gtsam/linear/NoiseModel.cpp

/* ----------------------------------------------------------------------------

 * 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

 * -------------------------------------------------------------------------- */

/*
 * NoiseModel
 *
 *  Created on: Jan 13, 2010
 *      Author: Richard Roberts
 *      Author: Frank Dellaert
 */

#include <limits>
#include <iostream>
#include <typeinfo>
#include <stdexcept>

#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/foreach.hpp>
#include <boost/random/linear_congruential.hpp>
#include <boost/random/normal_distribution.hpp>
#include <boost/random/variate_generator.hpp>

#include <gtsam/linear/NoiseModel.h>
#include <gtsam/linear/SharedDiagonal.h>

namespace ublas = boost::numeric::ublas;
typedef ublas::matrix_column<Matrix> column;

static double inf = std::numeric_limits<double>::infinity();
using namespace std;

namespace gtsam {

namespace noiseModel {

/* ************************************************************************* */
// update A, b
// A' \define A_{S}-ar and b'\define b-ad
// Linear algebra: takes away projection on latest orthogonal
// Graph: make a new factor on the separator S
// __attribute__ ((noinline))	// uncomment to prevent inlining when profiling
static void updateAb(Matrix& Ab, int j, const Vector& a, const Vector& rd) {
	size_t m = Ab.size1(), n = Ab.size2()-1;

	for (size_t i = 0; i < m; i++) { // update all rows
		double ai = a(i);
		double *Aij = Ab.data().begin() + i * (n+1) + j + 1;
		const double *rptr = rd.data().begin() + j + 1;
		// Ab(i,j+1:end) -= ai*rd(j+1:end)
		for (size_t j2 = j + 1; j2 < n+1; j2++, Aij++, rptr++)
			*Aij -= ai * (*rptr);
	}
}


/* ************************************************************************* */
Gaussian::shared_ptr Gaussian::Covariance(const Matrix& covariance, bool smart) {
	size_t m = covariance.size1(), n = covariance.size2();
	if (m != n) throw invalid_argument("Gaussian::Covariance: covariance not square");
	if (smart) {
		// check all non-diagonal entries
		size_t i,j;
		for (i = 0; i < m; i++)
			for (j = 0; j < n; j++)
				if (i != j && fabs(covariance(i, j) > 1e-9)) goto full;
		Vector variances(n);
		for (j = 0; j < n; j++) variances(j) = covariance(j,j);
		return Diagonal::Variances(variances,true);
	}
	full: return shared_ptr(new Gaussian(n, inverse_square_root(covariance)));
}

void Gaussian::print(const string& name) const {
	gtsam::print(thisR(), "Gaussian");
}

bool Gaussian::equals(const Base& expected, double tol) const {
	const Gaussian* p = dynamic_cast<const Gaussian*> (&expected);
	if (p == NULL) return false;
	if (typeid(*this) != typeid(*p)) return false;
	//if (!sqrt_information_) return true; // ALEX todo;
	return equal_with_abs_tol(R(), p->R(), sqrt(tol));
}

Vector Gaussian::whiten(const Vector& v) const {
	return thisR() * v;
}


Vector Gaussian::unwhiten(const Vector& v) const {
	return backSubstituteUpper(thisR(), v);
}

double Gaussian::Mahalanobis(const Vector& v) const {
	// Note: for Diagonal, which does ediv_, will be correct for constraints
	Vector w = whiten(v);
	return inner_prod(w, w);
}

Matrix Gaussian::Whiten(const Matrix& H) const {
	return thisR() * H;
}

void Gaussian::WhitenInPlace(Matrix& H) const {
	H = thisR() * H;
}

void Gaussian::WhitenInPlace(MatrixColMajor& H) const {
  H = ublas::prod(thisR(), H);
}

// General QR, see also special version in Constrained
/*SharedDiagonal Gaussian::QR(Matrix& Ab, boost::optional<vector<long>&> firstZeroRows) const {

	// get size(A) and maxRank
	// TODO: really no rank problems ?
	size_t m = Ab.size1(), n = Ab.size2()-1;
	size_t maxRank = min(m,n);

	// pre-whiten everything (cheaply if possible)
	WhitenInPlace(Ab);

	// Perform in-place Householder
#ifdef GT_USE_LAPACK
	if(firstZeroRows)
	  householder_denseqr(Ab, &(*firstZeroRows)[0]);
	else
	  householder_denseqr(Ab);
#else
householder(Ab, maxRank);
#endif

return Unit::Create(maxRank);
}*/

// Special version of QR for Constrained calls slower but smarter code
// that deals with possibly zero sigmas
// It is Gram-Schmidt orthogonalization rather than Householder
// Previously Diagonal::QR
SharedDiagonal Gaussian::QR(Matrix& Ab, boost::optional<std::vector<long>&> firstZeroRows) const {

	WhitenInPlace(Ab);
	// get size(A) and maxRank
	size_t m = Ab.size1(), n = Ab.size2()-1;
	size_t maxRank = min(m,n);

	// create storage for [R d]
	typedef boost::tuple<size_t, Vector, double> Triple;
	list<Triple> Rd;

	Vector pseudo(m); // allocate storage for pseudo-inverse
	Vector weights = ones(m); // calculate weights once

	// We loop over all columns, because the columns that can be eliminated
	// are not necessarily contiguous. For each one, estimate the corresponding
	// scalar variable x as d-rS, with S the separator (remaining columns).
	// Then update A and b by substituting x with d-rS, zero-ing out x's column.
	for (size_t j=0; j<n; ++j) {
		// extract the first column of A
		// ublas::matrix_column is slower ! TODO Really, why ????
		//  AGC: if you use column() you will automatically call ublas, use
		//      column_() to actually use the one in our library
		Vector a(column(Ab, j));

		// Calculate weighted pseudo-inverse and corresponding precision
		double precision = weightedPseudoinverse(a, weights, pseudo);

		// If precision is zero, no information on this column
		// This is actually not limited to constraints, could happen in Gaussian::QR
		// In that case, we're probably hosed. TODO: make sure Householder is rank-revealing
		if (precision < 1e-8) continue;

		// create solution [r d], rhs is automatically r(n)
		Vector rd(n+1); // uninitialized !
		rd(j)=1.0; // put 1 on diagonal
		for (size_t j2=j+1; j2<n+1; ++j2) // and fill in remainder with dot-products
			rd(j2) = inner_prod(pseudo, ublas::matrix_column<Matrix>(Ab, j2));

		// construct solution (r, d, sigma)
		Rd.push_back(boost::make_tuple(j, rd, precision));

		// exit after rank exhausted
		if (Rd.size()>=maxRank) break;

		// update Ab, expensive, using outer product
		updateAb(Ab, j, a, rd);
	}

	// Create storage for precisions
	Vector precisions(Rd.size());

	// Write back result in Ab, imperative as we are
	// TODO: test that is correct if a column was skipped !!!!
	size_t i = 0; // start with first row
	bool mixed = false;
	BOOST_FOREACH(const Triple& t, Rd) {
		const size_t& j  = t.get<0>();
		const Vector& rd = t.get<1>();
		precisions(i)    = t.get<2>();
		if (precisions(i)==inf) mixed = true;
		for (size_t j2=0; j2<j; ++j2) Ab(i,j2) = 0.0; // fill in zeros below diagonal anway
		for (size_t j2=j; j2<n+1; ++j2) // copy the j-the row TODO memcpy
			Ab(i,j2) = rd(j2);
		i+=1;
	}

	return Unit::Create(maxRank);
}


// General QR, see also special version in Constrained
SharedDiagonal Gaussian::QRColumnWise(ublas::matrix<double, ublas::column_major>& Ab, vector<long>& firstZeroRows) const {
	Matrix Abresult(Ab);
	SharedDiagonal result = QR(Abresult, firstZeroRows);
	Ab = Abresult;
	return result;
//  // get size(A) and maxRank
//  // TODO: really no rank problems ?
//  size_t m = Ab.size1(), n = Ab.size2()-1;
//  size_t maxRank = min(m,n);
//
//  // pre-whiten everything (cheaply if possible)
//  WhitenInPlace(Ab);
//
//  // Perform in-place Householder
//#ifdef GT_USE_LAPACK
//  householder_denseqr_colmajor(Ab, &firstZeroRows[0]);
//#else
//  householder(Ab, maxRank);
//#endif
//
//  return Unit::Create(maxRank);
}

/* ************************************************************************* */
Diagonal::Diagonal(const Vector& sigmas) :
		Gaussian(sigmas.size()), sigmas_(sigmas), invsigmas_(reciprocal(sigmas)) {
}

Diagonal::shared_ptr Diagonal::Variances(const Vector& variances, bool smart) {
	if (smart) {
		// check whether all the same entry
		int j, n = variances.size();
		for (j = 1; j < n; j++)
			if (variances(j) != variances(0)) goto full;
		return Isotropic::Variance(n, variances(0), true);
	}
	full: return shared_ptr(new Diagonal(esqrt(variances)));
}

Diagonal::shared_ptr Diagonal::Sigmas(const Vector& sigmas, bool smart) {
	if (smart) {
		// look for zeros to make a constraint
		for (size_t i=0; i<sigmas.size(); ++i)
			if (sigmas(i)<1e-8)
				return Constrained::MixedSigmas(sigmas);
	}
	return Diagonal::shared_ptr(new Diagonal(sigmas));
}

void Diagonal::print(const string& name) const {
	gtsam::print(sigmas_, "Diagonal sigmas " + name);
}

Vector Diagonal::whiten(const Vector& v) const {
	return emul(v, invsigmas_);
}

Vector Diagonal::unwhiten(const Vector& v) const {
	return emul(v, sigmas_);
}

Matrix Diagonal::Whiten(const Matrix& H) const {
	return vector_scale(invsigmas_, H);
}

void Diagonal::WhitenInPlace(Matrix& H) const {
	vector_scale_inplace(invsigmas_, H);
}

void Diagonal::WhitenInPlace(MatrixColMajor& H) const {

  vector_scale_inplace(invsigmas_, H);
}

Vector Diagonal::sample() const {
	Vector result(dim_);
	for (size_t i = 0; i < dim_; i++) {
		typedef boost::normal_distribution<double> Normal;
		Normal dist(0.0, this->sigmas_(i));
		boost::variate_generator<boost::minstd_rand&, Normal> norm(generator, dist);
		result(i) = norm();
	}
	return result;
}

/* ************************************************************************* */

void Constrained::print(const std::string& name) const {
	gtsam::print(sigmas_, "Constrained sigmas " + name);
}

Vector Constrained::whiten(const Vector& v) const {
	// ediv_ does the right thing with the errors
	return ediv_(v, sigmas_);
}

Matrix Constrained::Whiten(const Matrix& H) const {
	throw logic_error("noiseModel::Constrained cannot Whiten");
}

void Constrained::WhitenInPlace(Matrix& H) const {
	throw logic_error("noiseModel::Constrained cannot Whiten");
}

void Constrained::WhitenInPlace(MatrixColMajor& H) const {
  throw logic_error("noiseModel::Constrained cannot Whiten");
}

// Special version of QR for Constrained calls slower but smarter code
// that deals with possibly zero sigmas
// It is Gram-Schmidt orthogonalization rather than Householder
// Previously Diagonal::QR
SharedDiagonal Constrained::QR(Matrix& Ab, boost::optional<std::vector<long>&> firstZeroRows) const {
	bool verbose = false;
	if (verbose) cout << "\nStarting Constrained::QR" << endl;

	// get size(A) and maxRank
	size_t m = Ab.size1(), n = Ab.size2()-1;
	size_t maxRank = min(m,n);

	// create storage for [R d]
	typedef boost::tuple<size_t, Vector, double> Triple;
	list<Triple> Rd;

	Vector pseudo(m); // allocate storage for pseudo-inverse
	Vector weights = emul(invsigmas_,invsigmas_); // calculate weights once

	// We loop over all columns, because the columns that can be eliminated
	// are not necessarily contiguous. For each one, estimate the corresponding
	// scalar variable x as d-rS, with S the separator (remaining columns).
	// Then update A and b by substituting x with d-rS, zero-ing out x's column.
	for (size_t j=0; j<n; ++j) {
		// extract the first column of A
		// ublas::matrix_column is slower ! TODO Really, why ????
		//  AGC: if you use column() you will automatically call ublas, use
		//      column_() to actually use the one in our library
		Vector a(column(Ab, j));

		// Calculate weighted pseudo-inverse and corresponding precision
		double precision = weightedPseudoinverse(a, weights, pseudo);

		// If precision is zero, no information on this column
		// This is actually not limited to constraints, could happen in Gaussian::QR
		// In that case, we're probably hosed. TODO: make sure Householder is rank-revealing
		if (precision < 1e-8) continue;

		// create solution [r d], rhs is automatically r(n)
		Vector rd(n+1); // uninitialized !
		rd(j)=1.0; // put 1 on diagonal
		for (size_t j2=j+1; j2<n+1; ++j2) // and fill in remainder with dot-products
			rd(j2) = inner_prod(pseudo, ublas::matrix_column<Matrix>(Ab, j2));

		// construct solution (r, d, sigma)
		Rd.push_back(boost::make_tuple(j, rd, precision));

		// exit after rank exhausted
		if (Rd.size()>=maxRank) break;

		// update Ab, expensive, using outer product
		updateAb(Ab, j, a, rd);
	}

	// Create storage for precisions
	Vector precisions(Rd.size());

	// Write back result in Ab, imperative as we are
	// TODO: test that is correct if a column was skipped !!!!
	size_t i = 0; // start with first row
	bool mixed = false;
	BOOST_FOREACH(const Triple& t, Rd) {
		const size_t& j  = t.get<0>();
		const Vector& rd = t.get<1>();
		precisions(i)    = t.get<2>();
		if (precisions(i)==inf) mixed = true;
		for (size_t j2=0; j2<j; ++j2) Ab(i,j2) = 0.0; // fill in zeros below diagonal anway
		for (size_t j2=j; j2<n+1; ++j2) // copy the j-the row TODO memcpy
			Ab(i,j2) = rd(j2);
		i+=1;
	}

	return mixed ? Constrained::MixedPrecisions(precisions) : Diagonal::Precisions(precisions);
}

SharedDiagonal Constrained::QRColumnWise(ublas::matrix<double, ublas::column_major>& Ab, vector<long>& firstZeroRows) const {
//  Matrix AbRowWise(Ab);
//  SharedDiagonal result = this->QR(AbRowWise, firstZeroRows);
//  Ab = AbRowWise;
//  return result;
	Matrix Abresult(Ab);
	SharedDiagonal result = QR(Abresult, firstZeroRows);
	Ab = Abresult;
	return result;
}

/* ************************************************************************* */

Isotropic::shared_ptr Isotropic::Variance(size_t dim, double variance, bool smart)  {
	if (smart && fabs(variance-1.0)<1e-9) return Unit::Create(dim);
	return shared_ptr(new Isotropic(dim, sqrt(variance)));
}

void Isotropic::print(const string& name) const {
	cout << "Isotropic sigma " << name << " " << sigma_ << endl;
}

double Isotropic::Mahalanobis(const Vector& v) const {
	double dot = inner_prod(v, v);
	return dot * invsigma_ * invsigma_;
}

Vector Isotropic::whiten(const Vector& v) const {
	return v * invsigma_;
}

Vector Isotropic::unwhiten(const Vector& v) const {
	return v * sigma_;
}

Matrix Isotropic::Whiten(const Matrix& H) const {
	return invsigma_ * H;
}

void Isotropic::WhitenInPlace(Matrix& H) const {
	H *= invsigma_;
}

void Isotropic::WhitenInPlace(MatrixColMajor& H) const {
  H *= invsigma_;
}

// faster version
Vector Isotropic::sample() const {
	typedef boost::normal_distribution<double> Normal;
	Normal dist(0.0, this->sigma_);
	boost::variate_generator<boost::minstd_rand&, Normal> norm(generator, dist);
	Vector result(dim_);
	for (size_t i = 0; i < dim_; i++)
		result(i) = norm();
	return result;
}

/* ************************************************************************* */
void Unit::print(const std::string& name) const {
	cout << "Unit (" << dim_ << ") " << name << endl;
}

/* ************************************************************************* */

}
} // gtsam