6663b6c9
 adorian
projet complet av...
|
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
|
#include <quiz.h>
#include <string.h>
#include <assert.h>
#include <cmath>
#include "../sequence_store.h"
#include "../sequence_context.h"
using namespace Poincare;
namespace Sequence {
void check_sequences_defined_by(double result[2][10], Sequence::Type typeU, const char * definitionU, const char * conditionU1 = nullptr, const char * conditionU2 = nullptr, Sequence::Type typeV = Sequence::Type::Explicit, const char * definitionV = nullptr, const char * conditionV1 = nullptr, const char * conditionV2 = nullptr) {
GlobalContext globalContext;
SequenceStore store;
SequenceContext sequenceContext(&globalContext, &store);
Sequence * u = nullptr;
Sequence * v = nullptr;
if (definitionU) {
u = static_cast<Sequence *>(store.addEmptyModel());
assert(u->name()[0] == 'u');
u->setType(typeU);
u->setContent(definitionU);
if (conditionU1) {
u->setFirstInitialConditionContent(conditionU1);
}
if (conditionU2) {
u->setSecondInitialConditionContent(conditionU2);
}
}
if (definitionV) {
if (store.numberOfModels() == 0) {
Sequence * tempU = static_cast<Sequence *>(store.addEmptyModel());
v = static_cast<Sequence *>(store.addEmptyModel());
store.removeModel(tempU);
v = store.modelAtIndex(0);
} else {
assert(store.numberOfModels() == 1);
v = static_cast<Sequence *>(store.addEmptyModel());
}
v->setType(typeV);
v->setContent(definitionV);
if (conditionV1) {
v->setFirstInitialConditionContent(conditionV1);
}
if (conditionV2) {
v->setSecondInitialConditionContent(conditionV2);
}
}
for (int j = 0; j < 10; j++) {
if (u && u->isDefined()) {
double un = u->evaluateAtAbscissa((double)j, &sequenceContext);
assert((std::isnan(un) && std::isnan(result[0][j])) || (un == result[0][j]));
}
if (v && v->isDefined()) {
double vn = v->evaluateAtAbscissa((double)j, &sequenceContext);
assert((std::isnan(vn) && std::isnan(result[1][j])) || (vn == result[1][j]));
}
}
}
QUIZ_CASE(sequence_evaluation) {
// u(n) = n
double result0[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {}};
check_sequences_defined_by(result0, Sequence::Type::Explicit, "n");
// u(n+1) = u(n)+n, u(0) = 0
double result1[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}, {}};
check_sequences_defined_by(result1, Sequence::Type::SingleRecurrence, "u(n)+n", "0");
// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0
double result2[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}, {}};
check_sequences_defined_by(result2, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
// u independent, v defined with u
// u(n) = n; v(n) = u(n)+n
double result3[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
{0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0}};
check_sequences_defined_by(result3, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::Explicit, "u(n)+n");
// u(n+1) = u(n)+n, u(0) = 0; v(n) = u(n)+n
double result4[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
{0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0, 45.0}};
check_sequences_defined_by(result4, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::Explicit, "u(n)+n");
// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0; v(n) = u(n)+n
double result5[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
{0.0, 1.0, 2.0, 4.0, 7.0, 12.0, 20.0, 33.0, 54.0, 88.0}};
check_sequences_defined_by(result5, Sequence::Type::DoubleRecurrence, "n+u(n)+u(n+1)", "0", "0", Sequence::Type::Explicit, "u(n)+n");
// u(n) = n; v(n+1) = u(n)+u(n+1)+n, v(0) = 0
double result6[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
{0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0, 25.0}};
check_sequences_defined_by(result6, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::SingleRecurrence, "u(n)+u(n+1)+n", "0");
// u(n+1) = u(n)+n, u(0) = 0; v(n+1) = u(n)+u(n+1)+n, v(0) = 0
double result7[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}};
check_sequences_defined_by(result7, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::SingleRecurrence, "u(n)+u(n+1)+n", "0");
// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0; v(n+1) = u(n)+u(n+1)+n, v(0) = 0
double result8[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
{0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0, 133.0}};
check_sequences_defined_by(result8, Sequence::Type::DoubleRecurrence, "n+u(n)+u(n+1)", "0", "0", Sequence::Type::SingleRecurrence, "u(n)+u(n+1)+n", "0");
// u(n) = n; v(n+2) = u(n)+u(n+1)+n, v(0) = 0, v(1)=0
double result9[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
{0.0, 0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0}};
check_sequences_defined_by(result9, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
// u(n+1) = u(n)+n, u(0) = 0; v(n+2) = u(n)+u(n+1)+n, v(0) = 0, v(1)=0
double result10[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
{0.0, 0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0}};
check_sequences_defined_by(result10, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0; v(n+2) = u(n)+u(n+1)+n, v(0) = 0, v(1)=0
double result11[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}};
check_sequences_defined_by(result11, Sequence::Type::DoubleRecurrence, "n+u(n)+u(n+1)", "0", "0", Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
// v independent, u defined with v
// u(n) = v(n); v(n) = u(n)
double result12[2][10] = {{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN},
{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}};
check_sequences_defined_by(result12, Sequence::Type::Explicit, "v(n)", nullptr, nullptr, Sequence::Type::Explicit, "u(n)");
// u(n+1) = v(n)+n, u(0)=0; v(n) = u(n)+n
double result13[2][10] = {{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}, {0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81}};
check_sequences_defined_by(result13, Sequence::Type::SingleRecurrence, "v(n)+n", "0", nullptr, Sequence::Type::Explicit, "u(n)+n");
// u(n+2) = v(n+1)+u(n+1)+v(n)+u(n)+n, u(1) = 0; u(0)=0; v(n) = u(n)+n
double result14[2][10] = {{0.0, 0.0, 1.0, 6.0, 21.0, 64.0, 183.0, 510.0, 1405.0, 3852.0}, {0.0, 1.0, 3.0, 9.0, 25.0, 69.0, 189.0, 517.0, 1413.0, 3861.0}};
check_sequences_defined_by(result14, Sequence::Type::DoubleRecurrence, "v(n+1)+v(n)+u(n+1)+u(n)+n", "0", "0", Sequence::Type::Explicit, "u(n)+n");
// u(n) = v(n)+n; v(n+1) = u(n)+n, v(0)=0
double result15[2][10] = {{0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81},
{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}};
check_sequences_defined_by(result15, Sequence::Type::Explicit, "v(n)+n", nullptr, nullptr, Sequence::Type::SingleRecurrence, "u(n)+n", "0");
// u(n+1) = v(n)+n, u(0)=0; v(n+1) = u(n)+n, v(0)=0
double result16[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}, {0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}};
check_sequences_defined_by(result16, Sequence::Type::SingleRecurrence, "v(n)+n", "0", nullptr, Sequence::Type::SingleRecurrence, "u(n)+n", "0");
// u(n+2) = v(n+1)+u(n+1)+v(n)+u(n)+n, u(1) = 0, u(0) = 0; v(n+1) = u(n)+n, v(0)=0
double result17[2][10] = {{0.0, 0.0, 0.0, 2.0, 7.0, 19.0, 46.0, 105.0, 233.0, 509.0}, {0.0, 0.0, 1.0, 2.0, 5.0, 11.0, 24.0, 52.0, 112.0, 241.0}};
check_sequences_defined_by(result17, Sequence::Type::DoubleRecurrence, "v(n+1)+v(n)+u(n+1)+u(n)+n", "0", "0", Sequence::Type::SingleRecurrence, "u(n)+n", "0");
// u(n) = n; v undefined
double result18[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}};
check_sequences_defined_by(result18, Sequence::Type::Explicit, "n");
// u undefined; v(n) = n
double result19[2][10] = {{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}, {0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}};
check_sequences_defined_by(result19, Sequence::Type::Explicit, nullptr, nullptr, nullptr, Sequence::Type::Explicit, "n");
}
}
|