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[apps/sequence] Add tests on third sequence
This commit is contained in:
Émilie Feral
@@ -27,134 +27,300 @@ Sequence * addSequence(SequenceStore * store, Sequence::Type type, const char *
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return u;
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}
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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) {
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void check_sequences_defined_by(double result[MaxNumberOfSequences][10], Sequence::Type types[MaxNumberOfSequences], const char * definitions[MaxNumberOfSequences], const char * conditions1[MaxNumberOfSequences], const char * conditions2[MaxNumberOfSequences]) {
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Shared::GlobalContext globalContext;
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SequenceStore store;
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SequenceContext sequenceContext(&globalContext, &store);
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Sequence * u = nullptr;
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Sequence * v = nullptr;
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if (definitionU) {
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u = addSequence(&store, typeU, definitionU, conditionU1, conditionU2);
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quiz_assert(u->fullName()[0] == 'u');
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}
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if (definitionV) {
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if (store.numberOfModels() == 0) {
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Sequence * tempU = addSequence(&store, typeU, nullptr, nullptr, nullptr);
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v = addSequence(&store, typeV, definitionV, conditionV1, conditionV2);
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store.removeModel(*tempU);
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} else {
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quiz_assert(store.numberOfModels() == 1);
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v = addSequence(&store, typeV, definitionV, conditionV1, conditionV2);
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}
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Sequence * seqs[MaxNumberOfSequences];
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for (int i = 0; i < MaxNumberOfSequences; i++) {
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seqs[i] = addSequence(&store, types[i], definitions[i], conditions1[i], conditions2[i]);
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}
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for (int j = 0; j < 10; j++) {
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if (u && u->isDefined()) {
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double un = u->evaluateAtAbscissa((double)j, &sequenceContext);
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quiz_assert((std::isnan(un) && std::isnan(result[0][j])) || (un == result[0][j]));
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}
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if (v && v->isDefined()) {
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double vn = v->evaluateAtAbscissa((double)j, &sequenceContext);
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quiz_assert((std::isnan(vn) && std::isnan(result[1][j])) || (vn == result[1][j]));
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for (int i = 0; i < MaxNumberOfSequences; i++) {
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if (seqs[i]->isDefined()) {
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double un = seqs[i]->evaluateAtAbscissa((double)j, &sequenceContext);
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quiz_assert((std::isnan(un) && std::isnan(result[i][j])) || (un == result[i][j]));
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}
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}
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}
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store.removeAll();
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}
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QUIZ_CASE(sequence_evaluation) {
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Sequence::Type types[MaxNumberOfSequences] = {Sequence::Type::Explicit, Sequence::Type::Explicit, Sequence::Type::Explicit};
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const char * definitions[MaxNumberOfSequences] = {nullptr, nullptr, nullptr};
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const char * conditions1[MaxNumberOfSequences] = {nullptr, nullptr, nullptr};
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const char * conditions2[MaxNumberOfSequences] = {nullptr, nullptr, nullptr};
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// u(n) = n
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double result0[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {}};
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check_sequences_defined_by(result0, Sequence::Type::Explicit, "n");
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double results1[MaxNumberOfSequences][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {}, {}};
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definitions[0] = "n";
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check_sequences_defined_by(results1, types, definitions, conditions1, conditions2);
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// u(n+1) = u(n)+n, u(0) = 0
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double result1[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}, {}};
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check_sequences_defined_by(result1, Sequence::Type::SingleRecurrence, "u(n)+n", "0");
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double results2[MaxNumberOfSequences][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}, {}, {}};
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types[0] = Sequence::Type::SingleRecurrence;
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definitions[0] = "u(n)+n";
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conditions1[0] = "0";
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check_sequences_defined_by(results2, types, definitions, conditions1, conditions2);
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// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0
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double result2[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}, {}};
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check_sequences_defined_by(result2, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
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double results3[MaxNumberOfSequences][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}, {}, {}};
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types[0] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "u(n)+u(n+1)+n";
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conditions1[0] = "0";
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conditions2[0] = "0";
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check_sequences_defined_by(results3, types, definitions, conditions1, conditions2);
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// u independent, v defined with u
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// u(n) = n; v(n) = u(n)+n
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double result3[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0}};
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check_sequences_defined_by(result3, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::Explicit, "u(n)+n");
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double results4[MaxNumberOfSequences][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0},
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{}};
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types[0] = Sequence::Type::Explicit;
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definitions[0] = "n";
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definitions[1] = "u(n)+n";
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conditions1[0] = nullptr;
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conditions2[0] = nullptr;
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check_sequences_defined_by(results4, types, definitions, conditions1, conditions2);
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// u(n+1) = u(n)+n, u(0) = 0; v(n) = u(n)+n
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double result4[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0, 45.0}};
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check_sequences_defined_by(result4, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::Explicit, "u(n)+n");
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double results5[MaxNumberOfSequences][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0, 45.0}, {}};
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types[0] = Sequence::Type::SingleRecurrence;
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definitions[0] = "n+u(n)";
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conditions1[0] = "0";
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check_sequences_defined_by(results5, types, definitions, conditions1, conditions2);
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// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0; v(n) = u(n)+n
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double result5[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 1.0, 2.0, 4.0, 7.0, 12.0, 20.0, 33.0, 54.0, 88.0}};
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check_sequences_defined_by(result5, Sequence::Type::DoubleRecurrence, "n+u(n)+u(n+1)", "0", "0", Sequence::Type::Explicit, "u(n)+n");
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double results6[MaxNumberOfSequences][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 1.0, 2.0, 4.0, 7.0, 12.0, 20.0, 33.0, 54.0, 88.0}, {}};
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types[0] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "n+u(n)+u(n+1)";
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conditions2[0] = "0";
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check_sequences_defined_by(results6, types, definitions, conditions1, conditions2);
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// u(n) = n; v(n+1) = u(n)+u(n+1)+n, v(0) = 0
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double result6[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0, 25.0}};
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check_sequences_defined_by(result6, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::SingleRecurrence, "u(n)+u(n+1)+n", "0");
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double results7[MaxNumberOfSequences][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0, 25.0}, {}};
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types[0] = Sequence::Type::Explicit;
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types[1] = Sequence::Type::SingleRecurrence;
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definitions[0] = "n";
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definitions[1] = "n+u(n)+u(n+1)";
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conditions1[0] = nullptr;
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conditions1[1] = "0";
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conditions2[0] = nullptr;
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check_sequences_defined_by(results7, types, definitions, conditions1, conditions2);
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// u(n+1) = u(n)+n, u(0) = 0; v(n+1) = u(n)+u(n+1)+n, v(0) = 0
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double result7[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}};
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check_sequences_defined_by(result7, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::SingleRecurrence, "u(n)+u(n+1)+n", "0");
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double results8[MaxNumberOfSequences][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}, {}};
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types[0] = Sequence::Type::SingleRecurrence;
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definitions[0] = "n+u(n)";
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definitions[1] = "n+u(n)+u(n+1)";
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conditions1[0] = "0";
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check_sequences_defined_by(results8, types, definitions, conditions1, conditions2);
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// 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
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double result8[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0, 133.0}};
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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");
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double results9[MaxNumberOfSequences][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0, 133.0}, {}};
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types[0] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "n+u(n)+u(n+1)";
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conditions2[0] = "0";
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check_sequences_defined_by(results9, types, definitions, conditions1, conditions2);
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// u(n) = n; v(n+2) = u(n)+u(n+1)+n, v(0) = 0, v(1)=0
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double result9[2][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0}};
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check_sequences_defined_by(result9, Sequence::Type::Explicit, "n", nullptr, nullptr, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
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double results10[MaxNumberOfSequences][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0},
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{0.0, 0.0, 1.0, 4.0, 7.0, 10.0, 13.0, 16.0, 19.0, 22.0}, {}};
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types[0] = Sequence::Type::Explicit;
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types[1] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "n";
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conditions1[0] = nullptr;
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conditions2[0] = nullptr;
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conditions2[1] = "0";
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check_sequences_defined_by(results10, types, definitions, conditions1, conditions2);
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// u(n+1) = u(n)+n, u(0) = 0; v(n+2) = u(n)+u(n+1)+n, v(0) = 0, v(1)=0
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double result10[2][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0}};
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check_sequences_defined_by(result10, Sequence::Type::SingleRecurrence, "n+u(n)", "0", nullptr, Sequence::Type::DoubleRecurrence, "u(n)+u(n+1)+n", "0", "0");
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double results11[MaxNumberOfSequences][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0},
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{0.0, 0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0}, {}};
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types[0] = Sequence::Type::SingleRecurrence;
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definitions[0] = "n+u(n)";
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conditions1[0] = "0";
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check_sequences_defined_by(results11, types, definitions, conditions1, conditions2);
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// 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
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double result11[2][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}};
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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");
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double results12[MaxNumberOfSequences][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0},
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{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}, {}};
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types[0] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "u(n+1)+u(n)+n";
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conditions2[0] = "0";
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check_sequences_defined_by(results12, types, definitions, conditions1, conditions2);
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// v independent, u defined with v
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// u(n) = v(n); v(n) = u(n)
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double result12[2][10] = {{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN},
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{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}};
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check_sequences_defined_by(result12, Sequence::Type::Explicit, "v(n)", nullptr, nullptr, Sequence::Type::Explicit, "u(n)");
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double results13[MaxNumberOfSequences][10] = {{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN},
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{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}, {}};
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types[0] = Sequence::Type::Explicit;
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types[1] = Sequence::Type::Explicit;
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definitions[0] = "v(n)";
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definitions[1] = "u(n)";
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conditions1[0] = nullptr;
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conditions1[1] = nullptr;
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conditions2[0] = nullptr;
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conditions2[1] = nullptr;
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check_sequences_defined_by(results13, types, definitions, conditions1, conditions2);
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// u(n+1) = v(n)+n, u(0)=0; v(n) = u(n)+n
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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}};
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check_sequences_defined_by(result13, Sequence::Type::SingleRecurrence, "v(n)+n", "0", nullptr, Sequence::Type::Explicit, "u(n)+n");
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double results14[MaxNumberOfSequences][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}, {}};
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types[0] = Sequence::Type::SingleRecurrence;
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definitions[0] = "v(n)+n";
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definitions[1] = "u(n)+n";
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conditions1[0] = "0";
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check_sequences_defined_by(results14, types, definitions, conditions1, conditions2);
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// 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
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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}};
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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");
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double results15[MaxNumberOfSequences][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}, {}};
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types[0] = Sequence::Type::DoubleRecurrence;
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definitions[0] = "v(n+1)+v(n)+u(n+1)+u(n)+n";
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conditions1[0] = "0";
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conditions2[0] = "0";
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check_sequences_defined_by(results15, types, definitions, conditions1, conditions2);
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// u(n) = v(n)+n; v(n+1) = u(n)+n, v(0)=0
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double result15[2][10] = {{0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81},
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{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}};
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check_sequences_defined_by(result15, Sequence::Type::Explicit, "v(n)+n", nullptr, nullptr, Sequence::Type::SingleRecurrence, "u(n)+n", "0");
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double results16[MaxNumberOfSequences][10] = {{0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81},
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{0.0, 0.0, 2.0, 6.0, 12.0, 20.0, 30.0, 42.0, 56.0, 72.0}, {}};
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types[0] = Sequence::Type::Explicit;
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types[1] = Sequence::Type::SingleRecurrence;
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definitions[0] = "v(n)+n";
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conditions1[0] = nullptr;
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||||
conditions1[1] = "0";
|
||||
conditions2[0] = nullptr;
|
||||
check_sequences_defined_by(results16, types, definitions, conditions1, conditions2);
|
||||
|
||||
// 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");
|
||||
double results17[MaxNumberOfSequences][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}, {}};
|
||||
types[0] = Sequence::Type::SingleRecurrence;
|
||||
conditions1[0] = "0";
|
||||
check_sequences_defined_by(results17, types, definitions, conditions1, conditions2);
|
||||
|
||||
// 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");
|
||||
double results18[MaxNumberOfSequences][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}, {}};
|
||||
types[0] = Sequence::Type::DoubleRecurrence;
|
||||
definitions[0] = "v(n+1)+v(n)+u(n+1)+u(n)+n";
|
||||
conditions2[0] = "0";
|
||||
check_sequences_defined_by(results18, types, definitions, conditions1, conditions2);
|
||||
|
||||
// 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");
|
||||
double results19[MaxNumberOfSequences][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}, {}};
|
||||
types[0] = Sequence::Type::Explicit;
|
||||
types[1] = Sequence::Type::Explicit;
|
||||
definitions[0] = "n";
|
||||
definitions[1] = nullptr;
|
||||
conditions1[0] = nullptr;
|
||||
conditions1[1] = nullptr;
|
||||
conditions2[0] = nullptr;
|
||||
conditions2[1] = nullptr;
|
||||
check_sequences_defined_by(results19, types, definitions, conditions1, conditions2);
|
||||
|
||||
// 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");
|
||||
double results20[MaxNumberOfSequences][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}, {}};
|
||||
definitions[0] = nullptr;
|
||||
definitions[1] = "n";
|
||||
check_sequences_defined_by(results20, types, definitions, conditions1, conditions2);
|
||||
|
||||
// u, v, w independent
|
||||
|
||||
// u(n) = n; v(n+1) = 9+n, v(0) = 0; w(n) = n+2
|
||||
double results21[MaxNumberOfSequences][10] = {{0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {0.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0}, {2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0}};
|
||||
types[1] = Sequence::Type::SingleRecurrence;
|
||||
definitions[0] = "n";
|
||||
definitions[1] = "9+n";
|
||||
definitions[2] = "n+2";
|
||||
conditions1[1] = "0";
|
||||
check_sequences_defined_by(results21, types, definitions, conditions1, conditions2);
|
||||
|
||||
// u(n+2) = u(n+1)+u(n)+n, u(0) = 0, u(1) = 0; v(n) = 9+n; w(n+1) = w(n)+2, w(0) = 0
|
||||
double results22[MaxNumberOfSequences][10] = {{0.0, 0.0, 0.0, 1.0, 3.0, 7.0, 14.0, 26.0, 46.0, 79.0}, {9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0}, {0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0}};
|
||||
types[0] = Sequence::Type::DoubleRecurrence;
|
||||
types[1] = Sequence::Type::Explicit;
|
||||
types[2] = Sequence::Type::SingleRecurrence;
|
||||
definitions[0] = "u(n+1)+u(n)+n";
|
||||
definitions[2] = "2+w(n)";
|
||||
conditions1[0] = "0";
|
||||
conditions1[1] = nullptr;
|
||||
conditions1[2] = "0";
|
||||
conditions2[0] = "0";
|
||||
check_sequences_defined_by(results22, types, definitions, conditions1, conditions2);
|
||||
|
||||
// u(n+1) = u(n)+n, u(0) = 0; v(n) = 9+n; w(n+2) = w(n+1)+w(n)+2, w(0) = 0, w(1) = 0
|
||||
double results23[MaxNumberOfSequences][10] = {{0.0, 0.0, 1.0, 3.0, 6.0, 10.0, 15.0, 21.0, 28.0, 36.0}, {9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0}, {0.0, 0.0, 2.0, 4.0, 8.0, 14.0, 24.0, 40.0, 66.0, 108.0}};
|
||||
types[0] = Sequence::Type::SingleRecurrence;
|
||||
types[2] = Sequence::Type::DoubleRecurrence;
|
||||
definitions[0] = "u(n)+n";
|
||||
definitions[2] = "w(n+1)+w(n)+2";
|
||||
conditions2[2] = "0";
|
||||
conditions2[0] = nullptr;
|
||||
check_sequences_defined_by(results23, types, definitions, conditions1, conditions2);
|
||||
|
||||
// v depends on u, w depends on v & u independent
|
||||
// u(n) = n ; v(n+1) = u(n)+1, v(0) = 0, w(n) = 2+v(n)
|
||||
double results24[MaxNumberOfSequences][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, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0}};
|
||||
types[0] = Sequence::Type::Explicit;
|
||||
types[1] = Sequence::Type::SingleRecurrence;
|
||||
types[2] = Sequence::Type::Explicit;
|
||||
definitions[0] = "n";
|
||||
definitions[1] = "u(n)+1";
|
||||
definitions[2] = "2+v(n)";
|
||||
conditions1[1] = "0";
|
||||
check_sequences_defined_by(results24, types, definitions, conditions1, conditions2);
|
||||
|
||||
// u(n) = n ; v(n+1) = u(n)+1, v(0) = 0, w(n+1) = 2+v(n+1), w(0) = 0
|
||||
double results25[MaxNumberOfSequences][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, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {0.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0}};
|
||||
types[2] = Sequence::Type::SingleRecurrence;
|
||||
definitions[2] = "2+v(n+1)";
|
||||
conditions1[2] = "0";
|
||||
check_sequences_defined_by(results25, types, definitions, conditions1, conditions2);
|
||||
|
||||
// v depends on u, w depends on u and v & u independent
|
||||
// u(n) = n ; v(n+1) = u(n)+1, v(0) = 0, w(n+2) = 2+v(n+1)+u(n+1), w(0) = 0, w(1) = 0
|
||||
double results26[MaxNumberOfSequences][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, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0}, {0.0, 0.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 16.0, 18.0}};
|
||||
types[2] = Sequence::Type::DoubleRecurrence;
|
||||
definitions[2] = "2+v(n+1)+u(n+1)";
|
||||
conditions1[2] = "0";
|
||||
conditions2[2] = "0";
|
||||
check_sequences_defined_by(results26, types, definitions, conditions1, conditions2);
|
||||
|
||||
// v depends on u, w depends on v & u depends on w
|
||||
// u(n+1) = w(n)+1, u(0) = 0; v(n+1) = u(n)+1, v(0) = 0, w(n+1) = v(n)+2, w(0) = 0
|
||||
double results27[MaxNumberOfSequences][10] = {{0.0, 1.0, 3.0, 4.0, 5.0, 7.0, 8.0, 9.0, 11.0, 12.0}, {0.0, 1.0, 2.0, 4.0, 5.0, 6.0, 8.0, 9.0, 10.0, 12.0}, {0.0, 2.0, 3.0, 4.0, 6.0, 7.0, 8.0, 10.0, 11.0, 12.0}};
|
||||
types[0] = Sequence::Type::SingleRecurrence;
|
||||
types[2] = Sequence::Type::SingleRecurrence;
|
||||
definitions[0] = "w(n)+1";
|
||||
definitions[1] = "u(n)+1";
|
||||
definitions[2] = "v(n)+2";
|
||||
conditions1[0] = "0";
|
||||
conditions1[1] = "0";
|
||||
conditions1[2] = "0";
|
||||
conditions2[2] = nullptr;
|
||||
check_sequences_defined_by(results27, types, definitions, conditions1, conditions2);
|
||||
|
||||
// v depends on u, w depends on v & u depends on w
|
||||
// u(n) = w(n); v(n) = u(n), w(n) = v(n)
|
||||
double results28[MaxNumberOfSequences][10] = {{NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}, {NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}, {NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN}};
|
||||
types[0] = Sequence::Type::Explicit;
|
||||
types[1] = Sequence::Type::Explicit;
|
||||
types[2] = Sequence::Type::Explicit;
|
||||
definitions[0] = "w(n)";
|
||||
definitions[1] = "u(n)";
|
||||
definitions[2] = "v(n)";
|
||||
conditions1[0] = nullptr;
|
||||
conditions1[1] = nullptr;
|
||||
conditions1[2] = nullptr;
|
||||
conditions2[2] = nullptr;
|
||||
check_sequences_defined_by(results28, types, definitions, conditions1, conditions2);
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user