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
202
203
204
205
206
207
208
|
#include "Compare.hh"
#include "NEvaluator.hh"
#include <cmath>
using namespace cadabra;
// void NEvaluator::find_common_subexpressions(std::vector<Ex *>)
// {
// // Compute the hash value of every subtree, and collect matches.
// // Then compare subtrees with equal hash to find common subtrees.
// }
NEvaluator::NEvaluator(const Ex &ex_)
: ex(ex_)
{
}
NTensor NEvaluator::evaluate()
{
find_variable_locations();
// The vector below pairs LaTeX strings which can appear in the
// cadabra input to function names in the C++ standard library.
const std::vector<std::pair<nset_t::iterator, double (*)(double) >> elementary
= { { name_set.find("\\sin"), std::sin},
{ name_set.find("\\cos"), std::cos},
{ name_set.find("\\tan"), std::tan},
{ name_set.find("\\arcsin"), std::asin},
{ name_set.find("\\arccos"), std::acos},
{ name_set.find("\\arctan"), std::atan},
{ name_set.find("\\sinh"), std::sinh},
{ name_set.find("\\cosh"), std::cosh},
{ name_set.find("\\tanh"), std::tanh},
// { name_set.find("\\coth"), std::coth},
// { name_set.find("\\sech"), std::sech},
// { name_set.find("\\csch"), std::csch},
{ name_set.find("\\arcsinh"), std::asinh},
{ name_set.find("\\arccosh"), std::acosh},
{ name_set.find("\\arctanh"), std::atanh},
// { name_set.find("\\arccoth"), std::acoth},
// { name_set.find("\\arcsech"), std::asech},
// { name_set.find("\\arccsch"), std::acsch},
{ name_set.find("\\log"), std::log10},
{ name_set.find("\\ln"), std::log},
{ name_set.find("\\exp"), std::exp},
{ name_set.find("\\sqrt"), std::sqrt},
};
const auto n_pow = name_set.find("\\pow");
const auto n_prod = name_set.find("\\prod");
const auto n_sum = name_set.find("\\sum");
const auto n_pi = name_set.find("\\pi");
NTensor lastval(0);
auto it = ex.begin_post();
while(it != ex.end_post()) {
// Either this node is known in the subtree value map,
// or this node is a function which combines the values
// of child nodes.
auto fnd = subtree_values.find(Ex::iterator(it));
if(fnd!=subtree_values.end()) {
//std::cerr << it << " has value " << fnd->second << std::endl;
}
else {
bool found_elementary=false;
if(it->is_rational()) {
lastval = to_double(*it->multiplier);
found_elementary=true;
}
else {
for(const auto& el: elementary) {
if(it->name == el.first) {
auto arg = ex.begin(it);
auto argval = subtree_values.find(arg)->second;
lastval = argval.apply(el.second);
lastval *= to_double(*it->multiplier);
found_elementary=true;
break;
}
}
}
if(found_elementary==false) {
if(it->name==n_prod) {
for(auto cit = ex.begin(it); cit!=ex.end(it); ++cit) {
auto cfnd = subtree_values.find(Ex::iterator(cit));
if(cfnd==subtree_values.end())
throw std::logic_error("Inconsistent value tree.");
if(cit==ex.begin(it))
lastval = cfnd->second;
else
lastval *= cfnd->second;
}
lastval *= to_double(*it->multiplier);
}
else if(it->name==n_sum) {
for(auto cit = ex.begin(it); cit!=ex.end(it); ++cit) {
auto cfnd = subtree_values.find(Ex::iterator(cit));
if(cfnd==subtree_values.end())
throw std::logic_error("Inconsistent value tree.");
if(cit==ex.begin(it))
lastval = cfnd->second;
else
lastval += cfnd->second;
}
lastval *= to_double(*it->multiplier);
}
else if(it->name==n_pow) {
auto cit1 = Ex::begin(it);
auto cit2 = cit1;
++cit2;
auto cfnd1 = subtree_values.find(Ex::iterator(cit1));
auto cfnd2 = subtree_values.find(Ex::iterator(cit2));
if(cfnd1==subtree_values.end() || cfnd2==subtree_values.end())
throw std::logic_error("Inconsistent value tree at exponentiation node.");
lastval = cfnd1->second.pow( cfnd2->second );
lastval *= to_double(*it->multiplier);
// throw std::logic_error("Value unknown for subtree special function.");
}
else if(it->name==n_pi) {
lastval = 3.141592653589793238463;
lastval *= to_double(*it->multiplier);
}
else {
// Try variable substitution rules.
bool found=false;
for(const auto& var: variable_values) {
// std::cerr << "Comparing " << var.first << " with " << *it << std::endl;
Ex no_multiplier(it);
auto mult = *it->multiplier;
one( no_multiplier.begin()->multiplier );
if(var.variable == no_multiplier) {
subtree_values.insert(std::make_pair(it, var.values));
lastval = var.values;
lastval *= to_double(mult);
// std::cerr << "We know the value of " << *it << std::endl;
found=true;
break;
}
}
if(!found)
throw std::logic_error("Value unknown for subtree with head "+(*it->name)+".");
}
}
subtree_values.insert(std::make_pair(it, lastval));
}
++it;
}
return lastval;
}
void NEvaluator::set_variable(const Ex& var, const NTensor& val)
{
variable_values.push_back( VariableValues({var, val}) );
}
void NEvaluator::find_variable_locations()
{
// FIXME: we don't really need this anymore, as we do everything
// with broadcasting.
for(auto& var: variable_values) {
auto it = ex.begin_post();
while(it != ex.end_post()) {
if(var.variable == *it)
var.locations.push_back(it);
++it;
}
// std::cerr << "Variable " << var.variable << " at " << var.locations.size() << " places" << std::endl;
}
// Now insert subtree values which are such that for every
// variable node we have an NTensor which is broadcast to the
// shape of the full variable set NTensor.
// std::cerr << "full shape = ";
std::vector<size_t> fullshape;
for(const auto& var: variable_values) {
assert(var.values.shape.size()==1);
fullshape.push_back(var.values.shape[0]);
// std::cerr << var.values.shape[0] << ", ";
}
// std::cerr << std::endl;
for(size_t v=0; v<variable_values.size(); ++v) {
const auto& var = variable_values[v];
for(const auto& it: var.locations) {
subtree_values.insert(std::make_pair(it, var.values.broadcast( fullshape, v ) ) );
}
}
// std::cerr << "ready" << std::endl;
}
|
