (see THANKS for the full author list) - - * See LICENSE for the license information - - * -------------------------------------------------------------------------- */ - -/** - * @file GaussianFactorGraph.cpp - * @brief Linear Factor Graph where all factors are Gaussians - * @author Kai Ni - * @author Christian Potthast - * @author Richard Roberts - * @author Gerry Chen - * @author Frank Dellaert - */ - -#include // for autocomplete/intellisense - -namespace gtsam { - -/* ************************************************************************* */ -template -void GaussianFactorGraph::sparseJacobianInPlace(T& entries, - const Ordering& ordering, - size_t& nrows, - size_t& ncols) const { - gttic_(GaussianFactorGraph_sparseJacobianInPlace); - // First find dimensions of each variable - typedef std::map KeySizeMap; - KeySizeMap dims; - for (const sharedFactor& factor : *this) { - if (!static_cast(factor)) - continue; - - for (auto it = factor->begin(); it != factor->end(); ++it) { - dims[*it] = factor->getDim(it); - } - } - - // Compute first scalar column of each variable - ncols = 0; - KeySizeMap columnIndices = dims; - for (const auto key : ordering) { - columnIndices[key] = ncols; - ncols += dims[key]; - } - - // Iterate over all factors, adding sparse scalar entries - nrows = 0; - for (const sharedFactor& factor : *this) { - if (!static_cast(factor)) continue; - - // Convert to JacobianFactor if necessary - JacobianFactor::shared_ptr jacobianFactor( - boost::dynamic_pointer_cast(factor)); - if (!jacobianFactor) { - HessianFactor::shared_ptr hessian( - boost::dynamic_pointer_cast(factor)); - if (hessian) - jacobianFactor.reset(new JacobianFactor(*hessian)); - else - throw std::invalid_argument( - "GaussianFactorGraph contains a factor that is neither a JacobianFactor nor a HessianFactor."); - } - - // Whiten the factor and add entries for it - // iterate over all variables in the factor - const JacobianFactor whitened(jacobianFactor->whiten()); - for (JacobianFactor::const_iterator key = whitened.begin(); - key < whitened.end(); ++key) { - JacobianFactor::constABlock whitenedA = whitened.getA(key); - // find first column index for this key - size_t column_start = columnIndices[*key]; - for (size_t i = 0; i < (size_t) whitenedA.rows(); i++) - for (size_t j = 0; j < (size_t) whitenedA.cols(); j++) { - double s = whitenedA(i, j); - if (std::abs(s) > 1e-12) - entries.emplace_back(nrows + i, column_start + j, s); - } - } - - JacobianFactor::constBVector whitenedb(whitened.getb()); - for (size_t i = 0; i < (size_t) whitenedb.size(); i++) { - double s = whitenedb(i); - if (std::abs(s) > 1e-12) entries.emplace_back(nrows + i, ncols, s); - } - - // Increment row index - nrows += jacobianFactor->rows(); - } - - ncols++; // +1 for b-column -} - -} // namespace gtsam diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 825c6c5d2..b987ba24e 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -99,8 +99,82 @@ namespace gtsam { return result; } - using BoostTriplets = GaussianFactorGraph::SparseMatrixBoostTriplets; /* ************************************************************************* */ + template + void GaussianFactorGraph::sparseJacobianInPlace(T& entries, + const Ordering& ordering, + size_t& nrows, + size_t& ncols) const { + gttic_(GaussianFactorGraph_sparseJacobianInPlace); + // First find dimensions of each variable + typedef std::map KeySizeMap; + KeySizeMap dims; + for (const sharedFactor& factor : *this) { + if (!static_cast(factor)) continue; + + for (auto it = factor->begin(); it != factor->end(); ++it) { + dims[*it] = factor->getDim(it); + } + } + + // Compute first scalar column of each variable + ncols = 0; + KeySizeMap columnIndices = dims; + for (const auto key : ordering) { + columnIndices[key] = ncols; + ncols += dims[key]; + } + + // Iterate over all factors, adding sparse scalar entries + nrows = 0; + for (const sharedFactor& factor : *this) { + if (!static_cast(factor)) continue; + + // Convert to JacobianFactor if necessary + JacobianFactor::shared_ptr jacobianFactor( + boost::dynamic_pointer_cast(factor)); + if (!jacobianFactor) { + HessianFactor::shared_ptr hessian( + boost::dynamic_pointer_cast(factor)); + if (hessian) + jacobianFactor.reset(new JacobianFactor(*hessian)); + else + throw std::invalid_argument( + "GaussianFactorGraph contains a factor that is neither a " + "JacobianFactor nor a HessianFactor."); + } + + // Whiten the factor and add entries for it + // iterate over all variables in the factor + const JacobianFactor whitened(jacobianFactor->whiten()); + for (JacobianFactor::const_iterator key = whitened.begin(); + key < whitened.end(); ++key) { + JacobianFactor::constABlock whitenedA = whitened.getA(key); + // find first column index for this key + size_t column_start = columnIndices[*key]; + for (size_t i = 0; i < (size_t)whitenedA.rows(); i++) + for (size_t j = 0; j < (size_t)whitenedA.cols(); j++) { + double s = whitenedA(i, j); + if (std::abs(s) > 1e-12) + entries.emplace_back(nrows + i, column_start + j, s); + } + } + + JacobianFactor::constBVector whitenedb(whitened.getb()); + for (size_t i = 0; i < (size_t)whitenedb.size(); i++) { + double s = whitenedb(i); + if (std::abs(s) > 1e-12) entries.emplace_back(nrows + i, ncols, s); + } + + // Increment row index + nrows += jacobianFactor->rows(); + } + + ncols++; // +1 for b-column + } + + /* ************************************************************************* */ + using BoostTriplets = GaussianFactorGraph::SparseMatrixBoostTriplets; BoostTriplets GaussianFactorGraph::sparseJacobian( const Ordering& ordering, size_t& nrows, size_t& ncols) const { BoostTriplets entries; @@ -166,6 +240,35 @@ namespace gtsam { return sparseJacobian_(dummy1, dummy2); } + /* ************************************************************************* */ + using GtsamTriplets = GaussianFactorGraph::SparseMatrixGtsamTriplets; + GtsamTriplets GaussianFactorGraph::sparseJacobianFast( + const Ordering& ordering, size_t& nrows, size_t& ncols) const { + GtsamTriplets entries; + entries.reserve(60 * size()); + sparseJacobianInPlace(entries, ordering, nrows, ncols); + return entries; + } + + /* ************************************************************************* */ + GtsamTriplets GaussianFactorGraph::sparseJacobianFast( + const Ordering& ordering) const { + size_t dummy1, dummy2; + return sparseJacobianFast(ordering, dummy1, dummy2); + } + + /* ************************************************************************* */ + GtsamTriplets GaussianFactorGraph::sparseJacobianFast( + size_t& nrows, size_t& ncols) const { + return sparseJacobianFast(Ordering(this->keys()), nrows, ncols); + } + + /* ************************************************************************* */ + GtsamTriplets GaussianFactorGraph::sparseJacobianFast() const { + size_t dummy1, dummy2; + return sparseJacobianFast(dummy1, dummy2); + } + /* ************************************************************************* */ Matrix GaussianFactorGraph::augmentedJacobian( const Ordering& ordering) const { diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index f2ca3bd60..2f5bb582a 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -182,22 +182,8 @@ namespace gtsam { typedef std::vector> SparseMatrixBoostTriplets; ///< Sparse matrix representation as vector of tuples. - - /** - * Populates a container of triplets: (i, j, s) to generate an m-by-n sparse - * augmented Jacobian matrix, where i(k) and j(k) are the base 0 row and - * column indices, s(k) a double. - * The standard deviations are baked into A and b - * @param entries a container of triplets (i, j, s) which supports - * `emplace_back(size_t, size_t, double)` - * @param ordering the column ordering - * @param[out] nrows The number of rows in the Jacobian - * @param[out] ncols The number of columns in the Jacobian - * @return the sparse matrix in one of the 4 forms above - */ - template - void sparseJacobianInPlace(T& entries, const Ordering& ordering, - size_t& nrows, size_t& ncols) const; + typedef std::vector> + SparseMatrixGtsamTriplets; ///< Sparse matrix representation as vector of SparseTriplet's. /** * Return vector of i, j, and s to generate an m-by-n sparse augmented @@ -213,16 +199,16 @@ namespace gtsam { size_t& nrows, size_t& ncols) const; - /// Returns a sparse augmented Jacobian without outputting its dimensions + /** Returns a sparse augmented Jacobian without outputting its dimensions */ SparseMatrixBoostTriplets sparseJacobian( const Ordering& ordering) const; - /// Returns a sparse augmented Jacobian with default Ordering + /** Returns a sparse augmented Jacobian with default Ordering */ SparseMatrixBoostTriplets sparseJacobian(size_t& nrows, size_t& ncols) const; - /// Returns a sparse augmented Jacobian without with default ordering and - /// outputting its dimensions + /** Returns a sparse augmented Jacobian without with default ordering and + * outputting its dimensions */ SparseMatrixBoostTriplets sparseJacobian() const; /** @@ -231,23 +217,45 @@ namespace gtsam { * sparse. Note: i, j are 1-indexed. * The standard deviations are baked into A and b */ - Matrix sparseJacobian_(const Ordering& ordering, - size_t& nrows, - size_t& ncols) const; + Matrix sparseJacobian_(const Ordering& ordering, size_t& nrows, + size_t& ncols) const; - /// Returns a matrix-form sparse augmented Jacobian without outputting its - /// dimensions - Matrix sparseJacobian_( - const Ordering& ordering) const; + /** Returns a matrix-form sparse augmented Jacobian without outputting its + * dimensions + */ + Matrix sparseJacobian_(const Ordering& ordering) const; - /// Returns a matrix-form sparse augmented Jacobian with default Ordering - Matrix sparseJacobian_(size_t& nrows, - size_t& ncols) const; + /** Returns a matrix-form sparse augmented Jacobian with default Ordering + * @param[out] nrows The number of rows in the Jacobian + * @param[out] ncols The number of columns in the Jacobian + */ + Matrix sparseJacobian_(size_t& nrows, size_t& ncols) const; - /// Returns a matrix-form sparse augmented Jacobian with default ordering - /// and without outputting its dimensions + /** Returns a matrix-form sparse augmented Jacobian with default ordering + * and without outputting its dimensions */ Matrix sparseJacobian_() const; + /** Returns a sparse matrix with `int` indices instead of `size_t` for + * slightly faster performance */ + SparseMatrixGtsamTriplets sparseJacobianFast(const Ordering& ordering, + size_t& nrows, + size_t& ncols) const; + + /** Returns an int-indexed sparse matrix without outputting its dimensions + */ + SparseMatrixGtsamTriplets sparseJacobianFast(const Ordering& ordering) const; + + /** Returns an int-indexed sparse matrix with default ordering + * @param[out] nrows The number of rows in the Jacobian + * @param[out] ncols The number of columns in the Jacobian + */ + SparseMatrixGtsamTriplets sparseJacobianFast(size_t& nrows, + size_t& ncols) const; + + /** Returns an int-indexed sparse matrix with default ordering and without + * outputting its dimensions */ + SparseMatrixGtsamTriplets sparseJacobianFast() const; + /** * Return a dense \f$ [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \f$ * Jacobian matrix, augmented with b with the noise models baked @@ -429,7 +437,15 @@ namespace gtsam { ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base); } - public: + /** Performs in-place population of a sparse jacobian. Contains the + * common functionality amongst different sparseJacobian functions. + * @param entries a container of triplets that supports + * `emplace_back(size_t, size_t, double)`*/ + template + void sparseJacobianInPlace(T& entries, const Ordering& ordering, + size_t& nrows, size_t& ncols) const; + + public: /** \deprecated */ VectorValues optimize(boost::none_t, @@ -455,5 +471,3 @@ struct traits : public Testable { }; } // \ namespace gtsam - -#include diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index 72e77a021..bc99b5c89 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -32,7 +32,7 @@ namespace gtsam { /// Eigen-format sparse matrix. Note: ColMajor is ~20% faster since /// InnerIndices must be sorted -typedef Eigen::SparseMatrix SparseEigen; +typedef Eigen::SparseMatrix SparseEigen; /// Constructs an Eigen-format SparseMatrix of a GaussianFactorGraph SparseEigen sparseJacobianEigen( @@ -40,21 +40,18 @@ SparseEigen sparseJacobianEigen( gttic_(SparseEigen_sparseJacobianEigen); // intermediate `entries` vector is kind of unavoidable due to how expensive // factor->rows() is, which prevents us from populating SparseEigen directly. - // Triplet is about 11% faster than boost tuple. - std::vector> entries; - entries.reserve(60 * gfg.size()); size_t nrows, ncols; - gfg.sparseJacobianInPlace(entries, ordering, nrows, ncols); + auto entries = gfg.sparseJacobianFast(ordering, nrows, ncols); // declare sparse matrix SparseEigen Ab(nrows, ncols); // See Eigen::set_from_triplets. This is about 5% faster. // pass 1: count the nnz per inner-vector std::vector nnz(ncols, 0); - for (const auto &entry : entries) nnz[entry.col()]++; - // pass 2: insert the elements + for (const auto &entry : entries) nnz[std::get<1>(entry)]++; Ab.reserve(nnz); + // pass 2: insert the elements for (const auto &entry : entries) - Ab.insert(entry.row(), entry.col()) = entry.value(); + Ab.insert(std::get<0>(entry), std::get<1>(entry)) = std::get<2>(entry); return Ab; } From 570135c6f67ebd0652d34dfe2fef20b2c266ed2e Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 20 Jan 2021 17:02:51 -0500 Subject: [PATCH 55/65] revert Matrix.h --- gtsam/base/Matrix.h | 2 -- 1 file changed, 2 deletions(-) diff --git a/gtsam/base/Matrix.h b/gtsam/base/Matrix.h index b4ecf6f6a..a3a14c6c3 100644 --- a/gtsam/base/Matrix.h +++ b/gtsam/base/Matrix.h @@ -33,8 +33,6 @@ #include #include -#include - /** * Matrix is a typedef in the gtsam namespace * TODO: make a version to work with matlab wrapping From b63895426680b7cf774fd1d90cc0bf383758b8f3 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 20 Jan 2021 17:08:18 -0500 Subject: [PATCH 56/65] formatting --- gtsam/linear/GaussianFactorGraph.h | 22 ++++++++++++---------- 1 file changed, 12 insertions(+), 10 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 2f5bb582a..584eb02ce 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -180,10 +180,12 @@ namespace gtsam { ///@name Linear Algebra ///@{ + /// Sparse matrix representation as vector of tuples. typedef std::vector> - SparseMatrixBoostTriplets; ///< Sparse matrix representation as vector of tuples. - typedef std::vector> - SparseMatrixGtsamTriplets; ///< Sparse matrix representation as vector of SparseTriplet's. + SparseMatrixBoostTriplets; + /// Sparse matrix representation as vector of slightly more efficient + /// tuples. + typedef std::vector> SparseMatrixGtsamTriplets; /** * Return vector of i, j, and s to generate an m-by-n sparse augmented @@ -430,13 +432,6 @@ namespace gtsam { /// @} private: - /** Serialization function */ - friend class boost::serialization::access; - template - void serialize(ARCHIVE & ar, const unsigned int /*version*/) { - ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base); - } - /** Performs in-place population of a sparse jacobian. Contains the * common functionality amongst different sparseJacobian functions. * @param entries a container of triplets that supports @@ -445,6 +440,13 @@ namespace gtsam { void sparseJacobianInPlace(T& entries, const Ordering& ordering, size_t& nrows, size_t& ncols) const; + /** Serialization function */ + friend class boost::serialization::access; + template + void serialize(ARCHIVE & ar, const unsigned int /*version*/) { + ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base); + } + public: /** \deprecated */ From 5e8acf4378b41e695e477195ee9eb4762e4b33f9 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Mon, 25 Jan 2021 16:17:25 -0500 Subject: [PATCH 57/65] fix bug in Pose2 print --- gtsam/base/TestableAssertions.h | 9 +++++--- gtsam/geometry/Pose2.cpp | 2 +- gtsam/geometry/tests/testPose2.cpp | 33 ++++++++++++++++++++++-------- 3 files changed, 32 insertions(+), 12 deletions(-) diff --git a/gtsam/base/TestableAssertions.h b/gtsam/base/TestableAssertions.h index 88dd619e5..0e6e1c276 100644 --- a/gtsam/base/TestableAssertions.h +++ b/gtsam/base/TestableAssertions.h @@ -372,16 +372,19 @@ bool assert_stdout_equal(const std::string& expected, const V& actual) { /** * Capture print function output and compare against string. + * + * @param s: Optional string to pass to the print() method. */ -template -bool assert_print_equal(const std::string& expected, const V& actual) { +template +bool assert_print_equal(const std::string& expected, const V& actual, + const std::string& s = "") { // Redirect output to buffer so we can compare std::stringstream buffer; // Save the original output stream so we can reset later std::streambuf* old = std::cout.rdbuf(buffer.rdbuf()); // We test against actual std::cout for faithful reproduction - actual.print(); + actual.print(s); // Get output string and reset stdout std::string actual_ = buffer.str(); diff --git a/gtsam/geometry/Pose2.cpp b/gtsam/geometry/Pose2.cpp index bebe53dfa..8dafffee8 100644 --- a/gtsam/geometry/Pose2.cpp +++ b/gtsam/geometry/Pose2.cpp @@ -48,7 +48,7 @@ Matrix3 Pose2::matrix() const { /* ************************************************************************* */ void Pose2::print(const string& s) const { - cout << s << this << endl; + std::cout << (s.empty() ? s : s + " ") << *this << std::endl; } /* ************************************************************************* */ diff --git a/gtsam/geometry/tests/testPose2.cpp b/gtsam/geometry/tests/testPose2.cpp index 3d821502d..d17dc7689 100644 --- a/gtsam/geometry/tests/testPose2.cpp +++ b/gtsam/geometry/tests/testPose2.cpp @@ -14,16 +14,17 @@ * @brief Unit tests for Pose2 class */ -#include -#include -#include -#include -#include -#include - #include +#include +#include +#include +#include +#include +#include +#include + +#include // for operator += #include -#include // for operator += #include #include @@ -910,6 +911,22 @@ TEST(Pose2 , TransformCovariance3) { } } +/* ************************************************************************* */ +TEST(Pose2, Print) { + Pose2 pose(Rot2::identity(), Point2(1, 2)); + + // Generate the expected output + string s = "Planar Pose"; + string expected_stdout = "(1, 2, 0)"; + string expected1 = expected_stdout + "\n"; + string expected2 = s + " " + expected1; + + EXPECT(assert_stdout_equal(expected_stdout, pose)); + + EXPECT(assert_print_equal(expected1, pose)); + EXPECT(assert_print_equal(expected2, pose, s)); +} + /* ************************************************************************* */ int main() { TestResult tr; From ccd64fb08c21da3441cbe639a86a398398a7e1dd Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Mon, 25 Jan 2021 16:22:09 -0500 Subject: [PATCH 58/65] use standard function to check for empty string --- gtsam/base/Testable.h | 4 ++-- gtsam/navigation/CombinedImuFactor.cpp | 2 +- gtsam/navigation/ImuFactor.cpp | 4 ++-- gtsam/navigation/PreintegratedRotation.cpp | 2 +- gtsam/navigation/PreintegrationBase.cpp | 2 +- gtsam/nonlinear/Values.cpp | 2 +- gtsam/sfm/ShonanAveraging.h | 3 ++- 7 files changed, 10 insertions(+), 9 deletions(-) diff --git a/gtsam/base/Testable.h b/gtsam/base/Testable.h index 2145360df..e8cdbd8e0 100644 --- a/gtsam/base/Testable.h +++ b/gtsam/base/Testable.h @@ -72,10 +72,10 @@ namespace gtsam { }; // \ Testable inline void print(float v, const std::string& s = "") { - std::cout << (s == "" ? s : s + " ") << v << std::endl; + std::cout << (s.empty() ? s : s + " ") << v << std::endl; } inline void print(double v, const std::string& s = "") { - std::cout << (s == "" ? s : s + " ") << v << std::endl; + std::cout << (s.empty() ? s : s + " ") << v << std::endl; } /** Call equal on the object */ diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index e41a8de44..ca1c5b93a 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -167,7 +167,7 @@ gtsam::NonlinearFactor::shared_ptr CombinedImuFactor::clone() const { //------------------------------------------------------------------------------ void CombinedImuFactor::print(const string& s, const KeyFormatter& keyFormatter) const { - cout << (s == "" ? s : s + "\n") << "CombinedImuFactor(" + cout << (s.empty() ? s : s + "\n") << "CombinedImuFactor(" << keyFormatter(this->key1()) << "," << keyFormatter(this->key2()) << "," << keyFormatter(this->key3()) << "," << keyFormatter(this->key4()) << "," << keyFormatter(this->key5()) << "," << keyFormatter(this->key6()) diff --git a/gtsam/navigation/ImuFactor.cpp b/gtsam/navigation/ImuFactor.cpp index cebddf05d..98b1e6f9d 100644 --- a/gtsam/navigation/ImuFactor.cpp +++ b/gtsam/navigation/ImuFactor.cpp @@ -130,7 +130,7 @@ std::ostream& operator<<(std::ostream& os, const ImuFactor& f) { //------------------------------------------------------------------------------ void ImuFactor::print(const string& s, const KeyFormatter& keyFormatter) const { - cout << (s == "" ? s : s + "\n") << "ImuFactor(" << keyFormatter(this->key1()) + cout << (s.empty() ? s : s + "\n") << "ImuFactor(" << keyFormatter(this->key1()) << "," << keyFormatter(this->key2()) << "," << keyFormatter(this->key3()) << "," << keyFormatter(this->key4()) << "," << keyFormatter(this->key5()) << ")\n"; @@ -226,7 +226,7 @@ std::ostream& operator<<(std::ostream& os, const ImuFactor2& f) { //------------------------------------------------------------------------------ void ImuFactor2::print(const string& s, const KeyFormatter& keyFormatter) const { - cout << (s == "" ? s : s + "\n") << "ImuFactor2(" + cout << (s.empty() ? s : s + "\n") << "ImuFactor2(" << keyFormatter(this->key1()) << "," << keyFormatter(this->key2()) << "," << keyFormatter(this->key3()) << ")\n"; cout << *this << endl; diff --git a/gtsam/navigation/PreintegratedRotation.cpp b/gtsam/navigation/PreintegratedRotation.cpp index f827c7c59..ee30bee9e 100644 --- a/gtsam/navigation/PreintegratedRotation.cpp +++ b/gtsam/navigation/PreintegratedRotation.cpp @@ -26,7 +26,7 @@ using namespace std; namespace gtsam { void PreintegratedRotationParams::print(const string& s) const { - cout << (s == "" ? s : s + "\n") << endl; + cout << (s.empty() ? s : s + "\n") << endl; cout << "gyroscopeCovariance:\n[\n" << gyroscopeCovariance << "\n]" << endl; if (omegaCoriolis) cout << "omegaCoriolis = (" << omegaCoriolis->transpose() << ")" << endl; diff --git a/gtsam/navigation/PreintegrationBase.cpp b/gtsam/navigation/PreintegrationBase.cpp index 111594663..543cc5b59 100644 --- a/gtsam/navigation/PreintegrationBase.cpp +++ b/gtsam/navigation/PreintegrationBase.cpp @@ -46,7 +46,7 @@ ostream& operator<<(ostream& os, const PreintegrationBase& pim) { //------------------------------------------------------------------------------ void PreintegrationBase::print(const string& s) const { - cout << (s == "" ? s : s + "\n") << *this << endl; + cout << (s.empty() ? s : s + "\n") << *this << endl; } //------------------------------------------------------------------------------ diff --git a/gtsam/nonlinear/Values.cpp b/gtsam/nonlinear/Values.cpp index 89a4206ee..9b8f7645a 100644 --- a/gtsam/nonlinear/Values.cpp +++ b/gtsam/nonlinear/Values.cpp @@ -75,7 +75,7 @@ namespace gtsam { /* ************************************************************************* */ void Values::print(const string& str, const KeyFormatter& keyFormatter) const { - cout << str << (str == "" ? "" : "\n"); + cout << str << (str.empty() ? "" : "\n"); cout << "Values with " << size() << " values:\n"; for(const_iterator key_value = begin(); key_value != end(); ++key_value) { cout << "Value " << keyFormatter(key_value->key) << ": "; diff --git a/gtsam/sfm/ShonanAveraging.h b/gtsam/sfm/ShonanAveraging.h index 0a8bdc8c1..f00109cae 100644 --- a/gtsam/sfm/ShonanAveraging.h +++ b/gtsam/sfm/ShonanAveraging.h @@ -91,7 +91,8 @@ struct GTSAM_EXPORT ShonanAveragingParameters { bool getCertifyOptimality() const { return certifyOptimality; } /// Print the parameters and flags used for rotation averaging. - void print() const { + void print(const std::string &s = "") const { + std::cout << (s.empty() ? s : s + " "); std::cout << " ShonanAveragingParameters: " << std::endl; std::cout << " alpha: " << alpha << std::endl; std::cout << " beta: " << beta << std::endl; From dcf8a52b8b5ec68fdda2232e0cc333d37b9d3e39 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 10:27:32 -0500 Subject: [PATCH 59/65] remove unnecessary function overloads and typedefs --- gtsam/linear/GaussianFactorGraph.cpp | 72 +++------------------------- gtsam/linear/GaussianFactorGraph.h | 62 ++---------------------- 2 files changed, 12 insertions(+), 122 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index b987ba24e..c8446e6a7 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -174,40 +174,20 @@ namespace gtsam { } /* ************************************************************************* */ - using BoostTriplets = GaussianFactorGraph::SparseMatrixBoostTriplets; - BoostTriplets GaussianFactorGraph::sparseJacobian( - const Ordering& ordering, size_t& nrows, size_t& ncols) const { + using BoostTriplets = std::vector>; + BoostTriplets GaussianFactorGraph::sparseJacobian() const { BoostTriplets entries; entries.reserve(60 * size()); - sparseJacobianInPlace(entries, ordering, nrows, ncols); + size_t nrows, ncols; + sparseJacobianInPlace(entries, Ordering(this->keys()), nrows, ncols); return entries; } /* ************************************************************************* */ - BoostTriplets GaussianFactorGraph::sparseJacobian( - const Ordering& ordering) const { - size_t dummy1, dummy2; - return sparseJacobian(ordering, dummy1, dummy2); - } - - /* ************************************************************************* */ - BoostTriplets GaussianFactorGraph::sparseJacobian( - size_t& nrows, size_t& ncols) const { - return sparseJacobian(Ordering(this->keys()), nrows, ncols); - } - - /* ************************************************************************* */ - BoostTriplets GaussianFactorGraph::sparseJacobian() const { - size_t dummy1, dummy2; - return sparseJacobian(dummy1, dummy2); - } - - /* ************************************************************************* */ - Matrix GaussianFactorGraph::sparseJacobian_( - const Ordering& ordering, size_t& nrows, size_t& ncols) const { + Matrix GaussianFactorGraph::sparseJacobian_() const { gttic_(GaussianFactorGraph_sparseJacobian_matrix); // call sparseJacobian - auto result = sparseJacobian(ordering, nrows, ncols); + auto result = sparseJacobian(); // translate to base 1 matrix size_t nzmax = result.size(); @@ -222,26 +202,7 @@ namespace gtsam { } /* ************************************************************************* */ - Matrix GaussianFactorGraph::sparseJacobian_( - const Ordering& ordering) const { - size_t dummy1, dummy2; - return sparseJacobian_(ordering, dummy1, dummy2); - } - - /* ************************************************************************* */ - Matrix GaussianFactorGraph::sparseJacobian_( - size_t& nrows, size_t& ncols) const { - return sparseJacobian_(Ordering(this->keys()), nrows, ncols); - } - - /* ************************************************************************* */ - Matrix GaussianFactorGraph::sparseJacobian_() const { - size_t dummy1, dummy2; - return sparseJacobian_(dummy1, dummy2); - } - - /* ************************************************************************* */ - using GtsamTriplets = GaussianFactorGraph::SparseMatrixGtsamTriplets; + using GtsamTriplets = std::vector>; GtsamTriplets GaussianFactorGraph::sparseJacobianFast( const Ordering& ordering, size_t& nrows, size_t& ncols) const { GtsamTriplets entries; @@ -250,25 +211,6 @@ namespace gtsam { return entries; } - /* ************************************************************************* */ - GtsamTriplets GaussianFactorGraph::sparseJacobianFast( - const Ordering& ordering) const { - size_t dummy1, dummy2; - return sparseJacobianFast(ordering, dummy1, dummy2); - } - - /* ************************************************************************* */ - GtsamTriplets GaussianFactorGraph::sparseJacobianFast( - size_t& nrows, size_t& ncols) const { - return sparseJacobianFast(Ordering(this->keys()), nrows, ncols); - } - - /* ************************************************************************* */ - GtsamTriplets GaussianFactorGraph::sparseJacobianFast() const { - size_t dummy1, dummy2; - return sparseJacobianFast(dummy1, dummy2); - } - /* ************************************************************************* */ Matrix GaussianFactorGraph::augmentedJacobian( const Ordering& ordering) const { diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 584eb02ce..70327d9f4 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -180,38 +180,14 @@ namespace gtsam { ///@name Linear Algebra ///@{ - /// Sparse matrix representation as vector of tuples. - typedef std::vector> - SparseMatrixBoostTriplets; - /// Sparse matrix representation as vector of slightly more efficient - /// tuples. - typedef std::vector> SparseMatrixGtsamTriplets; - /** * Return vector of i, j, and s to generate an m-by-n sparse augmented * Jacobian matrix, where i(k) and j(k) are the base 0 row and column * indices, s(k) a double. * The standard deviations are baked into A and b - * @param ordering the column ordering - * @param[out] nrows The number of rows in the Jacobian - * @param[out] ncols The number of columns in the Jacobian * @return the sparse matrix in one of the 4 forms above */ - SparseMatrixBoostTriplets sparseJacobian(const Ordering& ordering, - size_t& nrows, - size_t& ncols) const; - - /** Returns a sparse augmented Jacobian without outputting its dimensions */ - SparseMatrixBoostTriplets sparseJacobian( - const Ordering& ordering) const; - - /** Returns a sparse augmented Jacobian with default Ordering */ - SparseMatrixBoostTriplets sparseJacobian(size_t& nrows, - size_t& ncols) const; - - /** Returns a sparse augmented Jacobian without with default ordering and - * outputting its dimensions */ - SparseMatrixBoostTriplets sparseJacobian() const; + std::vector> sparseJacobian() const; /** * Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] @@ -219,44 +195,16 @@ namespace gtsam { * sparse. Note: i, j are 1-indexed. * The standard deviations are baked into A and b */ - Matrix sparseJacobian_(const Ordering& ordering, size_t& nrows, - size_t& ncols) const; - - /** Returns a matrix-form sparse augmented Jacobian without outputting its - * dimensions - */ - Matrix sparseJacobian_(const Ordering& ordering) const; - - /** Returns a matrix-form sparse augmented Jacobian with default Ordering - * @param[out] nrows The number of rows in the Jacobian - * @param[out] ncols The number of columns in the Jacobian - */ - Matrix sparseJacobian_(size_t& nrows, size_t& ncols) const; - - /** Returns a matrix-form sparse augmented Jacobian with default ordering - * and without outputting its dimensions */ Matrix sparseJacobian_() const; /** Returns a sparse matrix with `int` indices instead of `size_t` for - * slightly faster performance */ - SparseMatrixGtsamTriplets sparseJacobianFast(const Ordering& ordering, - size_t& nrows, - size_t& ncols) const; - - /** Returns an int-indexed sparse matrix without outputting its dimensions - */ - SparseMatrixGtsamTriplets sparseJacobianFast(const Ordering& ordering) const; - - /** Returns an int-indexed sparse matrix with default ordering + * slightly faster performance + * @param ordering the column ordering * @param[out] nrows The number of rows in the Jacobian * @param[out] ncols The number of columns in the Jacobian */ - SparseMatrixGtsamTriplets sparseJacobianFast(size_t& nrows, - size_t& ncols) const; - - /** Returns an int-indexed sparse matrix with default ordering and without - * outputting its dimensions */ - SparseMatrixGtsamTriplets sparseJacobianFast() const; + std::vector> sparseJacobianFast( + const Ordering& ordering, size_t& nrows, size_t& ncols) const; /** * Return a dense \f$ [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \f$ From a17bd5c6d5d8bfe0c8e84db3d3bce6e3fc302cd9 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 10:44:31 -0500 Subject: [PATCH 60/65] remove InPlace jacobian from .h file --- gtsam/linear/GaussianFactorGraph.cpp | 24 ++++++++++++++++-------- gtsam/linear/GaussianFactorGraph.h | 8 -------- 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index c8446e6a7..4c0576934 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -100,16 +100,24 @@ namespace gtsam { } /* ************************************************************************* */ + /** Performs in-place population of a sparse jacobian. Contains the + * common functionality amongst different sparseJacobian functions. + * @param graph the factor graph to get the Jacobian from + * @param entries a container of triplets that supports + * `emplace_back(size_t, size_t, double) + * @param ordering the variable ordering + * @param[out] nrows the nurmber of rows in the Jacobian + * @param[out] ncols the number of columns in the Jacobian + */ template - void GaussianFactorGraph::sparseJacobianInPlace(T& entries, - const Ordering& ordering, - size_t& nrows, - size_t& ncols) const { + void sparseJacobianInPlace(const GaussianFactorGraph& graph, T& entries, + const Ordering& ordering, size_t& nrows, + size_t& ncols) { gttic_(GaussianFactorGraph_sparseJacobianInPlace); // First find dimensions of each variable typedef std::map KeySizeMap; KeySizeMap dims; - for (const sharedFactor& factor : *this) { + for (const auto& factor : graph) { if (!static_cast(factor)) continue; for (auto it = factor->begin(); it != factor->end(); ++it) { @@ -127,7 +135,7 @@ namespace gtsam { // Iterate over all factors, adding sparse scalar entries nrows = 0; - for (const sharedFactor& factor : *this) { + for (const auto& factor : graph) { if (!static_cast(factor)) continue; // Convert to JacobianFactor if necessary @@ -179,7 +187,7 @@ namespace gtsam { BoostTriplets entries; entries.reserve(60 * size()); size_t nrows, ncols; - sparseJacobianInPlace(entries, Ordering(this->keys()), nrows, ncols); + sparseJacobianInPlace(*this, entries, Ordering(this->keys()), nrows, ncols); return entries; } @@ -207,7 +215,7 @@ namespace gtsam { const Ordering& ordering, size_t& nrows, size_t& ncols) const { GtsamTriplets entries; entries.reserve(60 * size()); - sparseJacobianInPlace(entries, ordering, nrows, ncols); + sparseJacobianInPlace(*this, entries, ordering, nrows, ncols); return entries; } diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 70327d9f4..de4f2318b 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -380,14 +380,6 @@ namespace gtsam { /// @} private: - /** Performs in-place population of a sparse jacobian. Contains the - * common functionality amongst different sparseJacobian functions. - * @param entries a container of triplets that supports - * `emplace_back(size_t, size_t, double)`*/ - template - void sparseJacobianInPlace(T& entries, const Ordering& ordering, - size_t& nrows, size_t& ncols) const; - /** Serialization function */ friend class boost::serialization::access; template From fa6bdd4042094f6b4f8c6e033147d1b514072f5e Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 10:54:22 -0500 Subject: [PATCH 61/65] fix comment and remove whitespace diff --- gtsam/linear/GaussianFactorGraph.h | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index de4f2318b..b54799f52 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -185,7 +185,7 @@ namespace gtsam { * Jacobian matrix, where i(k) and j(k) are the base 0 row and column * indices, s(k) a double. * The standard deviations are baked into A and b - * @return the sparse matrix in one of the 4 forms above + * @return the sparse matrix as a std::vector of boost tuples */ std::vector> sparseJacobian() const; @@ -387,7 +387,7 @@ namespace gtsam { ar & BOOST_SERIALIZATION_BASE_OBJECT_NVP(Base); } - public: + public: /** \deprecated */ VectorValues optimize(boost::none_t, From 8063b9ae958b939cb8c264c19b362d7db781c3fc Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 10:58:26 -0500 Subject: [PATCH 62/65] disambiguate double template >> --- gtsam/linear/GaussianFactorGraph.cpp | 4 ++-- gtsam/linear/GaussianFactorGraph.h | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 4c0576934..6a359e9d1 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -182,7 +182,7 @@ namespace gtsam { } /* ************************************************************************* */ - using BoostTriplets = std::vector>; + using BoostTriplets = std::vector >; BoostTriplets GaussianFactorGraph::sparseJacobian() const { BoostTriplets entries; entries.reserve(60 * size()); @@ -210,7 +210,7 @@ namespace gtsam { } /* ************************************************************************* */ - using GtsamTriplets = std::vector>; + using GtsamTriplets = std::vector >; GtsamTriplets GaussianFactorGraph::sparseJacobianFast( const Ordering& ordering, size_t& nrows, size_t& ncols) const { GtsamTriplets entries; diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index b54799f52..661d0a4a8 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -187,7 +187,7 @@ namespace gtsam { * The standard deviations are baked into A and b * @return the sparse matrix as a std::vector of boost tuples */ - std::vector> sparseJacobian() const; + std::vector > sparseJacobian() const; /** * Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] @@ -203,7 +203,7 @@ namespace gtsam { * @param[out] nrows The number of rows in the Jacobian * @param[out] ncols The number of columns in the Jacobian */ - std::vector> sparseJacobianFast( + std::vector > sparseJacobianFast( const Ordering& ordering, size_t& nrows, size_t& ncols) const; /** From 2590b3b98098970eb51ba4013b7fdff6491b20e7 Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 15:25:01 -0500 Subject: [PATCH 63/65] replace sparseJacobian with "fast" version --- gtsam/linear/GaussianFactorGraph.cpp | 50 ++++++------------- gtsam/linear/GaussianFactorGraph.h | 26 +++++----- gtsam/linear/SparseEigen.h | 2 +- .../linear/tests/testGaussianFactorGraph.cpp | 16 +++--- 4 files changed, 36 insertions(+), 58 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 6a359e9d1..947d4745c 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -100,24 +100,15 @@ namespace gtsam { } /* ************************************************************************* */ - /** Performs in-place population of a sparse jacobian. Contains the - * common functionality amongst different sparseJacobian functions. - * @param graph the factor graph to get the Jacobian from - * @param entries a container of triplets that supports - * `emplace_back(size_t, size_t, double) - * @param ordering the variable ordering - * @param[out] nrows the nurmber of rows in the Jacobian - * @param[out] ncols the number of columns in the Jacobian - */ - template - void sparseJacobianInPlace(const GaussianFactorGraph& graph, T& entries, - const Ordering& ordering, size_t& nrows, - size_t& ncols) { - gttic_(GaussianFactorGraph_sparseJacobianInPlace); + using SparseTriplets = std::vector >; + SparseTriplets GaussianFactorGraph::sparseJacobian(const Ordering& ordering, + size_t& nrows, + size_t& ncols) const { + gttic_(GaussianFactorGraph_sparseJacobian); // First find dimensions of each variable typedef std::map KeySizeMap; KeySizeMap dims; - for (const auto& factor : graph) { + for (const auto& factor : *this) { if (!static_cast(factor)) continue; for (auto it = factor->begin(); it != factor->end(); ++it) { @@ -134,8 +125,10 @@ namespace gtsam { } // Iterate over all factors, adding sparse scalar entries + SparseTriplets entries; + entries.reserve(60 * size()); nrows = 0; - for (const auto& factor : graph) { + for (const auto& factor : *this) { if (!static_cast(factor)) continue; // Convert to JacobianFactor if necessary @@ -179,16 +172,13 @@ namespace gtsam { } ncols++; // +1 for b-column + return entries; } /* ************************************************************************* */ - using BoostTriplets = std::vector >; - BoostTriplets GaussianFactorGraph::sparseJacobian() const { - BoostTriplets entries; - entries.reserve(60 * size()); + SparseTriplets GaussianFactorGraph::sparseJacobian() const { size_t nrows, ncols; - sparseJacobianInPlace(*this, entries, Ordering(this->keys()), nrows, ncols); - return entries; + return sparseJacobian(Ordering(this->keys()), nrows, ncols); } /* ************************************************************************* */ @@ -202,23 +192,13 @@ namespace gtsam { Matrix IJS(3, nzmax); for (size_t k = 0; k < result.size(); k++) { const auto& entry = result[k]; - IJS(0, k) = double(entry.get<0>() + 1); - IJS(1, k) = double(entry.get<1>() + 1); - IJS(2, k) = entry.get<2>(); + IJS(0, k) = double(std::get<0>(entry) + 1); + IJS(1, k) = double(std::get<1>(entry) + 1); + IJS(2, k) = std::get<2>(entry); } return IJS; } - /* ************************************************************************* */ - using GtsamTriplets = std::vector >; - GtsamTriplets GaussianFactorGraph::sparseJacobianFast( - const Ordering& ordering, size_t& nrows, size_t& ncols) const { - GtsamTriplets entries; - entries.reserve(60 * size()); - sparseJacobianInPlace(*this, entries, ordering, nrows, ncols); - return entries; - } - /* ************************************************************************* */ Matrix GaussianFactorGraph::augmentedJacobian( const Ordering& ordering) const { diff --git a/gtsam/linear/GaussianFactorGraph.h b/gtsam/linear/GaussianFactorGraph.h index 661d0a4a8..e3304d5e8 100644 --- a/gtsam/linear/GaussianFactorGraph.h +++ b/gtsam/linear/GaussianFactorGraph.h @@ -181,13 +181,20 @@ namespace gtsam { ///@{ /** - * Return vector of i, j, and s to generate an m-by-n sparse augmented - * Jacobian matrix, where i(k) and j(k) are the base 0 row and column - * indices, s(k) a double. + * Returns a sparse augmented Jacbian matrix as a vector of i, j, and s, + * where i(k) and j(k) are the base 0 row and column indices, and s(k) is + * the entry as a double. * The standard deviations are baked into A and b - * @return the sparse matrix as a std::vector of boost tuples + * @return the sparse matrix as a std::vector of std::tuples + * @param ordering the column ordering + * @param[out] nrows The number of rows in the augmented Jacobian + * @param[out] ncols The number of columns in the augmented Jacobian */ - std::vector > sparseJacobian() const; + std::vector > sparseJacobian( + const Ordering& ordering, size_t& nrows, size_t& ncols) const; + + /** Returns a sparse augmented Jacobian matrix with default ordering */ + std::vector > sparseJacobian() const; /** * Matrix version of sparseJacobian: generates a 3*m matrix with [i,j,s] @@ -197,15 +204,6 @@ namespace gtsam { */ Matrix sparseJacobian_() const; - /** Returns a sparse matrix with `int` indices instead of `size_t` for - * slightly faster performance - * @param ordering the column ordering - * @param[out] nrows The number of rows in the Jacobian - * @param[out] ncols The number of columns in the Jacobian - */ - std::vector > sparseJacobianFast( - const Ordering& ordering, size_t& nrows, size_t& ncols) const; - /** * Return a dense \f$ [ \;A\;b\; ] \in \mathbb{R}^{m \times n+1} \f$ * Jacobian matrix, augmented with b with the noise models baked diff --git a/gtsam/linear/SparseEigen.h b/gtsam/linear/SparseEigen.h index bc99b5c89..483ae7f8d 100644 --- a/gtsam/linear/SparseEigen.h +++ b/gtsam/linear/SparseEigen.h @@ -41,7 +41,7 @@ SparseEigen sparseJacobianEigen( // intermediate `entries` vector is kind of unavoidable due to how expensive // factor->rows() is, which prevents us from populating SparseEigen directly. size_t nrows, ncols; - auto entries = gfg.sparseJacobianFast(ordering, nrows, ncols); + auto entries = gfg.sparseJacobian(ordering, nrows, ncols); // declare sparse matrix SparseEigen Ab(nrows, ncols); // See Eigen::set_from_triplets. This is about 5% faster. diff --git a/gtsam/linear/tests/testGaussianFactorGraph.cpp b/gtsam/linear/tests/testGaussianFactorGraph.cpp index 493e7667c..bb07a36aa 100644 --- a/gtsam/linear/tests/testGaussianFactorGraph.cpp +++ b/gtsam/linear/tests/testGaussianFactorGraph.cpp @@ -36,16 +36,16 @@ using namespace boost::assign; using namespace std; using namespace gtsam; -typedef boost::tuple BoostTriplet; -bool triplet_equal(BoostTriplet a, BoostTriplet b) { - if (a.get<0>() == b.get<0>() && a.get<1>() == b.get<1>() && - a.get<2>() == b.get<2>()) return true; +typedef std::tuple SparseTriplet; +bool triplet_equal(SparseTriplet a, SparseTriplet b) { + if (get<0>(a) == get<0>(b) && get<1>(a) == get<1>(b) && + get<2>(a) == get<2>(b)) return true; cout << "not equal:" << endl; cout << "\texpected: " - "(" << a.get<0>() << ", " << a.get<1>() << ") = " << a.get<2>() << endl; + "(" << get<0>(a) << ", " << get<1>(a) << ") = " << get<2>(a) << endl; cout << "\tactual: " - "(" << b.get<0>() << ", " << b.get<1>() << ") = " << b.get<2>() << endl; + "(" << get<0>(b) << ", " << get<1>(b) << ") = " << get<2>(b) << endl; return false; } @@ -119,14 +119,14 @@ TEST(GaussianFactorGraph, sparseJacobian) { EXPECT(assert_equal(expectedMatlab, actual)); - // BoostTriplets + // SparseTriplets auto boostActual = gfg.sparseJacobian(); // check the triplets size... EXPECT_LONGS_EQUAL(16, boostActual.size()); // check content for (int i = 0; i < 16; i++) { EXPECT(triplet_equal( - BoostTriplet(expected(i, 0) - 1, expected(i, 1) - 1, expected(i, 2)), + SparseTriplet(expected(i, 0) - 1, expected(i, 1) - 1, expected(i, 2)), boostActual.at(i))); } } From 53261a5e167733d8e2f0089eb69c702748fa7fed Mon Sep 17 00:00:00 2001 From: Gerry Chen Date: Wed, 27 Jan 2021 16:58:05 -0500 Subject: [PATCH 64/65] auto and reserve fewer --- gtsam/linear/GaussianFactorGraph.cpp | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/gtsam/linear/GaussianFactorGraph.cpp b/gtsam/linear/GaussianFactorGraph.cpp index 947d4745c..13eaee7e3 100644 --- a/gtsam/linear/GaussianFactorGraph.cpp +++ b/gtsam/linear/GaussianFactorGraph.cpp @@ -126,7 +126,7 @@ namespace gtsam { // Iterate over all factors, adding sparse scalar entries SparseTriplets entries; - entries.reserve(60 * size()); + entries.reserve(30 * size()); nrows = 0; for (const auto& factor : *this) { if (!static_cast(factor)) continue; @@ -148,8 +148,7 @@ namespace gtsam { // Whiten the factor and add entries for it // iterate over all variables in the factor const JacobianFactor whitened(jacobianFactor->whiten()); - for (JacobianFactor::const_iterator key = whitened.begin(); - key < whitened.end(); ++key) { + for (auto key = whitened.begin(); key < whitened.end(); ++key) { JacobianFactor::constABlock whitenedA = whitened.getA(key); // find first column index for this key size_t column_start = columnIndices[*key]; From a3d06f635fd489f19319f4aa8a8daee96f563526 Mon Sep 17 00:00:00 2001 From: Peter Mullen Date: Wed, 27 Jan 2021 21:48:10 -0800 Subject: [PATCH 65/65] type in test hidden by duplicate test values --- gtsam/base/tests/testNumericalDerivative.cpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/gtsam/base/tests/testNumericalDerivative.cpp b/gtsam/base/tests/testNumericalDerivative.cpp index d27e43040..90999674b 100644 --- a/gtsam/base/tests/testNumericalDerivative.cpp +++ b/gtsam/base/tests/testNumericalDerivative.cpp @@ -30,10 +30,10 @@ double f(const Vector2& x) { /* ************************************************************************* */ // TEST(testNumericalDerivative, numericalGradient) { - Vector2 x(1, 1); + Vector2 x(1, 1.1); Vector expected(2); - expected << cos(x(1)), -sin(x(0)); + expected << cos(x(0)), -sin(x(1)); Vector actual = numericalGradient(f, x); @@ -42,7 +42,7 @@ TEST(testNumericalDerivative, numericalGradient) { /* ************************************************************************* */ TEST(testNumericalDerivative, numericalHessian) { - Vector2 x(1, 1); + Vector2 x(1, 1.1); Matrix expected(2, 2); expected << -sin(x(0)), 0.0, 0.0, -cos(x(1));