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% LOS recovery with an iterative algorithm
losr_iterative : THEORY
BEGIN
IMPORTING repulsive,reals@sign3,trig@sincos
s,v,vo,vi : VAR Nz_vect2
nvo,nvo2 : VAR Vect2
minrelgs : VAR nnreal
step : VAR posreal
eps,dir : VAR Sign
maxtrk,
maxgs,mings : VAR posreal
i : VAR posnat
%% dir = 1 is right
incr_trk_vect(nvo,step,dir): {nvo2: Vect2 | trk_only?(nvo)(nvo2)} =
cos(dir*step)*nvo + sin(dir*step)*perpR(nvo)
losr_trk_iter_dir(s,vo,vi,step,eps): Sign3 =
IF repulsive_criteria(s,vo-vi,eps)(incr_trk_vect(vo,step,1)-vi)
THEN 1
ELSIF repulsive_criteria(s,vo-vi,eps)(incr_trk_vect(vo,step,-1)-vi)
THEN -1
ELSE 0 ENDIF
losr_trk_iter_i(s,vo,vi,minrelgs,maxtrk,step,i,dir,eps,
(nvo | trk_only?(vo)(nvo) AND
repulsive_criteria(s,vo-vi,eps)(nvo-vi))):
RECURSIVE {nvo2 | nz_vect2?(nvo2) =>
trk_only?(vo)(nvo2) AND
repulsive_criteria(s,vo-vi,eps)(nvo2-vi)} =
LET nvop = incr_trk_vect(nvo,step,dir) IN
IF i*step >= maxtrk OR NOT repulsive_criteria(s,nvo-vi,eps)(nvop-vi) THEN
nvo
ELSIF divergent?(s,nvop-vi) AND norm(nvop-vi) >= minrelgs THEN
nvop
ELSE
losr_trk_iter_i(s,vo,vi,minrelgs,maxtrk,step,i+1,dir,eps,nvop)
ENDIF
MEASURE max(0,floor(maxtrk/step)-i+1)
losr_trk_iter(s,vo,vi,minrelgs,maxtrk,step):
{nvo | nz_vect2?(nvo) =>
trk_only?(vo)(nvo) AND
repulsive_criteria(s,vo-vi,-sign(det(s,vo-vi)))(nvo-vi)} =
LET eps = -sign(det(s,vo-vi)),
dir3 = losr_trk_iter_dir(s,vo,vi,step,eps) IN
IF dir3 = 0 THEN
zero
ELSE LET nvo = incr_trk_vect(vo,step,dir3) IN
IF repulsive_criteria(s,vo-vi,eps)(nvo-vi) THEN
losr_trk_iter_i(s,vo,vi,minrelgs,maxtrk,step,1,dir3,eps,nvo)
ELSE
zero
ENDIF
ENDIF
%% dir = 1 is right
incr_gs_vect(vo,step,dir): {nvo: Vect2 | norm(vo)+dir*step > 0 IMPLIES gs_only?(vo)(nvo)} =
(norm(vo)+dir*step)*^(vo)
losr_gs_iter_dir(s,vo,vi,mings,maxgs,step,eps): Sign3 =
IF norm(vo) + step <= maxgs AND repulsive_criteria(s,vo-vi,eps)(incr_gs_vect(vo,step,1)-vi)
THEN 1
ELSIF norm(vo) - step >= mings AND repulsive_criteria(s,vo-vi,eps)(incr_gs_vect(vo,step,-1)-vi)
THEN -1
ELSE 0 ENDIF
losr_gs_iter_i(s,vo,vi,minrelgs,mings,maxgs,step,i,dir,eps,
(nvo | nvo = (norm(vo)+dir*i*step)*^(vo) AND norm(vo)+dir*i*step > 0 AND
repulsive_criteria(s,vo-vi,eps)(nvo-vi))):
RECURSIVE {nvo2 | nz_vect2?(nvo2) =>
gs_only?(vo)(nvo2) AND
repulsive_criteria(s,vo-vi,eps)(nvo2-vi)} =
LET nvop = incr_gs_vect(nvo,step,dir),
nnorm = norm(nvo)+dir*step IN
IF nnorm > maxgs OR nnorm < mings OR NOT repulsive_criteria(s,nvo-vi,eps)(nvop-vi) THEN
nvo
ELSIF divergent?(s,nvop-vi) AND norm(nvop-vi) >= minrelgs THEN
nvop
ELSE
losr_gs_iter_i(s,vo,vi,minrelgs,mings,maxgs,step,i+1,dir,eps,nvop)
ENDIF
MEASURE max(0,floor(IF dir >= 0 THEN (maxgs-norm(vo))/step ELSE (norm(vo)-mings)/step ENDIF)-i+1)
losr_gs_iter(s,vo,vi,minrelgs,mings,maxgs,step):
{nvo | nz_vect2?(nvo) =>
gs_only?(vo)(nvo) AND
repulsive_criteria(s,vo-vi,-sign(det(s,vo-vi)))(nvo-vi)} =
LET eps = -sign(det(s,vo-vi)),
dir3 = losr_gs_iter_dir(s,vo,vi,mings,maxgs,step,eps) IN
IF dir3 = 0 THEN
zero
ELSE LET nvo = incr_gs_vect(vo,step,dir3) IN
IF repulsive_criteria(s,vo-vi,eps)(nvo-vi) THEN
losr_gs_iter_i(s,vo,vi,minrelgs,mings,maxgs,step,1,dir3,eps,nvo)
ELSE
zero
ENDIF
ENDIF
END losr_iterative
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