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
|
//$$ solution.cpp // solve routines
// Copyright (C) 1994: R B Davies
#define WANT_STREAM // include.h will get stream fns
#define WANT_MATH // include.h will get math fns
#include "include.h"
#include "config.h"
#include "boolean.h"
#include "myexcept.h"
#include "solution.h"
#ifdef use_namespace
namespace RBD_COMMON {
#endif
void R1_R1::Set(Real X)
{
if ((!minXinf && X <= minX) || (!maxXinf && X >= maxX))
Throw(SolutionException("X value out of range"));
x = X; xSet = true;
}
R1_R1::operator Real()
{
if (!xSet) Throw(SolutionException("Value of X not set"));
Real y = operator()();
return y;
}
unsigned long SolutionException::Select;
SolutionException::SolutionException(const char* a_what) : BaseException()
{
Select = BaseException::Select;
AddMessage("Error detected by solution package\n");
AddMessage(a_what); AddMessage("\n");
if (a_what) Tracer::AddTrace();
};
inline Real square(Real x) { return x*x; }
void OneDimSolve::LookAt(int V)
{
lim--;
if (!lim) Throw(SolutionException("Does not converge"));
Last = V;
Real yy = function(x[V]) - YY;
Finish = (fabs(yy) <= accY) || (Captured && fabs(x[L]-x[U]) <= accX );
y[V] = vpol*yy;
}
void OneDimSolve::HFlip() { hpol=-hpol; State(U,C,L); }
void OneDimSolve::VFlip()
{ vpol = -vpol; y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2]; }
void OneDimSolve::Flip()
{
hpol=-hpol; vpol=-vpol; State(U,C,L);
y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2];
}
void OneDimSolve::State(int I, int J, int K) { L=I; C=J; U=K; }
void OneDimSolve::Linear(int I, int J, int K)
{
x[J] = (x[I]*y[K] - x[K]*y[I])/(y[K] - y[I]);
// cout << "Linear\n";
}
void OneDimSolve::Quadratic(int I, int J, int K)
{
// result to overwrite I
Real YJK, YIK, YIJ, XKI, XKJ;
YJK = y[J] - y[K]; YIK = y[I] - y[K]; YIJ = y[I] - y[J];
XKI = (x[K] - x[I]);
XKJ = (x[K]*y[J] - x[J]*y[K])/YJK;
if ( square(YJK/YIK)>(x[K] - x[J])/XKI ||
square(YIJ/YIK)>(x[J] - x[I])/XKI )
{
x[I] = XKJ;
// cout << "Quadratic - exceptional\n";
}
else
{
XKI = (x[K]*y[I] - x[I]*y[K])/YIK;
x[I] = (XKJ*y[I] - XKI*y[J])/YIJ;
// cout << "Quadratic - normal\n";
}
}
Real OneDimSolve::Solve(Real Y, Real X, Real Dev, int Lim)
{
enum Loop { start, captured1, captured2, binary, finish };
Tracer et("OneDimSolve::Solve");
lim=Lim; Captured = false;
if (Dev==0.0) Throw(SolutionException("Dev is zero"));
L=0; C=1; U=2; vpol=1; hpol=1; y[C]=0.0; y[U]=0.0;
if (Dev<0.0) { hpol=-1; Dev = -Dev; }
YY=Y; // target value
x[L] = X; // initial trial value
if (!function.IsValid(X))
Throw(SolutionException("Starting value is invalid"));
Loop TheLoop = start;
for (;;)
{
switch (TheLoop)
{
case start:
LookAt(L); if (Finish) { TheLoop = finish; break; }
if (y[L]>0.0) VFlip(); // so Y[L] < 0
x[U] = X + Dev * hpol;
if (!function.maxXinf && x[U] > function.maxX)
x[U] = (function.maxX + X) / 2.0;
if (!function.minXinf && x[U] < function.minX)
x[U] = (function.minX + X) / 2.0;
LookAt(U); if (Finish) { TheLoop = finish; break; }
if (y[U] > 0.0) { TheLoop = captured1; Captured = true; break; }
if (y[U] == y[L])
Throw(SolutionException("Function is flat"));
if (y[U] < y[L]) HFlip(); // Change direction
State(L,U,C);
for (i=0; i<20; i++)
{
// cout << "Searching for crossing point\n";
// Have L C then crossing point, Y[L]<Y[C]<0
x[U] = x[C] + Dev * hpol;
if (!function.maxXinf && x[U] > function.maxX)
x[U] = (function.maxX + x[C]) / 2.0;
if (!function.minXinf && x[U] < function.minX)
x[U] = (function.minX + x[C]) / 2.0;
LookAt(U); if (Finish) { TheLoop = finish; break; }
if (y[U] > 0) { TheLoop = captured2; Captured = true; break; }
if (y[U] < y[C])
Throw(SolutionException("Function is not monotone"));
Dev *= 2.0;
State(C,U,L);
}
if (TheLoop != start ) break;
Throw(SolutionException("Cannot locate a crossing point"));
case captured1:
// cout << "Captured - 1\n";
// We have 2 points L and U with crossing between them
Linear(L,C,U); // linear interpolation
// - result to C
LookAt(C); if (Finish) { TheLoop = finish; break; }
if (y[C] > 0.0) Flip(); // Want y[C] < 0
if (y[C] < 0.5*y[L]) { State(C,L,U); TheLoop = binary; break; }
case captured2:
// cout << "Captured - 2\n";
// We have L,C before crossing, U after crossing
Quadratic(L,C,U); // quad interpolation
// - result to L
State(C,L,U);
if ((x[C] - x[L])*hpol <= 0.0 || (x[C] - x[U])*hpol >= 0.0)
{ TheLoop = captured1; break; }
LookAt(C); if (Finish) { TheLoop = finish; break; }
// cout << "Through first stage\n";
if (y[C] > 0.0) Flip();
if (y[C] > 0.5*y[L]) { TheLoop = captured2; break; }
else { State(C,L,U); TheLoop = captured1; break; }
case binary:
// We have L, U around crossing - do binary search
// cout << "Binary\n";
for (i=3; i; i--)
{
x[C] = 0.5*(x[L]+x[U]);
LookAt(C); if (Finish) { TheLoop = finish; break; }
if (y[C]>0.0) State(L,U,C); else State(C,L,U);
}
if (TheLoop != binary) break;
TheLoop = captured1; break;
case finish:
return x[Last];
}
}
}
bool R1_R1::IsValid(Real X)
{
Set(X);
return (minXinf || x > minX) && (maxXinf || x < maxX);
}
#ifdef use_namespace
}
#endif
|
