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1 | // Created on: 1991-08-07 |
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_Householder_HeaderFile |
18 | #define _math_Householder_HeaderFile |
19 | |
20 | #include <Standard.hxx> |
21 | #include <Standard_DefineAlloc.hxx> |
22 | #include <Standard_Handle.hxx> |
23 | |
24 | #include <math_Matrix.hxx> |
25 | #include <Standard_Boolean.hxx> |
26 | #include <Standard_Integer.hxx> |
27 | #include <Standard_Real.hxx> |
28 | #include <math_Vector.hxx> |
29 | #include <Standard_OStream.hxx> |
30 | class StdFail_NotDone; |
31 | class Standard_OutOfRange; |
32 | class Standard_DimensionError; |
33 | class Standard_ConstructionError; |
34 | class math_Matrix; |
35 | |
36 | |
37 | //! This class implements the least square solution of a set of |
38 | //! linear equations of m unknowns (n >= m) using the Householder |
39 | //! method. It solves A.X = B. |
40 | //! This algorithm has more numerical stability than |
41 | //! GaussLeastSquare but is longer. |
42 | //! It must be used if the matrix is singular or nearly singular. |
43 | //! It is about 16% longer than GaussLeastSquare if there is only |
44 | //! one member B to solve. |
45 | //! It is about 30% longer if there are twenty B members to solve. |
46 | class math_Householder |
47 | { |
48 | public: |
49 | |
50 | DEFINE_STANDARD_ALLOC |
51 | |
52 | |
53 | //! Given an input matrix A with n>= m, given an input matrix B |
54 | //! this constructor performs the least square resolution of |
55 | //! the set of linear equations A.X = B for each column of B. |
56 | //! If a column norm is less than EPS, the resolution can't |
57 | //! be done. |
58 | //! Exception DimensionError is raised if the row number of B |
59 | //! is different from the A row number. |
60 | Standard_EXPORT math_Householder(const math_Matrix& A, const math_Matrix& B, const Standard_Real EPS = 1.0e-20); |
61 | |
62 | //! Given an input matrix A with n>= m, given an input matrix B |
63 | //! this constructor performs the least square resolution of |
64 | //! the set of linear equations A.X = B for each column of B. |
65 | //! If a column norm is less than EPS, the resolution can't |
66 | //! be done. |
67 | //! Exception DimensionError is raised if the row number of B |
68 | //! is different from the A row number. |
69 | Standard_EXPORT math_Householder(const math_Matrix& A, const math_Matrix& B, const Standard_Integer lowerArow, const Standard_Integer upperArow, const Standard_Integer lowerAcol, const Standard_Integer upperAcol, const Standard_Real EPS = 1.0e-20); |
70 | |
71 | //! Given an input matrix A with n>= m, given an input vector B |
72 | //! this constructor performs the least square resolution of |
73 | //! the set of linear equations A.X = B. |
74 | //! If a column norm is less than EPS, the resolution can't |
75 | //! be done. |
76 | //! Exception DimensionError is raised if the length of B |
77 | //! is different from the A row number. |
78 | Standard_EXPORT math_Householder(const math_Matrix& A, const math_Vector& B, const Standard_Real EPS = 1.0e-20); |
79 | |
80 | //! Returns true if the computations are successful, otherwise returns false. |
81 | Standard_Boolean IsDone() const; |
82 | |
83 | //! Given the integer Index, this routine returns the |
84 | //! corresponding least square solution sol. |
85 | //! Exception NotDone is raised if the resolution has not be |
86 | //! done. |
87 | //! Exception OutOfRange is raised if Index <=0 or |
88 | //! Index is more than the number of columns of B. |
89 | void Value (math_Vector& sol, const Standard_Integer Index = 1) const; |
90 | |
91 | //! Returns the matrix sol of all the solutions of the system |
92 | //! A.X = B. |
93 | //! Exception NotDone is raised is the resolution has not be |
94 | //! done. |
95 | const math_Matrix& AllValues() const; |
96 | |
97 | //! Prints informations on the current state of the object. |
98 | Standard_EXPORT void Dump (Standard_OStream& o) const; |
99 | |
100 | |
101 | |
102 | |
103 | protected: |
104 | |
105 | |
106 | //! This method is used internally for each constructor |
107 | //! above and can't be used directly. |
108 | Standard_EXPORT void Perform (const math_Matrix& A, const math_Matrix& B, const Standard_Real EPS); |
109 | |
110 | |
111 | |
112 | |
113 | private: |
114 | |
115 | |
116 | |
117 | math_Matrix Sol; |
118 | math_Matrix Q; |
119 | Standard_Boolean Done; |
120 | Standard_Integer mylowerArow; |
121 | Standard_Integer myupperArow; |
122 | Standard_Integer mylowerAcol; |
123 | Standard_Integer myupperAcol; |
124 | |
125 | |
126 | }; |
127 | |
128 | |
129 | #include <math_Householder.lxx> |
130 | |
131 | |
132 | |
133 | |
134 | |
135 | #endif // _math_Householder_HeaderFile |