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mdivide_left.hpp
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1 #ifndef STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_HPP
2 #define STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_HPP
3
4 #include <stan/math/prim/mat/fun/Eigen.hpp>
5 #include <stan/math/prim/mat/fun/typedefs.hpp>
6 #include <stan/math/prim/mat/err/check_multiplicable.hpp>
7 #include <stan/math/rev/core.hpp>
8 #include <stan/math/rev/mat/fun/typedefs.hpp>
9 #include <stan/math/prim/mat/err/check_square.hpp>
10 #include <vector>
11
12 namespace stan {
13 namespace math {
14
15 namespace {
16 template <int R1, int C1, int R2, int C2>
17 class mdivide_left_vv_vari : public vari {
18 public:
19 int M_; // A.rows() = A.cols() = B.rows()
20 int N_; // B.cols()
21 double* A_;
22 double* C_;
23 vari** _variRefA;
24 vari** _variRefB;
25 vari** _variRefC;
26
27 mdivide_left_vv_vari(const Eigen::Matrix<var, R1, C1> &A,
28 const Eigen::Matrix<var, R2, C2> &B)
29 : vari(0.0),
30 M_(A.rows()),
31 N_(B.cols()),
32 A_(reinterpret_cast<double*>
33 (stan::math::ChainableStack::memalloc_
34 .alloc(sizeof(double) * A.rows() * A.cols()))),
35 C_(reinterpret_cast<double*>
36 (stan::math::ChainableStack::memalloc_
37 .alloc(sizeof(double) * B.rows() * B.cols()))),
38 _variRefA(reinterpret_cast<vari**>
39 (stan::math::ChainableStack::memalloc_
40 .alloc(sizeof(vari*) * A.rows() * A.cols()))),
41 _variRefB(reinterpret_cast<vari**>
42 (stan::math::ChainableStack::memalloc_
43 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
44 _variRefC(reinterpret_cast<vari**>
45 (stan::math::ChainableStack::memalloc_
46 .alloc(sizeof(vari*) * B.rows() * B.cols()))) {
47 using Eigen::Matrix;
48 using Eigen::Map;
49
50 size_t pos = 0;
51 for (size_type j = 0; j < M_; j++) {
52 for (size_type i = 0; i < M_; i++) {
53 _variRefA[pos] = A(i, j).vi_;
54 A_[pos++] = A(i, j).val();
55 }
56 }
57
58 pos = 0;
59 for (size_type j = 0; j < N_; j++) {
60 for (size_type i = 0; i < M_; i++) {
61 _variRefB[pos] = B(i, j).vi_;
62 C_[pos++] = B(i, j).val();
63 }
64 }
65
66 Matrix<double, R1, C2> C(M_, N_);
67 C = Map<Matrix<double, R1, C2> >(C_, M_, N_);
68
69 C = Map<Matrix<double, R1, C1> >(A_, M_, M_)
70 .colPivHouseholderQr().solve(C);
71
72 pos = 0;
73 for (size_type j = 0; j < N_; j++) {
74 for (size_type i = 0; i < M_; i++) {
75 C_[pos] = C(i, j);
76 _variRefC[pos] = new vari(C_[pos], false);
77 pos++;
78 }
79 }
80 }
81
82 virtual void chain() {
83 using Eigen::Matrix;
84 using Eigen::Map;
85 Eigen::Matrix<double, R1, C1> adjA(M_, M_);
86 Eigen::Matrix<double, R2, C2> adjB(M_, N_);
87 Eigen::Matrix<double, R1, C2> adjC(M_, N_);
88
89 size_t pos = 0;
90 for (size_type j = 0; j < adjC.cols(); j++)
91 for (size_type i = 0; i < adjC.rows(); i++)
92 adjC(i, j) = _variRefC[pos++]->adj_;
93
94
95 adjB = Map<Matrix<double, R1, C1> >(A_, M_, M_)
96 .transpose().colPivHouseholderQr().solve(adjC);
97 adjA.noalias() = -adjB
98 * Map<Matrix<double, R1, C2> >(C_, M_, N_).transpose();
99
100 pos = 0;
101 for (size_type j = 0; j < adjA.cols(); j++)
102 for (size_type i = 0; i < adjA.rows(); i++)
103 _variRefA[pos++]->adj_ += adjA(i, j);
104
105 pos = 0;
106 for (size_type j = 0; j < adjB.cols(); j++)
107 for (size_type i = 0; i < adjB.rows(); i++)
108 _variRefB[pos++]->adj_ += adjB(i, j);
109 }
110 };
111
112 template <int R1, int C1, int R2, int C2>
113 class mdivide_left_dv_vari : public vari {
114 public:
115 int M_; // A.rows() = A.cols() = B.rows()
116 int N_; // B.cols()
117 double* A_;
118 double* C_;
119 vari** _variRefB;
120 vari** _variRefC;
121
122 mdivide_left_dv_vari(const Eigen::Matrix<double, R1, C1> &A,
123 const Eigen::Matrix<var, R2, C2> &B)
124 : vari(0.0),
125 M_(A.rows()),
126 N_(B.cols()),
127 A_(reinterpret_cast<double*>
128 (stan::math::ChainableStack::memalloc_
129 .alloc(sizeof(double) * A.rows() * A.cols()))),
130 C_(reinterpret_cast<double*>
131 (stan::math::ChainableStack::memalloc_
132 .alloc(sizeof(double) * B.rows() * B.cols()))),
133 _variRefB(reinterpret_cast<vari**>
134 (stan::math::ChainableStack::memalloc_
135 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
136 _variRefC(reinterpret_cast<vari**>
137 (stan::math::ChainableStack::memalloc_
138 .alloc(sizeof(vari*) * B.rows() * B.cols()))) {
139 using Eigen::Matrix;
140 using Eigen::Map;
141
142 size_t pos = 0;
143 for (size_type j = 0; j < M_; j++) {
144 for (size_type i = 0; i < M_; i++) {
145 A_[pos++] = A(i, j);
146 }
147 }
148
149 pos = 0;
150 for (size_type j = 0; j < N_; j++) {
151 for (size_type i = 0; i < M_; i++) {
152 _variRefB[pos] = B(i, j).vi_;
153 C_[pos++] = B(i, j).val();
154 }
155 }
156
157 Matrix<double, R1, C2> C(M_, N_);
158 C = Map<Matrix<double, R1, C2> >(C_, M_, N_);
159
160 C = Map<Matrix<double, R1, C1> >(A_, M_, M_)
161 .colPivHouseholderQr().solve(C);
162
163 pos = 0;
164 for (size_type j = 0; j < N_; j++) {
165 for (size_type i = 0; i < M_; i++) {
166 C_[pos] = C(i, j);
167 _variRefC[pos] = new vari(C_[pos], false);
168 pos++;
169 }
170 }
171 }
172
173 virtual void chain() {
174 using Eigen::Matrix;
175 using Eigen::Map;
176 Eigen::Matrix<double, R2, C2> adjB(M_, N_);
177 Eigen::Matrix<double, R1, C2> adjC(M_, N_);
178
179 size_t pos = 0;
180 for (size_type j = 0; j < adjC.cols(); j++)
181 for (size_type i = 0; i < adjC.rows(); i++)
182 adjC(i, j) = _variRefC[pos++]->adj_;
183
184 adjB = Map<Matrix<double, R1, C1> >(A_, M_, M_)
185 .transpose().colPivHouseholderQr().solve(adjC);
186
187 pos = 0;
188 for (size_type j = 0; j < adjB.cols(); j++)
189 for (size_type i = 0; i < adjB.rows(); i++)
190 _variRefB[pos++]->adj_ += adjB(i, j);
191 }
192 };
193
194 template <int R1, int C1, int R2, int C2>
195 class mdivide_left_vd_vari : public vari {
196 public:
197 int M_; // A.rows() = A.cols() = B.rows()
198 int N_; // B.cols()
199 double* A_;
200 double* C_;
201 vari** _variRefA;
202 vari** _variRefC;
203
204 mdivide_left_vd_vari(const Eigen::Matrix<var, R1, C1> &A,
205 const Eigen::Matrix<double, R2, C2> &B)
206 : vari(0.0),
207 M_(A.rows()),
208 N_(B.cols()),
209 A_(reinterpret_cast<double*>
210 (stan::math::ChainableStack::memalloc_
211 .alloc(sizeof(double) * A.rows() * A.cols()))),
212 C_(reinterpret_cast<double*>
213 (stan::math::ChainableStack::memalloc_
214 .alloc(sizeof(double) * B.rows() * B.cols()))),
215 _variRefA(reinterpret_cast<vari**>
216 (stan::math::ChainableStack::memalloc_
217 .alloc(sizeof(vari*) * A.rows() * A.cols()))),
218 _variRefC(reinterpret_cast<vari**>
219 (stan::math::ChainableStack::memalloc_
220 .alloc(sizeof(vari*) * B.rows() * B.cols()))) {
221 using Eigen::Matrix;
222 using Eigen::Map;
223
224 size_t pos = 0;
225 for (size_type j = 0; j < M_; j++) {
226 for (size_type i = 0; i < M_; i++) {
227 _variRefA[pos] = A(i, j).vi_;
228 A_[pos++] = A(i, j).val();
229 }
230 }
231
232 Matrix<double, R1, C2> C(M_, N_);
233 C = Map<Matrix<double, R1, C1> >(A_, M_, M_)
234 .colPivHouseholderQr().solve(B);
235
236 pos = 0;
237 for (size_type j = 0; j < N_; j++) {
238 for (size_type i = 0; i < M_; i++) {
239 C_[pos] = C(i, j);
240 _variRefC[pos] = new vari(C_[pos], false);
241 pos++;
242 }
243 }
244 }
245
246 virtual void chain() {
247 using Eigen::Matrix;
248 using Eigen::Map;
249 Eigen::Matrix<double, R1, C1> adjA(M_, M_);
250 Eigen::Matrix<double, R1, C2> adjC(M_, N_);
251
252 size_t pos = 0;
253 for (size_type j = 0; j < adjC.cols(); j++)
254 for (size_type i = 0; i < adjC.rows(); i++)
255 adjC(i, j) = _variRefC[pos++]->adj_;
256
257 // FIXME: add .noalias() to LHS
258 adjA = -Map<Matrix<double, R1, C1> >(A_, M_, M_)
259 .transpose()
260 .colPivHouseholderQr()
261 .solve(adjC*Map<Matrix<double, R1, C2> >(C_, M_, N_).transpose());
262
263 pos = 0;
264 for (size_type j = 0; j < adjA.cols(); j++)
265 for (size_type i = 0; i < adjA.rows(); i++)
266 _variRefA[pos++]->adj_ += adjA(i, j);
267 }
268 };
269 }
270
271 template <int R1, int C1, int R2, int C2>
272 inline
273 Eigen::Matrix<var, R1, C2>
274 mdivide_left(const Eigen::Matrix<var, R1, C1> &A,
275 const Eigen::Matrix<var, R2, C2> &b) {
276 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
277
278 stan::math::check_square("mdivide_left", "A", A);
279 stan::math::check_multiplicable("mdivide_left",
280 "A", A,
281 "b", b);
282
283 // NOTE: this is not a memory leak, this vari is used in the
284 // expression graph to evaluate the adjoint, but is not needed
285 // for the returned matrix. Memory will be cleaned up with the
286 // arena allocator.
287 mdivide_left_vv_vari<R1, C1, R2, C2> *baseVari
288 = new mdivide_left_vv_vari<R1, C1, R2, C2>(A, b);
289
290 size_t pos = 0;
291 for (size_type j = 0; j < res.cols(); j++)
292 for (size_type i = 0; i < res.rows(); i++)
293 res(i, j).vi_ = baseVari->_variRefC[pos++];
294
295 return res;
296 }
297
298 template <int R1, int C1, int R2, int C2>
299 inline
300 Eigen::Matrix<var, R1, C2>
301 mdivide_left(const Eigen::Matrix<var, R1, C1> &A,
302 const Eigen::Matrix<double, R2, C2> &b) {
303 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
304
305 stan::math::check_square("mdivide_left", "A", A);
306 stan::math::check_multiplicable("mdivide_left",
307 "A", A,
308 "b", b);
309
310 // NOTE: this is not a memory leak, this vari is used in the
311 // expression graph to evaluate the adjoint, but is not needed
312 // for the returned matrix. Memory will be cleaned up with the
313 // arena allocator.
314 mdivide_left_vd_vari<R1, C1, R2, C2> *baseVari
315 = new mdivide_left_vd_vari<R1, C1, R2, C2>(A, b);
316
317 size_t pos = 0;
318 for (size_type j = 0; j < res.cols(); j++)
319 for (size_type i = 0; i < res.rows(); i++)
320 res(i, j).vi_ = baseVari->_variRefC[pos++];
321
322 return res;
323 }
324
325 template <int R1, int C1, int R2, int C2>
326 inline
327 Eigen::Matrix<var, R1, C2>
328 mdivide_left(const Eigen::Matrix<double, R1, C1> &A,
329 const Eigen::Matrix<var, R2, C2> &b) {
330 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
331
332 stan::math::check_square("mdivide_left", "A", A);
333 stan::math::check_multiplicable("mdivide_left",
334 "A", A,
335 "b", b);
336
337 // NOTE: this is not a memory leak, this vari is used in the
338 // expression graph to evaluate the adjoint, but is not needed
339 // for the returned matrix. Memory will be cleaned up with the
340 // arena allocator.
341 mdivide_left_dv_vari<R1, C1, R2, C2> *baseVari
342 = new mdivide_left_dv_vari<R1, C1, R2, C2>(A, b);
343
344 size_t pos = 0;
345 for (size_type j = 0; j < res.cols(); j++)
346 for (size_type i = 0; i < res.rows(); i++)
347 res(i, j).vi_ = baseVari->_variRefC[pos++];
348
349 return res;
350 }
351
352 }
353 }
354 #endif
stan::math::mdivide_left
Eigen::Matrix< fvar< T >, R1, C2 > mdivide_left(const Eigen::Matrix< fvar< T >, R1, C1 > &A, const Eigen::Matrix< fvar< T >, R2, C2 > &b)
Definition: mdivide_left.hpp:24
core.hpp
check_multiplicable.hpp
C_
double * C_
Definition: mdivide_left.hpp:22
_variRefB
vari ** _variRefB
Definition: mdivide_left.hpp:24
stan::math::size_type
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >::Index size_type
Type for sizes and indexes in an Eigen matrix with double e.
Definition: typedefs.hpp:13
M_
int M_
Definition: mdivide_left.hpp:19
stan::math::rows
size_t rows(const Eigen::Matrix< T, R, C > &m)
Definition: rows.hpp:12
stan::math::ChainableStack
AutodiffStackStorage< chainable, chainable_alloc > ChainableStack
Definition: chainablestack.hpp:11
typedefs.hpp
stan::math::check_multiplicable
bool check_multiplicable(const char *function, const char *name1, const T1 &y1, const char *name2, const T2 &y2)
Return true if the matrices can be multiplied.
Definition: check_multiplicable.hpp:33
stan::math::cols
size_t cols(const Eigen::Matrix< T, R, C > &m)
Definition: cols.hpp:12
_variRefA
vari ** _variRefA
Definition: mdivide_left.hpp:23
Eigen.hpp
A_
double * A_
Definition: mdivide_left.hpp:21
stan::math::transpose
Eigen::Matrix< T, C, R > transpose(const Eigen::Matrix< T, R, C > &m)
Definition: transpose.hpp:12
stan::math::check_square
bool check_square(const char *function, const char *name, const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y)
Return true if the specified matrix is square.
Definition: check_square.hpp:28
N_
int N_
Definition: mdivide_left.hpp:20
_variRefC
vari ** _variRefC
Definition: mdivide_left.hpp:25
typedefs.hpp
check_square.hpp

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