lsst.astshim g38293774b4+62d12e78cb
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#include <ChebyMap.h>
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 | |
ChebyMap & | operator= (ChebyMap const &)=delete |
ChebyMap & | operator= (ChebyMap &&)=default |
std::shared_ptr< ChebyMap > | copy () 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 |
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virtual | ~Mapping () |
Mapping (Mapping const &)=default | |
Copy constructor: make a deep copy. More... | |
Mapping (Mapping &&)=default | |
Mapping & | operator= (Mapping const &)=delete |
Mapping & | operator= (Mapping &&)=default |
std::shared_ptr< Mapping > | copy () 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< Mapping > | inverted () 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< Mapping > | simplified () 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 |
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virtual | ~Object () |
Object (Object const &object) | |
Copy constructor: make a deep copy. More... | |
Object (Object &&)=default | |
Object & | operator= (Object const &)=delete |
Object & | operator= (Object &&)=default |
bool | operator== (Object const &rhs) const |
bool | operator!= (Object const &rhs) const |
std::shared_ptr< Object > | copy () 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< Object > | copyPolymorphic () const override |
ChebyMap (AstChebyMap *map) | |
Construct a ChebyMap from an raw AST pointer. More... | |
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Mapping (AstMapping *rawMap) | |
virtual std::shared_ptr< Object > | copyPolymorphic () const override |
template<typename Class > | |
std::shared_ptr< Class > | decompose (int i, bool copy) const |
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Object (AstObject *object) | |
template<typename T , typename AstT > | |
std::shared_ptr< T > | copyImpl () const |
virtual std::shared_ptr< Object > | copyPolymorphic () const =0 |
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 | |
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using | ObjectPtr = std::unique_ptr< AstObject, Deleter > |
unique pointer holding an AST raw pointer More... | |
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static std::shared_ptr< Object > | fromString (std::string const &str) |
template<typename Class > | |
static std::shared_ptr< Class > | fromAstObject (AstObject *rawObj, bool copy) |
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template<typename ShimT , typename AstT > | |
static std::shared_ptr< ShimT > | makeShim (AstObject *p) |
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), where
x'_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).
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.
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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.
[in] | coeff_f | A matrix of coefficients describing the forward transformation. If coeff_f is empty then no forward transformation is provided. |
[in] | coeff_i | A 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 other constructor for details. |
[in] | lbnd_f | Lower bounds for input data; one element per input axis |
[in] | ubnd_f | Upper bounds for input data; one element per input axis |
[in] | lbnd_i | Lower bounds for output data; one element per output axis |
[in] | ubnd_i | Upper bounds for output data; one element per output axis |
[in] | options | Comma-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.
std::invalid_argument | if neither transform is specified (coeff_f and coeff_i are both empty). |
std::invalid_argument | if the forward transform is specified (coeff_f is not empty) and lbnd_f or ubnd_f do not have nin elements. |
std::invalid_argument | if the inverse transform is specified (coeff_i is not empty) and lbnd_i or ubnd_i do not have nout elements. |
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:
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.
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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).
[in] | coeff_f | A (2 + nin) x ncoeff_f matrix of coefficients describing the forward transformation. |
[in] | nout | Number of output coordinates. |
[in] | lbnd_f | Lower bounds for input data; one element per input axis |
[in] | ubnd_f | Upper bounds for input data; one element per input axis |
[in] | options | Comma-separated list of attribute assignments. |
std::invalid_argument | if the forward transform is not defined (coeff_f is empty) |
std::invalid_argument | if lbnd_f or ubnd_f do not have nin elements |
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inlinevirtual |
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default |
Copy constructor: make a deep copy.
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default |
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protected |
Construct a ChebyMap from an raw AST pointer.
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inline |
Return a deep copy of this object.
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inlineoverrideprotectedvirtual |
Return a deep copy of this object. This is called by copy.
Each subclass must override this method. The standard implementation is:
for example Frame implements this as:
Reimplemented from ast::Mapping.
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.
[in] | forward | If true return the domain of the forward transform, else the inverse |
std::runtime_error | if the domain cannot be computed |
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.
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.
[in] | forward | If true the forward transformation is replaced. Otherwise the inverse transformation is replaced. |
[in] | acc | The 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] | maxacc | The 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] | maxorder | The 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] | lbnd | A 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] | ubnd | A 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 . |
std::invalid_argument | if 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.
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.
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