1 | // Copyright (C) 2012 Ryan Curtin |
---|
2 | // Copyright (C) 2012 Conrad Sanderson |
---|
3 | // |
---|
4 | // This Source Code Form is subject to the terms of the Mozilla Public |
---|
5 | // License, v. 2.0. If a copy of the MPL was not distributed with this |
---|
6 | // file, You can obtain one at http://mozilla.org/MPL/2.0/. |
---|
7 | |
---|
8 | |
---|
9 | //! \addtogroup spglue_times |
---|
10 | //! @{ |
---|
11 | |
---|
12 | |
---|
13 | |
---|
14 | template<typename T1, typename T2> |
---|
15 | inline |
---|
16 | void |
---|
17 | spglue_times::apply(SpMat<typename T1::elem_type>& out, const SpGlue<T1,T2,spglue_times>& X) |
---|
18 | { |
---|
19 | arma_extra_debug_sigprint(); |
---|
20 | |
---|
21 | typedef typename T1::elem_type eT; |
---|
22 | |
---|
23 | const SpProxy<T1> pa(X.A); |
---|
24 | const SpProxy<T2> pb(X.B); |
---|
25 | |
---|
26 | const bool is_alias = pa.is_alias(out) || pb.is_alias(out); |
---|
27 | |
---|
28 | if(is_alias == false) |
---|
29 | { |
---|
30 | spglue_times::apply_noalias(out, pa, pb); |
---|
31 | } |
---|
32 | else |
---|
33 | { |
---|
34 | SpMat<eT> tmp; |
---|
35 | spglue_times::apply_noalias(tmp, pa, pb); |
---|
36 | |
---|
37 | out.steal_mem(tmp); |
---|
38 | } |
---|
39 | } |
---|
40 | |
---|
41 | |
---|
42 | |
---|
43 | template<typename eT, typename T1, typename T2> |
---|
44 | arma_hot |
---|
45 | inline |
---|
46 | void |
---|
47 | spglue_times::apply_noalias(SpMat<eT>& c, const SpProxy<T1>& pa, const SpProxy<T2>& pb) |
---|
48 | { |
---|
49 | arma_extra_debug_sigprint(); |
---|
50 | |
---|
51 | const uword x_n_rows = pa.get_n_rows(); |
---|
52 | const uword x_n_cols = pa.get_n_cols(); |
---|
53 | const uword y_n_rows = pb.get_n_rows(); |
---|
54 | const uword y_n_cols = pb.get_n_cols(); |
---|
55 | |
---|
56 | arma_debug_assert_mul_size(x_n_rows, x_n_cols, y_n_rows, y_n_cols, "matrix multiplication"); |
---|
57 | |
---|
58 | // First we must determine the structure of the new matrix (column pointers). |
---|
59 | // This follows the algorithm described in 'Sparse Matrix Multiplication |
---|
60 | // Package (SMMP)' (R.E. Bank and C.C. Douglas, 2001). Their description of |
---|
61 | // "SYMBMM" does not include anything about memory allocation. In addition it |
---|
62 | // does not consider that there may be elements which space may be allocated |
---|
63 | // for but which evaluate to zero anyway. So we have to modify the algorithm |
---|
64 | // to work that way. For the "SYMBMM" implementation we will not determine |
---|
65 | // the row indices but instead just the column pointers. |
---|
66 | |
---|
67 | //SpMat<typename T1::elem_type> c(x_n_rows, y_n_cols); // Initializes col_ptrs to 0. |
---|
68 | c.zeros(x_n_rows, y_n_cols); |
---|
69 | |
---|
70 | //if( (pa.get_n_elem() == 0) || (pb.get_n_elem() == 0) ) |
---|
71 | if( (pa.get_n_nonzero() == 0) || (pb.get_n_nonzero() == 0) ) |
---|
72 | { |
---|
73 | return; |
---|
74 | } |
---|
75 | |
---|
76 | // Auxiliary storage which denotes when items have been found. |
---|
77 | podarray<uword> index(x_n_rows); |
---|
78 | index.fill(x_n_rows); // Fill with invalid links. |
---|
79 | |
---|
80 | typename SpProxy<T2>::const_iterator_type y_it = pb.begin(); |
---|
81 | typename SpProxy<T2>::const_iterator_type y_end = pb.end(); |
---|
82 | |
---|
83 | // SYMBMM: calculate column pointers for resultant matrix to obtain a good |
---|
84 | // upper bound on the number of nonzero elements. |
---|
85 | uword cur_col_length = 0; |
---|
86 | uword last_ind = x_n_rows + 1; |
---|
87 | do |
---|
88 | { |
---|
89 | const uword y_it_row = y_it.row(); |
---|
90 | |
---|
91 | // Look through the column that this point (*y_it) could affect. |
---|
92 | typename SpProxy<T1>::const_iterator_type x_it = pa.begin_col(y_it_row); |
---|
93 | |
---|
94 | while(x_it.col() == y_it_row) |
---|
95 | { |
---|
96 | // A point at x(i, j) and y(j, k) implies a point at c(i, k). |
---|
97 | if(index[x_it.row()] == x_n_rows) |
---|
98 | { |
---|
99 | index[x_it.row()] = last_ind; |
---|
100 | last_ind = x_it.row(); |
---|
101 | ++cur_col_length; |
---|
102 | } |
---|
103 | |
---|
104 | ++x_it; |
---|
105 | } |
---|
106 | |
---|
107 | const uword old_col = y_it.col(); |
---|
108 | ++y_it; |
---|
109 | |
---|
110 | // See if column incremented. |
---|
111 | if(old_col != y_it.col()) |
---|
112 | { |
---|
113 | // Set column pointer (this is not a cumulative count; that is done later). |
---|
114 | access::rw(c.col_ptrs[old_col + 1]) = cur_col_length; |
---|
115 | cur_col_length = 0; |
---|
116 | |
---|
117 | // Return index markers to zero. Use last_ind for traversal. |
---|
118 | while(last_ind != x_n_rows + 1) |
---|
119 | { |
---|
120 | const uword tmp = index[last_ind]; |
---|
121 | index[last_ind] = x_n_rows; |
---|
122 | last_ind = tmp; |
---|
123 | } |
---|
124 | } |
---|
125 | } |
---|
126 | while(y_it != y_end); |
---|
127 | |
---|
128 | // Accumulate column pointers. |
---|
129 | for(uword i = 0; i < c.n_cols; ++i) |
---|
130 | { |
---|
131 | access::rw(c.col_ptrs[i + 1]) += c.col_ptrs[i]; |
---|
132 | } |
---|
133 | |
---|
134 | // Now that we know a decent bound on the number of nonzero elements, allocate |
---|
135 | // the memory and fill it. |
---|
136 | c.mem_resize(c.col_ptrs[c.n_cols]); |
---|
137 | |
---|
138 | // Now the implementation of the NUMBMM algorithm. |
---|
139 | uword cur_pos = 0; // Current position in c matrix. |
---|
140 | podarray<eT> sums(x_n_rows); // Partial sums. |
---|
141 | sums.zeros(); |
---|
142 | |
---|
143 | // setting the size of 'sorted_indices' to x_n_rows is a better-than-nothing guess; |
---|
144 | // the correct minimum size is determined later |
---|
145 | podarray<uword> sorted_indices(x_n_rows); |
---|
146 | |
---|
147 | // last_ind is already set to x_n_rows, and cur_col_length is already set to 0. |
---|
148 | // We will loop through all columns as necessary. |
---|
149 | uword cur_col = 0; |
---|
150 | while(cur_col < c.n_cols) |
---|
151 | { |
---|
152 | // Skip to next column with elements in it. |
---|
153 | while((cur_col < c.n_cols) && (c.col_ptrs[cur_col] == c.col_ptrs[cur_col + 1])) |
---|
154 | { |
---|
155 | // Update current column pointer to actual number of nonzero elements up |
---|
156 | // to this point. |
---|
157 | access::rw(c.col_ptrs[cur_col]) = cur_pos; |
---|
158 | ++cur_col; |
---|
159 | } |
---|
160 | |
---|
161 | if(cur_col == c.n_cols) |
---|
162 | { |
---|
163 | break; |
---|
164 | } |
---|
165 | |
---|
166 | // Update current column pointer. |
---|
167 | access::rw(c.col_ptrs[cur_col]) = cur_pos; |
---|
168 | |
---|
169 | // Check all elements in this column. |
---|
170 | typename SpProxy<T2>::const_iterator_type y_col_it = pb.begin_col(cur_col); |
---|
171 | |
---|
172 | while(y_col_it.col() == cur_col) |
---|
173 | { |
---|
174 | // Check all elements in the column of the other matrix corresponding to |
---|
175 | // the row of this column. |
---|
176 | typename SpProxy<T1>::const_iterator_type x_col_it = pa.begin_col(y_col_it.row()); |
---|
177 | |
---|
178 | const eT y_value = (*y_col_it); |
---|
179 | |
---|
180 | while(x_col_it.col() == y_col_it.row()) |
---|
181 | { |
---|
182 | // A point at x(i, j) and y(j, k) implies a point at c(i, k). |
---|
183 | // Add to partial sum. |
---|
184 | const eT x_value = (*x_col_it); |
---|
185 | sums[x_col_it.row()] += (x_value * y_value); |
---|
186 | |
---|
187 | // Add point if it hasn't already been marked. |
---|
188 | if(index[x_col_it.row()] == x_n_rows) |
---|
189 | { |
---|
190 | index[x_col_it.row()] = last_ind; |
---|
191 | last_ind = x_col_it.row(); |
---|
192 | } |
---|
193 | |
---|
194 | ++x_col_it; |
---|
195 | } |
---|
196 | |
---|
197 | ++y_col_it; |
---|
198 | } |
---|
199 | |
---|
200 | // Now sort the indices that were used in this column. |
---|
201 | //podarray<uword> sorted_indices(c.col_ptrs[cur_col + 1] - c.col_ptrs[cur_col]); |
---|
202 | sorted_indices.set_min_size(c.col_ptrs[cur_col + 1] - c.col_ptrs[cur_col]); |
---|
203 | |
---|
204 | // .set_min_size() can only enlarge the array to the specified size, |
---|
205 | // hence if we request a smaller size than already allocated, |
---|
206 | // no new memory allocation is done |
---|
207 | |
---|
208 | |
---|
209 | uword cur_index = 0; |
---|
210 | while(last_ind != x_n_rows + 1) |
---|
211 | { |
---|
212 | const uword tmp = last_ind; |
---|
213 | |
---|
214 | // Check that it wasn't a "fake" nonzero element. |
---|
215 | if(sums[tmp] != eT(0)) |
---|
216 | { |
---|
217 | // Assign to next open position. |
---|
218 | sorted_indices[cur_index] = tmp; |
---|
219 | ++cur_index; |
---|
220 | } |
---|
221 | |
---|
222 | last_ind = index[tmp]; |
---|
223 | index[tmp] = x_n_rows; |
---|
224 | } |
---|
225 | |
---|
226 | // Now sort the indices. |
---|
227 | if (cur_index != 0) |
---|
228 | { |
---|
229 | op_sort::direct_sort_ascending(sorted_indices.memptr(), cur_index); |
---|
230 | |
---|
231 | for(uword k = 0; k < cur_index; ++k) |
---|
232 | { |
---|
233 | const uword row = sorted_indices[k]; |
---|
234 | access::rw(c.row_indices[cur_pos]) = row; |
---|
235 | access::rw(c.values[cur_pos]) = sums[row]; |
---|
236 | sums[row] = eT(0); |
---|
237 | ++cur_pos; |
---|
238 | } |
---|
239 | } |
---|
240 | |
---|
241 | // Move to next column. |
---|
242 | ++cur_col; |
---|
243 | } |
---|
244 | |
---|
245 | // Update last column pointer and resize to actual memory size. |
---|
246 | access::rw(c.col_ptrs[c.n_cols]) = cur_pos; |
---|
247 | c.mem_resize(cur_pos); |
---|
248 | } |
---|
249 | |
---|
250 | |
---|
251 | |
---|
252 | // |
---|
253 | // |
---|
254 | // spglue_times2: scalar*(A * B) |
---|
255 | |
---|
256 | |
---|
257 | |
---|
258 | template<typename T1, typename T2> |
---|
259 | inline |
---|
260 | void |
---|
261 | spglue_times2::apply(SpMat<typename T1::elem_type>& out, const SpGlue<T1,T2,spglue_times2>& X) |
---|
262 | { |
---|
263 | arma_extra_debug_sigprint(); |
---|
264 | |
---|
265 | typedef typename T1::elem_type eT; |
---|
266 | |
---|
267 | const SpProxy<T1> pa(X.A); |
---|
268 | const SpProxy<T2> pb(X.B); |
---|
269 | |
---|
270 | const bool is_alias = pa.is_alias(out) || pb.is_alias(out); |
---|
271 | |
---|
272 | if(is_alias == false) |
---|
273 | { |
---|
274 | spglue_times::apply_noalias(out, pa, pb); |
---|
275 | } |
---|
276 | else |
---|
277 | { |
---|
278 | SpMat<eT> tmp; |
---|
279 | spglue_times::apply_noalias(tmp, pa, pb); |
---|
280 | |
---|
281 | out.steal_mem(tmp); |
---|
282 | } |
---|
283 | |
---|
284 | out *= X.aux; |
---|
285 | } |
---|
286 | |
---|
287 | |
---|
288 | |
---|
289 | //! @} |
---|