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1 | -- Created on: 1991-05-14 |
2 | -- Created by: Laurent PAINNOT |
3 | -- Copyright (c) 1991-1999 Matra Datavision |
4 | -- Copyright (c) 1999-2012 OPEN CASCADE SAS |
5 | -- |
6 | -- The content of this file is subject to the Open CASCADE Technology Public |
7 | -- License Version 6.5 (the "License"). You may not use the content of this file |
8 | -- except in compliance with the License. Please obtain a copy of the License |
9 | -- at http://www.opencascade.org and read it completely before using this file. |
10 | -- |
11 | -- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its |
12 | -- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France. |
13 | -- |
14 | -- The Original Code and all software distributed under the License is |
15 | -- distributed on an "AS IS" basis, without warranty of any kind, and the |
16 | -- Initial Developer hereby disclaims all such warranties, including without |
17 | -- limitation, any warranties of merchantability, fitness for a particular |
18 | -- purpose or non-infringement. Please see the License for the specific terms |
19 | -- and conditions governing the rights and limitations under the License. |
20 | |
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21 | |
22 | |
23 | |
24 | class FunctionSetRoot from math |
25 | ---Purpose: The math_FunctionSetRoot class calculates the root |
26 | -- of a set of N functions of M variables (N<M, N=M or N>M). Knowing |
27 | -- an initial guess of the solution and using a minimization algorithm, a search |
28 | -- is made in the Newton direction and then in the Gradient direction if there |
29 | -- is no success in the Newton direction. This algorithm can also be |
30 | -- used for functions minimization. Knowledge of all the partial |
31 | -- derivatives (the Jacobian) is required. |
32 | |
33 | |
34 | uses Vector from math, |
35 | Matrix from math, |
36 | IntegerVector from math, |
37 | FunctionSetWithDerivatives from math, |
38 | OStream from Standard |
39 | |
40 | raises NotDone from StdFail, |
41 | DimensionError from Standard |
42 | |
43 | is |
44 | |
45 | Create(F: in out FunctionSetWithDerivatives; |
46 | Tolerance : Vector; |
47 | NbIterations: Integer = 100) |
48 | ---Purpose: is used in a sub-class to initialize correctly all the fields |
49 | -- of this class. |
50 | -- The range (1, F.NbVariables()) must be especially |
51 | -- respected for all vectors and matrix declarations. |
52 | |
53 | returns FunctionSetRoot from math; |
54 | |
55 | |
56 | |
57 | Create(F: in out FunctionSetWithDerivatives; |
58 | NbIterations: Integer = 100) |
59 | ---Purpose: is used in a sub-class to initialize correctly all the fields |
60 | -- of this class. |
61 | -- The range (1, F.NbVariables()) must be especially |
62 | -- respected for all vectors and matrix declarations. |
63 | -- The method SetTolerance must be called after this |
64 | -- constructor. |
65 | |
66 | returns FunctionSetRoot from math; |
67 | |
68 | |
69 | |
70 | Create(F: in out FunctionSetWithDerivatives; StartingPoint: Vector; |
71 | Tolerance: Vector; NbIterations: Integer = 100) |
72 | ---Purpose: is used to improve the root of the function F |
73 | -- from the initial guess StartingPoint. |
74 | -- The maximum number of iterations allowed is given by |
75 | -- NbIterations. |
76 | -- In this case, the solution is found when: |
77 | -- abs(Xi - Xi-1)(j) <= Tolerance(j) for all unknowns. |
78 | |
79 | returns FunctionSetRoot from math; |
80 | |
81 | |
82 | |
83 | Create(F: in out FunctionSetWithDerivatives; StartingPoint: Vector; |
84 | Tolerance: Vector; infBound, supBound: Vector; |
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85 | NbIterations: Integer = 100; theStopOnDivergent : Boolean from Standard = Standard_False) |
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86 | ---Purpose: is used to improve the root of the function F |
87 | -- from the initial guess StartingPoint. |
88 | -- The maximum number of iterations allowed is given |
89 | -- by NbIterations. |
90 | -- In this case, the solution is found when: |
91 | -- abs(Xi - Xi-1) <= Tolerance for all unknowns. |
92 | |
93 | returns FunctionSetRoot from math; |
94 | |
95 | |
96 | |
97 | Delete(me:out) is virtual; |
98 | ---C++: alias "Standard_EXPORT virtual ~math_FunctionSetRoot(){Delete();}" |
99 | |
100 | SetTolerance(me: in out; Tolerance: Vector) |
101 | ---Purpose: Initializes the tolerance values. |
102 | |
103 | is static; |
104 | |
105 | |
106 | |
107 | Perform(me: in out; F: in out FunctionSetWithDerivatives; |
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108 | StartingPoint: Vector; |
109 | infBound, supBound: Vector; theStopOnDivergent : Boolean from Standard = Standard_False) |
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110 | ---Purpose: Improves the root of function F from the initial guess |
111 | -- StartingPoint. infBound and supBound may be given to constrain the solution. |
112 | -- Warning |
113 | -- This method is called when computation of the solution is |
114 | -- not performed by the constructors. |
115 | |
116 | is static; |
117 | |
118 | |
119 | IsSolutionReached(me: in out; F: in out FunctionSetWithDerivatives) |
120 | ---Purpose: This routine is called at the end of each iteration |
121 | -- to check if the solution was found. It can be redefined |
122 | -- in a sub-class to implement a specific test to stop the |
123 | -- iterations. |
124 | -- In this case, the solution is found when: |
125 | -- abs(Xi - Xi-1) <= Tolerance for all unknowns. |
126 | |
127 | returns Boolean is virtual; |
128 | |
129 | |
130 | IsDone(me) |
131 | ---Purpose: |
132 | -- Returns true if the computations are successful, otherwise returns false. |
133 | ---C++: inline |
134 | returns Boolean |
135 | is static; |
136 | |
137 | |
138 | NbIterations(me) |
139 | ---Purpose: Returns the number of iterations really done |
140 | -- during the computation of the root. |
141 | -- Exception NotDone is raised if the root was not found. |
142 | ---C++: inline |
143 | returns Integer |
144 | raises NotDone |
145 | is static; |
146 | |
147 | |
148 | StateNumber(me) |
149 | ---Purpose: returns the stateNumber (as returned by |
150 | -- F.GetStateNumber()) associated to the root found. |
151 | ---C++: inline |
152 | returns Integer |
153 | raises NotDone |
154 | is static; |
155 | |
156 | |
157 | Root(me) |
158 | ---Purpose: Returns the value of the root of function F. |
159 | -- Exception NotDone is raised if the root was not found. |
160 | ---C++: inline |
161 | ---C++: return const& |
162 | returns Vector |
163 | raises NotDone, |
164 | DimensionError |
165 | is static; |
166 | |
167 | |
168 | Root(me; Root: out Vector) |
169 | ---Purpose: Outputs the root vector in Root. |
170 | -- Exception NotDone is raised if the root was not found. |
171 | -- Exception DimensionError is raised if the range of Root |
172 | -- is not equal to the range of the StartingPoint. |
173 | |
174 | raises NotDone from StdFail |
175 | is static; |
176 | |
177 | |
178 | Derivative(me) |
179 | ---Purpose: Returns the matrix value of the derivative at the root. |
180 | -- Exception NotDone is raised if the root was not found. |
181 | ---C++: inline |
182 | ---C++: return const& |
183 | |
184 | returns Matrix |
185 | raises NotDone |
186 | is static; |
187 | |
188 | |
189 | Derivative(me; Der: out Matrix) |
190 | ---Purpose: outputs the matrix value of the derivative |
191 | -- at the root in Der. |
192 | -- Exception NotDone is raised if the root was not found. |
193 | -- Exception DimensionError is raised if the column range |
194 | -- of <Der> is not equal to the range of the startingPoint. |
195 | ---C++: inline |
196 | |
197 | raises NotDone, |
198 | DimensionError |
199 | is static; |
200 | |
201 | |
202 | |
203 | FunctionSetErrors(me) |
204 | ---Purpose: returns the vector value of the error done |
205 | -- on the functions at the root. |
206 | -- Exception NotDone is raised if the root was not found. |
207 | ---C++: inline |
208 | ---C++: return const& |
209 | |
210 | returns Vector |
211 | raises NotDone |
212 | is static; |
213 | |
214 | |
215 | FunctionSetErrors(me; Err: out Vector) |
216 | ---Purpose: outputs the vector value of the error done |
217 | -- on the functions at the root in Err. |
218 | -- Exception NotDone is raised if the root was not found. |
219 | -- Exception DimensionError is raised if the range of Err |
220 | -- is not equal to the range of the StartingPoint. |
221 | |
222 | raises NotDone, |
223 | DimensionError |
224 | is static; |
225 | |
226 | |
227 | Dump(me; o: in out OStream) |
228 | ---Purpose: Prints on the stream o information on the current state |
229 | -- of the object. |
230 | -- Is used to redefine the operator <<. |
231 | |
232 | is static; |
233 | |
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234 | IsDivergent(me) |
235 | returns Boolean |
236 | is static; |
237 | |
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238 | |
239 | fields |
240 | |
241 | Done : Boolean; |
242 | Delta : Vector is protected; |
243 | Sol : Vector is protected; |
244 | DF : Matrix is protected; |
245 | Kount : Integer; |
246 | State : Integer; |
247 | Tol : Vector is protected; |
248 | Itermax : Integer; |
249 | |
250 | -- working tables |
251 | |
252 | InfBound : Vector; |
253 | SupBound : Vector; |
254 | |
255 | SolSave : Vector; |
256 | GH : Vector; |
257 | DH : Vector; |
258 | DHSave : Vector; |
259 | FF : Vector; |
260 | PreviousSolution : Vector; |
261 | Save : Vector; |
262 | Constraints : IntegerVector; |
263 | Temp1 : Vector; |
264 | Temp2 : Vector; |
265 | Temp3 : Vector; |
266 | Temp4 : Vector; |
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267 | myIsDivergent : Boolean from Standard; |
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268 | |
269 | end FunctionSetRoot; |