1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2013 Google Inc. All rights reserved.
3 // http://code.google.com/p/ceres-solver/
4 //
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6 // modification, are permitted provided that the following conditions are met:
7 //
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9 // this list of conditions and the following disclaimer.
10 // * Redistributions in binary form must reproduce the above copyright notice,
11 // this list of conditions and the following disclaimer in the documentation
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14 // used to endorse or promote products derived from this software without
15 // specific prior written permission.
16 //
17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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28 //
29 // Author: keir@google.com (Keir Mierle)
30
31 #include "ceres/small_blas.h"
32
33 #include "gtest/gtest.h"
34 #include "ceres/internal/eigen.h"
35
36 namespace ceres {
37 namespace internal {
38
TEST(BLAS,MatrixMatrixMultiply)39 TEST(BLAS, MatrixMatrixMultiply) {
40 const double kTolerance = 1e-16;
41 const int kRowA = 3;
42 const int kColA = 5;
43 Matrix A(kRowA, kColA);
44 A.setOnes();
45
46 const int kRowB = 5;
47 const int kColB = 7;
48 Matrix B(kRowB, kColB);
49 B.setOnes();
50
51 for (int row_stride_c = kRowA; row_stride_c < 3 * kRowA; ++row_stride_c) {
52 for (int col_stride_c = kColB; col_stride_c < 3 * kColB; ++col_stride_c) {
53 Matrix C(row_stride_c, col_stride_c);
54 C.setOnes();
55
56 Matrix C_plus = C;
57 Matrix C_minus = C;
58 Matrix C_assign = C;
59
60 Matrix C_plus_ref = C;
61 Matrix C_minus_ref = C;
62 Matrix C_assign_ref = C;
63 for (int start_row_c = 0; start_row_c + kRowA < row_stride_c; ++start_row_c) {
64 for (int start_col_c = 0; start_col_c + kColB < col_stride_c; ++start_col_c) {
65 C_plus_ref.block(start_row_c, start_col_c, kRowA, kColB) +=
66 A * B;
67
68 MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, 1>(
69 A.data(), kRowA, kColA,
70 B.data(), kRowB, kColB,
71 C_plus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
72
73 EXPECT_NEAR((C_plus_ref - C_plus).norm(), 0.0, kTolerance)
74 << "C += A * B \n"
75 << "row_stride_c : " << row_stride_c << "\n"
76 << "col_stride_c : " << col_stride_c << "\n"
77 << "start_row_c : " << start_row_c << "\n"
78 << "start_col_c : " << start_col_c << "\n"
79 << "Cref : \n" << C_plus_ref << "\n"
80 << "C: \n" << C_plus;
81
82
83 C_minus_ref.block(start_row_c, start_col_c, kRowA, kColB) -=
84 A * B;
85
86 MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, -1>(
87 A.data(), kRowA, kColA,
88 B.data(), kRowB, kColB,
89 C_minus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
90
91 EXPECT_NEAR((C_minus_ref - C_minus).norm(), 0.0, kTolerance)
92 << "C -= A * B \n"
93 << "row_stride_c : " << row_stride_c << "\n"
94 << "col_stride_c : " << col_stride_c << "\n"
95 << "start_row_c : " << start_row_c << "\n"
96 << "start_col_c : " << start_col_c << "\n"
97 << "Cref : \n" << C_minus_ref << "\n"
98 << "C: \n" << C_minus;
99
100 C_assign_ref.block(start_row_c, start_col_c, kRowA, kColB) =
101 A * B;
102
103 MatrixMatrixMultiply<kRowA, kColA, kRowB, kColB, 0>(
104 A.data(), kRowA, kColA,
105 B.data(), kRowB, kColB,
106 C_assign.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
107
108 EXPECT_NEAR((C_assign_ref - C_assign).norm(), 0.0, kTolerance)
109 << "C = A * B \n"
110 << "row_stride_c : " << row_stride_c << "\n"
111 << "col_stride_c : " << col_stride_c << "\n"
112 << "start_row_c : " << start_row_c << "\n"
113 << "start_col_c : " << start_col_c << "\n"
114 << "Cref : \n" << C_assign_ref << "\n"
115 << "C: \n" << C_assign;
116 }
117 }
118 }
119 }
120 }
121
TEST(BLAS,MatrixTransposeMatrixMultiply)122 TEST(BLAS, MatrixTransposeMatrixMultiply) {
123 const double kTolerance = 1e-16;
124 const int kRowA = 5;
125 const int kColA = 3;
126 Matrix A(kRowA, kColA);
127 A.setOnes();
128
129 const int kRowB = 5;
130 const int kColB = 7;
131 Matrix B(kRowB, kColB);
132 B.setOnes();
133
134 for (int row_stride_c = kColA; row_stride_c < 3 * kColA; ++row_stride_c) {
135 for (int col_stride_c = kColB; col_stride_c < 3 * kColB; ++col_stride_c) {
136 Matrix C(row_stride_c, col_stride_c);
137 C.setOnes();
138
139 Matrix C_plus = C;
140 Matrix C_minus = C;
141 Matrix C_assign = C;
142
143 Matrix C_plus_ref = C;
144 Matrix C_minus_ref = C;
145 Matrix C_assign_ref = C;
146 for (int start_row_c = 0; start_row_c + kColA < row_stride_c; ++start_row_c) {
147 for (int start_col_c = 0; start_col_c + kColB < col_stride_c; ++start_col_c) {
148 C_plus_ref.block(start_row_c, start_col_c, kColA, kColB) +=
149 A.transpose() * B;
150
151 MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, 1>(
152 A.data(), kRowA, kColA,
153 B.data(), kRowB, kColB,
154 C_plus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
155
156 EXPECT_NEAR((C_plus_ref - C_plus).norm(), 0.0, kTolerance)
157 << "C += A' * B \n"
158 << "row_stride_c : " << row_stride_c << "\n"
159 << "col_stride_c : " << col_stride_c << "\n"
160 << "start_row_c : " << start_row_c << "\n"
161 << "start_col_c : " << start_col_c << "\n"
162 << "Cref : \n" << C_plus_ref << "\n"
163 << "C: \n" << C_plus;
164
165 C_minus_ref.block(start_row_c, start_col_c, kColA, kColB) -=
166 A.transpose() * B;
167
168 MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, -1>(
169 A.data(), kRowA, kColA,
170 B.data(), kRowB, kColB,
171 C_minus.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
172
173 EXPECT_NEAR((C_minus_ref - C_minus).norm(), 0.0, kTolerance)
174 << "C -= A' * B \n"
175 << "row_stride_c : " << row_stride_c << "\n"
176 << "col_stride_c : " << col_stride_c << "\n"
177 << "start_row_c : " << start_row_c << "\n"
178 << "start_col_c : " << start_col_c << "\n"
179 << "Cref : \n" << C_minus_ref << "\n"
180 << "C: \n" << C_minus;
181
182 C_assign_ref.block(start_row_c, start_col_c, kColA, kColB) =
183 A.transpose() * B;
184
185 MatrixTransposeMatrixMultiply<kRowA, kColA, kRowB, kColB, 0>(
186 A.data(), kRowA, kColA,
187 B.data(), kRowB, kColB,
188 C_assign.data(), start_row_c, start_col_c, row_stride_c, col_stride_c);
189
190 EXPECT_NEAR((C_assign_ref - C_assign).norm(), 0.0, kTolerance)
191 << "C = A' * B \n"
192 << "row_stride_c : " << row_stride_c << "\n"
193 << "col_stride_c : " << col_stride_c << "\n"
194 << "start_row_c : " << start_row_c << "\n"
195 << "start_col_c : " << start_col_c << "\n"
196 << "Cref : \n" << C_assign_ref << "\n"
197 << "C: \n" << C_assign;
198 }
199 }
200 }
201 }
202 }
203
TEST(BLAS,MatrixVectorMultiply)204 TEST(BLAS, MatrixVectorMultiply) {
205 const double kTolerance = 1e-16;
206 const int kRowA = 5;
207 const int kColA = 3;
208 Matrix A(kRowA, kColA);
209 A.setOnes();
210
211 Vector b(kColA);
212 b.setOnes();
213
214 Vector c(kRowA);
215 c.setOnes();
216
217 Vector c_plus = c;
218 Vector c_minus = c;
219 Vector c_assign = c;
220
221 Vector c_plus_ref = c;
222 Vector c_minus_ref = c;
223 Vector c_assign_ref = c;
224
225 c_plus_ref += A * b;
226 MatrixVectorMultiply<kRowA, kColA, 1>(A.data(), kRowA, kColA,
227 b.data(),
228 c_plus.data());
229 EXPECT_NEAR((c_plus_ref - c_plus).norm(), 0.0, kTolerance)
230 << "c += A * b \n"
231 << "c_ref : \n" << c_plus_ref << "\n"
232 << "c: \n" << c_plus;
233
234 c_minus_ref -= A * b;
235 MatrixVectorMultiply<kRowA, kColA, -1>(A.data(), kRowA, kColA,
236 b.data(),
237 c_minus.data());
238 EXPECT_NEAR((c_minus_ref - c_minus).norm(), 0.0, kTolerance)
239 << "c += A * b \n"
240 << "c_ref : \n" << c_minus_ref << "\n"
241 << "c: \n" << c_minus;
242
243 c_assign_ref = A * b;
244 MatrixVectorMultiply<kRowA, kColA, 0>(A.data(), kRowA, kColA,
245 b.data(),
246 c_assign.data());
247 EXPECT_NEAR((c_assign_ref - c_assign).norm(), 0.0, kTolerance)
248 << "c += A * b \n"
249 << "c_ref : \n" << c_assign_ref << "\n"
250 << "c: \n" << c_assign;
251 }
252
TEST(BLAS,MatrixTransposeVectorMultiply)253 TEST(BLAS, MatrixTransposeVectorMultiply) {
254 const double kTolerance = 1e-16;
255 const int kRowA = 5;
256 const int kColA = 3;
257 Matrix A(kRowA, kColA);
258 A.setRandom();
259
260 Vector b(kRowA);
261 b.setRandom();
262
263 Vector c(kColA);
264 c.setOnes();
265
266 Vector c_plus = c;
267 Vector c_minus = c;
268 Vector c_assign = c;
269
270 Vector c_plus_ref = c;
271 Vector c_minus_ref = c;
272 Vector c_assign_ref = c;
273
274 c_plus_ref += A.transpose() * b;
275 MatrixTransposeVectorMultiply<kRowA, kColA, 1>(A.data(), kRowA, kColA,
276 b.data(),
277 c_plus.data());
278 EXPECT_NEAR((c_plus_ref - c_plus).norm(), 0.0, kTolerance)
279 << "c += A' * b \n"
280 << "c_ref : \n" << c_plus_ref << "\n"
281 << "c: \n" << c_plus;
282
283 c_minus_ref -= A.transpose() * b;
284 MatrixTransposeVectorMultiply<kRowA, kColA, -1>(A.data(), kRowA, kColA,
285 b.data(),
286 c_minus.data());
287 EXPECT_NEAR((c_minus_ref - c_minus).norm(), 0.0, kTolerance)
288 << "c += A' * b \n"
289 << "c_ref : \n" << c_minus_ref << "\n"
290 << "c: \n" << c_minus;
291
292 c_assign_ref = A.transpose() * b;
293 MatrixTransposeVectorMultiply<kRowA, kColA, 0>(A.data(), kRowA, kColA,
294 b.data(),
295 c_assign.data());
296 EXPECT_NEAR((c_assign_ref - c_assign).norm(), 0.0, kTolerance)
297 << "c += A' * b \n"
298 << "c_ref : \n" << c_assign_ref << "\n"
299 << "c: \n" << c_assign;
300 }
301
302 } // namespace internal
303 } // namespace ceres
304