Go to the documentation of this file.00001
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00010 #define WANT_STREAM // include.h will get stream fns
00011 #define WANT_MATH // include.h will get math fns
00012
00013 #include "include.h"
00014 #include "myexcept.h"
00015
00016 #include "solution.h"
00017
00018 #ifdef use_namespace
00019 namespace RBD_COMMON {
00020 #endif
00021
00022
00023 void R1_R1::Set(Real X)
00024 {
00025 if ((!minXinf && X <= minX) || (!maxXinf && X >= maxX))
00026 Throw(SolutionException("X value out of range"));
00027 x = X; xSet = true;
00028 }
00029
00030 R1_R1::operator Real()
00031 {
00032 if (!xSet) Throw(SolutionException("Value of X not set"));
00033 Real y = operator()();
00034 return y;
00035 }
00036
00037 unsigned long SolutionException::Select;
00038
00039 SolutionException::SolutionException(const char* a_what) : BaseException()
00040 {
00041 Select = BaseException::Select;
00042 AddMessage("Error detected by solution package\n");
00043 AddMessage(a_what); AddMessage("\n");
00044 if (a_what) Tracer::AddTrace();
00045 }
00046
00047 inline Real square(Real x) { return x*x; }
00048
00049 void OneDimSolve::LookAt(int V)
00050 {
00051 lim--;
00052 if (!lim) Throw(SolutionException("Does not converge"));
00053 Last = V;
00054 Real yy = function(x[V]) - YY;
00055 Finish = (fabs(yy) <= accY) || (Captured && fabs(x[L]-x[U]) <= accX );
00056 y[V] = vpol*yy;
00057 }
00058
00059 void OneDimSolve::HFlip() { hpol=-hpol; State(U,C,L); }
00060
00061 void OneDimSolve::VFlip()
00062 { vpol = -vpol; y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2]; }
00063
00064 void OneDimSolve::Flip()
00065 {
00066 hpol=-hpol; vpol=-vpol; State(U,C,L);
00067 y[0] = -y[0]; y[1] = -y[1]; y[2] = -y[2];
00068 }
00069
00070 void OneDimSolve::State(int I, int J, int K) { L=I; C=J; U=K; }
00071
00072 void OneDimSolve::Linear(int I, int J, int K)
00073 {
00074 x[J] = (x[I]*y[K] - x[K]*y[I])/(y[K] - y[I]);
00075
00076 }
00077
00078 void OneDimSolve::Quadratic(int I, int J, int K)
00079 {
00080
00081 Real YJK, YIK, YIJ, XKI, XKJ;
00082 YJK = y[J] - y[K]; YIK = y[I] - y[K]; YIJ = y[I] - y[J];
00083 XKI = (x[K] - x[I]);
00084 XKJ = (x[K]*y[J] - x[J]*y[K])/YJK;
00085 if ( square(YJK/YIK)>(x[K] - x[J])/XKI ||
00086 square(YIJ/YIK)>(x[J] - x[I])/XKI )
00087 {
00088 x[I] = XKJ;
00089
00090 }
00091 else
00092 {
00093 XKI = (x[K]*y[I] - x[I]*y[K])/YIK;
00094 x[I] = (XKJ*y[I] - XKI*y[J])/YIJ;
00095
00096 }
00097 }
00098
00099 Real OneDimSolve::Solve(Real Y, Real X, Real Dev, int Lim)
00100 {
00101 enum Loop { start, captured1, captured2, binary, finish };
00102 Tracer et("OneDimSolve::Solve");
00103 lim=Lim; Captured = false;
00104 if ( Dev == 0.0 ) Throw(SolutionException("Dev is zero"));
00105 L=0; C=1; U=2; vpol=1; hpol=1; y[C]=0.0; y[U]=0.0;
00106 if (Dev<0.0) { hpol=-1; Dev = -Dev; }
00107 YY=Y;
00108 x[L] = X;
00109 if (!function.IsValid(X))
00110 Throw(SolutionException("Starting value is invalid"));
00111 Loop TheLoop = start;
00112 for (;;)
00113 {
00114 switch (TheLoop)
00115 {
00116 case start:
00117 LookAt(L); if (Finish) { TheLoop = finish; break; }
00118 if (y[L]>0.0) VFlip();
00119
00120 x[U] = X + Dev * hpol;
00121 if (!function.maxXinf && x[U] > function.maxX)
00122 x[U] = (function.maxX + X) / 2.0;
00123 if (!function.minXinf && x[U] < function.minX)
00124 x[U] = (function.minX + X) / 2.0;
00125
00126 LookAt(U); if (Finish) { TheLoop = finish; break; }
00127 if (y[U] > 0.0) { TheLoop = captured1; Captured = true; break; }
00128 if (y[U] == y[L])
00129 Throw(SolutionException("Function is flat"));
00130 if (y[U] < y[L]) HFlip();
00131 State(L,U,C);
00132 for (i=0; i<20; i++)
00133 {
00134
00135
00136 x[U] = x[C] + Dev * hpol;
00137 if (!function.maxXinf && x[U] > function.maxX)
00138 x[U] = (function.maxX + x[C]) / 2.0;
00139 if (!function.minXinf && x[U] < function.minX)
00140 x[U] = (function.minX + x[C]) / 2.0;
00141
00142 LookAt(U); if (Finish) { TheLoop = finish; break; }
00143 if (y[U] > 0) { TheLoop = captured2; Captured = true; break; }
00144 if (y[U] < y[C])
00145 Throw(SolutionException("Function is not monotone"));
00146 Dev *= 2.0;
00147 State(C,U,L);
00148 }
00149 if (TheLoop != start ) break;
00150 Throw(SolutionException("Cannot locate a crossing point"));
00151
00152 case captured1:
00153
00154
00155 Linear(L,C,U);
00156
00157 LookAt(C); if (Finish) { TheLoop = finish; break; }
00158 if (y[C] > 0.0) Flip();
00159 if (y[C] < 0.5*y[L]) { State(C,L,U); TheLoop = binary; break; }
00160
00161 case captured2:
00162
00163
00164 Quadratic(L,C,U);
00165
00166 State(C,L,U);
00167 if ((x[C] - x[L])*hpol <= 0.0 || (x[C] - x[U])*hpol >= 0.0)
00168 { TheLoop = captured1; break; }
00169 LookAt(C); if (Finish) { TheLoop = finish; break; }
00170
00171 if (y[C] > 0.0) Flip();
00172 if (y[C] > 0.5*y[L]) { TheLoop = captured2; break; }
00173 else { State(C,L,U); TheLoop = captured1; break; }
00174
00175 case binary:
00176
00177
00178 for (i=3; i; i--)
00179 {
00180 x[C] = 0.5*(x[L]+x[U]);
00181 LookAt(C); if (Finish) { TheLoop = finish; break; }
00182 if (y[C]>0.0) State(L,U,C); else State(C,L,U);
00183 }
00184 if (TheLoop != binary) break;
00185 TheLoop = captured1; break;
00186
00187 case finish:
00188 return x[Last];
00189
00190 }
00191 }
00192 }
00193
00194 bool R1_R1::IsValid(Real X)
00195 {
00196 Set(X);
00197 return (minXinf || x > minX) && (maxXinf || x < maxX);
00198 }
00199
00200 #ifdef use_namespace
00201 }
00202 #endif
00203
00204