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mdivide_left_spd.hpp
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1 #ifndef STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_SPD_HPP
2 #define STAN_MATH_REV_MAT_FUN_MDIVIDE_LEFT_SPD_HPP
3
4 #include <stan/math/rev/core.hpp>
5 #include <stan/math/prim/mat/fun/Eigen.hpp>
6 #include <stan/math/prim/mat/fun/typedefs.hpp>
7 #include <stan/math/prim/mat/err/check_multiplicable.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_spd_alloc : public chainable_alloc {
18 public:
19 virtual ~mdivide_left_spd_alloc() {}
20
21 Eigen::LLT< Eigen::Matrix<double, R1, C1> > _llt;
22 Eigen::Matrix<double, R2, C2> C_;
23 };
24
25 template <int R1, int C1, int R2, int C2>
26 class mdivide_left_spd_vv_vari : public vari {
27 public:
28 int M_; // A.rows() = A.cols() = B.rows()
29 int N_; // B.cols()
30 vari** _variRefA;
31 vari** _variRefB;
32 vari** _variRefC;
33 mdivide_left_spd_alloc<R1, C1, R2, C2> *_alloc;
34
35 mdivide_left_spd_vv_vari(const Eigen::Matrix<var, R1, C1> &A,
36 const Eigen::Matrix<var, R2, C2> &B)
37 : vari(0.0),
38 M_(A.rows()),
39 N_(B.cols()),
40 _variRefA(reinterpret_cast<vari**>
41 (stan::math::ChainableStack::memalloc_
42 .alloc(sizeof(vari*) * A.rows() * A.cols()))),
43 _variRefB(reinterpret_cast<vari**>
44 (stan::math::ChainableStack::memalloc_
45 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
46 _variRefC(reinterpret_cast<vari**>
47 (stan::math::ChainableStack::memalloc_
48 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
49 _alloc(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
50 using Eigen::Matrix;
51 using Eigen::Map;
52
53 Matrix<double, R1, C1> Ad(A.rows(), A.cols());
54
55 size_t pos = 0;
56 for (size_type j = 0; j < M_; j++) {
57 for (size_type i = 0; i < M_; i++) {
58 _variRefA[pos] = A(i, j).vi_;
59 Ad(i, j) = A(i, j).val();
60 pos++;
61 }
62 }
63
64 pos = 0;
65 _alloc->C_.resize(M_, N_);
66 for (size_type j = 0; j < N_; j++) {
67 for (size_type i = 0; i < M_; i++) {
68 _variRefB[pos] = B(i, j).vi_;
69 _alloc->C_(i, j) = B(i, j).val();
70 pos++;
71 }
72 }
73
74 _alloc->_llt = Ad.llt();
75 _alloc->_llt.solveInPlace(_alloc->C_);
76
77 pos = 0;
78 for (size_type j = 0; j < N_; j++) {
79 for (size_type i = 0; i < M_; i++) {
80 _variRefC[pos] = new vari(_alloc->C_(i, j), false);
81 pos++;
82 }
83 }
84 }
85
86 virtual void chain() {
87 using Eigen::Matrix;
88 using Eigen::Map;
89 Eigen::Matrix<double, R1, C1> adjA(M_, M_);
90 Eigen::Matrix<double, R2, C2> adjB(M_, N_);
91
92 size_t pos = 0;
93 for (size_type j = 0; j < N_; j++)
94 for (size_type i = 0; i < M_; i++)
95 adjB(i, j) = _variRefC[pos++]->adj_;
96
97 _alloc->_llt.solveInPlace(adjB);
98 adjA.noalias() = -adjB * _alloc->C_.transpose();
99
100 pos = 0;
101 for (size_type j = 0; j < M_; j++)
102 for (size_type i = 0; i < M_; i++)
103 _variRefA[pos++]->adj_ += adjA(i, j);
104
105 pos = 0;
106 for (size_type j = 0; j < N_; j++)
107 for (size_type i = 0; i < M_; 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_spd_dv_vari : public vari {
114 public:
115 int M_; // A.rows() = A.cols() = B.rows()
116 int N_; // B.cols()
117 vari** _variRefB;
118 vari** _variRefC;
119 mdivide_left_spd_alloc<R1, C1, R2, C2> *_alloc;
120
121 mdivide_left_spd_dv_vari(const Eigen::Matrix<double, R1, C1> &A,
122 const Eigen::Matrix<var, R2, C2> &B)
123 : vari(0.0),
124 M_(A.rows()),
125 N_(B.cols()),
126 _variRefB(reinterpret_cast<vari**>
127 (stan::math::ChainableStack::memalloc_
128 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
129 _variRefC(reinterpret_cast<vari**>
130 (stan::math::ChainableStack::memalloc_
131 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
132 _alloc(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
133 using Eigen::Matrix;
134 using Eigen::Map;
135
136 size_t pos = 0;
137 _alloc->C_.resize(M_, N_);
138 for (size_type j = 0; j < N_; j++) {
139 for (size_type i = 0; i < M_; i++) {
140 _variRefB[pos] = B(i, j).vi_;
141 _alloc->C_(i, j) = B(i, j).val();
142 pos++;
143 }
144 }
145
146 _alloc->_llt = A.llt();
147 _alloc->_llt.solveInPlace(_alloc->C_);
148
149 pos = 0;
150 for (size_type j = 0; j < N_; j++) {
151 for (size_type i = 0; i < M_; i++) {
152 _variRefC[pos] = new vari(_alloc->C_(i, j), false);
153 pos++;
154 }
155 }
156 }
157
158 virtual void chain() {
159 using Eigen::Matrix;
160 using Eigen::Map;
161 Eigen::Matrix<double, R2, C2> adjB(M_, N_);
162
163 size_t pos = 0;
164 for (size_type j = 0; j < adjB.cols(); j++)
165 for (size_type i = 0; i < adjB.rows(); i++)
166 adjB(i, j) = _variRefC[pos++]->adj_;
167
168 _alloc->_llt.solveInPlace(adjB);
169
170 pos = 0;
171 for (size_type j = 0; j < adjB.cols(); j++)
172 for (size_type i = 0; i < adjB.rows(); i++)
173 _variRefB[pos++]->adj_ += adjB(i, j);
174 }
175 };
176
177 template <int R1, int C1, int R2, int C2>
178 class mdivide_left_spd_vd_vari : public vari {
179 public:
180 int M_; // A.rows() = A.cols() = B.rows()
181 int N_; // B.cols()
182 vari** _variRefA;
183 vari** _variRefC;
184 mdivide_left_spd_alloc<R1, C1, R2, C2> *_alloc;
185
186 mdivide_left_spd_vd_vari(const Eigen::Matrix<var, R1, C1> &A,
187 const Eigen::Matrix<double, R2, C2> &B)
188 : vari(0.0),
189 M_(A.rows()),
190 N_(B.cols()),
191 _variRefA(reinterpret_cast<vari**>
192 (stan::math::ChainableStack::memalloc_
193 .alloc(sizeof(vari*) * A.rows() * A.cols()))),
194 _variRefC(reinterpret_cast<vari**>
195 (stan::math::ChainableStack::memalloc_
196 .alloc(sizeof(vari*) * B.rows() * B.cols()))),
197 _alloc(new mdivide_left_spd_alloc<R1, C1, R2, C2>()) {
198 using Eigen::Matrix;
199 using Eigen::Map;
200
201 Matrix<double, R1, C1> Ad(A.rows(), A.cols());
202
203 size_t pos = 0;
204 for (size_type j = 0; j < M_; j++) {
205 for (size_type i = 0; i < M_; i++) {
206 _variRefA[pos] = A(i, j).vi_;
207 Ad(i, j) = A(i, j).val();
208 pos++;
209 }
210 }
211
212 _alloc->_llt = Ad.llt();
213 _alloc->C_ = _alloc->_llt.solve(B);
214
215 pos = 0;
216 for (size_type j = 0; j < N_; j++) {
217 for (size_type i = 0; i < M_; i++) {
218 _variRefC[pos] = new vari(_alloc->C_(i, j), false);
219 pos++;
220 }
221 }
222 }
223
224 virtual void chain() {
225 using Eigen::Matrix;
226 using Eigen::Map;
227 Eigen::Matrix<double, R1, C1> adjA(M_, M_);
228 Eigen::Matrix<double, R1, C2> adjC(M_, N_);
229
230 size_t pos = 0;
231 for (size_type j = 0; j < adjC.cols(); j++)
232 for (size_type i = 0; i < adjC.rows(); i++)
233 adjC(i, j) = _variRefC[pos++]->adj_;
234
235 adjA = -_alloc->_llt.solve(adjC*_alloc->C_.transpose());
236
237 pos = 0;
238 for (size_type j = 0; j < adjA.cols(); j++)
239 for (size_type i = 0; i < adjA.rows(); i++)
240 _variRefA[pos++]->adj_ += adjA(i, j);
241 }
242 };
243 }
244
245 template <int R1, int C1, int R2, int C2>
246 inline
247 Eigen::Matrix<var, R1, C2>
248 mdivide_left_spd(const Eigen::Matrix<var, R1, C1> &A,
249 const Eigen::Matrix<var, R2, C2> &b) {
250 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
251
252 stan::math::check_square("mdivide_left_spd", "A", A);
253 stan::math::check_multiplicable("mdivide_left_spd",
254 "A", A,
255 "b", b);
256
257 // NOTE: this is not a memory leak, this vari is used in the
258 // expression graph to evaluate the adjoint, but is not needed
259 // for the returned matrix. Memory will be cleaned up with the
260 // arena allocator.
261 mdivide_left_spd_vv_vari<R1, C1, R2, C2> *baseVari
262 = new mdivide_left_spd_vv_vari<R1, C1, R2, C2>(A, b);
263
264 size_t pos = 0;
265 for (size_type j = 0; j < res.cols(); j++)
266 for (size_type i = 0; i < res.rows(); i++)
267 res(i, j).vi_ = baseVari->_variRefC[pos++];
268
269 return res;
270 }
271
272 template <int R1, int C1, int R2, int C2>
273 inline
274 Eigen::Matrix<var, R1, C2>
275 mdivide_left_spd(const Eigen::Matrix<var, R1, C1> &A,
276 const Eigen::Matrix<double, R2, C2> &b) {
277 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
278
279 stan::math::check_square("mdivide_left_spd", "A", A);
280 stan::math::check_multiplicable("mdivide_left_spd",
281 "A", A,
282 "b", b);
283
284 // NOTE: this is not a memory leak, this vari is used in the
285 // expression graph to evaluate the adjoint, but is not needed
286 // for the returned matrix. Memory will be cleaned up with the
287 // arena allocator.
288 mdivide_left_spd_vd_vari<R1, C1, R2, C2> *baseVari
289 = new mdivide_left_spd_vd_vari<R1, C1, R2, C2>(A, b);
290
291 size_t pos = 0;
292 for (size_type j = 0; j < res.cols(); j++)
293 for (size_type i = 0; i < res.rows(); i++)
294 res(i, j).vi_ = baseVari->_variRefC[pos++];
295
296 return res;
297 }
298
299 template <int R1, int C1, int R2, int C2>
300 inline
301 Eigen::Matrix<var, R1, C2>
302 mdivide_left_spd(const Eigen::Matrix<double, R1, C1> &A,
303 const Eigen::Matrix<var, R2, C2> &b) {
304 Eigen::Matrix<var, R1, C2> res(b.rows(), b.cols());
305
306 stan::math::check_square("mdivide_left_spd", "A", A);
307 stan::math::check_multiplicable("mdivide_left_spd",
308 "A", A,
309 "b", b);
310
311 // NOTE: this is not a memory leak, this vari is used in the
312 // expression graph to evaluate the adjoint, but is not needed
313 // for the returned matrix. Memory will be cleaned up with the
314 // arena allocator.
315 mdivide_left_spd_dv_vari<R1, C1, R2, C2> *baseVari
316 = new mdivide_left_spd_dv_vari<R1, C1, R2, C2>(A, b);
317
318 size_t pos = 0;
319 for (size_type j = 0; j < res.cols(); j++)
320 for (size_type i = 0; i < res.rows(); i++)
321 res(i, j).vi_ = baseVari->_variRefC[pos++];
322
323 return res;
324 }
325
326 }
327 }
328 #endif
core.hpp
N_
int N_
Definition: mdivide_left_spd.hpp:29
_variRefB
vari ** _variRefB
Definition: mdivide_left_spd.hpp:31
check_multiplicable.hpp
_llt
Eigen::LLT< Eigen::Matrix< double, R1, C1 > > _llt
Definition: mdivide_left_spd.hpp:21
stan::math::mdivide_left_spd
Eigen::Matrix< typename boost::math::tools::promote_args< T1, T2 >::type, R1, C2 > mdivide_left_spd(const Eigen::Matrix< T1, R1, C1 > &A, const Eigen::Matrix< T2, R2, C2 > &b)
Returns the solution of the system Ax=b where A is symmetric positive definite.
Definition: mdivide_left_spd.hpp:28
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
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
M_
int M_
Definition: mdivide_left_spd.hpp:28
_alloc
mdivide_left_spd_alloc< R1, C1, R2, C2 > * _alloc
Definition: mdivide_left_spd.hpp:33
stan::math::cols
size_t cols(const Eigen::Matrix< T, R, C > &m)
Definition: cols.hpp:12
Eigen.hpp
_variRefC
vari ** _variRefC
Definition: mdivide_left_spd.hpp:32
_variRefA
vari ** _variRefA
Definition: mdivide_left_spd.hpp:30
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
C_
Eigen::Matrix< double, R2, C2 > C_
Definition: mdivide_left_spd.hpp:22
typedefs.hpp
check_square.hpp

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