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1 | // Created on: 1991-08-22 |
2 | // Created by: Laurent PAINNOT |
3 | // Copyright (c) 1991-1999 Matra Datavision |
4 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
5 | // |
6 | // This file is part of Open CASCADE Technology software library. |
7 | // |
8 | // This library is free software; you can redistribute it and/or modify it under |
9 | // the terms of the GNU Lesser General Public License version 2.1 as published |
10 | // by the Free Software Foundation, with special exception defined in the file |
11 | // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
12 | // distribution for complete text of the license and disclaimer of any warranty. |
13 | // |
14 | // Alternatively, this file may be used under the terms of Open CASCADE |
15 | // commercial license or contractual agreement. |
16 | |
17 | #ifndef _math_Uzawa_HeaderFile |
18 | #define _math_Uzawa_HeaderFile |
19 | |
20 | #include <Standard.hxx> |
21 | #include <Standard_DefineAlloc.hxx> |
22 | #include <Standard_Handle.hxx> |
23 | |
24 | #include <math_Vector.hxx> |
25 | #include <math_Matrix.hxx> |
26 | #include <Standard_Integer.hxx> |
27 | #include <Standard_Boolean.hxx> |
28 | #include <Standard_Real.hxx> |
29 | #include <Standard_OStream.hxx> |
30 | class StdFail_NotDone; |
31 | class Standard_ConstructionError; |
32 | class math_Matrix; |
33 | |
34 | |
35 | //! This class implements a system resolution C*X = B with |
36 | //! an approach solution X0. There are no conditions on the |
37 | //! number of equations. The algorithm used is the Uzawa |
38 | //! algorithm. It is possible to have equal or inequal (<) |
39 | //! equations to solve. The resolution is done with a |
40 | //! minimization of Norm(X-X0). |
41 | //! If there are only equal equations, the resolution is directly |
42 | //! done and is similar to Gauss resolution with an optimisation |
43 | //! because the matrix is a symmetric matrix. |
44 | //! (The resolution is done with Crout algorithm) |
45 | class math_Uzawa |
46 | { |
47 | public: |
48 | |
49 | DEFINE_STANDARD_ALLOC |
50 | |
51 | |
52 | //! Given an input matrix Cont, two input vectors Secont |
53 | //! and StartingPoint, it solves Cont*X = Secont (only |
54 | //! = equations) with a minimization of Norme(X-X0). |
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55 | //! The maximum iterations number allowed is fixed to |
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56 | //! NbIterations. |
57 | //! The tolerance EpsLic is fixed for the dual variable |
58 | //! convergence. The tolerance EpsLix is used for the |
59 | //! convergence of X. |
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60 | //! Exception ConstructionError is raised if the line number |
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61 | //! of Cont is different from the length of Secont. |
62 | Standard_EXPORT math_Uzawa(const math_Matrix& Cont, const math_Vector& Secont, const math_Vector& StartingPoint, const Standard_Real EpsLix = 1.0e-06, const Standard_Real EpsLic = 1.0e-06, const Standard_Integer NbIterations = 500); |
63 | |
64 | //! Given an input matrix Cont, two input vectors Secont |
65 | //! and StartingPoint, it solves Cont*X = Secont (the Nce |
66 | //! first equations are equal equations and the Nci last |
67 | //! equations are inequalities <) with a minimization |
68 | //! of Norme(X-X0). |
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69 | //! The maximum iterations number allowed is fixed to |
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70 | //! NbIterations. |
71 | //! The tolerance EpsLic is fixed for the dual variable |
72 | //! convergence. The tolerance EpsLix is used for the |
73 | //! convergence of X. |
74 | //! There are no conditions on Nce and Nci. |
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75 | //! Exception ConstructionError is raised if the line number |
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76 | //! of Cont is different from the length of Secont and from |
77 | //! Nce + Nci. |
78 | Standard_EXPORT math_Uzawa(const math_Matrix& Cont, const math_Vector& Secont, const math_Vector& StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix = 1.0e-06, const Standard_Real EpsLic = 1.0e-06, const Standard_Integer NbIterations = 500); |
79 | |
80 | //! Returns true if the computations are successful, otherwise returns false. |
81 | Standard_Boolean IsDone() const; |
82 | |
83 | //! Returns the vector solution of the system above. |
84 | //! An exception is raised if NotDone. |
85 | const math_Vector& Value() const; |
86 | |
87 | //! Returns the initial error Cont*StartingPoint-Secont. |
88 | //! An exception is raised if NotDone. |
89 | const math_Vector& InitialError() const; |
90 | |
91 | //! returns the duale variables V of the systeme. |
92 | Standard_EXPORT void Duale (math_Vector& V) const; |
93 | |
94 | //! Returns the difference between X solution and the |
95 | //! StartingPoint. |
96 | //! An exception is raised if NotDone. |
97 | const math_Vector& Error() const; |
98 | |
99 | //! returns the number of iterations really done. |
100 | //! An exception is raised if NotDone. |
101 | Standard_Integer NbIterations() const; |
102 | |
103 | //! returns the inverse matrix of (C * Transposed(C)). |
104 | //! This result is needed for the computation of the gradient |
105 | //! when approximating a curve. |
106 | const math_Matrix& InverseCont() const; |
107 | |
108 | //! Prints information on the current state of the object. |
109 | Standard_EXPORT void Dump (Standard_OStream& o) const; |
110 | |
111 | |
112 | |
113 | |
114 | protected: |
115 | |
116 | |
117 | //! Is used internally by the two constructors above. |
118 | Standard_EXPORT void Perform (const math_Matrix& Cont, const math_Vector& Secont, const math_Vector& StartingPoint, const Standard_Integer Nci, const Standard_Integer Nce, const Standard_Real EpsLix = 1.0e-06, const Standard_Real EpsLic = 1.0e-06, const Standard_Integer NbIterations = 500); |
119 | |
120 | |
121 | |
122 | |
123 | private: |
124 | |
125 | |
126 | |
127 | math_Vector Resul; |
128 | math_Vector Erruza; |
129 | math_Vector Errinit; |
130 | math_Vector Vardua; |
131 | math_Matrix CTCinv; |
132 | Standard_Integer NbIter; |
133 | Standard_Boolean Done; |
134 | |
135 | |
136 | }; |
137 | |
138 | |
139 | #include <math_Uzawa.lxx> |
140 | |
141 | |
142 | |
143 | |
144 | |
145 | #endif // _math_Uzawa_HeaderFile |