Approximate.cc

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// -*- LSST-C++ -*-
 
/*
 * LSST Data Management System
 * Copyright 2008-2015 AURA/LSST.
 *
 * This product includes software developed by the
 * LSST Project (http://www.lsst.org/).
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program 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
 * GNU General Public License for more details.
 *
 * You should have received a copy of the LSST License Statement and
 * the GNU General Public License along with this program.  If not,
 * see <https://www.lsstcorp.org/LegalNotices/>.
 */
 
/*
 * Approximate values for a set of x,y vector<>s
 */
#include <limits>
#include <algorithm>
#include <cmath>
#include <memory>
#include <numeric>
#include "Eigen/Core"
#include "Eigen/LU"
#include "boost/format.hpp"
#include "lsst/pex/exceptions.h"
#include "lsst/afw/math/FunctionLibrary.h"
#include "lsst/afw/image/MaskedImage.h"
#include "lsst/afw/math/Approximate.h"
 
namespace lsst {
namespace ex = pex::exceptions;
namespace afw {
namespace math {
 
ApproximateControl::ApproximateControl(Style style, int orderX, int orderY, bool weighting)
        : _style(style), _orderX(orderX), _orderY(orderY < 0 ? orderX : orderY), _weighting(weighting) {
    if (_orderX != _orderY) {
        throw LSST_EXCEPT(lsst::pex::exceptions::InvalidParameterError,
                          str(boost::format("X- and Y-orders must be equal (%d != %d) "
                                            "due to a limitation in math::Chebyshev1Function2") %
                              _orderX % _orderY));
    }
}
 
namespace {
template <typename PixelT>
class ApproximateChebyshev : public Approximate<PixelT> {
    template <typename T>
    friend std::shared_ptr<Approximate<T>> math::makeApproximate(std::vector<double> const& xVec,
                                                                 std::vector<double> const& yVec,
                                                                 image::MaskedImage<T> const& im,
                                                                 lsst::geom::Box2I const& bbox,
                                                                 ApproximateControl const& ctrl);
 
public:
    ~ApproximateChebyshev() override;
 
private:
    math::Chebyshev1Function2<double> _poly;
 
    ApproximateChebyshev(std::vector<double> const& xVec, std::vector<double> const& yVec,
                         image::MaskedImage<PixelT> const& im, lsst::geom::Box2I const& bbox,
                         ApproximateControl const& ctrl);
    std::shared_ptr<image::Image<typename Approximate<PixelT>::OutPixelT>> doGetImage(
            int orderX, int orderY) const override;
    std::shared_ptr<image::MaskedImage<typename Approximate<PixelT>::OutPixelT>> doGetMaskedImage(
            int orderX, int orderY) const override;
};
 
namespace {
// N.b. physically inlining these routines into ApproximateChebyshev
// causes clang++ 3.1 problems; I suspect a clang bug (see http://llvm.org/bugs/show_bug.cgi?id=14162)
inline void solveMatrix_Eigen(Eigen::MatrixXd& a, Eigen::VectorXd& b, Eigen::Map<Eigen::VectorXd>& c) {
    Eigen::PartialPivLU<Eigen::MatrixXd> lu(a);
    c = lu.solve(b);
}
}  // namespace
 
template <typename PixelT>
ApproximateChebyshev<PixelT>::ApproximateChebyshev(
        std::vector<double> const& xVec,       
        std::vector<double> const& yVec,       
        image::MaskedImage<PixelT> const& im,  
        lsst::geom::Box2I const& bbox,         
        ApproximateControl const& ctrl         
        )
        : Approximate<PixelT>(xVec, yVec, bbox, ctrl),
          _poly(math::Chebyshev1Function2<double>(ctrl.getOrderX(), lsst::geom::Box2D(bbox))) {
#if !defined(NDEBUG)
    {
        std::vector<double> const& coeffs = _poly.getParameters();
        assert(std::accumulate(coeffs.begin(), coeffs.end(), 0.0) ==
               0.0);  // i.e. coeffs is initialised to 0.0
    }
#endif
    int const nTerm = _poly.getNParameters();          // number of terms in polynomial
    int const nData = im.getWidth() * im.getHeight();  // number of data points
                                                       /*
                                                        * N.b. in the comments,
                                                        *      i     runs over the 0..nTerm-1 coefficients
                                                        *      alpha runs over the 0..nData-1 data points
                                                        */
 
    /*
     * We need the value of the polynomials evaluated at every data point, so it's more
     * efficient to pre-calculate the values:  termCoeffs[i][alpha]
     */
    std::vector<std::vector<double>> termCoeffs(nTerm);
 
    for (int i = 0; i != nTerm; ++i) {
        termCoeffs[i].reserve(nData);
    }
 
    for (int iy = 0; iy != im.getHeight(); ++iy) {
        double const y = yVec[iy];
 
        for (int ix = 0; ix != im.getWidth(); ++ix) {
            double const x = xVec[ix];
 
            for (int i = 0; i != nTerm; ++i) {
                _poly.setParameter(i, 1.0);
                termCoeffs[i].push_back(_poly(x, y));
                _poly.setParameter(i, 0.0);
            }
        }
    }
    // We'll solve A*c = b
    Eigen::MatrixXd A;
    A.setZero(nTerm, nTerm);  // We'll solve A*c = b
    Eigen::VectorXd b;
    b.setZero(nTerm);
    /*
     * Go through the data accumulating the values of the A and b matrix/vector
     */
    int alpha = 0;
    for (int iy = 0; iy != im.getHeight(); ++iy) {
        for (typename image::MaskedImage<PixelT>::const_x_iterator ptr = im.row_begin(iy),
                                                                   end = im.row_end(iy);
             ptr != end; ++ptr, ++alpha) {
            double const val = ptr.image();
            double const ivar = ctrl.getWeighting() ? 1 / ptr.variance() : 1.0;
            if (!std::isfinite(val + ivar)) {
                continue;
            }
 
            for (int i = 0; i != nTerm; ++i) {
                double const c_i = termCoeffs[i][alpha];
                double const tmp = c_i * ivar;
                b(i) += val * tmp;
                A(i, i) += c_i * tmp;
                for (int j = 0; j < i; ++j) {
                    double const c_j = termCoeffs[j][alpha];
                    A(i, j) += c_j * tmp;
                }
            }
        }
    }
    if (A.isZero()) {
        if (ctrl.getWeighting()) {
            throw LSST_EXCEPT(pex::exceptions::RuntimeError,
                              "No valid points to fit. Variance is likely zero. Try weighting=False");
        } else {
            throw LSST_EXCEPT(pex::exceptions::RuntimeError,
                              "No valid points to fit (even though weighting is False). "
                              "Check that binSize & approxOrderX settings are appropriate for image size.");
        }
    }
    // We only filled out the lower triangular part of A
    for (int j = 0; j != nTerm; ++j) {
        for (int i = j + 1; i != nTerm; ++i) {
            A(j, i) = A(i, j);
        }
    }
    /*
     * OK, now all we ned do is solve that...
     */
    std::vector<double> cvec(nTerm);
    Eigen::Map<Eigen::VectorXd> c(&cvec[0], nTerm);  // N.b. c shares memory with cvec
 
    solveMatrix_Eigen(A, b, c);
 
    _poly.setParameters(cvec);
}
 
template <typename PixelT>
ApproximateChebyshev<PixelT>::~ApproximateChebyshev() {}
 
template <typename PixelT>
std::shared_ptr<image::Image<typename Approximate<PixelT>::OutPixelT>>
ApproximateChebyshev<PixelT>::doGetImage(int orderX, int orderY) const {
    if (orderX < 0) orderX = Approximate<PixelT>::_ctrl.getOrderX();
    if (orderY < 0) orderY = Approximate<PixelT>::_ctrl.getOrderY();
 
    math::Chebyshev1Function2<double> poly = (orderX == Approximate<PixelT>::_ctrl.getOrderX() &&
                                              orderY == Approximate<PixelT>::_ctrl.getOrderY())
                                                     ? _poly
                                                     : _poly.truncate(orderX);
 
    typedef typename image::Image<typename Approximate<PixelT>::OutPixelT> ImageT;
 
    std::shared_ptr<ImageT> im(new ImageT(Approximate<PixelT>::_bbox));
    for (int iy = 0; iy != im->getHeight(); ++iy) {
        double const y = iy;
 
        int ix = 0;
        for (typename ImageT::x_iterator ptr = im->row_begin(iy), end = im->row_end(iy); ptr != end;
             ++ptr, ++ix) {
            double const x = ix;
 
            *ptr = poly(x, y);
        }
    }
 
    return im;
}
template <typename PixelT>
std::shared_ptr<image::MaskedImage<typename Approximate<PixelT>::OutPixelT>>
ApproximateChebyshev<PixelT>::doGetMaskedImage(int orderX, int orderY) const {
    typedef typename image::MaskedImage<typename Approximate<PixelT>::OutPixelT> MImageT;
 
    std::shared_ptr<MImageT> mi(new MImageT(Approximate<PixelT>::_bbox));
    std::shared_ptr<typename MImageT::Image> im = mi->getImage();
 
    for (int iy = 0; iy != im->getHeight(); ++iy) {
        double const y = iy;
 
        int ix = 0;
        for (typename MImageT::Image::x_iterator ptr = im->row_begin(iy), end = im->row_end(iy); ptr != end;
             ++ptr, ++ix) {
            double const x = ix;
 
            *ptr = _poly(x, y);
        }
    }
 
    return mi;
}
}  // namespace
 
template <typename PixelT>
std::shared_ptr<Approximate<PixelT>> makeApproximate(std::vector<double> const& x,
                                                     std::vector<double> const& y,
                                                     image::MaskedImage<PixelT> const& im,
                                                     lsst::geom::Box2I const& bbox,
                                                     ApproximateControl const& ctrl) {
    switch (ctrl.getStyle()) {
        case ApproximateControl::CHEBYSHEV:
            return std::shared_ptr<Approximate<PixelT>>(
                    new ApproximateChebyshev<PixelT>(x, y, im, bbox, ctrl));
        default:
            throw LSST_EXCEPT(lsst::pex::exceptions::InvalidParameterError,
                              str(boost::format("Unknown ApproximationStyle: %d") % ctrl.getStyle()));
    }
}
/*
 * Explicit instantiations
 *
 */
#define INSTANTIATE(PIXEL_T)                                                      \
    template std::shared_ptr<Approximate<PIXEL_T>> makeApproximate(               \
            std::vector<double> const& x, std::vector<double> const& y,           \
            image::MaskedImage<PIXEL_T> const& im, lsst::geom::Box2I const& bbox, \
            ApproximateControl const& ctrl)
 
INSTANTIATE(float);
// INSTANTIATE(int);
 
}  // namespace math
}  // namespace afw
}  // namespace lsst