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: G4ErrorMatrix.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 HepMatrix class |
---|
32 | |
---|
33 | // History: |
---|
34 | // - Imported from CLHEP and modified: P. Arce May 2007 |
---|
35 | // -------------------------------------------------------------------- |
---|
36 | |
---|
37 | #ifndef G4ErrorMatrix_hh |
---|
38 | #define G4ErrorMatrix_hh |
---|
39 | |
---|
40 | #include <vector> |
---|
41 | |
---|
42 | class G4ErrorSymMatrix; |
---|
43 | |
---|
44 | typedef std::vector<G4double >::iterator G4ErrorMatrixIter; |
---|
45 | typedef std::vector<G4double >::const_iterator G4ErrorMatrixConstIter; |
---|
46 | |
---|
47 | class G4ErrorMatrix |
---|
48 | { |
---|
49 | |
---|
50 | public: // with description |
---|
51 | |
---|
52 | G4ErrorMatrix(); |
---|
53 | // Default constructor. Gives 0 x 0 matrix. |
---|
54 | // Another G4ErrorMatrix can be assigned to it. |
---|
55 | |
---|
56 | G4ErrorMatrix(G4int p, G4int q); |
---|
57 | // Constructor. Gives an unitialized p x q matrix. |
---|
58 | |
---|
59 | G4ErrorMatrix(G4int p, G4int q, G4int i); |
---|
60 | // Constructor. Gives an initialized p x q matrix. |
---|
61 | // If i=0, it is initialized to all 0. If i=1, the diagonal elements |
---|
62 | // are set to 1.0. |
---|
63 | |
---|
64 | G4ErrorMatrix(const G4ErrorMatrix &m1); |
---|
65 | // Copy constructor. |
---|
66 | |
---|
67 | G4ErrorMatrix(const G4ErrorSymMatrix &m1); |
---|
68 | // Constructors from G4ErrorSymG4ErrorMatrix, DiagG4ErrorMatrix and Vector. |
---|
69 | |
---|
70 | virtual ~G4ErrorMatrix(); |
---|
71 | // Destructor. |
---|
72 | |
---|
73 | inline virtual G4int num_row() const; |
---|
74 | // Returns the number of rows. |
---|
75 | |
---|
76 | inline virtual G4int num_col() const; |
---|
77 | // Returns the number of columns. |
---|
78 | |
---|
79 | inline virtual const G4double & operator()(G4int row, G4int col) const; |
---|
80 | inline virtual G4double & operator()(G4int row, G4int col); |
---|
81 | // Read or write a matrix element. |
---|
82 | // ** Note that the indexing starts from (1,1). ** |
---|
83 | |
---|
84 | G4ErrorMatrix & operator *= (G4double t); |
---|
85 | // Multiply a G4ErrorMatrix by a floating number. |
---|
86 | |
---|
87 | G4ErrorMatrix & operator /= (G4double t); |
---|
88 | // Divide a G4ErrorMatrix by a floating number. |
---|
89 | |
---|
90 | G4ErrorMatrix & operator += ( const G4ErrorMatrix &m2); |
---|
91 | G4ErrorMatrix & operator += ( const G4ErrorSymMatrix &m2); |
---|
92 | G4ErrorMatrix & operator -= ( const G4ErrorMatrix &m2); |
---|
93 | G4ErrorMatrix & operator -= ( const G4ErrorSymMatrix &m2); |
---|
94 | // Add or subtract a G4ErrorMatrix. |
---|
95 | // When adding/subtracting Vector, G4ErrorMatrix must have num_col of one. |
---|
96 | |
---|
97 | G4ErrorMatrix & operator = ( const G4ErrorMatrix &m2); |
---|
98 | G4ErrorMatrix & operator = ( const G4ErrorSymMatrix &m2); |
---|
99 | // Assignment operators. |
---|
100 | |
---|
101 | G4ErrorMatrix operator- () const; |
---|
102 | // unary minus, ie. flip the sign of each element. |
---|
103 | |
---|
104 | G4ErrorMatrix apply(G4double (*f)(G4double, G4int, G4int)) const; |
---|
105 | // Apply a function to all elements of the matrix. |
---|
106 | |
---|
107 | G4ErrorMatrix T() const; |
---|
108 | // Returns the transpose of a G4ErrorMatrix. |
---|
109 | |
---|
110 | G4ErrorMatrix sub(G4int min_row, G4int max_row, |
---|
111 | G4int min_col, G4int max_col) const; |
---|
112 | // Returns a sub matrix of a G4ErrorMatrix. |
---|
113 | // WARNING: rows and columns are numbered from 1 |
---|
114 | |
---|
115 | void sub(G4int row, G4int col, const G4ErrorMatrix &m1); |
---|
116 | // Sub matrix of this G4ErrorMatrix is replaced with m1. |
---|
117 | // WARNING: rows and columns are numbered from 1 |
---|
118 | |
---|
119 | inline G4ErrorMatrix inverse(G4int& ierr) const; |
---|
120 | // Invert a G4ErrorMatrix. G4ErrorMatrix must be square and is not changed. |
---|
121 | // Returns ierr = 0 (zero) when successful, otherwise non-zero. |
---|
122 | |
---|
123 | virtual void invert(G4int& ierr); |
---|
124 | // Invert a G4ErrorMatrix. G4ErrorMatrix must be square. |
---|
125 | // N.B. the contents of the matrix are replaced by the inverse. |
---|
126 | // Returns ierr = 0 (zero) when successful, otherwise non-zero. |
---|
127 | // This method has less overhead then inverse(). |
---|
128 | |
---|
129 | G4double determinant() const; |
---|
130 | // calculate the determinant of the matrix. |
---|
131 | |
---|
132 | G4double trace() const; |
---|
133 | // calculate the trace of the matrix (sum of diagonal elements). |
---|
134 | |
---|
135 | class G4ErrorMatrix_row |
---|
136 | { |
---|
137 | typedef std::vector<G4double >::const_iterator G4ErrorMatrixConstIter; |
---|
138 | public: |
---|
139 | inline G4ErrorMatrix_row(G4ErrorMatrix&,G4int); |
---|
140 | G4double & operator[](G4int); |
---|
141 | private: |
---|
142 | G4ErrorMatrix& _a; |
---|
143 | G4int _r; |
---|
144 | }; |
---|
145 | class G4ErrorMatrix_row_const |
---|
146 | { |
---|
147 | public: |
---|
148 | inline G4ErrorMatrix_row_const (const G4ErrorMatrix&,G4int); |
---|
149 | const G4double & operator[](G4int) const; |
---|
150 | private: |
---|
151 | const G4ErrorMatrix& _a; |
---|
152 | G4int _r; |
---|
153 | }; |
---|
154 | // helper classes for implementing m[i][j] |
---|
155 | |
---|
156 | inline G4ErrorMatrix_row operator[] (G4int); |
---|
157 | inline const G4ErrorMatrix_row_const operator[] (G4int) const; |
---|
158 | // Read or write a matrix element. |
---|
159 | // While it may not look like it, you simply do m[i][j] to get an element. |
---|
160 | // ** Note that the indexing starts from [0][0]. ** |
---|
161 | |
---|
162 | protected: |
---|
163 | |
---|
164 | virtual inline G4int num_size() const; |
---|
165 | virtual void invertHaywood4(G4int& ierr); |
---|
166 | virtual void invertHaywood5(G4int& ierr); |
---|
167 | virtual void invertHaywood6(G4int& ierr); |
---|
168 | |
---|
169 | public: |
---|
170 | |
---|
171 | static void error(const char *s); |
---|
172 | |
---|
173 | private: |
---|
174 | |
---|
175 | friend class G4ErrorMatrix_row; |
---|
176 | friend class G4ErrorMatrix_row_const; |
---|
177 | friend class G4ErrorSymMatrix; |
---|
178 | // Friend classes. |
---|
179 | |
---|
180 | friend G4ErrorMatrix operator+(const G4ErrorMatrix &m1, |
---|
181 | const G4ErrorMatrix &m2); |
---|
182 | friend G4ErrorMatrix operator-(const G4ErrorMatrix &m1, |
---|
183 | const G4ErrorMatrix &m2); |
---|
184 | friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1, |
---|
185 | const G4ErrorMatrix &m2); |
---|
186 | friend G4ErrorMatrix operator*(const G4ErrorMatrix &m1, |
---|
187 | const G4ErrorSymMatrix &m2); |
---|
188 | friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
189 | const G4ErrorMatrix &m2); |
---|
190 | friend G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, |
---|
191 | const G4ErrorSymMatrix &m2); |
---|
192 | // Multiply a G4ErrorMatrix by a G4ErrorMatrix or Vector. |
---|
193 | |
---|
194 | // solve the system of linear eq |
---|
195 | |
---|
196 | friend G4ErrorMatrix qr_solve(G4ErrorMatrix *, const G4ErrorMatrix &b); |
---|
197 | friend void tridiagonal(G4ErrorSymMatrix *a,G4ErrorMatrix *hsm); |
---|
198 | friend void row_house(G4ErrorMatrix *,const G4ErrorMatrix &, G4double, |
---|
199 | G4int, G4int, G4int, G4int); |
---|
200 | friend void back_solve(const G4ErrorMatrix &R, G4ErrorMatrix *b); |
---|
201 | friend void col_givens(G4ErrorMatrix *A, G4double c, |
---|
202 | G4double s, G4int k1, G4int k2, |
---|
203 | G4int rowmin, G4int rowmax); |
---|
204 | // Does a column Givens update. |
---|
205 | |
---|
206 | friend void row_givens(G4ErrorMatrix *A, G4double c, |
---|
207 | G4double s, G4int k1, G4int k2, |
---|
208 | G4int colmin, G4int colmax); |
---|
209 | friend void col_house(G4ErrorMatrix *,const G4ErrorMatrix &, G4double, |
---|
210 | G4int, G4int, G4int, G4int); |
---|
211 | friend void house_with_update(G4ErrorMatrix *a,G4int row,G4int col); |
---|
212 | friend void house_with_update(G4ErrorMatrix *a,G4ErrorMatrix *v, |
---|
213 | G4int row, G4int col); |
---|
214 | friend void house_with_update2(G4ErrorSymMatrix *a,G4ErrorMatrix *v, |
---|
215 | G4int row, G4int col); |
---|
216 | |
---|
217 | G4int dfact_matrix(G4double &det, G4int *ir); |
---|
218 | // factorize the matrix. If successful, the return code is 0. On |
---|
219 | // return, det is the determinant and ir[] is row-interchange |
---|
220 | // matrix. See CERNLIB's DFACT routine. |
---|
221 | |
---|
222 | G4int dfinv_matrix(G4int *ir); |
---|
223 | // invert the matrix. See CERNLIB DFINV. |
---|
224 | |
---|
225 | std::vector<G4double > m; |
---|
226 | |
---|
227 | G4int nrow, ncol; |
---|
228 | G4int size; |
---|
229 | }; |
---|
230 | |
---|
231 | // Operations other than member functions for G4ErrorMatrix |
---|
232 | |
---|
233 | G4ErrorMatrix operator*(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2); |
---|
234 | G4ErrorMatrix operator*(G4double t, const G4ErrorMatrix &m1); |
---|
235 | G4ErrorMatrix operator*(const G4ErrorMatrix &m1, G4double t); |
---|
236 | // Multiplication operators |
---|
237 | // Note that m *= m1 is always faster than m = m * m1. |
---|
238 | |
---|
239 | G4ErrorMatrix operator/(const G4ErrorMatrix &m1, G4double t); |
---|
240 | // m = m1 / t. (m /= t is faster if you can use it.) |
---|
241 | |
---|
242 | G4ErrorMatrix operator+(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2); |
---|
243 | // m = m1 + m2; |
---|
244 | // Note that m += m1 is always faster than m = m + m1. |
---|
245 | |
---|
246 | G4ErrorMatrix operator-(const G4ErrorMatrix &m1, const G4ErrorMatrix &m2); |
---|
247 | // m = m1 - m2; |
---|
248 | // Note that m -= m1 is always faster than m = m - m1. |
---|
249 | |
---|
250 | G4ErrorMatrix dsum(const G4ErrorMatrix&, const G4ErrorMatrix&); |
---|
251 | // Direct sum of two matrices. The direct sum of A and B is the matrix |
---|
252 | // A 0 |
---|
253 | // 0 B |
---|
254 | |
---|
255 | std::ostream& operator<<(std::ostream &s, const G4ErrorMatrix &q); |
---|
256 | // Read in, write out G4ErrorMatrix into a stream. |
---|
257 | |
---|
258 | // |
---|
259 | // Specialized linear algebra functions |
---|
260 | // |
---|
261 | |
---|
262 | G4ErrorMatrix qr_solve(const G4ErrorMatrix &A, const G4ErrorMatrix &b); |
---|
263 | G4ErrorMatrix qr_solve(G4ErrorMatrix *A, const G4ErrorMatrix &b); |
---|
264 | // Works like backsolve, except matrix does not need to be upper |
---|
265 | // triangular. For nonsquare matrix, it solves in the least square sense. |
---|
266 | |
---|
267 | G4ErrorMatrix qr_inverse(const G4ErrorMatrix &A); |
---|
268 | G4ErrorMatrix qr_inverse(G4ErrorMatrix *A); |
---|
269 | // Finds the inverse of a matrix using QR decomposition. Note, often what |
---|
270 | // you really want is solve or backsolve, they can be much quicker than |
---|
271 | // inverse in many calculations. |
---|
272 | |
---|
273 | |
---|
274 | void qr_decomp(G4ErrorMatrix *A, G4ErrorMatrix *hsm); |
---|
275 | G4ErrorMatrix qr_decomp(G4ErrorMatrix *A); |
---|
276 | // Does a QR decomposition of a matrix. |
---|
277 | |
---|
278 | void back_solve(const G4ErrorMatrix &R, G4ErrorMatrix *b); |
---|
279 | // Solves R*x = b where R is upper triangular. Also has a variation that |
---|
280 | // solves a number of equations of this form in one step, where b is a matrix |
---|
281 | // with each column a different vector. See also solve. |
---|
282 | |
---|
283 | void col_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4double vnormsq, |
---|
284 | G4int row, G4int col, G4int row_start, G4int col_start); |
---|
285 | void col_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4int row, G4int col, |
---|
286 | G4int row_start, G4int col_start); |
---|
287 | // Does a column Householder update. |
---|
288 | |
---|
289 | void col_givens(G4ErrorMatrix *A, G4double c, G4double s, |
---|
290 | G4int k1, G4int k2, G4int row_min=1, G4int row_max=0); |
---|
291 | // do a column Givens update |
---|
292 | |
---|
293 | void row_givens(G4ErrorMatrix *A, G4double c, G4double s, |
---|
294 | G4int k1, G4int k2, G4int col_min=1, G4int col_max=0); |
---|
295 | // do a row Givens update |
---|
296 | |
---|
297 | void givens(G4double a, G4double b, G4double *c, G4double *s); |
---|
298 | // algorithm 5.1.5 in Golub and Van Loan |
---|
299 | |
---|
300 | // Returns a Householder vector to zero elements. |
---|
301 | |
---|
302 | void house_with_update(G4ErrorMatrix *a, G4int row=1, G4int col=1); |
---|
303 | void house_with_update(G4ErrorMatrix *a, G4ErrorMatrix *v, |
---|
304 | G4int row=1, G4int col=1); |
---|
305 | // Finds and does Householder reflection on matrix. |
---|
306 | |
---|
307 | void row_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4double vnormsq, |
---|
308 | G4int row, G4int col, G4int row_start, G4int col_start); |
---|
309 | void row_house(G4ErrorMatrix *a, const G4ErrorMatrix &v, G4int row, G4int col, |
---|
310 | G4int row_start, G4int col_start); |
---|
311 | // Does a row Householder update. |
---|
312 | |
---|
313 | #include "G4ErrorMatrix.icc" |
---|
314 | |
---|
315 | #endif |
---|