Class ChebyshevBoundedField

Inheritance Relationships

Base Types

Class Documentation

class ChebyshevBoundedField : public lsst::afw::table::io::PersistableFacade<ChebyshevBoundedField>, public lsst::afw::math::BoundedField

A BoundedField based on 2-d Chebyshev polynomials of the first kind.

The 2-d Chebyshev polynomial used here is defined as:

\[ f(x,y) = \sum_i \sum_j a_{i,j} T_i(x) T_j(y) \]

where \(T_n(x)\) is the n-th order Chebyshev polynomial of \(x\) and \(a_{i,j}\) is the corresponding coefficient of the (i,j) polynomial term.

ChebyshevBoundedField supports fitting to gridded and non-gridded data, as well coefficient matrices with different x- and y-order.

There is currently quite a bit of duplication of functionality between ChebyshevBoundedField, ApproximateChebyshev, and Chebyshev1Function2; the intent is that ChebyshevBoundedField will ultimately replace ApproximateChebyshev and should be preferred over Chebyshev1Function2 when the parametrization interface that is part of the Function2 class is not needed.

Public Types

typedef ChebyshevBoundedFieldControl Control

Public Functions

ChebyshevBoundedField(lsst::geom::Box2I const &bbox, ndarray::Array<double const, 2, 2> const &coefficients)

Initialize the field from its bounding box an coefficients.

This constructor is mostly intended for testing purposes and persistence, but it also provides a way to initialize the object from Chebyshev coefficients derived from some external source.

Note that because the bounding box provided is always an integer bounding box, and LSST convention puts the center of each pixel at an integer, the actual floating-point domain of the Chebyshev functions is lsst::geom::Box2D(bbox), that is, the box that contains the entirety of all the pixels included in the integer bounding box.

The coefficients are ordered [y,x], so the shape is (orderY+1, orderX+1), and the arguments to the Chebyshev functions are transformed such that the region lsst::geom::Box2D(bbox) is mapped to [-1, 1]x[-1, 1].

Example: 

bbox = lsst::geom::Box2I(lsst::geom::Point2I(10, 20), lsst::geom::Point2I(30, 40));
ndarray::Array<double, 2, 2> coeffs = ndarray::allocate(ndarray::makeVector(2, 2));
coeffs[0][0] = 1;
coeffs[1][0] = 2;
coeffs[0][1] = 3;
coeffs[1][1] = 4;
ndarray::Array<double, 2, 2> coeffs = ndarray::external(data);
poly = ChebyshevBoundedField(bbox, coeffs);

will result in the following polynomial:

\[ f(x,y) = 1 T_0(x) T_0(y) + 2 T_0(x) T_1(y) + 3 T_1(x) T_0(y) + 4 T_1(x) T_1(y) \]

ChebyshevBoundedField(ChebyshevBoundedField const&)
ChebyshevBoundedField(ChebyshevBoundedField&&)
ChebyshevBoundedField &operator=(ChebyshevBoundedField const&)
ChebyshevBoundedField &operator=(ChebyshevBoundedField&&)
~ChebyshevBoundedField()
ndarray::Array<double const, 2, 2> getCoefficients() const

Return the coefficient matrix.

The coefficients are ordered [y,x], so the shape is (orderY+1, orderX+1).

std::shared_ptr<ChebyshevBoundedField> truncate(Control const &ctrl) const

Return a new ChebyshevBoudedField with maximum orders set by the given control object.

std::shared_ptr<ChebyshevBoundedField> relocate(lsst::geom::Box2I const &bbox) const

Return a new ChebyshevBoundedField with domain set to the given bounding box.

Because this leaves the coefficients unchanged, it is equivalent to transforming the function by the affine transform that maps the old box to the new one.

double evaluate(lsst::geom::Point2D const &position) const

Evaluate the field at the given point.

This is the only abstract method to be implemented by subclasses.

Subclasses should not provide bounds checking on the given position; this is the responsibility of the user, who can almost always do it more efficiently.

double integrate() const

Compute the integral of this function over its bounding-box.

Return

The value of the integral.

double mean() const

Compute the mean of this function over its bounding-box.

Return

The value of the mean.

bool isPersistable() const

ChebyshevBoundedField is always persistable.

std::shared_ptr<BoundedField> operator*(double const scale) const

Return a scaled BoundedField

Parameters

  • [in] scale: Scaling factor

bool operator==(BoundedField const &rhs) const

BoundedFields (of the same sublcass) are equal if their bounding boxes and parameters are equal.

Public Static Functions

static std::shared_ptr<ChebyshevBoundedField> fit(lsst::geom::Box2I const &bbox, ndarray::Array<double const, 1> const &x, ndarray::Array<double const, 1> const &y, ndarray::Array<double const, 1> const &z, Control const &ctrl)

Fit a Chebyshev approximation to non-gridded data with equal weights.

Parameters

  • [in] bbox: Integer bounding box of the resulting approximation. All given points must lie within lsst::geom::Box2D(bbox).

  • [in] x: Array of x coordinate values.

  • [in] y: Array of y coordinate values.

  • [in] z: Array of field values to be fit at each (x,y) point.

  • [in] ctrl: Specifies the orders and triangularity of the coefficient matrix.

static std::shared_ptr<ChebyshevBoundedField> fit(lsst::geom::Box2I const &bbox, ndarray::Array<double const, 1> const &x, ndarray::Array<double const, 1> const &y, ndarray::Array<double const, 1> const &z, ndarray::Array<double const, 1> const &w, Control const &ctrl)

Fit a Chebyshev approximation to non-gridded data with unequal weights.

Parameters

  • [in] bbox: Integer bounding box of the resulting approximation. All given points must lie within lsst::geom::Box2D(bbox).

  • [in] x: Array of x coordinate values.

  • [in] y: Array of y coordinate values.

  • [in] z: Array of field values to be fit at each (x,y) point.

  • [in] w: Array of weights for each point in the fit. For points with Gaussian noise, w = 1/sigma.

  • [in] ctrl: Specifies the orders and triangularity of the coefficient matrix.

template<typename T>
static std::shared_ptr<ChebyshevBoundedField> fit(image::Image<T> const &image, Control const &ctrl)

Fit a Chebyshev approximation to gridded data with equal weights.

Instantiated for float and double.

Parameters

  • [in] image: The Image containing the data to fit. image.getBBox(PARENT) is used as the bounding box of the BoundedField.

  • [in] ctrl: Specifies the orders and triangularity of the coefficient matrix.

Note

if the image to be fit is a binned version of the actual image the field should correspond to, call relocate() with the unbinned image’s bounding box after fitting.

Protected Functions

std::string getPersistenceName() const

Return the unique name used to persist this object and look up its factory.

Must be less than ArchiveIndexSchema::MAX_NAME_LENGTH characters.

std::string getPythonModule() const

Return the fully-qualified Python module that should be imported to guarantee that its factory is registered.

Must be less than ArchiveIndexSchema::MAX_MODULE_LENGTH characters.

Will be ignored if empty.

void write(OutputArchiveHandle &handle) const

Write the object to one or more catalogs.

The handle object passed to this function provides an interface for adding new catalogs and adding nested objects to the same archive (while checking for duplicates). See OutputArchiveHandle for more information.