// Check that the small body has the right degrees of freedom in the frame of
// the big body.
TEST_F(BodyCentredNonRotatingDynamicFrameTest, SmallBodyInBigFrame) {
int const kSteps = 100;
Bivector<double, ICRFJ2000Equator> const axis({0, 0, 1});
RelativeDegreesOfFreedom<ICRFJ2000Equator> const initial_big_to_small =
small_initial_state_ - big_initial_state_;
ContinuousTrajectory<ICRFJ2000Equator>::Hint hint;
for (Instant t = t0_; t < t0_ + 1 * period_; t += period_ / kSteps) {
DegreesOfFreedom<ICRFJ2000Equator> const small_in_inertial_frame_at_t =
solar_system_.trajectory(*ephemeris_, kSmall).
EvaluateDegreesOfFreedom(t, &hint);
auto const rotation_in_big_frame_at_t =
Rotation<ICRFJ2000Equator, Big>(-2 * π * (t - t0_) * Radian / period_,
axis);
DegreesOfFreedom<Big> const small_in_big_frame_at_t(
rotation_in_big_frame_at_t(initial_big_to_small.displacement()) +
Big::origin,
rotation_in_big_frame_at_t(initial_big_to_small.velocity()));
auto const to_big_frame_at_t = big_frame_->ToThisFrameAtTime(t);
EXPECT_THAT(AbsoluteError(
to_big_frame_at_t(small_in_inertial_frame_at_t).position(),
small_in_big_frame_at_t.position()),
Lt(0.3 * Milli(Metre)));
EXPECT_THAT(AbsoluteError(
to_big_frame_at_t(small_in_inertial_frame_at_t).velocity(),
small_in_big_frame_at_t.velocity()),
Lt(4 * Milli(Metre) / Second));
}
}
void
Matrix::lu(Matrix& L, Matrix& U) const
{
if (m_nrows != m_ncols)
throw Error(" matrix is not square ");
Matrix A = *this;
Matrix Lf(m_nrows), dI(m_nrows), P(m_nrows);
dI = dI + dI;
for (size_t i = 0; i < m_nrows - 1; i++)
{
/*
// check if pivot == 0
// if so, try to find a valid pivot
// if no valid pivot found, matrix isn't invertible (quit)
// update permutation matrix
//
*/
Matrix Lt(m_nrows);
for (size_t j = i + 1; j < m_nrows; j++)
Lt(j, i) = -A(j, i) / A(i, i);
A = Lt * A;
Lf = Lf * (dI - Lt);
}
U = A;
L = Lf;
}
void TestSymplecticity(Integrator const& integrator,
Energy const& expected_energy_error) {
Length const q_initial = 1 * Metre;
Speed const v_initial = 0 * Metre / Second;
Instant const t_initial;
Instant const t_final = t_initial + 500 * Second;
Time const step = 0.2 * Second;
Mass const m = 1 * Kilogram;
Stiffness const k = SIUnit<Stiffness>();
Energy const initial_energy =
0.5 * m * Pow<2>(v_initial) + 0.5 * k * Pow<2>(q_initial);
std::vector<ODE::SystemState> solution;
ODE harmonic_oscillator;
harmonic_oscillator.compute_acceleration =
std::bind(ComputeHarmonicOscillatorAcceleration,
_1, _2, _3, /*evaluations=*/nullptr);
IntegrationProblem<ODE> problem;
problem.equation = harmonic_oscillator;
ODE::SystemState const initial_state = {{q_initial}, {v_initial}, t_initial};
problem.initial_state = &initial_state;
auto append_state = [&solution](ODE::SystemState const& state) {
solution.push_back(state);
};
auto const instance =
integrator.NewInstance(problem, std::move(append_state), step);
integrator.Solve(t_final, *instance);
std::size_t const length = solution.size();
std::vector<Energy> energy_error(length);
std::vector<Time> time(length);
Energy max_energy_error;
for (std::size_t i = 0; i < length; ++i) {
Length const q_i = solution[i].positions[0].value;
Speed const v_i = solution[i].velocities[0].value;
time[i] = solution[i].time.value - t_initial;
energy_error[i] =
AbsoluteError(initial_energy,
0.5 * m * Pow<2>(v_i) + 0.5 * k * Pow<2>(q_i));
max_energy_error = std::max(energy_error[i], max_energy_error);
}
double const correlation =
PearsonProductMomentCorrelationCoefficient(time, energy_error);
LOG(INFO) << "Correlation between time and energy error : " << correlation;
EXPECT_THAT(correlation, Lt(1e-2));
Power const slope = Slope(time, energy_error);
LOG(INFO) << "Slope : " << slope;
EXPECT_THAT(Abs(slope), Lt(2e-6 * SIUnit<Power>()));
LOG(INFO) << "Maximum energy error : " <<
max_energy_error;
EXPECT_EQ(expected_energy_error, max_energy_error);
}
TEST_F(RandomTests, NextNumber_TwoArgument) {
int a = rnd.nextInt(10, 20);
EXPECT_THAT(a, Ge(10));
EXPECT_THAT(a, Lt(20));
long long b = rnd.nextLongLong(1000000000000ll, 2000000000000ll);
EXPECT_THAT(b, Ge(1000000000000ll));
EXPECT_THAT(b, Lt(2000000000000ll));
double c = rnd.nextDouble(100.0, 200.0);
EXPECT_THAT(c, Ge(100.0));
EXPECT_THAT(c, Le(200.0));
}
unsigned int
Matrix::lup(Matrix& L, Matrix& U, Matrix& P) const
{
if (m_nrows != m_ncols)
throw Error(" matrix is not square ");
unsigned int permutations = 0;
Matrix A = *this;
Matrix Lf(m_nrows), dI(m_nrows), Per(m_nrows);
dI = dI + dI;
for (size_t i = 0; i < m_nrows - 1; i++)
{
if (Matrix::precision >= std::fabs(A(i, i)))
{
bool p = 0;
for (size_t k = i + 1; k < m_nrows; k++)
if (Matrix::precision >= std::fabs(A(k, i)))
{
A.swapRows(i, k);
Per.swapRows(i, k);
p = true;
break;
}
if (!p)
throw Error("matrix is not invertible");
else
permutations++;
}
Matrix Lt(m_nrows); // gaussian matrix
for (size_t j = i + 1; j < m_nrows; j++)
Lt(j, i) = -A(j, i) / A(i, i);
/*
A = Lt * A;
Lf = Lf * (dI - Lt);
*/
A = Lt.multiply(A);
Lf = Lf.multiply((dI - Lt)); // dI-Lt is the inverse of Lt (gaussian matrix)
}
P = Per;
U = A;
L = Lf;
return permutations;
}
TEST_F(BodyCentredNonRotatingDynamicFrameTest, GeometricAcceleration) {
int const kSteps = 10;
RelativeDegreesOfFreedom<ICRFJ2000Equator> const initial_big_to_small =
small_initial_state_ - big_initial_state_;
Length const big_to_small = initial_big_to_small.displacement().Norm();
Acceleration const small_on_big =
small_gravitational_parameter_ / (big_to_small * big_to_small);
for (Length y = big_to_small / kSteps;
y < big_to_small;
y += big_to_small / kSteps) {
Position<Big> const position(Big::origin +
Displacement<Big>({0 * Kilo(Metre),
y,
0 * Kilo(Metre)}));
Acceleration const big_on_position =
-big_gravitational_parameter_ / (y * y);
Acceleration const small_on_position =
small_gravitational_parameter_ /
((big_to_small - y) * (big_to_small - y));
Vector<Acceleration, Big> const expected_acceleration(
{0 * SIUnit<Acceleration>(),
small_on_position + big_on_position - small_on_big,
0 * SIUnit<Acceleration>()});
EXPECT_THAT(AbsoluteError(
big_frame_->GeometricAcceleration(
t0_,
DegreesOfFreedom<Big>(position, Velocity<Big>())),
expected_acceleration),
Lt(1E-10 * SIUnit<Acceleration>()));
}
}
Spectrum ExPhotonIntegrator::LPhoton(
KdTree<Photon, PhotonProcess> *map,
int nPaths, int nLookup, BSDF *bsdf,
const Intersection &isect, const Vector &wo,
float maxDistSquared) {
Spectrum L(0.);
if (!map) return L;
BxDFType nonSpecular = BxDFType(BSDF_REFLECTION |
BSDF_TRANSMISSION | BSDF_DIFFUSE | BSDF_GLOSSY);
if (bsdf->NumComponents(nonSpecular) == 0)
return L;
static StatsCounter lookups("Photon Map", "Total lookups"); // NOBOOK
// Initialize _PhotonProcess_ object, _proc_, for photon map lookups
PhotonProcess proc(nLookup, isect.dg.p);
proc.photons =
(ClosePhoton *)alloca(nLookup * sizeof(ClosePhoton));
// Do photon map lookup
++lookups; // NOBOOK
map->Lookup(isect.dg.p, proc, maxDistSquared);
// Accumulate light from nearby photons
static StatsRatio foundRate("Photon Map", "Photons found per lookup"); // NOBOOK
foundRate.Add(proc.foundPhotons, 1); // NOBOOK
// Estimate reflected light from photons
ClosePhoton *photons = proc.photons;
int nFound = proc.foundPhotons;
Normal Nf = Dot(wo, bsdf->dgShading.nn) < 0 ? -bsdf->dgShading.nn :
bsdf->dgShading.nn;
if (bsdf->NumComponents(BxDFType(BSDF_REFLECTION |
BSDF_TRANSMISSION | BSDF_GLOSSY)) > 0) {
// Compute exitant radiance from photons for glossy surface
for (int i = 0; i < nFound; ++i) {
const Photon *p = photons[i].photon;
BxDFType flag = Dot(Nf, p->wi) > 0.f ?
BSDF_ALL_REFLECTION : BSDF_ALL_TRANSMISSION;
float k = kernel(p, isect.dg.p, maxDistSquared);
L += (k / nPaths) * bsdf->f(wo, p->wi, flag) * p->alpha;
}
}
else {
// Compute exitant radiance from photons for diffuse surface
Spectrum Lr(0.), Lt(0.);
for (int i = 0; i < nFound; ++i) {
if (Dot(Nf, photons[i].photon->wi) > 0.f) {
float k = kernel(photons[i].photon, isect.dg.p,
maxDistSquared);
Lr += (k / nPaths) * photons[i].photon->alpha;
}
else {
float k = kernel(photons[i].photon, isect.dg.p,
maxDistSquared);
Lt += (k / nPaths) * photons[i].photon->alpha;
}
}
L += Lr * bsdf->rho(wo, BSDF_ALL_REFLECTION) * INV_PI +
Lt * bsdf->rho(wo, BSDF_ALL_TRANSMISSION) * INV_PI;
}
return L;
}
TEST_P(SimpleHarmonicMotionTest, Symplecticity) {
parameters_.initial.positions.emplace_back(SIUnit<Length>());
parameters_.initial.momenta.emplace_back(Speed());
parameters_.initial.time = Time();
Stiffness const k = SIUnit<Stiffness>();
Mass const m = SIUnit<Mass>();
Length const q0 = parameters_.initial.positions[0].value;
Speed const v0 = parameters_.initial.momenta[0].value;
Energy const initial_energy = 0.5 * m * Pow<2>(v0) + 0.5 * k * Pow<2>(q0);
parameters_.tmax = 500.0 * SIUnit<Time>();
parameters_.Δt = 0.2 * Second;
parameters_.sampling_period = 1;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
std::size_t const length = solution_.size();
std::vector<Energy> energy_error(length);
std::vector<Time> time_steps(length);
Energy max_energy_error = 0 * SIUnit<Energy>();
for (std::size_t i = 0; i < length; ++i) {
Length const q_i = solution_[i].positions[0].value;
Speed const v_i = solution_[i].momenta[0].value;
time_steps[i] = solution_[i].time.value;
energy_error[i] = Abs(0.5 * m * Pow<2>(v_i) + 0.5 * k * Pow<2>(q_i) -
initial_energy);
max_energy_error = std::max(energy_error[i], max_energy_error);
}
#if 0
LOG(INFO) << "Energy error as a function of time:\n" <<
BidimensionalDatasetMathematicaInput(time_steps, energy_error);
#endif
double const correlation =
PearsonProductMomentCorrelationCoefficient(time_steps, energy_error);
LOG(INFO) << GetParam();
LOG(INFO) << "Correlation between time and energy error : " << correlation;
EXPECT_THAT(correlation, Lt(2E-3));
Power const slope = Slope(time_steps, energy_error);
LOG(INFO) << "Slope : " << slope;
EXPECT_THAT(Abs(slope), Lt(2E-6 * SIUnit<Power>()));
LOG(INFO) << "Maximum energy error : " <<
max_energy_error;
EXPECT_EQ(GetParam().expected_energy_error, max_energy_error);
}
Spectrum LPhoton(KdTree<Photon> *map, int nPaths, int nLookup,
MemoryArena &arena, BSDF *bsdf, RNG &rng, const Intersection &isect,
const Vector &wo, float maxDistSquared) {
Spectrum L(0.);
BxDFType nonSpecular = BxDFType(BSDF_REFLECTION |
BSDF_TRANSMISSION | BSDF_DIFFUSE | BSDF_GLOSSY);
if (map && bsdf->NumComponents(nonSpecular) > 0) {
PBRT_PHOTON_MAP_STARTED_LOOKUP(const_cast<DifferentialGeometry *>(&isect.dg));
// Do photon map lookup at intersection point
PhotonProcess proc(nLookup, arena.Alloc<ClosePhoton>(nLookup));
map->Lookup(isect.dg.p, proc, maxDistSquared);
// Estimate reflected radiance due to incident photons
ClosePhoton *photons = proc.photons;
int nFound = proc.nFound;
Normal Nf = Faceforward(bsdf->dgShading.nn, wo);
if (bsdf->NumComponents(BxDFType(BSDF_REFLECTION |
BSDF_TRANSMISSION | BSDF_GLOSSY)) > 0) {
// Compute exitant radiance from photons for glossy surface
for (int i = 0; i < nFound; ++i) {
const Photon *p = photons[i].photon;
float k = kernel(p, isect.dg.p, maxDistSquared);
L += (k / (nPaths * maxDistSquared)) * bsdf->f(wo, p->wi) *
p->alpha;
}
}
else {
// Compute exitant radiance from photons for diffuse surface
Spectrum Lr(0.), Lt(0.);
for (int i = 0; i < nFound; ++i) {
if (Dot(Nf, photons[i].photon->wi) > 0.f) {
float k = kernel(photons[i].photon, isect.dg.p,
maxDistSquared);
Lr += (k / (nPaths * maxDistSquared)) * photons[i].photon->alpha;
}
else {
float k = kernel(photons[i].photon, isect.dg.p,
maxDistSquared);
Lt += (k / (nPaths * maxDistSquared)) * photons[i].photon->alpha;
}
}
const int sqrtRhoSamples = 4;
float rhoRSamples[2*sqrtRhoSamples*sqrtRhoSamples];
StratifiedSample2D(rhoRSamples, sqrtRhoSamples, sqrtRhoSamples, rng);
float rhoTSamples[2*sqrtRhoSamples*sqrtRhoSamples];
StratifiedSample2D(rhoTSamples, sqrtRhoSamples, sqrtRhoSamples, rng);
L += Lr * bsdf->rho(wo, sqrtRhoSamples*sqrtRhoSamples, rhoRSamples,
BSDF_ALL_REFLECTION) * INV_PI +
Lt * bsdf->rho(wo, sqrtRhoSamples*sqrtRhoSamples, rhoTSamples,
BSDF_ALL_TRANSMISSION) * INV_PI;
}
PBRT_PHOTON_MAP_FINISHED_LOOKUP(const_cast<DifferentialGeometry *>(&isect.dg),
proc.nFound, proc.nLookup, &L);
}
return L;
}
tmp<volScalarField::Internal> kOmegaSSTDES<BasicTurbulenceModel>::FDES
(
const volScalarField::Internal& F1,
const volScalarField::Internal& F2
) const
{
switch (FSST_)
{
case 0:
return max(Lt()/(CDES_*this->delta()()), scalar(1));
case 1:
return max(Lt()*(1 - F1)/(CDES_*this->delta()()), scalar(1));
case 2:
return max(Lt()*(1 - F2)/(CDES_*this->delta()()), scalar(1));
default:
FatalErrorInFunction
<< "Incorrect FSST = " << FSST_ << ", should be 0, 1 or 2"
<< exit(FatalError);
return F1;
}
}
bool cellLess(Cell cell, const ArrayData* val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(Cell cell, double val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(Cell cell, const StringData* val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(Cell cell, bool val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(Cell cell, int64_t val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(Cell c1, Cell c2) {
return cellRelOp(Lt(), c1, c2);
}
static bool Eq(Value lhs, Value rhs) { return !Lt(lhs, rhs) && !Gt(lhs, rhs); }
bool cellLess(const Cell* cell, double val) {
return cellRelOp(Lt(), cell, val);
}
bool cellLess(const Cell* c1, const Cell* c2) {
return cellRelOp(Lt(), c1, c2);
}
TEST_F(ManœuvreTest, Apollo8SIVB) {
// Data from NASA's Saturn V Launch Vehicle, Flight Evaluation Report AS-503,
// Apollo 8 Mission (1969),
// http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690015314.pdf.
// We use the reconstructed or actual values.
// Table 2-2. Significant Event Times Summary.
Instant const range_zero;
Instant const s_ivb_1st_90_percent_thrust = range_zero + 530.53 * Second;
Instant const s_ivb_1st_eco = range_zero + 684.98 * Second;
// Initiate S-IVB Restart Sequence and Start of Time Base 6 (T6).
Instant const t6 = range_zero + 9659.54 * Second;
Instant const s_ivb_2nd_90_percent_thrust = range_zero + 10'240.02 * Second;
Instant const s_ivb_2nd_eco = range_zero + 10'555.51 * Second;
// From Table 7-2. S-IVB Steady State Performance - First Burn.
Force thrust_1st = 901'557 * Newton;
Speed specific_impulse_1st = 4'204.1 * Newton * Second / Kilogram;
Variation<Mass> lox_flowrate_1st = 178.16 * Kilogram / Second;
Variation<Mass> fuel_flowrate_1st = 36.30 * Kilogram / Second;
// From Table 7-7. S-IVB Steady State Performance - Second Burn.
Force thrust_2nd = 897'548 * Newton;
Speed specific_impulse_2nd = 4199.2 * Newton * Second / Kilogram;
Variation<Mass> lox_flowrate_2nd = 177.70 * Kilogram / Second;
Variation<Mass> fuel_flowrate_2nd = 36.01 * Kilogram / Second;
// Table 21-5. Total Vehicle Mass, S-IVB First Burn Phase, Kilograms.
Mass total_vehicle_at_s_ivb_1st_90_percent_thrust = 161143 * Kilogram;
Mass total_vehicle_at_s_ivb_1st_eco = 128095 * Kilogram;
// Table 21-7. Total Vehicle Mass, S-IVB Second Burn Phase, Kilograms.
Mass total_vehicle_at_s_ivb_2nd_90_percent_thrust = 126780 * Kilogram;
Mass total_vehicle_at_s_ivb_2nd_eco = 59285 * Kilogram;
// An arbitrary direction, we're not testing this.
Vector<double, World> e_y({0, 1, 0});
Manœuvre<World> first_burn(thrust_1st,
total_vehicle_at_s_ivb_1st_90_percent_thrust,
specific_impulse_1st, e_y);
EXPECT_THAT(RelativeError(lox_flowrate_1st + fuel_flowrate_1st,
first_burn.mass_flow()),
Lt(1E-4));
first_burn.set_duration(s_ivb_1st_eco - s_ivb_1st_90_percent_thrust);
EXPECT_THAT(
RelativeError(total_vehicle_at_s_ivb_1st_eco, first_burn.final_mass()),
Lt(1E-3));
first_burn.set_initial_time(s_ivb_1st_90_percent_thrust);
EXPECT_EQ(s_ivb_1st_eco, first_burn.final_time());
// Accelerations from Figure 4-4. Ascent Trajectory Acceleration Comparison.
// Final acceleration from Table 4-2. Comparison of Significant Trajectory
// Events.
EXPECT_THAT(
first_burn.acceleration()(first_burn.initial_time()).Norm(),
AllOf(Gt(5 * Metre / Pow<2>(Second)), Lt(6.25 * Metre / Pow<2>(Second))));
EXPECT_THAT(first_burn.acceleration()(range_zero + 600 * Second).Norm(),
AllOf(Gt(6.15 * Metre / Pow<2>(Second)),
Lt(6.35 * Metre / Pow<2>(Second))));
EXPECT_THAT(first_burn.acceleration()(first_burn.final_time()).Norm(),
AllOf(Gt(7.03 * Metre / Pow<2>(Second)),
Lt(7.05 * Metre / Pow<2>(Second))));
Manœuvre<World> second_burn(thrust_2nd,
total_vehicle_at_s_ivb_2nd_90_percent_thrust,
specific_impulse_2nd, e_y);
EXPECT_THAT(RelativeError(lox_flowrate_2nd + fuel_flowrate_2nd,
second_burn.mass_flow()),
Lt(2E-4));
second_burn.set_duration(s_ivb_2nd_eco - s_ivb_2nd_90_percent_thrust);
EXPECT_THAT(
RelativeError(total_vehicle_at_s_ivb_2nd_eco, second_burn.final_mass()),
Lt(2E-3));
second_burn.set_initial_time(s_ivb_2nd_90_percent_thrust);
EXPECT_EQ(s_ivb_2nd_eco, second_burn.final_time());
// Accelerations from Figure 4-9. Injection Phase Acceleration Comparison.
// Final acceleration from Table 4-2. Comparison of Significant Trajectory
// Events.
EXPECT_THAT(second_burn.acceleration()(second_burn.initial_time()).Norm(),
AllOf(Gt(7 * Metre / Pow<2>(Second)),
Lt(7.5 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.acceleration()(t6 + 650 * Second).Norm(),
AllOf(Gt(8 * Metre / Pow<2>(Second)),
Lt(8.02 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.acceleration()(t6 + 700 * Second).Norm(),
AllOf(Gt(8.8 * Metre / Pow<2>(Second)),
Lt(9 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.acceleration()(t6 + 750 * Second).Norm(),
AllOf(Gt(9.9 * Metre / Pow<2>(Second)),
Lt(10 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.acceleration()(t6 + 850 * Second).Norm(),
AllOf(Gt(12.97 * Metre / Pow<2>(Second)),
Lt(13 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.acceleration()(second_burn.final_time()).Norm(),
AllOf(Gt(15.12 * Metre / Pow<2>(Second)),
Lt(15.17 * Metre / Pow<2>(Second))));
EXPECT_THAT(second_burn.Δv(),
AllOf(Gt(3 * Kilo(Metre) / Second),
Lt(3.25 * Kilo(Metre) / Second)));
// From the Apollo 8 flight journal.
EXPECT_THAT(AbsoluteError(10'519.6 * Foot / Second, second_burn.Δv()),
Lt(20 * Metre / Second));
}
bool cellLess(const Cell* cell, int64_t val) {
return cellRelOp(Lt(), cell, val);
}
void TestConvergence(Integrator const& integrator,
Time const& beginning_of_convergence) {
Length const q_initial = 1 * Metre;
Speed const v_initial = 0 * Metre / Second;
Speed const v_amplitude = 1 * Metre / Second;
AngularFrequency const ω = 1 * Radian / Second;
Instant const t_initial;
Instant const t_final = t_initial + 100 * Second;
Time step = beginning_of_convergence;
int const step_sizes = 50;
double const step_reduction = 1.1;
std::vector<double> log_step_sizes;
log_step_sizes.reserve(step_sizes);
std::vector<double> log_q_errors;
log_step_sizes.reserve(step_sizes);
std::vector<double> log_p_errors;
log_step_sizes.reserve(step_sizes);
std::vector<ODE::SystemState> solution;
ODE harmonic_oscillator;
harmonic_oscillator.compute_acceleration =
std::bind(ComputeHarmonicOscillatorAcceleration,
_1, _2, _3, /*evaluations=*/nullptr);
IntegrationProblem<ODE> problem;
problem.equation = harmonic_oscillator;
ODE::SystemState const initial_state = {{q_initial}, {v_initial}, t_initial};
problem.initial_state = &initial_state;
ODE::SystemState final_state;
auto const append_state = [&final_state](ODE::SystemState const& state) {
final_state = state;
};
for (int i = 0; i < step_sizes; ++i, step /= step_reduction) {
auto const instance = integrator.NewInstance(problem, append_state, step);
integrator.Solve(t_final, *instance);
Time const t = final_state.time.value - t_initial;
Length const& q = final_state.positions[0].value;
Speed const& v = final_state.velocities[0].value;
double const log_q_error = std::log10(
AbsoluteError(q / q_initial, Cos(ω * t)));
double const log_p_error = std::log10(
AbsoluteError(v / v_amplitude, -Sin(ω * t)));
if (log_q_error <= -13 || log_p_error <= -13) {
// If we keep going the effects of finite precision will drown out
// convergence.
break;
}
log_step_sizes.push_back(std::log10(step / Second));
log_q_errors.push_back(log_q_error);
log_p_errors.push_back(log_p_error);
}
double const q_convergence_order = Slope(log_step_sizes, log_q_errors);
double const q_correlation =
PearsonProductMomentCorrelationCoefficient(log_step_sizes, log_q_errors);
LOG(INFO) << "Convergence order in q : " << q_convergence_order;
LOG(INFO) << "Correlation : " << q_correlation;
#if !defined(_DEBUG)
EXPECT_THAT(RelativeError(integrator.order, q_convergence_order),
Lt(0.05));
EXPECT_THAT(q_correlation, AllOf(Gt(0.99), Lt(1.01)));
#endif
double const v_convergence_order = Slope(log_step_sizes, log_p_errors);
double const v_correlation =
PearsonProductMomentCorrelationCoefficient(log_step_sizes, log_p_errors);
LOG(INFO) << "Convergence order in p : " << v_convergence_order;
LOG(INFO) << "Correlation : " << v_correlation;
#if !defined(_DEBUG)
// SPRKs with odd convergence order have a higher convergence order in p.
EXPECT_THAT(
RelativeError(integrator.order + (integrator.order % 2),
v_convergence_order),
Lt(0.03));
EXPECT_THAT(v_correlation, AllOf(Gt(0.99), Lt(1.01)));
#endif
}
void Parser::executeAction(int production) try {
if (d_token__ != _UNDETERMINED_)
pushToken__(d_token__); // save an already available token
// $insert defaultactionreturn
// save default non-nested block $$
if (int size = s_productionInfo[production].d_size)
d_val__ = d_vsp__[1 - size];
switch (production) {
// $insert actioncases
case 1:
#line 43 "parser.yy"
{
d_val__.get<Tag__::basic>() = d_vsp__[0].data<Tag__::basic>();
res = d_val__.get<Tag__::basic>();
} break;
case 2:
#line 51 "parser.yy"
{
d_val__.get<Tag__::basic>() = add(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>());
} break;
case 3:
#line 54 "parser.yy"
{
d_val__.get<Tag__::basic>() = sub(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>());
} break;
case 4:
#line 57 "parser.yy"
{
d_val__.get<Tag__::basic>() = mul(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>());
} break;
case 5:
#line 60 "parser.yy"
{
d_val__.get<Tag__::basic>() = div(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>());
} break;
case 6:
#line 63 "parser.yy"
{
auto tup = parse_implicit_mul(d_vsp__[-2].data<Tag__::string>());
if (neq(*std::get<1>(tup), *one)) {
d_val__.get<Tag__::basic>() = mul(
std::get<0>(tup),
pow(std::get<1>(tup), d_vsp__[0].data<Tag__::basic>()));
} else {
d_val__.get<Tag__::basic>()
= pow(std::get<0>(tup), d_vsp__[0].data<Tag__::basic>());
}
} break;
case 7:
#line 73 "parser.yy"
{
d_val__.get<Tag__::basic>() = pow(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>());
} break;
case 8:
#line 76 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
Lt(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>()));
} break;
case 9:
#line 79 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
Gt(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>()));
} break;
case 10:
#line 82 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
Le(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>()));
} break;
case 11:
#line 85 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
Ge(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>()));
} break;
case 12:
#line 88 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
Eq(d_vsp__[-2].data<Tag__::basic>(),
d_vsp__[0].data<Tag__::basic>()));
} break;
case 13:
#line 91 "parser.yy"
{
set_boolean s;
s.insert(rcp_static_cast<const Boolean>(
d_vsp__[-2].data<Tag__::basic>()));
s.insert(rcp_static_cast<const Boolean>(
d_vsp__[0].data<Tag__::basic>()));
d_val__.get<Tag__::basic>()
= rcp_static_cast<const Basic>(logical_or(s));
} break;
case 14:
#line 99 "parser.yy"
{
set_boolean s;
s.insert(rcp_static_cast<const Boolean>(
d_vsp__[-2].data<Tag__::basic>()));
s.insert(rcp_static_cast<const Boolean>(
d_vsp__[0].data<Tag__::basic>()));
d_val__.get<Tag__::basic>()
= rcp_static_cast<const Basic>(logical_and(s));
} break;
case 15:
#line 107 "parser.yy"
{
vec_boolean s;
s.push_back(rcp_static_cast<const Boolean>(
d_vsp__[-2].data<Tag__::basic>()));
s.push_back(rcp_static_cast<const Boolean>(
d_vsp__[0].data<Tag__::basic>()));
d_val__.get<Tag__::basic>()
= rcp_static_cast<const Basic>(logical_xor(s));
} break;
case 16:
#line 115 "parser.yy"
{
d_val__.get<Tag__::basic>() = d_vsp__[-1].data<Tag__::basic>();
} break;
case 17:
#line 118 "parser.yy"
{
d_val__.get<Tag__::basic>() = neg(d_vsp__[0].data<Tag__::basic>());
} break;
case 18:
#line 121 "parser.yy"
{
d_val__.get<Tag__::basic>() = rcp_static_cast<const Basic>(
logical_not(rcp_static_cast<const Boolean>(
d_vsp__[0].data<Tag__::basic>())));
} break;
case 19:
#line 124 "parser.yy"
{
d_val__.get<Tag__::basic>()
= rcp_static_cast<const Basic>(d_vsp__[0].data<Tag__::basic>());
} break;
case 20:
#line 129 "parser.yy"
{
d_val__.get<Tag__::basic>()
= parse_identifier(d_vsp__[0].data<Tag__::string>());
} break;
case 21:
#line 134 "parser.yy"
{
auto tup = parse_implicit_mul(d_vsp__[0].data<Tag__::string>());
d_val__.get<Tag__::basic>()
= mul(std::get<0>(tup), std::get<1>(tup));
} break;
case 22:
#line 140 "parser.yy"
{
d_val__.get<Tag__::basic>()
= parse_numeric(d_vsp__[0].data<Tag__::string>());
} break;
case 23:
#line 145 "parser.yy"
{
d_val__.get<Tag__::basic>() = d_vsp__[0].data<Tag__::basic>();
} break;
case 24:
#line 152 "parser.yy"
{
d_val__.get<Tag__::basic>()
= functionify(d_vsp__[-3].data<Tag__::string>(),
d_vsp__[-1].data<Tag__::basic_vec>());
} break;
case 25:
#line 160 "parser.yy"
{
d_val__.get<Tag__::basic_vec>()
= d_vsp__[-2].data<Tag__::basic_vec>();
d_val__.get<Tag__::basic_vec>().push_back(
d_vsp__[0].data<Tag__::basic>());
} break;
case 26:
#line 166 "parser.yy"
{
d_val__.get<Tag__::basic_vec>()
= vec_basic(1, d_vsp__[0].data<Tag__::basic>());
} break;
}
} catch (std::exception const &exc) {
exceptionHandler__(exc);
}
TEST_P(SimpleHarmonicMotionTest, Convergence) {
parameters_.initial.positions.emplace_back(SIUnit<Length>());
parameters_.initial.momenta.emplace_back(Speed());
parameters_.initial.time = Time();
#if defined(_DEBUG)
parameters_.tmax = 1 * SIUnit<Time>();
#else
parameters_.tmax = 100 * SIUnit<Time>();
#endif
parameters_.sampling_period = 0;
parameters_.Δt = GetParam().beginning_of_convergence;
int const step_sizes = 50;
double const step_reduction = 1.1;
std::vector<double> log_step_sizes;
log_step_sizes.reserve(step_sizes);
std::vector<double> log_q_errors;
log_step_sizes.reserve(step_sizes);
std::vector<double> log_p_errors;
log_step_sizes.reserve(step_sizes);
for (int i = 0; i < step_sizes; ++i, parameters_.Δt /= step_reduction) {
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
double const log_q_error = std::log10(
std::abs(solution_[0].positions[0].value / SIUnit<Length>() -
Cos(solution_[0].time.value *
SIUnit<AngularFrequency>())));
double const log_p_error = std::log10(
std::abs(solution_[0].momenta[0].value / SIUnit<Speed>() +
Sin(solution_[0].time.value *
SIUnit<AngularFrequency>())));
if (log_q_error <= -13 || log_p_error <= -13) {
// If we keep going the effects of finite precision will drown out
// convergence.
break;
}
log_step_sizes.push_back(std::log10(parameters_.Δt / SIUnit<Time>()));
log_q_errors.push_back(log_q_error);
log_p_errors.push_back(log_p_error);
}
double const q_convergence_order = Slope(log_step_sizes, log_q_errors);
double const q_correlation =
PearsonProductMomentCorrelationCoefficient(log_step_sizes, log_q_errors);
LOG(INFO) << GetParam();
LOG(INFO) << "Convergence order in q : " << q_convergence_order;
LOG(INFO) << "Correlation : " << q_correlation;
#if 0
LOG(INFO) << "Convergence data for q :\n" <<
BidimensionalDatasetMathematicaInput(log_step_sizes, log_q_errors);
#endif
#if !defined(_DEBUG)
EXPECT_THAT(RelativeError(GetParam().convergence_order, q_convergence_order),
Lt(0.02));
EXPECT_THAT(q_correlation, AllOf(Gt(0.99), Lt(1.01)));
#endif
double const v_convergence_order = Slope(log_step_sizes, log_p_errors);
double const v_correlation =
PearsonProductMomentCorrelationCoefficient(log_step_sizes, log_p_errors);
LOG(INFO) << "Convergence order in p : " << v_convergence_order;
LOG(INFO) << "Correlation : " << v_correlation;
#if 0
LOG(INFO) << "Convergence data for p :\n" <<
BidimensionalDatasetMathematicaInput(log_step_sizes, log_q_errors);
#endif
#if !defined(_DEBUG)
// SPRKs with odd convergence order have a higher convergence order in p.
EXPECT_THAT(
RelativeError(((GetParam().convergence_order + 1) / 2) * 2,
v_convergence_order),
Lt(0.02));
EXPECT_THAT(v_correlation, AllOf(Gt(0.99), Lt(1.01)));
#endif
}
bool cellLess(Cell cell, const ObjectData* val) {
return cellRelOp(Lt(), cell, val);
}
HOT_FUNC
bool tvLess(const TypedValue* tv1, const TypedValue* tv2) {
return tvRelOp(Lt(), tv1, tv2);
}
bool cellLess(Cell cell, const ResourceData* val) {
return cellRelOp(Lt(), cell, val);
}
TEST_F(EmbeddedExplicitRungeKuttaNyströmIntegratorTest,
MaxSteps) {
AdaptiveStepSizeIntegrator<ODE> const& integrator =
DormandElMikkawyPrince1986RKN434FM<Length>();
Length const x_initial = 1 * Metre;
Speed const v_initial = 0 * Metre / Second;
Speed const v_amplitude = 1 * Metre / Second;
Time const period = 2 * π * Second;
AngularFrequency const ω = 1 * Radian / Second;
Instant const t_initial;
Instant const t_final = t_initial + 10 * period;
Length const length_tolerance = 1 * Milli(Metre);
Speed const speed_tolerance = 1 * Milli(Metre) / Second;
// The number of steps if no step limit is set.
std::int64_t const steps_forward = 132;
int evaluations = 0;
auto const step_size_callback = [](bool tolerable) {};
std::vector<ODE::SystemState> solution;
ODE harmonic_oscillator;
harmonic_oscillator.compute_acceleration =
std::bind(ComputeHarmonicOscillatorAcceleration,
_1, _2, _3, &evaluations);
IntegrationProblem<ODE> problem;
problem.equation = harmonic_oscillator;
ODE::SystemState const initial_state = {{x_initial}, {v_initial}, t_initial};
problem.initial_state = &initial_state;
problem.t_final = t_final;
problem.append_state = [&solution](ODE::SystemState const& state) {
solution.push_back(state);
};
AdaptiveStepSize<ODE> adaptive_step_size;
adaptive_step_size.first_time_step = t_final - t_initial;
adaptive_step_size.safety_factor = 0.9;
adaptive_step_size.tolerance_to_error_ratio =
std::bind(HarmonicOscillatorToleranceRatio,
_1, _2, length_tolerance, speed_tolerance, step_size_callback);
adaptive_step_size.max_steps = 100;
auto const outcome = integrator.Solve(problem, adaptive_step_size);
EXPECT_EQ(termination_condition::ReachedMaximalStepCount, outcome.error());
EXPECT_THAT(AbsoluteError(
x_initial * Cos(ω * (solution.back().time.value - t_initial)),
solution.back().positions[0].value),
AllOf(Ge(8e-4 * Metre), Le(9e-4 * Metre)));
EXPECT_THAT(AbsoluteError(
-v_amplitude *
Sin(ω * (solution.back().time.value - t_initial)),
solution.back().velocities[0].value),
AllOf(Ge(1e-3 * Metre / Second), Le(2e-3 * Metre / Second)));
EXPECT_THAT(solution.back().time.value, Lt(t_final));
EXPECT_EQ(100, solution.size());
// Check that a |max_steps| greater than or equal to the unconstrained number
// of steps has no effect.
for (std::int64_t const max_steps :
{steps_forward, steps_forward + 1234}) {
solution.clear();
adaptive_step_size.max_steps = steps_forward;
auto const outcome = integrator.Solve(problem, adaptive_step_size);
EXPECT_EQ(termination_condition::Done, outcome.error());
EXPECT_THAT(AbsoluteError(x_initial, solution.back().positions[0].value),
AllOf(Ge(3e-4 * Metre), Le(4e-4 * Metre)));
EXPECT_THAT(AbsoluteError(v_initial, solution.back().velocities[0].value),
AllOf(Ge(2e-3 * Metre / Second), Le(3e-3 * Metre / Second)));
EXPECT_EQ(t_final, solution.back().time.value);
EXPECT_EQ(steps_forward, solution.size());
}
}
bool tvLess(TypedValue tv1, TypedValue tv2) {
return tvRelOp(Lt(), tv1, tv2);
}
TEST_P(SRKNTest, ExactInexactTMax) {
parameters_.initial.positions.emplace_back(SIUnit<Length>());
parameters_.initial.momenta.emplace_back(Speed());
parameters_.initial.time = Time();
parameters_.tmax = 10.0 * SIUnit<Time>();
parameters_.sampling_period = 1;
parameters_.Δt = (1.0 / 3.000001) * SIUnit<Time>();
parameters_.tmax_is_exact = false;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(30, solution_.size());
EXPECT_THAT(solution_.back().time.value, Lt(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Ne(0.0 * SIUnit<Time>()));
parameters_.tmax_is_exact = true;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(30, solution_.size());
EXPECT_THAT(solution_.back().time.value, Eq(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Eq(0.0 * SIUnit<Time>()));
parameters_.Δt = (1.0 / 2.999999) * SIUnit<Time>();
parameters_.tmax_is_exact = false;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(29, solution_.size());
EXPECT_THAT(solution_.back().time.value, Lt(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Ne(0.0 * SIUnit<Time>()));
parameters_.tmax_is_exact = true;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(30, solution_.size());
EXPECT_THAT(solution_.back().time.value, Eq(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Eq(0.0 * SIUnit<Time>()));
parameters_.Δt = 11.0 * SIUnit<Time>();
parameters_.tmax_is_exact = false;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(0, solution_.size());
parameters_.tmax_is_exact = true;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(1, solution_.size());
EXPECT_THAT(solution_.back().time.value, Eq(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Eq(0.0 * SIUnit<Time>()));
parameters_.Δt = 100.0 * SIUnit<Time>();
parameters_.tmax_is_exact = false;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(0, solution_.size());
parameters_.tmax_is_exact = true;
integrator_->SolveTrivialKineticEnergyIncrement<Length>(
&ComputeHarmonicOscillatorAcceleration,
parameters_,
&solution_);
EXPECT_EQ(1, solution_.size());
EXPECT_THAT(solution_.back().time.value, Eq(parameters_.tmax));
EXPECT_THAT(solution_.back().time.error, Eq(0.0 * SIUnit<Time>()));
}