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Datei: vardirselector.pvs Sprache: PVS

Original von: PVS^©

% 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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