
:: String  indentification of caller location for easier debugging
 > fa   > fa   Check internal consistency and report problem if any.




:: fa  this parameter is not used except for type checking
 > domra   > ranra  



:: fa  this parameter is not used except for type checking
 > ranra   > domra  



Get the internal degree of quality (usually polynomial degree)
of the approximation.



Set an upper bound on the degree of this function approximation.
This reduces the degree immediately if necessary and also
affects all operations performed with this value later.
May also set the maximum size of the approximations to a default
based on the degree and the dimension of this enclosure.



Get the current uppend bound on the degree associated
with this function approximation.



Get the internal size of the approximation
(usually number of polynomial terms).



Set an upper bound on the size of this function approximation.
This reduces the size immediately if necessary and also
affects all operations performed with this value later.



Get the current uppend bound on the size associated
with this function approximation.


getVariables :: fa > [varid]  Source 

List all variables that are actually used in the approximation.



Give a close upper bound of the precision of the range
at the best approximated point in the domain.


getRangeApprox :: fa > ranra  Source 

Find some upper and lower bounds of the function over [1,1]^n.



Combine several functions with the same domain into one tuple function.



Reveal how many functions are bundled together.


applyTupleFn :: ([fa] > [fa]) > fa > fa  Source 

Modify a tuple of functions in a way
that does not treat the tuple elements uniformly.



Find close upper and lower bounds of the volume of the entire enclosure.
A negative volume means that the enclosure is certainly inconsistent.


scale :: ranra > fa > fa  Source 

Multiply a function approximation by a real number approximation.



:: EffortIndex   > box  the subdomain; defined by clipping the range of some variables
 > fa  the enclosure to be used on the subdomain (but defined on the whole domain)
 > fa  function to improve by intersecting its subdomain
 > fa   Intersect one approximation by another but only on a box within its domain.



intersectMeasureImprovement  Source 



eval :: box > fa > [ranra]  Source 

Evaluate the function at the given point.


partialEval :: box > fa > fa  Source 

Fix some variables in the function to the given exact values.



:: fa  enclosure of f, f is nondecreasing in variable var
 > varid  variable var to get substituted in f
 > fa  enclosure of f_var, to be substituted for var
 > fa  enclosure of f[var > f_var]
BEWARE: Enclosure is probably incorrect where values of
f_v are outside the domain of v in f.
 A simple and limited composition of functions applicable
only when the rangedefining function is nondecreasing.




:: fa  enclosure of f, f is nonincreasing in variable var
 > varid  variable var to get substituted in f
 > fa  enclosure of f_var, to be substituted for var
 > fa  enclosure of f[var > f_var]
BEWARE: Enclosure is probably incorrect where values of
f_v are outside the domain of v in f.
 A simple and limited composition of functions applicable
only when the rangedefining function is nonincreasing.

