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
|
// This file is generated by WOK (CPPExt).
// Please do not edit this file; modify original file instead.
// The copyright and license terms as defined for the original file apply to
// this header file considered to be the "object code" form of the original source.
#ifndef _math_FunctionSetRoot_HeaderFile
#define _math_FunctionSetRoot_HeaderFile
#ifndef _Standard_HeaderFile
#include <Standard.hxx>
#endif
#ifndef _Standard_Macro_HeaderFile
#include <Standard_Macro.hxx>
#endif
#ifndef _Standard_Boolean_HeaderFile
#include <Standard_Boolean.hxx>
#endif
#ifndef _math_Vector_HeaderFile
#include <math_Vector.hxx>
#endif
#ifndef _math_Matrix_HeaderFile
#include <math_Matrix.hxx>
#endif
#ifndef _Standard_Integer_HeaderFile
#include <Standard_Integer.hxx>
#endif
#ifndef _math_IntegerVector_HeaderFile
#include <math_IntegerVector.hxx>
#endif
#ifndef _Standard_OStream_HeaderFile
#include <Standard_OStream.hxx>
#endif
class StdFail_NotDone;
class Standard_DimensionError;
class math_FunctionSetWithDerivatives;
class math_Vector;
class math_Matrix;
//! The math_FunctionSetRoot class calculates the root <br>
//! of a set of N functions of M variables (N<M, N=M or N>M). Knowing <br>
//! an initial guess of the solution and using a minimization algorithm, a search <br>
//! is made in the Newton direction and then in the Gradient direction if there <br>
//! is no success in the Newton direction. This algorithm can also be <br>
//! used for functions minimization. Knowledge of all the partial <br>
//! derivatives (the Jacobian) is required. <br>
class math_FunctionSetRoot {
public:
void* operator new(size_t,void* anAddress)
{
return anAddress;
}
void* operator new(size_t size)
{
return Standard::Allocate(size);
}
void operator delete(void *anAddress)
{
if (anAddress) Standard::Free((Standard_Address&)anAddress);
}
//! is used in a sub-class to initialize correctly all the fields <br>
//! of this class. <br>
//! The range (1, F.NbVariables()) must be especially <br>
//! respected for all vectors and matrix declarations. <br>
Standard_EXPORT math_FunctionSetRoot(math_FunctionSetWithDerivatives& F,const math_Vector& Tolerance,const Standard_Integer NbIterations = 100);
//! is used in a sub-class to initialize correctly all the fields <br>
//! of this class. <br>
//! The range (1, F.NbVariables()) must be especially <br>
//! respected for all vectors and matrix declarations. <br>
//! The method SetTolerance must be called after this <br>
//! constructor. <br>
Standard_EXPORT math_FunctionSetRoot(math_FunctionSetWithDerivatives& F,const Standard_Integer NbIterations = 100);
//! is used to improve the root of the function F <br>
//! from the initial guess StartingPoint. <br>
//! The maximum number of iterations allowed is given by <br>
//! NbIterations. <br>
//! In this case, the solution is found when: <br>
//! abs(Xi - Xi-1)(j) <= Tolerance(j) for all unknowns. <br>
Standard_EXPORT math_FunctionSetRoot(math_FunctionSetWithDerivatives& F,const math_Vector& StartingPoint,const math_Vector& Tolerance,const Standard_Integer NbIterations = 100);
//! is used to improve the root of the function F <br>
//! from the initial guess StartingPoint. <br>
//! The maximum number of iterations allowed is given <br>
//! by NbIterations. <br>
//! In this case, the solution is found when: <br>
//! abs(Xi - Xi-1) <= Tolerance for all unknowns. <br>
Standard_EXPORT math_FunctionSetRoot(math_FunctionSetWithDerivatives& F,const math_Vector& StartingPoint,const math_Vector& Tolerance,const math_Vector& infBound,const math_Vector& supBound,const Standard_Integer NbIterations = 100);
Standard_EXPORT virtual void Delete() ;
Standard_EXPORT virtual ~math_FunctionSetRoot(){Delete();}
//! Initializes the tolerance values. <br>
Standard_EXPORT void SetTolerance(const math_Vector& Tolerance) ;
//! Improves the root of function F from the initial guess <br>
//! StartingPoint. infBound and supBound may be given to constrain the solution. <br>
//! Warning <br>
//! This method is called when computation of the solution is <br>
//! not performed by the constructors. <br>
Standard_EXPORT void Perform(math_FunctionSetWithDerivatives& F,const math_Vector& StartingPoint,const math_Vector& infBound,const math_Vector& supBound) ;
//! This routine is called at the end of each iteration <br>
//! to check if the solution was found. It can be redefined <br>
//! in a sub-class to implement a specific test to stop the <br>
//! iterations. <br>
//! In this case, the solution is found when: <br>
//! abs(Xi - Xi-1) <= Tolerance for all unknowns. <br>
Standard_EXPORT virtual Standard_Boolean IsSolutionReached(math_FunctionSetWithDerivatives& F) ;
//! Returns true if the computations are successful, otherwise returns false. <br>
Standard_Boolean IsDone() const;
//! Returns the number of iterations really done <br>
//! during the computation of the root. <br>
//! Exception NotDone is raised if the root was not found. <br>
Standard_Integer NbIterations() const;
//! returns the stateNumber (as returned by <br>
//! F.GetStateNumber()) associated to the root found. <br>
Standard_Integer StateNumber() const;
//! Returns the value of the root of function F. <br>
//! Exception NotDone is raised if the root was not found. <br>
const math_Vector& Root() const;
//! Outputs the root vector in Root. <br>
//! Exception NotDone is raised if the root was not found. <br>
//! Exception DimensionError is raised if the range of Root <br>
//! is not equal to the range of the StartingPoint. <br>
Standard_EXPORT void Root(math_Vector& Root) const;
//! Returns the matrix value of the derivative at the root. <br>
//! Exception NotDone is raised if the root was not found. <br>
const math_Matrix& Derivative() const;
//! outputs the matrix value of the derivative <br>
//! at the root in Der. <br>
//! Exception NotDone is raised if the root was not found. <br>
//! Exception DimensionError is raised if the column range <br>
//! of <Der> is not equal to the range of the startingPoint. <br>
void Derivative(math_Matrix& Der) const;
//! returns the vector value of the error done <br>
//! on the functions at the root. <br>
//! Exception NotDone is raised if the root was not found. <br>
const math_Vector& FunctionSetErrors() const;
//! outputs the vector value of the error done <br>
//! on the functions at the root in Err. <br>
//! Exception NotDone is raised if the root was not found. <br>
//! Exception DimensionError is raised if the range of Err <br>
//! is not equal to the range of the StartingPoint. <br>
Standard_EXPORT void FunctionSetErrors(math_Vector& Err) const;
//! Prints on the stream o information on the current state <br>
//! of the object. <br>
//! Is used to redefine the operator <<. <br>
Standard_EXPORT void Dump(Standard_OStream& o) const;
protected:
math_Vector Delta;
math_Vector Sol;
math_Matrix DF;
math_Vector Tol;
private:
Standard_Boolean Done;
Standard_Integer Kount;
Standard_Integer State;
Standard_Integer Itermax;
math_Vector InfBound;
math_Vector SupBound;
math_Vector SolSave;
math_Vector GH;
math_Vector DH;
math_Vector DHSave;
math_Vector FF;
math_Vector PreviousSolution;
math_Vector Save;
math_IntegerVector Constraints;
math_Vector Temp1;
math_Vector Temp2;
math_Vector Temp3;
math_Vector Temp4;
};
#include <math_FunctionSetRoot.lxx>
// other Inline functions and methods (like "C++: function call" methods)
#endif
|
