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ConjugateGradientSolver.h
Go to the documentation of this file.
/* ----------------------------------------------------------------------------
* 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
* -------------------------------------------------------------------------- */
#pragma once
#include <gtsam/linear/IterativeSolver.h>
namespace gtsam {
class GTSAM_EXPORT ConjugateGradientParameters : public IterativeOptimizationParameters {
public:
typedef IterativeOptimizationParameters Base;
typedef boost::shared_ptr<ConjugateGradientParameters> shared_ptr;
size_t minIterations_;
size_t maxIterations_;
size_t reset_;
double epsilon_rel_;
double epsilon_abs_;
/* Matrix Operation Kernel */
enum BLASKernel {
GTSAM = 0,
} blas_kernel_ ;
ConjugateGradientParameters()
: minIterations_(1), maxIterations_(500), reset_(501), epsilon_rel_(1e-3),
epsilon_abs_(1e-3), blas_kernel_(GTSAM) {}
ConjugateGradientParameters(size_t minIterations, size_t maxIterations, size_t reset,
double epsilon_rel, double epsilon_abs, BLASKernel blas)
: minIterations_(minIterations), maxIterations_(maxIterations), reset_(reset),
epsilon_rel_(epsilon_rel), epsilon_abs_(epsilon_abs), blas_kernel_(blas) {}
ConjugateGradientParameters(const ConjugateGradientParameters &p)
: Base(p), minIterations_(p.minIterations_), maxIterations_(p.maxIterations_), reset_(p.reset_),
epsilon_rel_(p.epsilon_rel_), epsilon_abs_(p.epsilon_abs_), blas_kernel_(GTSAM) {}
/* general interface */
inline size_t minIterations() const { return minIterations_; }
inline size_t maxIterations() const { return maxIterations_; }
inline size_t reset() const { return reset_; }
inline double epsilon() const { return epsilon_rel_; }
inline double epsilon_rel() const { return epsilon_rel_; }
inline double epsilon_abs() const { return epsilon_abs_; }
inline size_t getMinIterations() const { return minIterations_; }
inline size_t getMaxIterations() const { return maxIterations_; }
inline size_t getReset() const { return reset_; }
inline double getEpsilon() const { return epsilon_rel_; }
inline double getEpsilon_rel() const { return epsilon_rel_; }
inline double getEpsilon_abs() const { return epsilon_abs_; }
inline void setMinIterations(size_t value) { minIterations_ = value; }
inline void setMaxIterations(size_t value) { maxIterations_ = value; }
inline void setReset(size_t value) { reset_ = value; }
inline void setEpsilon(double value) { epsilon_rel_ = value; }
inline void setEpsilon_rel(double value) { epsilon_rel_ = value; }
inline void setEpsilon_abs(double value) { epsilon_abs_ = value; }
void print() const { Base::print(); }
void print(std::ostream &os) const override;
static std::string blasTranslator(const BLASKernel k) ;
static BLASKernel blasTranslator(const std::string &s) ;
};
/*
* A template for the linear preconditioned conjugate gradient method.
* System class should support residual(v, g), multiply(v,Av), scal(alpha,v), dot(v,v), axpy(alpha,x,y)
* leftPrecondition(v, L^{-1}v, rightPrecondition(v, L^{-T}v) where preconditioner M = L*L^T
* Note that the residual is in the preconditioned domain. Refer to Section 9.2 of Saad's book.
*
** REFERENCES:
* [1] Y. Saad, "Preconditioned Iterations," in Iterative Methods for Sparse Linear Systems,
* 2nd ed. SIAM, 2003, ch. 9, sec. 2, pp.276-281.
*/
template<class S, class V>
V preconditionedConjugateGradient(const S &system, const V &initial,
const ConjugateGradientParameters &parameters) {
V estimate, residual, direction, q1, q2;
estimate = residual = direction = q1 = q2 = initial;
system.residual(estimate, q1); /* q1 = b-Ax */
system.leftPrecondition(q1, residual); /* r = L^{-1} (b-Ax) */
system.rightPrecondition(residual, direction);/* p = L^{-T} r */
double currentGamma = system.dot(residual, residual), prevGamma, alpha, beta;
const size_t iMaxIterations = parameters.maxIterations(),
iMinIterations = parameters.minIterations(),
iReset = parameters.reset() ;
const double threshold = std::max(parameters.epsilon_abs(),
parameters.epsilon() * parameters.epsilon() * currentGamma);
if (parameters.verbosity() >= ConjugateGradientParameters::COMPLEXITY )
std::cout << "[PCG] epsilon = " << parameters.epsilon()
<< ", max = " << parameters.maxIterations()
<< ", reset = " << parameters.reset()
<< ", ||r0||^2 = " << currentGamma
<< ", threshold = " << threshold << std::endl;
size_t k;
for ( k = 1 ; k <= iMaxIterations && (currentGamma > threshold || k <= iMinIterations) ; k++ ) {
if ( k % iReset == 0 ) {
system.residual(estimate, q1); /* q1 = b-Ax */
system.leftPrecondition(q1, residual); /* r = L^{-1} (b-Ax) */
system.rightPrecondition(residual, direction); /* p = L^{-T} r */
currentGamma = system.dot(residual, residual);
}
system.multiply(direction, q1); /* q1 = A p */
alpha = currentGamma / system.dot(direction, q1); /* alpha = gamma / (p' A p) */
system.axpy(alpha, direction, estimate); /* estimate += alpha * p */
system.leftPrecondition(q1, q2); /* q2 = L^{-1} * q1 */
system.axpy(-alpha, q2, residual); /* r -= alpha * q2 */
prevGamma = currentGamma;
currentGamma = system.dot(residual, residual); /* gamma = |r|^2 */
beta = currentGamma / prevGamma;
system.rightPrecondition(residual, q1); /* q1 = L^{-T} r */
system.scal(beta, direction);
system.axpy(1.0, q1, direction); /* p = q1 + beta * p */
if (parameters.verbosity() >= ConjugateGradientParameters::ERROR )
std::cout << "[PCG] k = " << k
<< ", alpha = " << alpha
<< ", beta = " << beta
<< ", ||r||^2 = " << currentGamma
// << "\nx =\n" << estimate
// << "\nr =\n" << residual
<< std::endl;
}
if (parameters.verbosity() >= ConjugateGradientParameters::COMPLEXITY )
std::cout << "[PCG] iterations = " << k
<< ", ||r||^2 = " << currentGamma
<< std::endl;
return estimate;
}
}
IterativeSolver.h
Some support classes for iterative solvers.
gtsam
Global functions in a separate testing namespace.
Definition chartTesting.h:28
gtsam::print
void print(const Matrix &A, const string &s, ostream &stream)
print without optional string, must specify cout yourself
Definition Matrix.cpp:156
gtsam::ConjugateGradientParameters
parameters for the conjugate gradient method
Definition ConjugateGradientSolver.h:29
gtsam::ConjugateGradientParameters::minIterations_
size_t minIterations_
minimum number of cg iterations
Definition ConjugateGradientSolver.h:35
gtsam::ConjugateGradientParameters::reset_
size_t reset_
number of iterations before reset
Definition ConjugateGradientSolver.h:37
gtsam::ConjugateGradientParameters::BLASKernel
BLASKernel
Definition ConjugateGradientSolver.h:42
gtsam::ConjugateGradientParameters::GTSAM
@ GTSAM
Jacobian Factor Graph of GTSAM.
Definition ConjugateGradientSolver.h:43
gtsam::ConjugateGradientParameters::epsilon_rel_
double epsilon_rel_
threshold for relative error decrease
Definition ConjugateGradientSolver.h:38
gtsam::ConjugateGradientParameters::maxIterations_
size_t maxIterations_
maximum number of cg iterations
Definition ConjugateGradientSolver.h:36
gtsam::ConjugateGradientParameters::epsilon_abs_
double epsilon_abs_
threshold for absolute error decrease
Definition ConjugateGradientSolver.h:39