source: trunk/source/error_propagation/include/G4ErrorSymMatrix.hh@ 1305

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1//
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4// * *
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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 *
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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
42class G4ErrorMatrix;
43
44class 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
243std::ostream& operator<<(std::ostream &s, const G4ErrorSymMatrix &q);
244// Write out Matrix, G4ErrorSymMatrix, DiagMatrix and Vector into ostream.
245
246G4ErrorMatrix operator*(const G4ErrorMatrix &m1,
247 const G4ErrorSymMatrix &m2);
248G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,
249 const G4ErrorMatrix &m2);
250G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1,
251 const G4ErrorSymMatrix &m2);
252G4ErrorSymMatrix operator*(G4double t, const G4ErrorSymMatrix &s1);
253G4ErrorSymMatrix operator*(const G4ErrorSymMatrix &s1, G4double t);
254// Multiplication operators.
255// Note that m *= m1 is always faster than m = m * m1
256
257G4ErrorSymMatrix operator/(const G4ErrorSymMatrix &m1, G4double t);
258// s = s1 / t. (s /= t is faster if you can use it.)
259
260G4ErrorMatrix operator+(const G4ErrorMatrix &m1,
261 const G4ErrorSymMatrix &s2);
262G4ErrorMatrix operator+(const G4ErrorSymMatrix &s1,
263 const G4ErrorMatrix &m2);
264G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &s1,
265 const G4ErrorSymMatrix &s2);
266// Addition operators
267
268G4ErrorMatrix operator-(const G4ErrorMatrix &m1,
269 const G4ErrorSymMatrix &s2);
270G4ErrorMatrix operator-(const G4ErrorSymMatrix &m1,
271 const G4ErrorMatrix &m2);
272G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &s1,
273 const G4ErrorSymMatrix &s2);
274// subtraction operators
275
276G4ErrorSymMatrix dsum(const G4ErrorSymMatrix &s1,
277 const G4ErrorSymMatrix &s2);
278// Direct sum of two symmetric matrices;
279
280G4double condition(const G4ErrorSymMatrix &m);
281// Find the conditon number of a symmetric matrix.
282
283void diag_step(G4ErrorSymMatrix *t, G4int begin, G4int end);
284void diag_step(G4ErrorSymMatrix *t, G4ErrorMatrix *u, G4int begin, G4int end);
285// Implicit symmetric QR step with Wilkinson Shift
286
287G4ErrorMatrix diagonalize(G4ErrorSymMatrix *s);
288// Diagonalize a symmetric matrix.
289// It returns the matrix U so that s_old = U * s_diag * U.T()
290
291void house_with_update2(G4ErrorSymMatrix *a, G4ErrorMatrix *v,
292 G4int row=1, G4int col=1);
293// Finds and does Householder reflection on matrix.
294
295void tridiagonal(G4ErrorSymMatrix *a, G4ErrorMatrix *hsm);
296G4ErrorMatrix tridiagonal(G4ErrorSymMatrix *a);
297// Does a Householder tridiagonalization of a symmetric matrix.
298
299#include "G4ErrorSymMatrix.icc"
300
301#endif
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