1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
#pragma once
#include <eigen3/Eigen/Dense>
#include <iterator>
#include "types.hpp"
#include "tensor.hpp"
#include "factorial.hpp"
template <typename Derived>
Vector<typename Derived::Scalar> normalize(const Eigen::MatrixBase<Derived>& z) {
return z * sqrt((Real)z.size() / (typename Derived::Scalar)(z.transpose() * z));
}
template <typename Scalar, int... ps>
class pSpinModel {
private:
std::tuple<Matrix<Scalar>, Tensor<Scalar, 3>> hamGradTensorHelper(const Vector<Scalar>& z, const Tensor<Scalar, 2>& J) const {
Tensor<Scalar, 3> J3(z.size(), z.size(), z.size());;
J3.setZero();
Matrix<Scalar> Jz = Eigen::Map<const Matrix<Scalar>>(J.data(), z.size(), z.size());
return {Jz, J3};
}
template <int p>
std::tuple<Matrix<Scalar>, Tensor<Scalar, 3>> hamGradTensorHelper(const Vector<Scalar>& z, const Tensor<Scalar, p>& J) const {
Tensor<Scalar, 3> J3 = contractDown(J, z);
Tensor<Scalar, 1> zT = Eigen::TensorMap<Tensor<const Scalar, 1>>(z.data(), {z.size()});
Tensor<Scalar, 2> J3zT = J3.contract(zT, ip00);
Matrix<Scalar> Jz = Eigen::Map<const Matrix<Scalar>>(J3zT.data(), z.size(), z.size());
return {Jz, J3};
}
template <int p, int... qs>
std::tuple<Scalar, Vector<Scalar>, Matrix<Scalar>, Tensor<Scalar, 3>> hamGradHessHelper(const Vector<Scalar>& z, const Tensor<Scalar, p>& J, const Tensor<Scalar, qs>& ...Js) const {
auto [Jz, J3] = hamGradTensorHelper(z, J);
Vector<Scalar> Jzz = Jz * z;
Scalar Jzzz = Jzz.transpose() * z;
Real pBang = factorial(p);
Tensor<Scalar, 3> dddH = ((p - 2) * (p - 1) * p / pBang) * J3;
Matrix<Scalar> ddH = ((p - 1) * p / pBang) * Jz;
Vector<Scalar> dH = (p / pBang) * Jzz;
Scalar H = Jzzz / pBang;
if constexpr (sizeof...(Js) > 0) {
auto [Hs, dHs, ddHs, dddHs] = hamGradHessHelper(z, Js...);
H += Hs;
dH += dHs;
ddH += ddHs;
dddH += dddHs;
}
return {H, dH, ddH, dddH};
}
public:
std::tuple<Tensor<Scalar, ps>...> Js;
pSpinModel() {}
pSpinModel(const std::tuple<Tensor<Scalar, ps>...>& Js) : Js(Js) {}
template <class Generator, typename... T>
pSpinModel<Real>(unsigned N, Generator& r, T... μs) {
Js = std::make_tuple(μs * generateRealPSpinCouplings<Real, ps>(N, r)...);
}
unsigned dimension() const {
return std::get<0>(Js).dimension(0);
}
template <typename NewScalar>
pSpinModel<NewScalar, ps...> cast() const {
return std::apply(
[] (const Tensor<Scalar, ps>& ...Ks) -> std::tuple<Tensor<NewScalar, ps>...> {
return std::make_tuple(Ks.template cast<NewScalar>()...);
}, Js
);
}
template <typename T>
pSpinModel<Scalar, ps...>& operator*=(T x) {
std::tuple<Tensor<Scalar, ps>...> newJs = std::apply(
[x] (const Tensor<Scalar, ps>& ...Ks) -> std::tuple<Tensor<Scalar, ps>...> {
return std::make_tuple((x * Ks)...);
}, Js
);
Js = newJs;
return *this;
}
std::tuple<Scalar, Vector<Scalar>, Matrix<Scalar>, Tensor<Scalar, 3>> hamGradHess(const Vector<Scalar>& z) const {
return std::apply([&z, this](const Tensor<Scalar, ps>& ...Ks) -> std::tuple<Scalar, Vector<Scalar>, Matrix<Scalar>, Tensor<Scalar, 3>> { return hamGradHessHelper(z, Ks...); }, Js);
}
Scalar getHamiltonian(const Vector<Scalar>& z) const {
Scalar H;
std::tie(H, std::ignore, std::ignore, std::ignore) = hamGradHess(z);
return H;
}
Vector<Scalar> getGradient(const Vector<Scalar>& z) const {
Vector<Scalar> dH;
std::tie(std::ignore, dH, std::ignore, std::ignore) = hamGradHess(z);
return dH;
}
Matrix<Scalar> getHessian(const Vector<Scalar>& z) const {
Matrix<Scalar> ddH;
std::tie(std::ignore, std::ignore, ddH, std::ignore) = hamGradHess(z);
return ddH;
}
};
template <class Scalar>
Vector<Scalar> zDot(const Vector<Scalar>& z, const Vector<Scalar>& dH) {
return -dH.conjugate() + (dH.dot(z) / z.squaredNorm()) * z.conjugate();
}
template <class Scalar>
Matrix<Scalar> dzDot(const Vector<Scalar>& z, const Vector<Scalar>& dH) {
Real z² = z.squaredNorm();
return (dH.conjugate() - (dH.dot(z) / z²) * z.conjugate()) * z.adjoint() / z²;
}
template <class Scalar>
Matrix<Scalar> dzDotConjugate(const Vector<Scalar>& z, const Vector<Scalar>& dH, const Matrix<Scalar>& ddH) {
Real z² = z.squaredNorm();
return -ddH + (ddH * z.conjugate()) * z.transpose() / z²
+ (z.dot(dH) / z²) * (
Matrix<Scalar>::Identity(ddH.rows(), ddH.cols()) - z.conjugate() * z.transpose() / z²
);
}
template <class Scalar>
Tensor<Scalar, 3> ddzDot(const Vector<Scalar>& z, const Vector<Scalar>& dH) {
Tensor<Scalar, 1> zT = Eigen::TensorMap<Tensor<const Scalar, 1>>(z.data(), {z.size()});
Tensor<Scalar, 1> dHT = Eigen::TensorMap<Tensor<const Scalar, 1>>(dH.data(), {dH.size()});
Eigen::array<Eigen::IndexPair<int>, 0> ei = {};
Scalar z² = z.squaredNorm();
return - zT.conjugate().contract(dHT.conjugate(), ei).contract(zT.conjugate(), ei) / pow(z², 2)
- dHT.conjugate().contract(zT.conjugate(), ei).contract(zT.conjugate(), ei) / pow(z², 2)
+ zT.conjugate().contract(zT.conjugate(), ei).contract(zT.conjugate(), ei) * ((Real)2 * dH.dot(z) / pow(z², 3));
}
template <class Scalar>
Tensor<Scalar, 3> dcdzDot(const Vector<Scalar>& z, const Vector<Scalar>& dH, const Matrix<Scalar>& ddH) {
Tensor<Scalar, 1> zT = Eigen::TensorMap<Tensor<const Scalar, 1>>(z.data(), {z.size()});
Tensor<Scalar, 1> dHT = Eigen::TensorMap<Tensor<const Scalar, 1>>(dH.data(), {dH.size()});
Tensor<Scalar, 2> ddHT = Eigen::TensorMap<Tensor<const Scalar, 2>>(ddH.data(), {dH.size(), dH.size()});
Matrix<Scalar> I = Matrix<Real>::Identity(z.size(), z.size());
Tensor<Scalar, 2> IT = Eigen::TensorMap<Tensor<const Scalar, 2>>(I.data(), {z.size(), z.size()});
Eigen::array<Eigen::IndexPair<int>, 0> ei = {};
Scalar z² = z.squaredNorm();
return ddHT.conjugate().contract(zT.conjugate(), ei) / z²
+IT.contract(dHT.conjugate(), ei).shuffle((std::array<int, 3>){0,2,1}) / z²
-zT.contract(dHT.conjugate(), ei).contract(zT.conjugate(), ei) / pow(z², 2)
-ddHT.conjugate().contract(zT, ip00).contract(zT.conjugate(), ei).contract(zT.conjugate(), ei) / pow(z², 2)
-IT.contract(zT.conjugate(), ei) * (dH.dot(z) / pow(z², 2))
-IT.contract(zT.conjugate(), ei).shuffle((std::array<int, 3>){0,2,1}) * (dH.dot(z) / pow(z², 2))
+zT.contract(zT.conjugate(), ei).contract(zT.conjugate(), ei) * ((Real)2 * dH.dot(z) / pow(z², 3))
;
}
template <class Scalar>
Tensor<Scalar, 3> ddzDotConjugate(const Vector<Scalar>& z, const Vector<Scalar>& dH, const Matrix<Scalar>& ddH, const Tensor<Scalar, 3>& dddH) {
Tensor<Scalar, 1> zT = Eigen::TensorMap<Tensor<const Scalar, 1>>(z.data(), {z.size()});
Tensor<Scalar, 1> dHT = Eigen::TensorMap<Tensor<const Scalar, 1>>(dH.data(), {dH.size()});
Tensor<Scalar, 2> ddHT = Eigen::TensorMap<Tensor<const Scalar, 2>>(ddH.data(), {z.size(), z.size()});
Matrix<Scalar> I = Matrix<Real>::Identity(z.size(), z.size());
Tensor<Scalar, 2> IT = Eigen::TensorMap<Tensor<const Scalar, 2>>(I.data(), {z.size(), z.size()});
Eigen::array<Eigen::IndexPair<int>, 0> ei = {};
Eigen::array<Eigen::IndexPair<int>, 1> ip00 = {Eigen::IndexPair<int>(0, 0)};
Scalar z² = z.squaredNorm();
return - dddH + dddH.contract(zT.conjugate(), ip00).contract(zT, ei) / z²
+ IT.contract(ddHT.contract(zT.conjugate(), ip00), ei).shuffle((std::array<int, 3>){0, 2, 1}) / z²
+ ddHT.contract(zT.conjugate(), ip00).contract(IT, ei) / z²
- zT.conjugate().contract(ddHT.contract(zT.conjugate(), ip00), ei).contract(zT, ei) / pow(z², 2)
- zT.conjugate().contract(IT, ei) * (z.dot(dH) / pow(z², 2))
- IT.contract(zT.conjugate(), ei).shuffle((std::array<int, 3>){0, 2, 1}) * (z.dot(dH) / pow(z², 2))
- ddHT.contract(zT.conjugate(), ip00).contract(zT.conjugate(), ei).contract(zT, ei) / pow(z², 2)
+ zT.conjugate().contract(zT.conjugate(), ei).contract(zT, ei) * ((Real)2 * z.dot(dH) / pow(z², 3));
}
|
