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% This theory contains the following strategies for selecting a variable:
% AltVarLeftRight : Select variables in alternate way, split left first
% AltVarRightLeft : Select variables in alternate way, split right first
% MaxVarMinDir : Select the variable of maximum variation and the direction with the minimum coefficient
% MaxVarMaxDir : Select the variable of maximum variation and the direction with the maximum coefficient
vardirselector : THEORY
BEGIN
IMPORTING multi_bernstein
bspoly : VAR MultiBernstein
bsdegmono : VAR DegreeMono
nvars,terms : VAR posnat
cf : VAR Coeff
level,v : VAR nat
% Parameters are bspoly,bsdegmono,nvars,terms,cf,level (bool=true is Left)
VarSelector : TYPE = [[MultiBernstein,DegreeMono,posnat,posnat,Coeff,nat]->[bool,nat]]
% Alternate variable, Left-Right direction
AltVarLeftRight(bspoly,bsdegmono,nvars,terms,cf,level): [bool,nat] =
(true,level)
% Alternate variable, Right-Left direction
AltVarRightLeft(bspoly,bsdegmono,nvars,terms,cf,level): [bool,nat] =
(false,level)
var_coeff_range_rec(bspoly,bsdegmono,nvars,terms,cf,v,(iup:upto(bsdegmono(v)))) :
RECURSIVE [# currmin: real, currmax:real, firstc:real,lastc:real #] =
LET coefffun = multibscoeff(bspoly,bsdegmono,cf,nvars,terms),
thismono = zeroes WITH [(v):=iup],
thiscoeff = coefffun(thismono)
IN
IF iup=0 THEN
(# currmin := thiscoeff,
currmax := thiscoeff,
firstc := thiscoeff,
lastc := thiscoeff #)
ELSE
LET vcrrlast = var_coeff_range_rec(bspoly,bsdegmono,nvars,terms,cf,v,iup-1) IN
(# currmin := min(vcrrlast`currmin,thiscoeff),
currmax := max(vcrrlast`currmax,thiscoeff),
firstc := vcrrlast`firstc,
lastc := IF iup=bsdegmono(v) THEN thiscoeff ELSE vcrrlast`lastc ENDIF #)
ENDIF
MEASURE iup
var_maxcoeff_rec(bspoly,bsdegmono,nvars,terms,cf,v):
RECURSIVE [# variable:nat,firstc:real,lastc:real #] =
LET vcrr = var_coeff_range_rec(bspoly,bsdegmono,nvars,terms,cf,v,bsdegmono(v)),
thisanswer = (# variable := v,
firstc := vcrr`firstc,
lastc := vcrr`lastc #)
IN
IF v = 0 THEN thisanswer
ELSE
LET vmr = var_maxcoeff_rec(bspoly,bsdegmono,nvars,terms,cf,v-1),
vcrrlast = var_coeff_range_rec(bspoly,bsdegmono,nvars,terms,cf,vmr`variable,
bsdegmono(vmr`variable)),
lastanswer = (# variable :=vmr`variable,
firstc :=vcrrlast`firstc,
lastc :=vcrrlast`lastc #) IN
IF vcrr`currmax-vcrr`currmin > vcrrlast`currmax-vcrrlast`currmin THEN
thisanswer
ELSE
lastanswer
ENDIF
ENDIF
MEASURE v
MaxVarMinDir(bspoly,bsdegmono,nvars,terms,cf,level): [bool,nat] =
LET vcrr = var_maxcoeff_rec(bspoly,bsdegmono,nvars,terms,cf,nvars-1) IN
(vcrr`firstc<=vcrr`lastc,vcrr`variable)
MaxVarMaxDir(bspoly,bsdegmono,nvars,terms,cf,level): [bool,nat] =
LET vcrr = var_maxcoeff_rec(bspoly,bsdegmono,nvars,terms,cf,nvars-1) IN
(vcrr`firstc > vcrr`lastc,vcrr`variable)
END vardirselector
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