lsst.astshim  20.0.0-4-g45278ab+d529cf1a41
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ast::ChebyMap Class Reference

#include <ChebyMap.h>

Inheritance diagram for ast::ChebyMap:
ast::Mapping ast::Object

Public Member Functions

 ChebyMap (ConstArray2D const &coeff_f, ConstArray2D const &coeff_i, std::vector< double > const &lbnd_f, std::vector< double > const &ubnd_f, std::vector< double > const &lbnd_i, std::vector< double > const &ubnd_i, std::string const &options="")
 
 ChebyMap (ConstArray2D const &coeff_f, int nout, std::vector< double > const &lbnd_f, std::vector< double > const &ubnd_f, std::string const &options="IterInverse=0")
 
virtual ~ChebyMap ()
 
 ChebyMap (ChebyMap const &)=default
 Copy constructor: make a deep copy. More...
 
 ChebyMap (ChebyMap &&)=default
 
ChebyMapoperator= (ChebyMap const &)=delete
 
ChebyMapoperator= (ChebyMap &&)=default
 
std::shared_ptr< ChebyMapcopy () const
 Return a deep copy of this object. More...
 
ChebyDomain getDomain (bool forward) const
 
ChebyMap polyTran (bool forward, double acc, double maxacc, int maxorder, std::vector< double > const &lbnd, std::vector< double > const &ubnd) const
 
ChebyMap polyTran (bool forward, double acc, double maxacc, int maxorder) const
 
- Public Member Functions inherited from ast::Mapping
virtual ~Mapping ()
 
 Mapping (Mapping const &)=default
 Copy constructor: make a deep copy. More...
 
 Mapping (Mapping &&)=default
 
Mappingoperator= (Mapping const &)=delete
 
Mappingoperator= (Mapping &&)=default
 
std::shared_ptr< Mappingcopy () const
 Return a deep copy of this object. More...
 
int getNIn () const
 
int getNOut () const
 
bool getIsSimple () const
 
bool isInverted () const
 
bool getIsLinear () const
 
bool getReport () const
 
bool hasForward () const
 
bool hasInverse () const
 
std::shared_ptr< Mappinginverted () const
 
Array2D linearApprox (PointD const &lbnd, PointD const &ubnd, double tol) const
 
SeriesMap then (Mapping const &next) const
 
ParallelMap under (Mapping const &next) const
 
double rate (PointD const &at, int ax1, int ax2) const
 
void setReport (bool report)
 
std::shared_ptr< Mappingsimplified () const
 
void applyForward (ConstArray2D const &from, Array2D const &to) const
 
Array2D applyForward (ConstArray2D const &from) const
 
std::vector< double > applyForward (std::vector< double > const &from) const
 
void applyInverse (ConstArray2D const &from, Array2D const &to) const
 
Array2D applyInverse (ConstArray2D const &from) const
 
std::vector< double > applyInverse (std::vector< double > const &from) const
 
void tranGridForward (PointI const &lbnd, PointI const &ubnd, double tol, int maxpix, Array2D const &to) const
 
Array2D tranGridForward (PointI const &lbnd, PointI const &ubnd, double tol, int maxpix, int nPts) const
 
void tranGridInverse (PointI const &lbnd, PointI const &ubnd, double tol, int maxpix, Array2D const &to) const
 
Array2D tranGridInverse (PointI const &lbnd, PointI const &ubnd, double tol, int maxpix, int nPts) const
 
- Public Member Functions inherited from ast::Object
virtual ~Object ()
 
 Object (Object const &object)
 Copy constructor: make a deep copy. More...
 
 Object (Object &&)=default
 
Objectoperator= (Object const &)=delete
 
Objectoperator= (Object &&)=default
 
bool operator== (Object const &rhs) const
 
bool operator!= (Object const &rhs) const
 
std::shared_ptr< Objectcopy () const
 Return a deep copy of this object. More...
 
void clear (std::string const &attrib)
 
bool hasAttribute (std::string const &attrib) const
 
std::string getClassName () const
 
std::string getID () const
 Get ID: object identification string that is not copied. More...
 
std::string getIdent () const
 Get Ident: object identification string that is copied. More...
 
int getNObject () const
 
int getObjSize () const
 Get ObjSize: the in-memory size of the AST object in bytes. More...
 
int getRefCount () const
 
bool getUseDefs () const
 Get UseDefs: allow use of default values for Object attributes? More...
 
void lock (bool wait)
 
bool same (Object const &other) const
 
void setID (std::string const &id)
 Set ID: object identification string that is not copied. More...
 
void setIdent (std::string const &ident)
 Set Ident: object identification string that is copied. More...
 
void setUseDefs (bool usedefs)
 Set UseDefs: allow use of default values for Object attributes? More...
 
void show (std::ostream &os, bool showComments=true) const
 
std::string show (bool showComments=true) const
 
bool test (std::string const &attrib) const
 
void unlock (bool report=false)
 
AstObject const * getRawPtr () const
 
AstObject * getRawPtr ()
 

Protected Member Functions

virtual std::shared_ptr< ObjectcopyPolymorphic () const override
 
 ChebyMap (AstChebyMap *map)
 Construct a ChebyMap from an raw AST pointer. More...
 
- Protected Member Functions inherited from ast::Mapping
 Mapping (AstMapping *rawMap)
 
template<typename Class >
std::shared_ptr< Class > decompose (int i, bool copy) const
 
- Protected Member Functions inherited from ast::Object
 Object (AstObject *object)
 
template<typename T , typename AstT >
std::shared_ptr< T > copyImpl () const
 
bool getB (std::string const &attrib) const
 
std::string const getC (std::string const &attrib) const
 
double getD (std::string const &attrib) const
 
float getF (std::string const &attrib) const
 
int getI (std::string const &attrib) const
 
long int getL (std::string const &attrib) const
 
void set (std::string const &setting)
 
void setB (std::string const &attrib, bool value)
 
void setC (std::string const &attrib, std::string const &value)
 
void setD (std::string const &attrib, double value)
 
void setF (std::string const &attrib, float value)
 
void setI (std::string const &attrib, int value)
 
void setL (std::string const &attrib, long int value)
 

Friends

class Object
 

Additional Inherited Members

- Public Types inherited from ast::Object
using ObjectPtr = std::unique_ptr< AstObject, Deleter >
 unique pointer holding an AST raw pointer More...
 
- Static Public Member Functions inherited from ast::Object
static std::shared_ptr< ObjectfromString (std::string const &str)
 
template<typename Class >
static std::shared_ptr< Class > fromAstObject (AstObject *rawObj, bool copy)
 
- Static Protected Member Functions inherited from ast::Object
template<typename ShimT , typename AstT >
static std::shared_ptr< ShimT > makeShim (AstObject *p)
 

Detailed Description

A ChebyMap is a form of Mapping which performs a Chebyshev polynomial transformation. Each output coordinate is a linear combination of Chebyshev polynomials of the first kind, of order zero up to a specified maximum order, evaluated at the input coordinates. The coefficients to be used in the linear combination are specified separately for each output coordinate.

For a 1-dimensional ChebyMap, the forward transformation is defined as follows:

f(x) = c0 T0(x') + c1 T1(x') + c2 T2(x') + ...

where:

For an N-dimensional ChebyMap, the forward transformation is a generalisation of the above form. Each output axis value is the sum of ncoeff terms, where each term is the product of a single coefficient value and N factors of the form ‘Tn(x’_i), wherex'_i` is the normalised value of the i'th input axis value.

The forward and inverse transformations are defined independantly by separate sets of coefficients, supplied when the ChebyMap is created. If no coefficients are supplied to define the inverse transformation, the polyTran method can instead be used to create an inverse transformation. The inverse transformation so generated will be a Chebyshev polynomial with coefficients chosen to minimise the residuals left by a round trip (forward transformation followed by inverse transformation).

Attributes

All those of Mapping. In addition, the forward and inverse bounds can be retrieved using getDomain

Strictly speaking, ChebyMap it has all the attributes of PolyMap, but the only attributes PolyMap adds to Mapping are iterative inverse parameters and those are ignored by ChebyMap because it does not (yet) support an iterative inverse.

Constructor & Destructor Documentation

◆ ChebyMap() [1/5]

ast::ChebyMap::ChebyMap ( ConstArray2D const &  coeff_f,
ConstArray2D const &  coeff_i,
std::vector< double > const &  lbnd_f,
std::vector< double > const &  ubnd_f,
std::vector< double > const &  lbnd_i,
std::vector< double > const &  ubnd_i,
std::string const &  options = "" 
)
inlineexplicit

Construct a ChebyMap with a specified forward and/or inverse transforms.

The two sets of coefficients are independent of each other: the inverse transform need not undo the forward transform.

Parameters
[in]coeff_fA matrix of coefficients describing the forward transformation. If coeff_f is empty then no forward transformation is provided.
[in]coeff_iA matrix of coefficients describing the inverse transformation. If coeff_i is empty then no inverse transformation is provided, unless you specify suitable options to request an iterative inverse; see the ChebyMap(ConstArray2D const &, int, std::vector<double> const &, std::string const &) "other constructor" for details.
[in]lbnd_fLower bounds for input data; one element per input axis
[in]ubnd_fUpper bounds for input data; one element per input axis
[in]lbnd_iLower bounds for output data; one element per output axis
[in]ubnd_iUpper bounds for output data; one element per output axis
[in]optionsComma-separated list of attribute assignments.

If a transform is not specified then the corresponding bounds are ignored (not even length-checked) and can be empty. For example if coeff_f is empty then lbnd_f and ubnd_f are ignored.

Exceptions
std::invalid_argumentif neither transform is specified (coeff_f and coeff_i are both empty).
std::invalid_argumentif the forward transform is specified (coeff_f is not empty) and lbnd_f or ubnd_f do not have nin elements.
std::invalid_argumentif the inverse transform is specified (coeff_i is not empty) and lbnd_i or ubnd_i do not have nout elements.

@anchor ChebyMap_CoefficientMatrices Coefficient Matrices

The coefficients describing a forward transformation are specified as 2-dimensional ndarray, with one row per coefficient. Each row contains the following consecutive (2 + nin) values:

  • The first element is the coefficient value.
  • The next element is the integer index of the ChebyMap output which uses the coefficient within its defining polynomial (the first output has index 1).
  • The remaining elements give the Chebyshev order to use with each corresponding input coordinate value, or 0 to ignore that input coordinate. Powers must not be negative and floating point values are rounded to the nearest integer.

For example, suppose you want to make a ChebyMap with 3 inputs and 2 outputs. Then each row of coeff_f must have 5 = 2 + nin elements. A row with values (1.2, 2, 6, 3, 0) describes a coefficient that increments output 2 as follows:

`out2 += 1.2 * T6(in1') * T3(in2') * T0(in3')`

and a row with values (-1.5, 1, 0, 0, 0) describes a coefficient that increments output 1 with a constant value of -1.5 (since all powers are 0):

`out1 += -1.5 * T0(in1') * T0(in2') * T0(in3')`

where inI' is the normalized value of input axis I.

The final value of each output coordinate is the sum of all values specified by coefficients which increment that output coordinate, or 0 if there are no such coefficients.

The coefficients describing the inverse transformation work the same way, of course, but each coefficient is described by (2 + nout) values.

◆ ChebyMap() [2/5]

ast::ChebyMap::ChebyMap ( ConstArray2D const &  coeff_f,
int  nout,
std::vector< double > const &  lbnd_f,
std::vector< double > const &  ubnd_f,
std::string const &  options = "IterInverse=0" 
)
inlineexplicit

Construct a ChebyMap with only the forward transform specified.

If the polynomial is invertible and you want an inverse can you call polyTran to fit one (at this time the iterative inverse offered by PolyMap is not available for ChebyMap).

Parameters
[in]coeff_fA (2 + nin) x ncoeff_f matrix of coefficients describing the forward transformation.
[in]noutNumber of output coordinates.
[in]lbnd_fLower bounds for input data; one element per input axis
[in]ubnd_fUpper bounds for input data; one element per input axis
[in]optionsComma-separated list of attribute assignments.
Exceptions
std::invalid_argumentif the forward transform is not defined (coeff_f is empty)
std::invalid_argumentif lbnd_f or ubnd_f do not have nin elements

◆ ~ChebyMap()

virtual ast::ChebyMap::~ChebyMap ( )
inlinevirtual

◆ ChebyMap() [3/5]

ast::ChebyMap::ChebyMap ( ChebyMap const &  )
default

Copy constructor: make a deep copy.

◆ ChebyMap() [4/5]

ast::ChebyMap::ChebyMap ( ChebyMap &&  )
default

◆ ChebyMap() [5/5]

ast::ChebyMap::ChebyMap ( AstChebyMap *  map)
protected

Construct a ChebyMap from an raw AST pointer.

Member Function Documentation

◆ copy()

std::shared_ptr<ChebyMap> ast::ChebyMap::copy ( ) const
inline

Return a deep copy of this object.

◆ copyPolymorphic()

virtual std::shared_ptr<Object> ast::ChebyMap::copyPolymorphic ( ) const
inlineoverrideprotectedvirtual

Return a deep copy of this object. This is called by copy.

Each subclass must override this method. The standard implementation is:

return copyImpl<astshim_class, ast_class>();

for example Frame implements this as:

return copyImpl<Frame, AstFrame>();

Reimplemented from ast::Mapping.

◆ getDomain()

ChebyDomain ast::ChebyMap::getDomain ( bool  forward) const

Return the bounding box of the domain of a ChebyMap.

Return the upper and lower limits of the box defining the domain of either the forward or inverse transformation of a ChebyMap. These are the values that were supplied when the ChebyMap was created.

If the requested direction was fit using polyTran, and so does not have a user-specified domain bounding box, this method returns a box determined by calling MapBox on opposite direction's transformation.

Parameters
[in]forwardIf true return the domain of the forward transform, else the inverse
Exceptions
std::runtime_errorif the domain cannot be computed

◆ operator=() [1/2]

ChebyMap& ast::ChebyMap::operator= ( ChebyMap &&  )
default

◆ operator=() [2/2]

ChebyMap& ast::ChebyMap::operator= ( ChebyMap const &  )
delete

◆ polyTran() [1/2]

ChebyMap ast::ChebyMap::polyTran ( bool  forward,
double  acc,
double  maxacc,
int  maxorder 
) const

This method is the same as polyTran except that the bounds are those originally provided when the polynomial whose inverse is being fit was specified.

◆ polyTran() [2/2]

ChebyMap ast::ChebyMap::polyTran ( bool  forward,
double  acc,
double  maxacc,
int  maxorder,
std::vector< double > const &  lbnd,
std::vector< double > const &  ubnd 
) const

This function creates a new ChebyMap which is a copy of this one, in which a specified transformation (forward or inverse) has been replaced by a new Chebyshev polynomial transformation. The coefficients of the new transformation are estimated by sampling the other transformation and performing a least squares polynomial fit in the opposite direction to the sampled positions and values.

This method can only be used on (1-input,1-output) or (2-input, 2-output) ChebyMaps.

Parameters
[in]forwardIf true the forward transformation is replaced. Otherwise the inverse transformation is replaced.
[in]accThe target accuracy, expressed as a geodesic distance within the ChebyMap's input space (if forward is false) or output space (if forward is true).
[in]maxaccThe maximum allowed accuracy for an acceptable polynomial, expressed as a geodesic distance within the ChebyMap's input space (if forward is false) or output space (if forward is true).
[in]maxorderThe maximum allowed polynomial order. This is one more than the maximum power of either input axis. So for instance, a value of 3 refers to a quadratic polynomial. Note, cross terms with total powers greater than or equal to maxorder are not inlcuded in the fit. So the maximum number of terms in each of the fitted polynomials is maxorder*(maxorder + 1)/2.
[in]lbndA vector holding the lower bounds of a rectangular region within the ChebyMap's input space (if forward is false) or output space (if forward is true). If both lbnd and ubnd are empty (the default) then they will be estimated. The new polynomial will be evaluated over this rectangle. The length should equal getNIn() or getNOut(), depending on forward.
[in]ubndA vector holding the upper bounds of a rectangular region within the ChebyMap's input space (if forward is false) or output space (if forward is true). If both lbnd and ubnd are empty (the default) then they will be estimated. The new polynomial will be evaluated over this rectangle. The length should equal getNIn() or getNOut(), depending on forward.
Exceptions
std::invalid_argumentif the size of lbnd or ubnd does not match getNIn() (if forward false) or getNOut() (if forward true).

The variant that takes omits the lbnd and ubnd arguments uses the full domain of the polynomial whose inverse is being fit.

Note

The transformation to create is specified by the forward parameter. In what follows "X" refers to the inputs of the ChebyMap, and "Y" to the outputs of the ChebyMap. The forward transformation transforms input values (X) into output values (Y), and the inverse transformation transforms output values (Y) into input values (X). Within a ChebyMap, each transformation is represented by an independent set of polynomials, P_f or P_i: Y=P_f(X) for the forward transformation and X=P_i(Y) for the inverse transformation.

The forward parameter specifies the transformation to be replaced. If it is true, a new forward transformation is created by first finding the input values (X) using the inverse transformation (which must be available) at a regular grid of points (Y) covering a rectangular region of the ChebyMap's output space. The coefficients of the required forward polynomial, Y=P_f(X), are chosen in order to minimise the sum of the squared residuals between the sampled values of Y and P_f(X).

If forward is false (probably the most likely case), a new inverse transformation is created by first finding the output values (Y) using the forward transformation (which must be available) at a regular grid of points (X) covering a rectangular region of the ChebyMap's input space. The coefficients of the required inverse polynomial, X=P_i(Y), are chosen in order to minimise the sum of the squared residuals between the sampled values of X and P_i(Y).

This fitting process is performed repeatedly with increasing polynomial orders (starting with linear) until the target accuracy is achieved, or a specified maximum order is reached. If the target accuracy cannot be achieved even with this maximum-order polynomial, the best fitting maximum-order polynomial is returned so long as its accuracy is better than "maxacc". If it is not, an error is reported.

Friends And Related Function Documentation

◆ Object

friend class Object
friend

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