Fit a PolyMap inverse or forward transformation
This method can only be used on (1-input,1-output) or (2-input,2-output) PolyMaps.
The transformation to create is specified by the " forward" parameter. In what follows
" X" refers to the inputs of the PolyMap, and " Y" to the outputs of the PolyMap. 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
PolyMap, 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
non-zero, 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 PolyMap’ 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 zero (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
PolyMap’ 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, a
NULL pointer is returned but no error is reported.
’ s input space (if " forward" is zero) or output space (if " forward" is
non-zero). ’ s input space (if " forward" is
zero) or output space (if " forward" is non-zero). ’ s input space (if " forward" is zero) or output space (if "
forward" is non-zero). The new polynomial will be evaluated over this rectangle.
The length of this array should equal the value of the PolyMap’ s Nin or Nout
attribute, depending on " forward" . ’ s input space
(if " forward" is zero) or output space (if " forward" is non-zero). The new
polynomial will be evaluated over this rectangle. The length of this array
should equal the value of the PolyMap’ s Nin or Nout attribute, depending on "
forward" . " lbnd" and/or " ubnd" , in which case the corresponding bounds
supplied when the ChebyMap was created are used. The returned PolyMap will be a
ChebyMap, and the new transformation will be defined as a weighted sum of Chebyshev
functions of the first kind. " maxacc" , but no error will be reported. The IterInverse attribute is always cleared in the returned PolyMap. This means that the returned PolyMap will always use the new fit by default, rather than the iterative inverse, regardless of the setting of IterInverse in the supplied PolyMap.
This function can only be used on 1D or 2D PolyMaps which have the same number of inputs and outputs.
A null Object pointer (AST__NULL) will be returned if this function is invoked with the AST error status set, or if it should fail for any reason.