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trace_inv_quad_form_ldlt.hpp
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1 #ifndef STAN_MATH_REV_MAT_FUN_TRACE_INV_QUAD_FORM_LDLT_HPP
2 #define STAN_MATH_REV_MAT_FUN_TRACE_INV_QUAD_FORM_LDLT_HPP
3
4 #include <stan/math/prim/mat/fun/Eigen.hpp>
5 #include <stan/math/rev/core.hpp>
6 #include <stan/math/rev/mat/fun/LDLT_alloc.hpp>
7 #include <stan/math/rev/mat/fun/LDLT_factor.hpp>
8 #include <boost/utility/enable_if.hpp>
9 #include <stan/math/prim/mat/err/check_multiplicable.hpp>
10 #include <stan/math/rev/scal/meta/is_var.hpp>
11
12 namespace stan {
13 namespace math {
14 namespace {
15 template <typename T2, int R2, int C2, typename T3, int R3, int C3>
16 class trace_inv_quad_form_ldlt_impl : public chainable_alloc {
17 protected:
18 inline void initializeB(const Eigen::Matrix<var, R3, C3> &B,
19 bool haveD) {
20 Eigen::Matrix<double, R3, C3> Bd(B.rows(), B.cols());
21 _variB.resize(B.rows(), B.cols());
22 for (int j = 0; j < B.cols(); j++) {
23 for (int i = 0; i < B.rows(); i++) {
24 _variB(i, j) = B(i, j).vi_;
25 Bd(i, j) = B(i, j).val();
26 }
27 }
28 AinvB_ = _ldlt.solve(Bd);
29 if (haveD)
30 C_.noalias() = Bd.transpose()*AinvB_;
31 else
32 _value = (Bd.transpose()*AinvB_).trace();
33 }
34 inline void initializeB(const Eigen::Matrix<double, R3, C3> &B,
35 bool haveD) {
36 AinvB_ = _ldlt.solve(B);
37 if (haveD)
38 C_.noalias() = B.transpose()*AinvB_;
39 else
40 _value = (B.transpose()*AinvB_).trace();
41 }
42
43 template<int R1, int C1>
44 inline void initializeD(const Eigen::Matrix<var, R1, C1> &D) {
45 D_.resize(D.rows(), D.cols());
46 _variD.resize(D.rows(), D.cols());
47 for (int j = 0; j < D.cols(); j++) {
48 for (int i = 0; i < D.rows(); i++) {
49 _variD(i, j) = D(i, j).vi_;
50 D_(i, j) = D(i, j).val();
51 }
52 }
53 }
54 template<int R1, int C1>
55 inline void initializeD(const Eigen::Matrix<double, R1, C1> &D) {
56 D_ = D;
57 }
58
59 public:
60 template<typename T1, int R1, int C1>
61 trace_inv_quad_form_ldlt_impl(const Eigen::Matrix<T1, R1, C1> &D,
62 const stan::math::LDLT_factor<T2, R2, C2>
63 &A,
64 const Eigen::Matrix<T3, R3, C3> &B)
65 : Dtype_(stan::is_var<T1>::value),
66 _ldlt(A) {
67 initializeB(B, true);
68 initializeD(D);
69
70 _value = (D_*C_).trace();
71 }
72
73 trace_inv_quad_form_ldlt_impl(const stan::math::LDLT_factor<T2, R2, C2>
74 &A,
75 const Eigen::Matrix<T3, R3, C3> &B)
76 : Dtype_(2),
77 _ldlt(A) {
78 initializeB(B, false);
79 }
80
81 const int Dtype_; // 0 = double, 1 = var, 2 = missing
82 stan::math::LDLT_factor<T2, R2, C2> _ldlt;
83 Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> D_;
84 Eigen::Matrix<vari*, Eigen::Dynamic, Eigen::Dynamic> _variD;
85 Eigen::Matrix<vari*, R3, C3> _variB;
86 Eigen::Matrix<double, R3, C3> AinvB_;
87 Eigen::Matrix<double, C3, C3> C_;
88 double _value;
89 };
90
91 template <typename T2, int R2, int C2, typename T3, int R3, int C3>
92 class trace_inv_quad_form_ldlt_vari : public vari {
93 protected:
94 static inline
95 void
96 chainA(const double &adj,
97 trace_inv_quad_form_ldlt_impl<double, R2, C2, T3, R3, C3>
98 *impl) {
99 }
100 static inline
101 void
102 chainB(const double &adj,
103 trace_inv_quad_form_ldlt_impl<T2, R2, C2, double, R3, C3>
104 *impl) {
105 }
106
107 static inline
108 void
109 chainA(const double &adj,
110 trace_inv_quad_form_ldlt_impl<var, R2, C2, T3, R3, C3> *impl) {
111 Eigen::Matrix<double, R2, C2> aA;
112
113 if (impl->Dtype_ != 2)
114 aA.noalias() = -adj * (impl->AinvB_ * impl->D_.transpose()
115 * impl->AinvB_.transpose());
116 else
117 aA.noalias() = -adj*(impl->AinvB_ * impl->AinvB_.transpose());
118
119 for (int j = 0; j < aA.cols(); j++)
120 for (int i = 0; i < aA.rows(); i++)
121 impl->_ldlt._alloc->_variA(i, j)->adj_ += aA(i, j);
122 }
123 static inline
124 void
125 chainB(const double &adj,
126 trace_inv_quad_form_ldlt_impl<T2, R2, C2, var, R3, C3> *impl) {
127 Eigen::Matrix<double, R3, C3> aB;
128
129 if (impl->Dtype_ != 2)
130 aB.noalias() = adj*impl->AinvB_*(impl->D_ + impl->D_.transpose());
131 else
132 aB.noalias() = 2*adj*impl->AinvB_;
133
134 for (int j = 0; j < aB.cols(); j++)
135 for (int i = 0; i < aB.rows(); i++)
136 impl->_variB(i, j)->adj_ += aB(i, j);
137 }
138
139 public:
140 explicit trace_inv_quad_form_ldlt_vari
141 (trace_inv_quad_form_ldlt_impl<T2, R2, C2, T3, R3, C3> *impl)
142 : vari(impl->_value), _impl(impl)
143 { }
144
145 virtual void chain() {
146 // F = trace(D * B' * inv(A) * B)
147 // aA = -aF * inv(A') * B * D' * B' * inv(A')
148 // aB = aF*(inv(A) * B * D + inv(A') * B * D')
149 // aD = aF*(B' * inv(A) * B)
150 chainA(adj_, _impl);
151
152 chainB(adj_, _impl);
153
154 if (_impl->Dtype_ == 1) {
155 for (int j = 0; j < _impl->_variD.cols(); j++)
156 for (int i = 0; i < _impl->_variD.rows(); i++)
157 _impl->_variD(i, j)->adj_ += adj_*_impl->C_(i, j);
158 }
159 }
160
161 trace_inv_quad_form_ldlt_impl<T2, R2, C2, T3, R3, C3> *_impl;
162 };
163
164 }
165
166
172 template <typename T2, int R2, int C2, typename T3, int R3, int C3>
173 inline typename
174 boost::enable_if_c<stan::is_var<T2>::value ||
175 stan::is_var<T3>::value,
176 var>::type
177 trace_inv_quad_form_ldlt(const stan::math::LDLT_factor<T2, R2, C2> &A,
178 const Eigen::Matrix<T3, R3, C3> &B) {
179 stan::math::check_multiplicable("trace_inv_quad_form_ldlt",
180 "A", A,
181 "B", B);
182
183 trace_inv_quad_form_ldlt_impl<T2, R2, C2, T3, R3, C3> *_impl
184 = new trace_inv_quad_form_ldlt_impl<T2, R2, C2, T3, R3, C3>(A, B);
185
186 return var(new trace_inv_quad_form_ldlt_vari<T2, R2, C2, T3, R3, C3>
187 (_impl));
188 }
189
190 }
191 }
192
193 #endif
core.hpp
LDLT_alloc.hpp
check_multiplicable.hpp
stan
Definition: log_sum_exp.hpp:8
stan::is_var
Definition: is_var.hpp:7
_variD
Eigen::Matrix< vari *, Eigen::Dynamic, Eigen::Dynamic > _variD
Definition: trace_inv_quad_form_ldlt.hpp:84
Dtype_
const int Dtype_
Definition: trace_inv_quad_form_ldlt.hpp:81
C_
Eigen::Matrix< double, C3, C3 > C_
Definition: trace_inv_quad_form_ldlt.hpp:87
_value
double _value
Definition: trace_inv_quad_form_ldlt.hpp:88
stan::math::trace_inv_quad_form_ldlt
boost::enable_if_c<!stan::is_var< T1 >::value &&!stan::is_var< T2 >::value, typename boost::math::tools::promote_args< T1, T2 >::type >::type trace_inv_quad_form_ldlt(const stan::math::LDLT_factor< T1, R2, C2 > &A, const Eigen::Matrix< T2, R3, C3 > &B)
Definition: trace_inv_quad_form_ldlt.hpp:27
stan::math::var
Independent (input) and dependent (output) variables for gradients.
Definition: var.hpp:31
D_
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > D_
Definition: trace_inv_quad_form_ldlt.hpp:83
stan::math::LDLT_factor
Definition: LDLT_factor.hpp:18
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
_ldlt
stan::math::LDLT_factor< T2, R2, C2 > _ldlt
Definition: trace_inv_quad_form_ldlt.hpp:82
LDLT_factor.hpp
Eigen.hpp
AinvB_
Eigen::Matrix< double, R3, C3 > AinvB_
Definition: trace_inv_quad_form_ldlt.hpp:86
stan::math::trace
T trace(const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
Returns the trace of the specified matrix.
Definition: trace.hpp:20
is_var.hpp
_variB
Eigen::Matrix< vari *, R3, C3 > _variB
Definition: trace_inv_quad_form_ldlt.hpp:85
_impl
trace_inv_quad_form_ldlt_impl< T2, R2, C2, T3, R3, C3 > * _impl
Definition: trace_inv_quad_form_ldlt.hpp:161

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