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7c3070ec | 1 | |
2 | /*********************************************************************************/ | |
3 | /* Symmetric Band Diagonal matrix with half band width W (+1 for diagonal) */ | |
4 | /* Only lower triangle is stored in the "profile" format */ | |
5 | /* */ | |
6 | /* */ | |
7 | /* Author: ruben.shahoyan@cern.ch */ | |
8 | /* */ | |
9 | /*********************************************************************************/ | |
10 | #include <stdlib.h> | |
11 | #include <stdio.h> | |
12 | #include <iostream> | |
13 | #include <float.h> | |
14 | // | |
15 | #include "TClass.h" | |
16 | #include "TMath.h" | |
17 | #include "AliSymBDMatrix.h" | |
18 | // | |
19 | ||
20 | using namespace std; | |
21 | ||
22 | ClassImp(AliSymBDMatrix) | |
23 | ||
24 | ||
25 | //___________________________________________________________ | |
26 | AliSymBDMatrix::AliSymBDMatrix() | |
27 | : fElems(0) | |
28 | { | |
29 | // def. c-tor | |
30 | fSymmetric = kTRUE; | |
31 | } | |
32 | ||
33 | //___________________________________________________________ | |
34 | AliSymBDMatrix::AliSymBDMatrix(Int_t size, Int_t w) | |
35 | : AliMatrixSq(),fElems(0) | |
36 | { | |
37 | // c-tor for given size | |
38 | // | |
39 | fNcols = size; // number of rows | |
40 | if (w<0) w = 0; | |
41 | if (w>=size) w = size-1; | |
42 | fNrows = w; | |
43 | fRowLwb = w+1; | |
44 | fSymmetric = kTRUE; | |
45 | // | |
46 | // total number of stored elements | |
47 | fNelems = size*(w+1) - w*(w+1)/2; | |
48 | // | |
49 | fElems = new Double_t[fNcols*fRowLwb]; | |
50 | memset(fElems,0,fNcols*fRowLwb*sizeof(Double_t)); | |
51 | // | |
52 | } | |
53 | ||
54 | //___________________________________________________________ | |
55 | AliSymBDMatrix::AliSymBDMatrix(const AliSymBDMatrix &src) | |
56 | : AliMatrixSq(src),fElems(0) | |
57 | { | |
58 | // copy c-tor | |
59 | if (src.GetSize()<1) return; | |
60 | fNcols = src.GetSize(); | |
61 | fNrows = src.GetBandHWidth(); | |
62 | fRowLwb = fNrows+1; | |
63 | fNelems = src.GetNElemsStored(); | |
64 | fElems = new Double_t[fNcols*fRowLwb]; | |
65 | memcpy(fElems,src.fElems,fNcols*fRowLwb*sizeof(Double_t)); | |
66 | // | |
67 | } | |
68 | ||
69 | //___________________________________________________________ | |
70 | AliSymBDMatrix::~AliSymBDMatrix() | |
71 | { | |
72 | // d-tor | |
73 | Clear(); | |
74 | } | |
75 | ||
76 | //___________________________________________________________ | |
77 | AliSymBDMatrix& AliSymBDMatrix::operator=(const AliSymBDMatrix& src) | |
78 | { | |
79 | // assignment | |
80 | // | |
81 | if (this != &src) { | |
82 | TObject::operator=(src); | |
83 | if (fNcols!=src.fNcols) { | |
84 | // recreate the matrix | |
85 | if (fElems) delete[] fElems; | |
86 | fNcols = src.GetSize(); | |
87 | fNrows = src.GetBandHWidth(); | |
88 | fNelems = src.GetNElemsStored(); | |
89 | fRowLwb = src.fRowLwb; | |
90 | fElems = new Double_t[fNcols*fRowLwb]; | |
91 | } | |
92 | memcpy(fElems,src.fElems,fNcols*fRowLwb*sizeof(Double_t)); | |
93 | fSymmetric = kTRUE; | |
94 | } | |
95 | // | |
96 | return *this; | |
97 | // | |
98 | } | |
99 | ||
100 | //___________________________________________________________ | |
101 | void AliSymBDMatrix::Clear(Option_t*) | |
102 | { | |
103 | // clear dynamic part | |
104 | if (fElems) {delete[] fElems; fElems = 0;} | |
105 | // | |
106 | fNelems = fNcols = fNrows = fRowLwb = 0; | |
107 | // | |
108 | } | |
109 | ||
110 | //___________________________________________________________ | |
111 | Float_t AliSymBDMatrix::GetDensity() const | |
112 | { | |
113 | // get fraction of non-zero elements | |
114 | if (!fNelems) return 0; | |
115 | Int_t nel = 0; | |
116 | for (int i=fNelems;i--;) if (TMath::Abs(fElems[i])>DBL_MIN) nel++; | |
117 | return nel/fNelems; | |
118 | } | |
119 | ||
120 | //___________________________________________________________ | |
121 | void AliSymBDMatrix::Print(Option_t* option) const | |
122 | { | |
123 | // print data | |
124 | printf("Symmetric Band-Diagonal Matrix : Size = %d, half bandwidth = %d\n", | |
125 | GetSize(),GetBandHWidth()); | |
126 | TString opt = option; opt.ToLower(); | |
127 | if (opt.IsNull()) return; | |
128 | opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d|"; | |
129 | for (Int_t i=0;i<GetSize();i++) { | |
130 | printf(opt,i); | |
131 | for (Int_t j=TMath::Max(0,i-GetBandHWidth());j<=i;j++) printf("%+.3e|",GetEl(i,j)); | |
132 | printf("\n"); | |
133 | } | |
134 | } | |
135 | ||
136 | //___________________________________________________________ | |
137 | void AliSymBDMatrix::MultiplyByVec(Double_t *vecIn,Double_t *vecOut) const | |
138 | { | |
139 | // fill vecOut by matrix*vecIn | |
140 | // vector should be of the same size as the matrix | |
141 | if (IsDecomposed()) { | |
142 | for (int i=0;i<GetSize();i++) { | |
143 | double sm = 0; | |
144 | int jmax = TMath::Min(GetSize(),i+fRowLwb); | |
145 | for (int j=i+1;j<jmax;j++) sm += vecIn[j]*Query(j,i); | |
146 | vecOut[i] = QueryDiag(i)*(vecIn[i]+sm); | |
147 | } | |
148 | for (int i=GetSize();i--;) { | |
149 | double sm = 0; | |
150 | int jmin = TMath::Max(0,i - GetBandHWidth()); | |
151 | int jmax = i-1; | |
152 | for (int j=jmin;j<jmax;j++) sm += vecOut[j]*Query(i,j); | |
153 | vecOut[i] += sm; | |
154 | } | |
155 | } | |
156 | else { // not decomposed | |
157 | for (int i=GetSize();i--;) { | |
158 | vecOut[i] = 0.0; | |
159 | int jmin = TMath::Max(0,i - GetBandHWidth()); | |
160 | int jmax = TMath::Min(GetSize(),i + fRowLwb); | |
161 | for (int j=jmin;j<jmax;j++) vecOut[i] += vecIn[j]*Query(i,j); | |
162 | } | |
163 | } | |
164 | // | |
165 | } | |
166 | ||
167 | //___________________________________________________________ | |
168 | void AliSymBDMatrix::Reset() | |
169 | { | |
170 | // set all elems to 0 | |
171 | if (fElems) memset(fElems,0,fNcols*fRowLwb*sizeof(Double_t)); | |
c130d912 | 172 | SetDecomposed(kFALSE); |
7c3070ec | 173 | // |
174 | } | |
175 | ||
176 | //___________________________________________________________ | |
177 | void AliSymBDMatrix::AddToRow(Int_t r, Double_t *valc,Int_t *indc,Int_t n) | |
178 | { | |
179 | // add list of elements to row r | |
180 | for (int i=0;i<n;i++) (*this)(r,indc[i]) = valc[i]; | |
181 | } | |
182 | ||
183 | //___________________________________________________________ | |
184 | void AliSymBDMatrix::DecomposeLDLT() | |
185 | { | |
186 | // decomposition to L Diag L^T | |
187 | if (IsDecomposed()) return; | |
188 | // | |
189 | Double_t eps = std::numeric_limits<double>::epsilon()*std::numeric_limits<double>::epsilon(); | |
190 | // | |
191 | Double_t dtmp,gamma=0.0,xi=0.0; | |
192 | int iDiag; | |
193 | // | |
194 | // find max diag and number of non-0 diag.elements | |
195 | for (dtmp=0.0,iDiag=0;iDiag<GetSize();iDiag++) { | |
196 | if ( (dtmp=QueryDiag(iDiag)) <=0.0) break; | |
197 | if (gamma < dtmp) gamma = dtmp; | |
198 | } | |
199 | // | |
200 | // find max. off-diag element | |
201 | for (int ir=1;ir<iDiag;ir++) { | |
202 | for (int ic=ir-GetBandHWidth();ic<ir;ic++) { | |
203 | if (ic<0) continue; | |
204 | dtmp = TMath::Abs(Query(ir,ic)); | |
205 | if (xi<dtmp) xi = dtmp; | |
206 | } | |
207 | } | |
208 | double delta = eps*TMath::Max(1.0,xi+gamma); | |
209 | // | |
210 | double sn = GetSize()>1 ? 1.0/TMath::Sqrt( GetSize()*GetSize() - 1.0) : 1.0; | |
211 | double beta = TMath::Sqrt(TMath::Max(eps,TMath::Max(gamma,xi*sn))); | |
212 | // | |
213 | for (int kr=1;kr<GetSize();kr++) { | |
214 | int colKmin = TMath::Max(0,kr - GetBandHWidth()); | |
215 | double theta = 0.0; | |
216 | // | |
217 | for (int jr=colKmin;jr<=kr;jr++) { | |
218 | int colJmin = TMath::Max(0,jr - GetBandHWidth()); | |
219 | // | |
220 | dtmp = 0.0; | |
221 | for (int i=TMath::Max(colKmin,colJmin);i<jr;i++) | |
222 | dtmp += Query(kr,i)*QueryDiag(i)*Query(jr,i); | |
223 | dtmp = (*this)(kr,jr) -= dtmp; | |
224 | // | |
225 | theta = TMath::Max(theta, TMath::Abs(dtmp)); | |
226 | // | |
227 | if (jr!=kr) { | |
228 | if (TMath::Abs(QueryDiag(jr))>DBL_MIN) (*this)(kr,jr) /= QueryDiag(jr); | |
229 | else (*this)(kr,jr) = 0.0; | |
230 | } | |
231 | else if (kr<iDiag) { | |
232 | dtmp = theta/beta; | |
233 | dtmp *= dtmp; | |
234 | dtmp = TMath::Max(dtmp, delta); | |
235 | (*this)(kr,jr) = TMath::Max( TMath::Abs(Query(kr,jr)), dtmp); | |
236 | } | |
237 | } // jr | |
238 | } // kr | |
239 | // | |
240 | for (int i=0;i<GetSize();i++) { | |
241 | dtmp = QueryDiag(i); | |
242 | if (TMath::Abs(dtmp)>DBL_MIN) DiagElem(i) = 1./dtmp; | |
243 | } | |
244 | // | |
245 | SetDecomposed(); | |
246 | } | |
247 | ||
248 | //___________________________________________________________ | |
249 | void AliSymBDMatrix::Solve(Double_t *rhs) | |
250 | { | |
251 | // solve matrix equation | |
252 | // | |
253 | if (!IsDecomposed()) DecomposeLDLT(); | |
254 | // | |
255 | for (int kr=0;kr<GetSize();kr++) | |
256 | for (int jr=TMath::Max(0,kr-GetBandHWidth());jr<kr;jr++) rhs[kr] -= Query(kr,jr)*rhs[jr]; | |
257 | // | |
258 | for (int kr=GetSize();kr--;) rhs[kr] *= QueryDiag(kr); | |
259 | // | |
260 | for (int kr=GetSize();kr--;) | |
261 | for (int jr=TMath::Max(0,kr - GetBandHWidth());jr<kr;jr++) rhs[jr] -= Query(kr,jr)*rhs[kr]; | |
262 | // | |
263 | } | |
264 | ||
265 | //___________________________________________________________ | |
266 | void AliSymBDMatrix::Solve(const Double_t *rhs,Double_t *sol) | |
267 | { | |
268 | // solve matrix equation | |
269 | memcpy(sol,rhs,GetSize()*sizeof(Double_t)); | |
270 | Solve(sol); | |
271 | // | |
272 | } |