least_squares Namespace Reference
Typedefs |
| typedef Vx::value_type | T |
Functions |
| template<class T > |
| void | invert (M(T)&m) |
| | Invert a matrix, in-place, using Gauss-Jordan elimination.
|
| template void | invert (M(float)&m) |
| template void | invert (M(double)&m) |
| template<class T > |
| | V (T) linearFit(const M(T)&x |
| | Returns parameters 'a' via ordinary least squares such that y = x·a.
|
| template | V (float) linearFit(const M(float)&x |
| template | V (double) linearFit(const M(double)&x |
| template<class Vx , class Vy > |
| | V (typename Vx::value_type) polyFit(size_t degree |
| | Returns fit 'a' of degree powers of x: y = [ 1 x .. xⁿ ] · a.
|
| const Vx const Vy &y | if (degree >0) |
| | if (y.size()< degree) |
| | M (T) xn(V(T)(1 |
| return | linearFit (xn, V(T)(&y[0], N)) |
Variables |
| const Vx & | x |
| const Vx const Vy & | y |
| const size_t | N = y.size() |
| | degree |
Detailed Description
Least Squares Solver by Ethan Tira-Thompson, © 2011
Solves linear systems using Ordinary Least Squares.
Provides the namespace 'least_squares'.
There are two solver functions:
linearFit(x,y) Returns the parameters 'a' such that y = x·a minimizes squared error. x should be a valarray< valarray<T> >, where each x[i] is a column of data with length matching that of the valarray y.
polyFit(degree,x,y) Performs a polynomial fit of degree n: y = [ 1 x .. xⁿ ] · a given x and y (as vector or valarray) Results will be in order of increasing power (i.e. index 0 is constant term, 1 is linear term, etc.)
Additionally, there are two helper functions:
polyApply(poly,x) Computes the polynomial of 'x' given polynomial terms 'poly'. These arguments can be either vector or valarray.
invert(x) Inverts a square valarray matrix 'x', overwriting results in-place. Throws std::underflow_error if the matrix is deficient.
TODO: does not handle degenerate/low-rank conditions very well. Ideally, the fit functions should handle internally instead of allowing invert()'s std::underflow_error to pass through
LICENSE: least_squares is free software: you can redistribute it and/or modify it under the terms of the Lesser GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version, waiving any requirement to distribute the license document itself.
least_squares is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Lesser GNU General Public License for more details.
Typedef Documentation
Function Documentation
| least_squares::if |
( |
degree |
, |
|
|
0 |
| |
|
) |
| | |
| template void least_squares::invert |
( |
M(double)& |
m |
) |
|
| template void least_squares::invert |
( |
M(float)& |
m |
) |
|
template<class T >
| void least_squares::invert |
( |
M(T)& |
m |
) |
|
Invert a matrix, in-place, using Gauss-Jordan elimination.
Throws std::underflow_error if the matrix is deficient.
| return least_squares::linearFit |
( |
xn |
, |
|
|
V(T)&[0], |
N | |
|
) |
| | |
template<class Vx , class Vy >
| least_squares::V |
( |
typename Vx::value_type |
|
) |
|
Returns fit 'a' of degree powers of x: y = [ 1 x .. xⁿ ] · a.
Computes the polynomial of x given terms from poly.
Accepts vector or valarray... results will be in order of increasing power (i.e. 0 is constant term, 1 is linear term, etc.)
TODO: does not handle degenerate/low-rank conditions. Ideally, this should be handled internally instead of allowing invert()'s std::underflow_error to pass through.
Accepts either vector and valarray arguments... poly terms should be in order of increasing degree à la polyFit()
| template const least_squares::V |
( |
double |
|
) |
const |
| template const least_squares::V |
( |
float |
|
) |
const |
template<class T >
| const least_squares::V |
( |
T |
|
) |
const |
Returns parameters 'a' via ordinary least squares such that y = x·a.
Each element of x should be a valarray with length matching that of y. Will then compute invert(x' * x) * x' * y to find the fit.
TODO: does not handle degenerate/low-rank conditions. Ideally, this should be handled internally instead of allowing invert()'s std::underflow_error to pass through.
Definition at line 71 of file least_squares.cc.
Variable Documentation
Definition at line 120 of file least_squares.h.
Referenced by fmat::abs(), fmat::Row< N, R >::abs(), fmat::Column< 2, float >::abs(), fmat::SubVector< H, R >::abs(), CBracketGrasperPredicate< N >::admissible(), fmat::Row< N, R >::apply(), fmat::Column< 2, float >::apply(), fmat::SubVector< H, R >::apply(), BoundingBox< 3 >::BoundingBox(), CBracketGrasperPredicate< N >::CBracketGrasperPredicate(), GJK::collides(), BoundingBox< 3 >::collides(), RRTNode3DR< N >::CollisionChecker::CollisionChecker(), RRTNode2DR< N >::CollisionChecker::CollisionChecker(), fmat::Column< 2, float >::Column(), RRTNode3DR< N >::distance(), RRTNode2DR< N >::distance(), fmat::dotProduct(), fmat::Row< N, R >::exportTo(), fmat::Column< 2, float >::exportTo(), fmat::SubVector< H, R >::exportTo(), fmat::Row< N, R >::fmt(), fmat::Column< 2, float >::fmt(), fmat::SubVector< H, R >::fmt(), RRTNode3DR< N >::generateSample(), RRTNode2DR< N >::generateSample(), BoundingBox< 3 >::getCorner(), BoundingBox< 3 >::getRandom(), CBracketGrasperPredicate< N >::gripperPosition(), fmat::Row< N, R >::importFrom(), fmat::Column< 2, float >::importFrom(), fmat::SubVector< H, R >::importFrom(), RRTNode3DR< N >::interpolate(), RRTNode2DR< N >::interpolate(), fmat::Row< N, R >::map(), fmat::Column< 2, float >::map(), fmat::SubVector< H, R >::map(), fmat::Row< N, R >::max(), fmat::Column< 2, float >::max(), fmat::SubVector< H, R >::max(), fmat::Row< N, R >::maximize(), fmat::Column< 2, float >::maximize(), fmat::SubVector< H, R >::maximize(), fmat::Row< N, R >::min(), fmat::Column< 2, float >::min(), fmat::SubVector< H, R >::min(), fmat::Row< N, R >::minimize(), fmat::Column< 2, float >::minimize(), fmat::SubVector< H, R >::minimize(), fmat::Row< N, R >::norm(), fmat::Column< 2, float >::norm(), fmat::SubVector< H, R >::norm(), fmat::Row< N, R >::operator!=(), fmat::Column< 2, float >::operator!=(), fmat::SubVector< H, R >::operator!=(), fmat::TransformT< R >::operator*(), fmat::Row< N, R >::operator*=(), fmat::Column< 2, float >::operator*=(), fmat::SubVector< H, R >::operator*=(), fmat::Row< N, R >::operator+=(), fmat::Column< 2, float >::operator+=(), fmat::SubVector< H, R >::operator+=(), fmat::Row< N, R >::operator-(), fmat::Column< 2, float >::operator-(), fmat::SubVector< H, R >::operator-(), fmat::Row< N, R >::operator-=(), fmat::Column< 2, float >::operator-=(), fmat::SubVector< H, R >::operator-=(), fmat::Row< N, R >::operator/=(), fmat::Column< 2, float >::operator/=(), fmat::SubVector< H, R >::operator/=(), fmat::Row< N, R >::operator<(), fmat::Column< 2, float >::operator<(), fmat::SubVector< H, R >::operator<(), fmat::Row< N, R >::operator<<(), fmat::Column< 2, float >::operator<<(), fmat::SubVector< H, R >::operator<<(), fmat::Row< N, R >::operator=(), fmat::Column< 2, float >::operator=(), fmat::SubVector< H, R >::operator=(), fmat::Row< N, R >::operator==(), fmat::Column< 2, float >::operator==(), fmat::SubVector< H, R >::operator==(), fmat::pack(), GJK::processTriangle(), BoundingBox< 3 >::rotate(), fmat::rotationZN(), fmat::Row< N, R >::Row(), CBracketGrasperPredicate< N >::stateOrien(), fmat::SubVector< H, R >::SubVector(), fmat::Row< N, R >::sum(), fmat::Column< 2, float >::sum(), fmat::SubVector< H, R >::sum(), fmat::Row< N, R >::sumSq(), fmat::Column< 2, float >::sumSq(), fmat::SubVector< H, R >::sumSq(), RRTNode3DR< N >::toString(), RRTNode2DR< N >::toString(), fmat::Row< N, R >::transpose(), fmat::Column< 2, float >::transpose(), and fmat::SubVector< H, R >::transpose().
Definition at line 83 of file least_squares.h.
Referenced by Kinematics::baseToLocal(), RawImage::buildNextLayer(), LedEngine::calcCycle(), InterleavedYUVGenerator::calcImage(), CMVision::CheckRuns(), SiftMatch::computeBoundingBox(), VL::Sift::computeKeypointDescriptor(), VL::Sift::computeKeypointOrientations(), IKThreeLink::computeSecondLinkRevolute(), VL::Detail::copyAndDownsample(), VL::Detail::copyAndUpsampleRows(), ListMemBuf< T_t, MAX, idx_t >::countb(), ListMemBuf< T_t, MAX, idx_t >::countf(), LoadSave::decode(), VL::Sift::detectKeypoints(), DualCoding::ShapeSLAMParticleEvaluator::determineDeletions(), VisualTargetCloseTrans::doEvent(), SmoothCompareTrans< T >::doEvent(), DualCoding::Pilot::PushObjectMachine::AdjustPush::doStart(), DualCoding::Pilot::PushObjectMachine::FetchObj::doStart(), BufferedImageGenerator::downsampleImage(), DRanNormalTail(), DRanNormalZig(), DRanNormalZig32(), DRanNormalZig32Vec(), DRanNormalZigVec(), PGMImg::drawKeypoint(), PGMImg::drawLine(), Graphics::drawLine(), LoadSave::encode(), CMVision::EncodeRuns(), CMVision::EncodeRunsUseEdges(), fmat::Matrix< 4, 2 >::exportTo(), fmat::SubMatrix< H, W, R >::exportTo(), fmat::SubVector< H, R >::exportTo(), fmat::Matrix< 4, 2 >::exportToNewmat(), fmat::SubMatrix< H, W, R >::exportToNewmat(), AprilTags::TagDetector::extractTags(), plist::Angle::get(), AprilTags::FloatImage::get(), EllipsoidObstacle::get2Support(), Wireless::getIPAddress(), Kodu::VisualNavErrMonTask::getMapBuilderRequest(), EllipticalObstacle::getOrientation(), SineMC::getPhase(), EllipticalObstacle::getPointOnEdge(), LoadSave::getSerializedSize(), EllipsoidObstacle::getSupport(), EllipticalObstacle::getSupport(), GaitedFootsteps::State::hash(), debuget::hexout(), fmat::Matrix< 4, 2 >::importFrom(), fmat::SubMatrix< H, W, R >::importFrom(), fmat::Matrix< 4, 2 >::importFromNewmat(), fmat::SubMatrix< H, W, R >::importFromNewmat(), OpticalFlow::initializePositions(), fmat::invert(), DualCoding::MapBuilder::isBadGazePoint(), OpticalFlow::iterativeLucasKanade(), AprilTags::Gridder< T >::Iterator::Iterator(), ListMemBuf< T_t, MAX, idx_t >::ListMemBuf(), RLEGenerator::loadBuffer(), AprilTags::GLine2D::lsqFitXYW(), EventBase::makeClassTypeID(), MotionManager::MotionManager(), fmat::fmat_internal::mvops< M, V >::multiply(), fmat::fmat_internal::mmops< T1, T2 >::multiply(), fmat::SubVector< H, R >::norm(), fmat::SubVector< H, R >::operator<(), fmat::operator<<(), fmat::SubVector< H, R >::operator<<(), operator>>(), RawImage::printImage(), RawCameraGenerator::reconstructImage(), WaypointWalkControl::refresh(), CMVision::RmapToRgb(), BoundingBox< 3 >::rotate(), GreedySampler::sample(), RLEGenerator::saveBuffer(), ArmController::sendReachablePoints(), plist::RGBColor< T >::set(), plist::NamedEnumeration< shutter_speeds >::set(), AprilTags::FloatImage::set(), MotionSequenceEngine::setOutputCmd(), HeadPointerMC::setWeight(), siftdriver(), RawImage::spatialGradientMatrix(), fmat::SubVector< H, R >::sumSq(), and SineMC::sync().
Definition at line 83 of file least_squares.h.
Referenced by Kinematics::baseToLocal(), RawImage::buildNextLayer(), InterleavedYUVGenerator::calcImage(), CMVision::CheckRuns(), SiftMatch::computeBoundingBox(), VL::Sift::computeKeypointDescriptor(), VL::Sift::computeKeypointOrientations(), VL::Detail::copyAndDownsample(), VL::Detail::copyAndUpsampleRows(), image_util::decodePNGToDepth(), VL::Sift::detectKeypoints(), DualCoding::ShapeSLAMParticleEvaluator::determineDeletions(), VisualTargetCloseTrans::doEvent(), DualCoding::Pilot::PushObjectMachine::AdjustPush::doStart(), DualCoding::Pilot::PushObjectMachine::FetchObj::doStart(), dProbN(), DRanNormalTail(), DRanNormalZig32(), DRanNormalZig32Vec(), PGMImg::drawKeypoint(), PGMImg::drawLine(), Graphics::drawLine(), CMVision::EncodeRuns(), CMVision::EncodeRunsUseEdges(), AprilTags::TagDetector::extractTags(), AprilTags::FloatImage::get(), Kodu::VisualNavErrMonTask::getMapBuilderRequest(), GaitedFootsteps::State::hash(), OpticalFlow::initializePositions(), DualCoding::MapBuilder::isBadGazePoint(), OpticalFlow::iterativeLucasKanade(), AprilTags::Gridder< T >::Iterator::Iterator(), RLEGenerator::loadBuffer(), AprilTags::GLine2D::lsqFitXYW(), VL::Sift::prepareGrad(), RawImage::printImage(), RawCameraGenerator::reconstructImage(), WaypointWalkControl::refresh(), CMVision::RmapToRgb(), RawCameraGenerator::saveBuffer(), CDTGenerator::saveBuffer(), BufferedImageGenerator::saveBuffer(), RawCameraGenerator::saveFileStream(), BufferedImageGenerator::saveFileStream(), ArmController::sendReachablePoints(), AprilTags::FloatImage::set(), siftdriver(), IKCalliope::solve(), and RawImage::spatialGradientMatrix().
|
