lsst::afw::math::detail::Spline Class Reference

#include <Spline.h>

Inheritance diagram for lsst::afw::math::detail::Spline:

Public Member Functions
virtual	~Spline ()=default
	Spline (Spline const &)=default
	Spline (Spline &&)=default
Spline &	operator= (Spline const &)=default
Spline &	operator= (Spline &&)=default
void	interpolate (std::vector< double > const &x, std::vector< double > &y) const
	Interpolate a Spline.
void	derivative (std::vector< double > const &x, std::vector< double > &dydx) const
	Find the derivative of a Spline.
std::vector< double >	roots (double const value, double const x0, double const x1) const
	Find the roots of Spline - val = 0 in the range [x0, x1).

Protected Member Functions
	Spline ()=default
void	_allocateSpline (int const nknot)
	Allocate the storage a Spline needs.

Protected Attributes
std::vector< double >	_knots
std::vector< std::vector< double > >	_coeffs

Detailed Description

Definition at line 14 of file Spline.h.

Constructor & Destructor Documentation

~Spline()

virtual lsst::afw::math::detail::Spline::~Spline ( )

virtualdefault

Spline() [1/3]

lsst::afw::math::detail::Spline::Spline ( Spline const & )

default

Spline() [2/3]

lsst::afw::math::detail::Spline::Spline ( Spline && )

default

Spline() [3/3]

lsst::afw::math::detail::Spline::Spline ( )

protecteddefault

Member Function Documentation

_allocateSpline()

void lsst::afw::math::detail::Spline::_allocateSpline ( int const nknot )

protected

Allocate the storage a Spline needs.

Definition at line 21 of file Spline.cc.

                                            {
    _knots.resize(nknot);
    _coeffs.resize(4);
    for (unsigned int i = 0; i != _coeffs.size(); ++i) {
        _coeffs[i].reserve(nknot);
    }
}

derivative()

void lsst::afw::math::detail::Spline::derivative	(	std::vector< double > const &	x,
		std::vector< double > &	dydx ) const

Find the derivative of a Spline.

Parameters

[in]	x	points to evaluate derivative at
[out]	dydx	derivatives at x

Definition at line 57 of file Spline.cc.

                                                                                 {
    int const nknot = _knots.size();
    int const n = x.size();
 
    dydx.resize(n);  // may default-construct elements which is a little inefficient
                     /*
                      * For _knots[i] <= x <= _knots[i+1], the * interpolant has the form
                      *    val = _coeff[0][i] +dx*(_coeff[1][i] + dx*(_coeff[2][i]/2 + dx*_coeff[3][i]/6))
                      * with
                      *    dx = x - knots[i]
                      * so the derivative is
                      *    val = _coeff[1][i] + dx*(_coeff[2][i] + dx*_coeff[3][i]/2))
                      */
 
    int ind = -1;  // no idea initially
    for (int i = 0; i != n; ++i) {
        ind = search_array(x[i], &_knots[0], nknot, ind);
 
        if (ind < 0) {  // off bottom
            ind = 0;
        } else if (ind >= nknot) {  // off top
            ind = nknot - 1;
        }
 
        double const dx = x[i] - _knots[ind];
        dydx[i] = _coeffs[1][ind] + dx * (_coeffs[2][ind] + dx * _coeffs[3][ind] / 2);
    }
}

interpolate()

void lsst::afw::math::detail::Spline::interpolate	(	std::vector< double > const &	x,
		std::vector< double > &	y ) const

Interpolate a Spline.

Parameters

[in]	x	points to interpolate at
[out]	y	values of spline interpolation at x

Definition at line 29 of file Spline.cc.

                                                                               {
    int const nknot = _knots.size();
    int const n = x.size();
 
    y.resize(n);   // may default-construct elements which is a little inefficient
                   /*
                    * For _knots[i] <= x <= _knots[i+1], the interpolant
                    * has the form
                    *    val = _coeff[0][i] +dx*(_coeff[1][i] + dx*(_coeff[2][i]/2 + dx*_coeff[3][i]/6))
                    * with
                    *    dx = x - knots[i]
                    */
    int ind = -1;  // no idea initially
    for (int i = 0; i != n; ++i) {
        ind = search_array(x[i], &_knots[0], nknot, ind);
 
        if (ind < 0) {  // off bottom
            ind = 0;
        } else if (ind >= nknot) {  // off top
            ind = nknot - 1;
        }
 
        double const dx = x[i] - _knots[ind];
        y[i] = _coeffs[0][ind] +
               dx * (_coeffs[1][ind] + dx * (_coeffs[2][ind] / 2 + dx * _coeffs[3][ind] / 6));
    }
}

operator=() [1/2]

Spline & lsst::afw::math::detail::Spline::operator= ( Spline && )

default

operator=() [2/2]

Spline & lsst::afw::math::detail::Spline::operator= ( Spline const & )

default

roots()

std::vector< double > lsst::afw::math::detail::Spline::roots	(	double const	value,
		double const	x0,
		double const	x1 ) const

Find the roots of Spline - val = 0 in the range [x0, x1).

Return a vector of all the roots found

Parameters

value	desired value
x0,x1	specify desired range is [x0,x1)

Definition at line 1226 of file Spline.cc.

                                                                                  {
    /*
     * Strategy: we know that the interpolant has the form
     *    val = coef[0][i] +dx*(coef[1][i] + dx*(coef[2][i]/2 + dx*coef[3][i]/6))
     * so we can use the usual analytic solution for a cubic. Note that the
     * cubic quoted above returns dx, the distance from the previous knot,
     * rather than x itself
     */
    std::vector<double> roots; /* the roots found */
    double x0 = a;             // lower end of current range
    double const x1 = b;
    int const nknot = _knots.size();
 
    int i0 = search_array(x0, &_knots[0], nknot, -1);
    int const i1 = search_array(x1, &_knots[0], nknot, i0);
    assert(i1 >= i0 && i1 <= nknot - 1);
 
    std::vector<double> newRoots;  // the roots we find in some interval
                                   /*
                                    * Deal with special case that x0 may be off one end or the other of
                                    * the array of knots.
                                    */
    if (i0 < 0) {                  /* off bottom */
        i0 = 0;
        do_cubic(_coeffs[3][i0] / 6, _coeffs[2][i0] / 2, _coeffs[1][i0], _coeffs[0][i0] - value, newRoots);
        //
        // Could use
        //    std::transform(newRoots.begin(), newRoots.end(), newRoots.begin(),
        //                   std::bind(std::plus<double>(), _1, _knots[i0]));
        // but let's not
        //
        for (unsigned int j = 0; j != newRoots.size(); ++j) {
            newRoots[j] += _knots[i0];
        }
        keep_valid_roots(roots, newRoots, x0, _knots[i0]);
 
        x0 = _knots[i0];
    } else if (i0 >= nknot) { /* off top */
        i0 = nknot - 1;
        assert(i0 >= 0);
        do_cubic(_coeffs[3][i0] / 6, _coeffs[2][i0] / 2, _coeffs[1][i0], _coeffs[0][i0] - value, newRoots);
 
        for (unsigned int j = 0; j != newRoots.size(); ++j) {
            newRoots[j] += _knots[i0];
        }
        keep_valid_roots(roots, newRoots, x0, x1);
 
        return roots;
    }
    /*
     * OK, now search in main body of spline. Note that i1 may be nknot - 1, and
     * in any case the right hand limit of the last segment is at x1, not a knot
     */
    for (int i = i0; i <= i1; i++) {
        do_cubic(_coeffs[3][i] / 6, _coeffs[2][i] / 2, _coeffs[1][i], _coeffs[0][i] - value, newRoots);
 
        for (unsigned int j = 0; j != newRoots.size(); ++j) {
            newRoots[j] += _knots[i];
        }
        keep_valid_roots(roots, newRoots, ((i == i0) ? x0 : _knots[i]), ((i == i1) ? x1 : _knots[i + 1]));
    }
 
    return roots;
}

Member Data Documentation

_coeffs

std::vector<std::vector<double> > lsst::afw::math::detail::Spline::_coeffs

protected

Definition at line 56 of file Spline.h.

_knots

std::vector<double> lsst::afw::math::detail::Spline::_knots

protected

Definition at line 55 of file Spline.h.

---

The documentation for this class was generated from the following files:

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-12.0.0/Linux/afw/g083dd6704c+2e189452a7/include/lsst/afw/math/detail/Spline.h
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-12.0.0/Linux/afw/g083dd6704c+2e189452a7/src/math/Spline.cc