-
Notifications
You must be signed in to change notification settings - Fork 0
/
diffincl.cpp
249 lines (229 loc) · 9.69 KB
/
diffincl.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
///////////////////////////////////////////////////////////////////////////
// diffincl.cpp : exponential of interval matrices
///////////////////////////////////////////////////////////////////////////
#include <codac.h>
#include <iostream>
#include <vector>
#include <array>
#include <cstdio>
#include <cstring>
// #include "expIMat.h"
#include "vibes.h"
#include "diffincl.h"
using namespace codac;
namespace diffincl {
DiffInclusion::DiffInclusion(unsigned int dim, unsigned int udim,
const TFunction* tfun,
Interval& time, unsigned int nbsteps) :
dim(dim), udim(udim), ctc(NULL),
time(time), nbsteps(nbsteps),
with_delay(false), with_init(false)
{
ctc = new codac2::CtcDiffInclusion(*tfun);
}
DiffInclusion::DiffInclusion(std::istream& input) {
char str[256], *token;
bool fini = false;
this->ctc = NULL;
this->dim=-1;
this->udim=0;
this->nbsteps=0;
this->with_delay=false;
this->with_init=false;
while (!input.eof()) {
input.getline(str,255);
std::cout << str << "\n";
token=strtok(str," :=");
if (token==NULL) continue;
if (strncasecmp(token,"dim",3)==0) {
token=strtok(NULL," :=");
if (token==NULL) continue;
sscanf(token,"%d",&(this->dim));
if (this->dim<=0) {
std::cerr << "Invalid dimension.\n";
}
} else if (strncasecmp(token,"udim",4)==0) {
token=strtok(NULL," :=");
if (token==NULL) continue;
sscanf(token,"%d",&(this->udim));
if (this->udim<=0) {
std::cerr << "Invalid dimension.\n";
}
} else if (strncasecmp(token,"time",4)==0) {
double v1=0.0,v2=0.0;
token=strtok(NULL," :=");
if (token==NULL) continue;
sscanf(token,"[%lg,%lg]",&v1,&v2);
if (v1>=v2) {
std::cerr << "Invalid time : " << v1 << " " << v2 << "\n";
}
ibex::Interval iv(v1,v2);
std::cerr << "Interval : " << v1 << " " << v2 << "\n";
this->time = iv;
} else if (strncasecmp(token,"delay",5)==0) {
double v1=0.0,v2=0.0;
token=strtok(NULL," :=");
if (token==NULL) continue;
sscanf(token,"[%lg,%lg]",&v1,&v2);
if (v1>=v2 || v1<=0.0) {
std::cerr << "Invalid delay : " << v1 << " " << v2 << "\n";
}
ibex::Interval iv(-v2,-v1);
std::cerr << "Delay : " << v1 << " " << v2 << "\n";
this->delay = iv;
this->with_delay=true;
} else if (strncasecmp(token,"withinit",8)==0) {
double v1=0.0,v2=0.0;
token=strtok(NULL," :=");
if (token==NULL) continue;
this->with_init=strchr("tTyYoO",token[0]);
std::cerr << "With_init : " << this->with_init << "\n";
} else if (strncasecmp(token,"function",8)==0) {
assert(this->dim>0);
const char *xdyn[this->dim+this->udim];
for (int i=0;i<this->dim+this->udim;i=i+1) {
token=strtok(NULL,"(,) :=");
xdyn[i] = token;
}
token=strtok(NULL," :");
for (int i=0;i<this->dim+this->udim;i=i+1) {
std::cout << xdyn[i] << "\n";
}
std::cout << token << "\n";
TFunction *tfun = new TFunction(dim+udim,xdyn,token);
this->ctc = new codac2::CtcDiffInclusion(*tfun);
} else if (strncasecmp(token,"nbsteps",7)==0) {
token=strtok(NULL," :=");
if (token==NULL) continue;
sscanf(token,"%d",&(this->nbsteps));
assert(this->nbsteps>0);
} else {
std::cerr << "Invalid line!";
}
}
assert(this->dim>0);
assert(this->fun!=NULL || this->tfun!=NULL);
assert(this->nbsteps>0);
assert(!(this->time.is_degenerated()));
}
///// forward differential inclusion X' = f(X,t)
codac2::Tube<codac2::IParals> *DiffInclusion::fwd_inclusion
(const IntervalVector& frame,
const IntervalVector* u_val,
const IntervalVector& X0,
VIBesFig *fig,
int nbsl)
{
std::shared_ptr<codac2::TDomain> tdom = codac2::create_tdomain(this->time,this->time.diam()/nbsteps,true);
codac2::Tube<codac2::IParals>* Res = new codac2::Tube<codac2::IParals>(tdom,dim);
// codac2::TDomain *tdom = new codac2::TDomain(this->time,this->time.diam()/nbsteps,true);
// codac2::Tube<codac2::IParals>* Res = new codac2::Tube<codac2::IParals>(*tdom,dim);
Res->set(frame);
Res->first_slice().next_slice_ptr()->set(X0);
std::cout << "first slice " << *Res << "\n";
assert(X0.dim()==dim);
assert(ctc!=NULL);
codac2::Tube<codac2::IParals> *UDom=NULL;
if (u_val && this->udim>0) {
UDom = new codac2::Tube<codac2::IParals>(tdom,udim);
UDom->set(*u_val);
}
ctc->contract(*Res,UDom,TimePropag::FORWARD);
if (UDom!=NULL) delete UDom;
return Res;
}
///// forward differential inclusion X' = f(X,t)
codac2::Tube<codac2::IParals> *DiffInclusion::fwd_inclusion
(const IntervalVector& frame,
const TFunction& ufun,
const IntervalVector& X0,
VIBesFig *fig,
int nbsl)
{
std::shared_ptr<codac2::TDomain> tdom = codac2::create_tdomain(this->time,this->time.diam()/nbsteps,true);
codac2::Tube<codac2::IParals>* Res = new codac2::Tube<codac2::IParals>(tdom,dim);
// codac2::TDomain *tdom = new codac2::TDomain(this->time,this->time.diam()/nbsteps,true);
// codac2::Tube<codac2::IParals>* Res = new codac2::Tube<codac2::IParals>(*tdom,dim);
Res->set(frame);
Res->first_slice().next_slice_ptr()->set(X0);
std::cout << "first slice " << *Res << "\n";
assert(X0.dim()==dim);
assert(ctc!=NULL);
assert(this->udim>0);
// codac2::Tube<codac2::IParals> *UDom = new codac2::Tube<codac2::IParals>(tdom,ufun);
codac2::Tube<codac2::IParals> UDom(tdom,ufun);
ctc->contract(*Res,&UDom,TimePropag::FORWARD);
//delete(UDom);
return Res;
}
///// forward and backward from a slice inclusion X' = f(X,t)
void DiffInclusion::fwdbwd_contract(codac2::Tube<codac2::IParals> ¤t,
std::shared_ptr<codac2::Slice<codac2::IParals>> gate,
const IntervalVector* u_val) {
codac2::Tube<codac2::IParals> *UDom=NULL;
if (u_val && this->udim>0) {
UDom = new codac2::Tube<codac2::IParals>(current.tdomain(),udim);
UDom->set(*u_val);
}
ctc->contract_from_slice(current,UDom,gate,TimePropag::FORWARD |
TimePropag::BACKWARD);
if (UDom!=NULL) delete UDom;
}
#if 0
///// differential inclusion X' = f(X)
// dim : number of variables
// fun : function f of dim variables
// frame : global frame (no computation outside)
// X0 : initial position
// time : time interval [0,time]
// steps : number of steps
// result : list of each steps
// proj : projection for display ( matrix 2*dim )
void diffInclusion(unsigned int dim, const ibex::Function& fun,
const ibex::IntervalVector& frame, const ibex::IntervalVector& X0,
double time, unsigned int nbsteps,
std::vector<ibex::IntervalVector>& res,
const ibex::IntervalMatrix& proj) {
// time step
const double tsteps = time/nbsteps;
ibex::IntervalVector fp = proj * frame;
vibes::drawBox(fp[0].lb(),fp[0].ub(),fp[1].lb(),fp[1].ub(),"blue[cyan]");
ibex::IntervalVector Cent(X0.mid());
const ibex::IntervalVector X0c = X0-Cent; // centered "initial" place
const ibex::Matrix Id = ibex::Matrix::eye(dim);
ibex::IntervalMatrix prodExpM(Id); // products of exponential
ibex::IntervalVector Xbox(X0); // recomputed box
res.push_back(X0);
for (int currentstep=1;currentstep<=nbsteps;currentstep++) {
double currenttime=currentstep*tsteps;
ibex::IntervalVector approxbox =
this->extend_box_basic(fun,frame,Xbox,tsteps);
ibex::Vector center_Approxbox = approxbox.mid();
ibex::IntervalMatrix jac = fun.jacobian(approxbox);
ibex::Matrix center_jac = jac.mid();
jac = jac - center_jac;
ibex::IntervalVector uncert = jac*(approxbox-center_Approxbox);
ibex::IntervalVector fun_eval = fun.eval_vector(center_Approxbox)
- center_jac*center_Approxbox; // FIXME : check
ibex::Vector fun_evalc = fun_eval.mid();
std::cout << "uncert : " << uncert << "\n";
uncert += (fun_eval-fun_evalc);
ibex::IntervalVector u2 = fun.eval_vector(approxbox)-fun.eval_vector(center_Approxbox) - (approxbox-center_Approxbox)*center_jac;
std::cout << "uncert2 : " << u2 << "\n";
uncert &= u2;
std::cout << "uncert : " << uncert << "\n";
compute_next_step(dim,fun_evalc,Cent,prodExpM,
center_jac,uncert,tsteps);
// std::cout << center_jac << "\n" << prodExpM << "\n\n";
Xbox = Cent +prodExpM * X0c ;
if (!Xbox.is_subset(approxbox)) {
std::cerr << "Erreur Xbox//approxbox !!!\n" <<
Xbox << " " << approxbox << "\n\n";
exit(-1);
}
display_state(Cent,Xbox,proj,"black[magenta]","red[magenta]");
res.push_back(Xbox);
}
}
#endif
}