1 | // |
---|
2 | // ******************************************************************** |
---|
3 | // * License and Disclaimer * |
---|
4 | // * * |
---|
5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
7 | // * conditions of the Geant4 Software License, included in the file * |
---|
8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
9 | // * include a list of copyright holders. * |
---|
10 | // * * |
---|
11 | // * Neither the authors of this software system, nor their employing * |
---|
12 | // * institutes,nor the agencies providing financial support for this * |
---|
13 | // * work make any representation or warranty, express or implied, * |
---|
14 | // * regarding this software system or assume any liability for its * |
---|
15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
16 | // * for the full disclaimer and the limitation of liability. * |
---|
17 | // * * |
---|
18 | // * This code implementation is the result of the scientific and * |
---|
19 | // * technical work of the GEANT4 collaboration. * |
---|
20 | // * By using, copying, modifying or distributing the software (or * |
---|
21 | // * any work based on the software) you agree to acknowledge its * |
---|
22 | // * use in resulting scientific publications, and indicate your * |
---|
23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
24 | // ******************************************************************** |
---|
25 | // |
---|
26 | // $Id: G4ErrorSymMatrix.hh,v 1.2 2007/06/01 12:43:28 gcosmo Exp $ |
---|
27 | // GEANT4 tag $Name: geant4-09-03 $ |
---|
28 | // |
---|
29 | // Class Description: |
---|
30 | // |
---|
31 | // Simplified version of CLHEP HepSymMatrix class. |
---|
32 | |
---|
33 | // History: |
---|
34 | // - Imported from CLHEP and modified: P. Arce May 2007 |
---|
35 | // -------------------------------------------------------------------- |
---|
36 | |
---|
37 | #ifndef G4ErrorSymMatrix_hh |
---|
38 | #define G4ErrorSymMatrix_hh |
---|
39 | |
---|
40 | #include <vector> |
---|
41 | |
---|
42 | class G4ErrorMatrix; |
---|
43 | |
---|
44 | class G4ErrorSymMatrix |
---|
45 | { |
---|
46 | public: //with description |
---|
47 | |
---|
48 | inline G4ErrorSymMatrix(); |
---|
49 | // Default constructor. Gives 0x0 symmetric matrix. |
---|
50 | // Another G4ErrorSymMatrix can be assigned to it. |
---|
51 | |
---|
52 | explicit G4ErrorSymMatrix(G4int p); |
---|
53 | G4ErrorSymMatrix(G4int p, G4int); |
---|
54 | // Constructor. Gives p x p symmetric matrix. |
---|
55 | // With a second argument, the matrix is initialized. 0 means a zero |
---|
56 | // matrix, 1 means the identity matrix. |
---|
57 | |
---|
58 | G4ErrorSymMatrix(const G4ErrorSymMatrix &m1); |
---|
59 | // Copy constructor. |
---|
60 | |
---|
61 | // Constructor from DiagMatrix |
---|
62 | |
---|
63 | virtual ~G4ErrorSymMatrix(); |
---|
64 | // Destructor. |
---|
65 | |
---|
66 | inline G4int num_row() const; |
---|
67 | inline G4int num_col() const; |
---|
68 | // Returns number of rows/columns. |
---|
69 | |
---|
70 | const G4double & operator()(G4int row, G4int col) const; |
---|
71 | G4double & operator()(G4int row, G4int col); |
---|
72 | // Read and write a G4ErrorSymMatrix element. |
---|
73 | // ** Note that indexing starts from (1,1). ** |
---|
74 | |
---|
75 | const G4double & fast(G4int row, G4int col) const; |
---|
76 | G4double & fast(G4int row, G4int col); |
---|
77 | // fast element access. |
---|
78 | // Must be row>=col; |
---|
79 | // ** Note that indexing starts from (1,1). ** |
---|
80 | |
---|
81 | void assign(const G4ErrorMatrix &m2); |
---|
82 | // Assigns m2 to s, assuming m2 is a symmetric matrix. |
---|
83 | |
---|
84 | void assign(const G4ErrorSymMatrix &m2); |
---|
85 | // Another form of assignment. For consistency. |
---|
86 | |
---|
87 | G4ErrorSymMatrix & operator*=(G4double t); |
---|
88 | // Multiply a G4ErrorSymMatrix by a floating number. |
---|
89 | |
---|
90 | G4ErrorSymMatrix & operator/=(G4double t); |
---|
91 | // Divide a G4ErrorSymMatrix by a floating number. |
---|
92 | |
---|
93 | G4ErrorSymMatrix & operator+=( const G4ErrorSymMatrix &m2); |
---|
94 | G4ErrorSymMatrix & operator-=( const G4ErrorSymMatrix &m2); |
---|
95 | // Add or subtract a G4ErrorSymMatrix. |
---|
96 | |
---|
97 | G4ErrorSymMatrix & operator=( const G4ErrorSymMatrix &m2); |
---|
98 | // Assignment operators. Notice that there is no G4ErrorSymMatrix = Matrix. |
---|
99 | |
---|
100 | G4ErrorSymMatrix operator- () const; |
---|
101 | // unary minus, ie. flip the sign of each element. |
---|
102 | |
---|
103 | G4ErrorSymMatrix T() const; |
---|
104 | // Returns the transpose of a G4ErrorSymMatrix (which is itself). |
---|
105 | |
---|
106 | G4ErrorSymMatrix apply(G4double (*f)(G4double, G4int, G4int)) const; |
---|
107 | // Apply a function to all elements of the matrix. |
---|
108 | |
---|
109 | G4ErrorSymMatrix similarity(const G4ErrorMatrix &m1) const; |
---|
110 | G4ErrorSymMatrix similarity(const G4ErrorSymMatrix &m1) const; |
---|
111 | // Returns m1*s*m1.T(). |
---|
112 | |
---|
113 | G4ErrorSymMatrix similarityT(const G4ErrorMatrix &m1) const; |
---|
114 | // temporary. test of new similarity. |
---|
115 | // Returns m1.T()*s*m1. |
---|
116 | |
---|
117 | G4ErrorSymMatrix sub(G4int min_row, G4int max_row) const; |
---|
118 | // Returns a sub matrix of a G4ErrorSymMatrix. |
---|
119 | |
---|
120 | void sub(G4int row, const G4ErrorSymMatrix &m1); |
---|
121 | // Sub matrix of this G4ErrorSymMatrix is replaced with m1. |
---|
122 | |
---|
123 | G4ErrorSymMatrix sub(G4int min_row, G4int max_row); |
---|
124 | // SGI CC bug. I have to have both with/without const. I should not need |
---|
125 | // one without const. |
---|
126 | |
---|
127 | inline G4ErrorSymMatrix inverse(G4int &ifail) const; |
---|
128 | // Invert a Matrix. The matrix is not changed |
---|
129 | // Returns 0 when successful, otherwise non-zero. |
---|
130 | |
---|
131 | void invert(G4int &ifail); |
---|
132 | // Invert a Matrix. |
---|
133 | // N.B. the contents of the matrix are replaced by the inverse. |
---|
134 | // Returns ierr = 0 when successful, otherwise non-zero. |
---|
135 | // This method has less overhead then inverse(). |
---|
136 | |
---|
137 | G4double determinant() const; |
---|
138 | // calculate the determinant of the matrix. |
---|
139 | |
---|
140 | G4double trace() const; |
---|
141 | // calculate the trace of the matrix (sum of diagonal elements). |
---|
142 | |
---|
143 | class G4ErrorSymMatrix_row |
---|
144 | { |
---|
145 | public: |
---|
146 | inline G4ErrorSymMatrix_row(G4ErrorSymMatrix&,G4int); |
---|
147 | inline G4double & operator[](G4int); |
---|
148 | private: |
---|
149 | G4ErrorSymMatrix& _a; |
---|
150 | G4int _r; |
---|
151 | }; |
---|
152 | class G4ErrorSymMatrix_row_const |
---|
153 | { |
---|
154 | public: |
---|
155 | inline G4ErrorSymMatrix_row_const(const G4ErrorSymMatrix&,G4int); |
---|
156 | inline const G4double & operator[](G4int) const; |
---|
157 | private: |
---|
158 | const G4ErrorSymMatrix& _a; |
---|
159 | G4int _r; |
---|
160 | }; |
---|
161 | // helper class to implement m[i][j] |
---|
162 | |
---|
163 | inline G4ErrorSymMatrix_row operator[] (G4int); |
---|
164 | inline G4ErrorSymMatrix_row_const operator[] (G4int) const; |
---|
165 | // Read or write a matrix element. |
---|
166 | // While it may not look like it, you simply do m[i][j] to get an |
---|
167 | // element. |
---|
168 | // ** Note that the indexing starts from [0][0]. ** |
---|
169 | |
---|
170 | // Special-case inversions for 5x5 and 6x6 symmetric positive definite: |
---|
171 | // These set ifail=0 and invert if the matrix was positive definite; |
---|
172 | // otherwise ifail=1 and the matrix is left unaltered. |
---|
173 | |
---|
174 | void invertCholesky5 (G4int &ifail); |
---|
175 | void invertCholesky6 (G4int &ifail); |
---|
176 | |
---|
177 | // Inversions for 5x5 and 6x6 forcing use of specific methods: The |
---|
178 | // behavior (though not the speed) will be identical to invert(ifail). |
---|
179 | |
---|
180 | void invertHaywood4 (G4int & ifail); |
---|
181 | void invertHaywood5 (G4int &ifail); |
---|
182 | void invertHaywood6 (G4int &ifail); |
---|
183 | void invertBunchKaufman (G4int &ifail); |
---|
184 | |
---|
185 | protected: |
---|
186 | |
---|
187 | inline G4int num_size() const; |
---|
188 | |
---|
189 | private: |
---|
190 | |
---|
191 | friend class G4ErrorSymMatrix_row; |
---|
192 | friend class G4ErrorSymMatrix_row_const; |
---|
193 | friend class G4ErrorMatrix; |
---|
194 | |
---|
195 | friend void tridiagonal(G4ErrorSymMatrix *a, G4ErrorMatrix *hsm); |
---|
196 | friend G4double condition(const G4ErrorSymMatrix &m); |
---|
197 | friend void diag_step(G4ErrorSymMatrix *t, G4int begin, G4int end); |
---|
198 | friend void diag_step(G4ErrorSymMatrix *t, G4ErrorMatrix *u, |
---|
199 | G4int begin, G4int end); |
---|
200 | friend G4ErrorMatrix diagonalize(G4ErrorSymMatrix *s); |
---|
201 | friend void house_with_update2(G4ErrorSymMatrix *a, G4ErrorMatrix *v, |
---|
202 | G4int row, G4int col); |
---|
203 | |
---|
204 | friend G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &m1, |
---|
205 | const G4ErrorSymMatrix &m2); |
---|
206 | friend G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &m1, |
---|
207 | const G4ErrorSymMatrix &m2); |
---|
208 | friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
209 | const G4ErrorSymMatrix &m2); |
---|
210 | friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
211 | const G4ErrorMatrix &m2); |
---|
212 | friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1, |
---|
213 | const G4ErrorSymMatrix &m2); |
---|
214 | // Multiply a Matrix by a Matrix or Vector. |
---|
215 | |
---|
216 | // Returns v * v.T(); |
---|
217 | |
---|
218 | std::vector<G4double > m; |
---|
219 | |
---|
220 | G4int nrow; |
---|
221 | G4int size; // total number of elements |
---|
222 | |
---|
223 | static G4double posDefFraction5x5; |
---|
224 | static G4double adjustment5x5; |
---|
225 | static const G4double CHOLESKY_THRESHOLD_5x5; |
---|
226 | static const G4double CHOLESKY_CREEP_5x5; |
---|
227 | |
---|
228 | static G4double posDefFraction6x6; |
---|
229 | static G4double adjustment6x6; |
---|
230 | static const G4double CHOLESKY_THRESHOLD_6x6; |
---|
231 | static const G4double CHOLESKY_CREEP_6x6; |
---|
232 | |
---|
233 | void invert4 (G4int & ifail); |
---|
234 | void invert5 (G4int & ifail); |
---|
235 | void invert6 (G4int & ifail); |
---|
236 | }; |
---|
237 | |
---|
238 | // |
---|
239 | // Operations other than member functions for Matrix, G4ErrorSymMatrix, |
---|
240 | // DiagMatrix and Vectors |
---|
241 | // |
---|
242 | |
---|
243 | std::ostream& operator<<(std::ostream &s, const G4ErrorSymMatrix &q); |
---|
244 | // Write out Matrix, G4ErrorSymMatrix, DiagMatrix and Vector into ostream. |
---|
245 | |
---|
246 | G4ErrorMatrix operator*(const G4ErrorMatrix &m1, |
---|
247 | const G4ErrorSymMatrix &m2); |
---|
248 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
249 | const G4ErrorMatrix &m2); |
---|
250 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
251 | const G4ErrorSymMatrix &m2); |
---|
252 | G4ErrorSymMatrix operator*(G4double t, const G4ErrorSymMatrix &s1); |
---|
253 | G4ErrorSymMatrix operator*(const G4ErrorSymMatrix &s1, G4double t); |
---|
254 | // Multiplication operators. |
---|
255 | // Note that m *= m1 is always faster than m = m * m1 |
---|
256 | |
---|
257 | G4ErrorSymMatrix operator/(const G4ErrorSymMatrix &m1, G4double t); |
---|
258 | // s = s1 / t. (s /= t is faster if you can use it.) |
---|
259 | |
---|
260 | G4ErrorMatrix operator+(const G4ErrorMatrix &m1, |
---|
261 | const G4ErrorSymMatrix &s2); |
---|
262 | G4ErrorMatrix operator+(const G4ErrorSymMatrix &s1, |
---|
263 | const G4ErrorMatrix &m2); |
---|
264 | G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &s1, |
---|
265 | const G4ErrorSymMatrix &s2); |
---|
266 | // Addition operators |
---|
267 | |
---|
268 | G4ErrorMatrix operator-(const G4ErrorMatrix &m1, |
---|
269 | const G4ErrorSymMatrix &s2); |
---|
270 | G4ErrorMatrix operator-(const G4ErrorSymMatrix &m1, |
---|
271 | const G4ErrorMatrix &m2); |
---|
272 | G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &s1, |
---|
273 | const G4ErrorSymMatrix &s2); |
---|
274 | // subtraction operators |
---|
275 | |
---|
276 | G4ErrorSymMatrix dsum(const G4ErrorSymMatrix &s1, |
---|
277 | const G4ErrorSymMatrix &s2); |
---|
278 | // Direct sum of two symmetric matrices; |
---|
279 | |
---|
280 | G4double condition(const G4ErrorSymMatrix &m); |
---|
281 | // Find the conditon number of a symmetric matrix. |
---|
282 | |
---|
283 | void diag_step(G4ErrorSymMatrix *t, G4int begin, G4int end); |
---|
284 | void diag_step(G4ErrorSymMatrix *t, G4ErrorMatrix *u, G4int begin, G4int end); |
---|
285 | // Implicit symmetric QR step with Wilkinson Shift |
---|
286 | |
---|
287 | G4ErrorMatrix diagonalize(G4ErrorSymMatrix *s); |
---|
288 | // Diagonalize a symmetric matrix. |
---|
289 | // It returns the matrix U so that s_old = U * s_diag * U.T() |
---|
290 | |
---|
291 | void house_with_update2(G4ErrorSymMatrix *a, G4ErrorMatrix *v, |
---|
292 | G4int row=1, G4int col=1); |
---|
293 | // Finds and does Householder reflection on matrix. |
---|
294 | |
---|
295 | void tridiagonal(G4ErrorSymMatrix *a, G4ErrorMatrix *hsm); |
---|
296 | G4ErrorMatrix tridiagonal(G4ErrorSymMatrix *a); |
---|
297 | // Does a Householder tridiagonalization of a symmetric matrix. |
---|
298 | |
---|
299 | #include "G4ErrorSymMatrix.icc" |
---|
300 | |
---|
301 | #endif |
---|