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32 // This file is a modified version of ilut.h from ITL.
33 // See http://osl.iu.edu/research/itl/
34 // Following the corresponding Copyright notice.
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63 
64 #ifndef GMM_PRECOND_ILUT_H
65 #define GMM_PRECOND_ILUT_H
66 
67 /**@file gmm_precond_ilut.h
68    @author  Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu>
69    @date June 5, 2003.
70    @brief ILUT:  Incomplete LU with threshold and K fill-in Preconditioner.
71 */
72 
73 /*
74   Performane comparing for SSOR, ILU and ILUT based on sherman 5 matrix
75   in Harwell-Boeing collection on Sun Ultra 30 UPA/PCI (UltraSPARC-II 296MHz)
76   Preconditioner & Factorization time  &  Number of Iteration \\ \hline
77   SSOR        &   0.010577  & 41 \\
78   ILU         &   0.019336  & 32 \\
79   ILUT with 0 fill-in and threshold of 1.0e-6 & 0.343612 &  23 \\
80   ILUT with 5 fill-in and threshold of 1.0e-6 & 0.343612 &  18 \\ \hline
81 */
82 
83 #include "gmm_precond.h"
84 
85 namespace gmm {
86 
87   template<typename T> struct elt_rsvector_value_less_ {
operatorelt_rsvector_value_less_88     inline bool operator()(const elt_rsvector_<T>& a,
89 			   const elt_rsvector_<T>& b) const
90     { return (gmm::abs(a.e) > gmm::abs(b.e)); }
91   };
92 
93   /** Incomplete LU with threshold and K fill-in Preconditioner.
94 
95   The algorithm of ILUT(A, 0, 1.0e-6) is slower than ILU(A). If No
96   fill-in is arrowed, you can use ILU instead of ILUT.
97 
98   Notes: The idea under a concrete Preconditioner such as ilut is to
99   create a Preconditioner object to use in iterative methods.
100   */
101   template <typename Matrix>
102   class ilut_precond  {
103   public :
104     typedef typename linalg_traits<Matrix>::value_type value_type;
105     typedef wsvector<value_type> _wsvector;
106     typedef rsvector<value_type> _rsvector;
107     typedef row_matrix<_rsvector> LU_Matrix;
108 
109     bool invert;
110     LU_Matrix L, U;
111 
112   protected:
113     size_type K;
114     double eps;
115 
116     template<typename M> void do_ilut(const M&, row_major);
117     void do_ilut(const Matrix&, col_major);
118 
119   public:
120     void build_with(const Matrix& A, int k_ = -1, double eps_ = double(-1)) {
121       if (k_ >= 0) K = k_;
122       if (eps_ >= double(0)) eps = eps_;
123       invert = false;
124       gmm::resize(L, mat_nrows(A), mat_ncols(A));
125       gmm::resize(U, mat_nrows(A), mat_ncols(A));
126       do_ilut(A, typename principal_orientation_type<typename
127 	      linalg_traits<Matrix>::sub_orientation>::potype());
128     }
ilut_precond(const Matrix & A,int k_,double eps_)129     ilut_precond(const Matrix& A, int k_, double eps_)
130       : L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)),
131 	K(k_), eps(eps_) { build_with(A); }
ilut_precond(size_type k_,double eps_)132     ilut_precond(size_type k_, double eps_) :  K(k_), eps(eps_) {}
ilut_precond(void)133     ilut_precond(void) { K = 10; eps = 1E-7; }
memsize()134     size_type memsize() const {
135       return sizeof(*this) + (nnz(U)+nnz(L))*sizeof(value_type);
136     }
137   };
138 
139   template<typename Matrix> template<typename M>
do_ilut(const M & A,row_major)140   void ilut_precond<Matrix>::do_ilut(const M& A, row_major) {
141     typedef value_type T;
142     typedef typename number_traits<T>::magnitude_type R;
143 
144     size_type n = mat_nrows(A);
145     if (n == 0) return;
146     std::vector<T> indiag(n);
147     _wsvector w(mat_ncols(A));
148     _rsvector ww(mat_ncols(A)), wL(mat_ncols(A)), wU(mat_ncols(A));
149     T tmp;
150     gmm::clear(U); gmm::clear(L);
151     R prec = default_tol(R());
152     R max_pivot = gmm::abs(A(0,0)) * prec;
153 
154     for (size_type i = 0; i < n; ++i) {
155       gmm::copy(mat_const_row(A, i), w);
156       double norm_row = gmm::vect_norm2(w);
157 
158       typename _wsvector::iterator wkold = w.end();
159       for (typename _wsvector::iterator wk = w.begin();
160 	   wk != w.end() && wk->first < i; ) {
161 	size_type k = wk->first;
162 	tmp = (wk->second) * indiag[k];
163 	if (gmm::abs(tmp) < eps * norm_row) w.erase(k);
164 	else { wk->second += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); }
165 	if (wkold == w.end()) wk = w.begin(); else { wk = wkold; ++wk; }
166 	if (wk != w.end() && wk->first == k)
167 	  { if (wkold == w.end()) wkold = w.begin(); else ++wkold; ++wk; }
168       }
169       tmp = w[i];
170 
171       if (gmm::abs(tmp) <= max_pivot) {
172 	GMM_WARNING2("pivot " << i << " too small. try with ilutp ?");
173 	w[i] = tmp = T(1);
174       }
175 
176       max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
177       indiag[i] = T(1) / tmp;
178       gmm::clean(w, eps * norm_row);
179       gmm::copy(w, ww);
180       std::sort(ww.begin(), ww.end(), elt_rsvector_value_less_<T>());
181       typename _rsvector::const_iterator wit = ww.begin(), wite = ww.end();
182 
183       size_type nnl = 0, nnu = 0;
184       wL.base_resize(K); wU.base_resize(K+1);
185       typename _rsvector::iterator witL = wL.begin(), witU = wU.begin();
186       for (; wit != wite; ++wit)
187 	if (wit->c < i) { if (nnl < K) { *witL++ = *wit; ++nnl; } }
188 	else { if (nnu < K  || wit->c == i) { *witU++ = *wit; ++nnu; } }
189       wL.base_resize(nnl); wU.base_resize(nnu);
190       std::sort(wL.begin(), wL.end());
191       std::sort(wU.begin(), wU.end());
192       gmm::copy(wL, L.row(i));
193       gmm::copy(wU, U.row(i));
194     }
195 
196   }
197 
198   template<typename Matrix>
do_ilut(const Matrix & A,col_major)199   void ilut_precond<Matrix>::do_ilut(const Matrix& A, col_major) {
200     do_ilut(gmm::transposed(A), row_major());
201     invert = true;
202   }
203 
204   template <typename Matrix, typename V1, typename V2> inline
mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)205   void mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
206     gmm::copy(v1, v2);
207     if (P.invert) {
208       gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
209       gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
210     }
211     else {
212       gmm::lower_tri_solve(P.L, v2, true);
213       gmm::upper_tri_solve(P.U, v2, false);
214     }
215   }
216 
217   template <typename Matrix, typename V1, typename V2> inline
transposed_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)218   void transposed_mult(const ilut_precond<Matrix>& P,const V1 &v1,V2 &v2) {
219     gmm::copy(v1, v2);
220     if (P.invert) {
221       gmm::lower_tri_solve(P.L, v2, true);
222       gmm::upper_tri_solve(P.U, v2, false);
223     }
224     else {
225       gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
226       gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
227     }
228   }
229 
230   template <typename Matrix, typename V1, typename V2> inline
left_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)231   void left_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
232     copy(v1, v2);
233     if (P.invert) gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
234     else gmm::lower_tri_solve(P.L, v2, true);
235   }
236 
237   template <typename Matrix, typename V1, typename V2> inline
right_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)238   void right_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
239     copy(v1, v2);
240     if (P.invert) gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
241     else gmm::upper_tri_solve(P.U, v2, false);
242   }
243 
244   template <typename Matrix, typename V1, typename V2> inline
transposed_left_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)245   void transposed_left_mult(const ilut_precond<Matrix>& P, const V1 &v1,
246 			    V2 &v2) {
247     copy(v1, v2);
248     if (P.invert) gmm::upper_tri_solve(P.U, v2, false);
249     else gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
250   }
251 
252   template <typename Matrix, typename V1, typename V2> inline
transposed_right_mult(const ilut_precond<Matrix> & P,const V1 & v1,V2 & v2)253   void transposed_right_mult(const ilut_precond<Matrix>& P, const V1 &v1,
254 			     V2 &v2) {
255     copy(v1, v2);
256     if (P.invert) gmm::lower_tri_solve(P.L, v2, true);
257     else gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
258   }
259 
260 }
261 
262 #endif
263 
264