def run():
from leap.rk.imex import KennedyCarpenterIMEXARK4MethodBuilder
from dagrt.codegen import PythonCodeGenerator
# Construct the method generator.
mgen = KennedyCarpenterIMEXARK4MethodBuilder("y", atol=_atol)
# Generate the code for the method.
code = mgen.generate()
from leap.implicit import replace_AssignImplicit
code = replace_AssignImplicit(code, {"solve": solver_hook})
IMEXIntegrator = PythonCodeGenerator("IMEXIntegrator").get_class(code)
# Set up the problem and run the method.
from functools import partial
problem = KapsProblem(epsilon=0.001)
integrator = IMEXIntegrator(
function_map={
"<func>expl_y": problem.nonstiff,
"<func>impl_y": problem.stiff,
"<func>solver": partial(solver, problem.stiff, problem.jacobian),
"<func>j": problem.jacobian
})
integrator.set_up(t_start=problem.t_start,
dt_start=1.0e-1,
context={"y": problem.initial()})
t = None
y = None
for event in integrator.run(t_end=problem.t_end):
if isinstance(event, integrator.StateComputed):
t = event.t
y = event.state_component
print("Error: " + str(np.linalg.norm(y - problem.exact(t))))
from leap.rk.imex import KennedyCarpenterIMEXARK4MethodBuilder
from mirgecom.steppers import advance_state
@pytest.mark.parametrize(("method", "method_order"), [
(ODE23MethodBuilder("y", use_high_order=False), 2),
(ODE23MethodBuilder("y", use_high_order=True), 3),
(ODE45MethodBuilder("y", use_high_order=False), 4),
(ODE45MethodBuilder("y", use_high_order=True), 5),
(ForwardEulerMethodBuilder("y"), 1),
(MidpointMethodBuilder("y"), 2),
(HeunsMethodBuilder("y"), 2),
(RK3MethodBuilder("y"), 3),
(RK4MethodBuilder("y"), 4),
(RK5MethodBuilder("y"), 5),
(LSRK4MethodBuilder("y"), 4),
(KennedyCarpenterIMEXARK4MethodBuilder(
"y", use_implicit=False, explicit_rhs_name="y"), 4),
(SSPRK22MethodBuilder("y"), 2),
(SSPRK33MethodBuilder("y"), 3),
])
def test_leapgen_integration_order(method, method_order):
"""Test that time integrators have correct order."""
def exact_soln(t):
return np.exp(-t)
def rhs(t, y):
return -np.exp(-t)
from pytools.convergence import EOCRecorder
integrator_eoc = EOCRecorder()
dt = 1.0
def solver_hook(solve_expr, solve_var, solver_id, guess):
from dagrt.expression import match, substitute
pieces = match("unk - <func>rhs(t=t, y=sub_y + coeff*unk)",
solve_expr,
pre_match={"unk": solve_var})
pieces["guess"] = guess
return substitute("<func>solver(t, sub_y, coeff, guess)", pieces)
@pytest.mark.parametrize("problem, method, expected_order", [
[
KapsProblem(epsilon=0.9),
KennedyCarpenterIMEXARK4MethodBuilder("y", use_high_order=False), 3
],
[KapsProblem(epsilon=0.9),
KennedyCarpenterIMEXARK4MethodBuilder("y"), 4],
])
def test_convergence(python_method_impl, problem, method, expected_order):
pytest.importorskip("scipy")
code = method.generate()
from leap.implicit import replace_AssignImplicit
code = replace_AssignImplicit(code, {"solve": solver_hook})
from pytools.convergence import EOCRecorder
eocrec = EOCRecorder()
def main():
component_id = 'y'
stepper = KennedyCarpenterIMEXARK4MethodBuilder(component_id)
# stepper = KennedyCarpenterIMEXARK3MethodBuilder(component_id)
from dagrt.function_registry import (base_function_registry,
register_function, UserType)
# This stays unchanged from the existing explicit RK4 RHS.
freg = register_function(base_function_registry,
"<func>expl_" + component_id, ("y", "t"),
result_names=("result", ),
result_kinds=(UserType("y"), ))
freg = freg.register_codegen(
"<func>expl_" + component_id, "cxx",
cxx.CallCode("""
// Purely homogeneous chemistry simulation.
for (int i = 0;i < NS+1;i++){
${result}[i] = 0.0;
}
"""))
# Here, we need to call a new chemistry RHS that loops through
# all the points *under the hood.*
freg = register_function(freg,
"<func>impl_" + component_id, ("y", "t"),
result_names=("result", ),
result_kinds=(UserType("y"), ))
freg = freg.register_codegen(
"<func>impl_" + component_id, "cxx",
cxx.CallCode("""
// PyJac inputs.
double jac[(NS+1)*(NS+1)];
double jac_trans[(NS+1)*(NS+1)];
double phi[(NS+1)];
double phi_guess[(NS+1)];
double phi_old[(NS+1)];
double dphi[(NS+1)];
double dphi_old[(NS+1)];
double corr[(NS+1)];
double corr_weights[(NS+1)];
double corr_weighted[(NS+1)];
double reltol = 1e-6;
double abstol = 1e-12;
/* For Lapack */
int ipiv[NS+1], info;
int nrhs = 1;
int nsp_l = NS+1;
// Dummy time for pyJac.
double tout = 0;
// Work array for PyJac.
double* rwk_dphi = (double*)malloc(245 * sizeof(double));
memset(rwk_dphi, 0, 245 * sizeof(double));
double massFractions[NS];
double mw[NS];
// FIXME: Assumes the last (inert) species is nitrogen.
mw[NS-1] = 2*14.00674;
for (int i = 0; i < NS-1; ++i ){
mw[i] = mw[NS-1]*mw_factor[i];
}
double rho = 0.2072648773462248;
double vol = 1.0 / rho;
double tol = 1e-10;
double mass_sum = 0.0;
for (int i = 2; i <= NS; ++i ){
massFractions[i-2] = ${y}[i]*mw[i-2];
mass_sum += massFractions[i-2];
}
//massFractions[8] = 1 - mass_sum;
massFractions[8] = 0.0;
// PyJac converted input state.
//phi[0] = ${y}[0];
//phi[1] = ${y}[1];
// Update temperature and pressure using Cantera
Cantera::IdealGasMix * GasMixture;
//GasMixture = new Cantera::IdealGasMix("Mechanisms/sanDiego.xml");
GasMixture = new Cantera::IdealGasMix("Mechanisms/SanDiegoN9.xml");
// Reduced mechanism internal energy.
//double int_energy = 788261.179011143;
// Full mechanism internal energy.
//double int_energy = 786837.6552762145;
// N9 mechanism internal energy.
double int_energy = 1288730.465811496;
GasMixture->setMassFractions(massFractions);
GasMixture->setState_UV(int_energy, vol, tol);
phi[0] = GasMixture->temperature();
phi[1] = GasMixture->pressure();
delete GasMixture;
for (int j=2;j <= NS; j++) {
phi[j] = massFractions[j-2]/mw[j-2];
}
// PyJac call for source term
species_rates (&tout, &vol, phi, dphi, rwk_dphi);
for (int j=0;j <= NS; j++) {
${result}[j] = dphi[j];
}
"""))
# The tricky part - this is going to require a
# nonlinear solve of some kind.
freg = register_function(freg,
"<func>solver", ("y", "coeff"),
result_names=("result", ),
result_kinds=(UserType("y"), ))
freg = freg.register_codegen(
"<func>solver", "cxx",
cxx.CallCode("""
// PyJac inputs.
double jac[(NS+1)*(NS+1)];
double jac_trans[(NS+1)*(NS+1)];
double jac_sub[(NS-1)*(NS-1)];
double phi[(NS+1)];
double phi_guess[(NS+1)];
double phi_old[(NS+1)];
double dphi[(NS+1)];
double dphi_sub[(NS-1)];
double dphi_old[(NS+1)];
double corr[(NS+1)];
double corr_weights[(NS+1)];
double corr_weighted[(NS+1)];
double reltol = 1e-6;
double abstol = 1e-12;
/* For Lapack */
int ipiv[NS-1], info;
int nrhs = 1;
int nsp_l = NS-1;
int nsp_l_full = NS+1;
// Dummy time for pyJac.
double tout = 0;
// Work array for PyJac.
double* rwk_dphi = (double*)malloc(245 * sizeof(double));
memset(rwk_dphi, 0, 245 * sizeof(double));
double* rwk_jac = (double*)malloc(245 * sizeof(double));
memset(rwk_jac, 0, 245 * sizeof(double));
/* 1D point-sized identity matrix */
double ident[(NS-1)*(NS-1)];
for (int i=0; i < (NS-1)*(NS-1); i++) {
if (i % (NS) == 0) {
ident[i] = 1;
} else {
ident[i] = 0;
}
}
// THIS IS WHERE ALL OF THE
// NEWTON/PYJAC STUFF GOES.
// Get chemical state at this point.
double massFractions[NS];
double mw[NS];
// FIXME: Assumes the last (inert) species is nitrogen.
mw[NS-1] = 2*14.00674;
for (int i = 0; i < NS-1; ++i ){
mw[i] = mw[NS-1]*mw_factor[i];
}
double rho = 0.2072648773462248;
double mass_sum = 0.0;
for (int i = 2; i <= NS; ++i ){
massFractions[i-2] = ${y}[i]*mw[i-2];
mass_sum += massFractions[i-2];
}
//massFractions[8] = 1 - mass_sum;
massFractions[8] = 0.0;
double vol = 1.0 / 0.2072648773462248;
double tol = 1e-10;
// PyJac converted input state.
//phi[0] = ${y}[0];
//phi[1] = ${y}[1];
// Update temperature and pressure using Cantera
Cantera::IdealGasMix * GasMixture;
//GasMixture = new Cantera::IdealGasMix("Mechanisms/sanDiego.xml");
GasMixture = new Cantera::IdealGasMix("Mechanisms/SanDiegoN9.xml");
// Reduced mechanism internal energy.
//double int_energy = 788261.179011143;
// Full mechanism internal energy.
//double int_energy = 786837.6552762145;
// N9 mechanism internal energy.
double int_energy = 1288730.465811496;
GasMixture->setMassFractions(massFractions);
GasMixture->setState_UV(int_energy, vol, tol);
phi[0] = GasMixture->temperature();
phi[1] = GasMixture->pressure();
//delete GasMixture;
for (int j=2;j <= NS; j++) {
phi[j] = massFractions[j-2]/mw[j-2];
}
for (int j=0;j <= NS; j++) {
phi_old[j] = phi[j];
}
for (int j=0;j <= NS; j++) {
phi_guess[j] = phi[j];
}
// Newton loop within this point (for now).
double corr_norm = 1.0;
// PyJac call for source term
species_rates (&tout, &vol, phi, dphi_old, rwk_dphi);
//while (abs(corr_norm) >= reltol) {
while (abs(corr_norm) >= 1e-8) {
species_rates (&tout, &vol, phi_guess, dphi, rwk_dphi);
// Get Jacobian at this point.
jacobian (&tout, &vol, phi_guess, jac, rwk_jac);
for (int j=0;j <= NS; j++) {
// IMEX ARK
dphi[j] = phi_guess[j] - phi_old[j] - ${coeff} * dphi[j];
}
// Take subset of RHS vector.
for (int j=2;j <= NS; j++) {
dphi_sub[j-2] = dphi[j];
}
// Transpose the Jacobian.
// PYJAC outputs Fortran-ordering
for (int i = 0; i < (NS+1); ++i )
{
for (int j = 0; j < (NS+1); ++j )
{
// Index in the original matrix.
int index1 = i*(NS+1)+j;
// Index in the transpose matrix.
int index2 = j*(NS+1)+i;
jac_trans[index2] = jac[index1];
}
}
for (int i=0; i<(NS+1)*(NS+1); i++) {
jac[i] = jac_trans[i];
}
// Take subset of Jacobian for algebraic changes.
for (int i = 0; i < (NS-1); ++i )
{
for (int j = 0; j < (NS-1); ++j )
{
jac_sub[i*(NS-1)+j] = jac[(i+2)*(NS+1)+2+j];
}
}
// Make the algebraic changes,
// using PyJac routines as needed.
// Get internal energies.
double int_energies[NS];
eval_u(phi_guess, int_energies);
// Get CVs.
double cvs[NS];
eval_cv(phi_guess, cvs);
// Get total CV.
double mass_sum = 0.0;
for (int i = 2; i <= NS; ++i ){
massFractions[i-2] = phi_guess[i]*mw[i-2];
mass_sum += massFractions[i-2];
}
//massFractions[8] = 1 - mass_sum;
massFractions[8] = 0.0;
double cv_total = 0.0;
for (int i = 0; i <= NS-1; ++i ){
cv_total += cvs[i]*(massFractions[i]/mw[i]);
}
// Modify the Jacobian for the algebraic constraint.
for (int i = 0; i < (NS-1); ++i )
{
for (int j = 0; j < (NS-1); ++j )
{
//jac_sub[i*(NS-1)+j] -= jac[(i+2)*(NS+1)]*int_energies[j]/cv_total;
jac_sub[i*(NS-1)+j] -= jac[j+2]*int_energies[i]/cv_total;
}
}
/* Subtract from identity to get jac for Newton */
for (int j=0;j < (NS-1)*(NS-1); j++) {
jac_sub[j] = ident[j] - ${coeff} * jac_sub[j]; // IMEX ARK
jac_sub[j] = -jac_sub[j];
}
// Do the inversion with the assistance of Lapack.
dgesv_(&nsp_l, &nrhs, jac_sub, &nsp_l, ipiv, dphi_sub, &nsp_l, &info);
// Add the correction to the buffer.
mass_sum = 0.0;
for (int i = 2; i <= NS; ++i ){
massFractions[i-2] = (phi_guess[i] + dphi_sub[i-2])*mw[i-2];
mass_sum += massFractions[i-2];
}
//massFractions[8] = 1 - mass_sum;
massFractions[8] = 0.0;
GasMixture->setMassFractions(massFractions);
GasMixture->setState_UV(int_energy, vol, tol);
corr[0] = GasMixture->temperature() - phi_guess[0];
corr[1] = GasMixture->pressure() - phi_guess[1];
for (int j=2;j <= NS; j++) {
corr[j] = dphi_sub[j-2];
}
for (int j=0;j <= NS; j++) {
corr_weights[j] = 1.0 / (reltol * abs(phi_guess[j]) + abstol);
corr_weighted[j] = corr[j]*corr_weights[j];
}
//corr_norm = dnrm2_(&nsp_l, corr, &nrhs);
corr_norm = dnrm2_(&nsp_l_full, corr_weighted, &nrhs);
//std::cout << "Correction norm: " << corr_norm << std::endl;
for (int j=0;j <= NS; j++) {
phi_guess[j] = phi_guess[j] + corr[j];
}
}
// Now outside the Newton loop (presumably having converged),
// we update the RHS using the actual state.
species_rates (&tout, &vol, phi_guess, dphi, rwk_dphi);
for (int j=0;j <= NS; j++) {
${result}[j] = dphi[j];
}
// Also compare the relative internal energies and chec the mass sum.
//std::cout << std::setprecision(16) << (GasMixture->intEnergy_mass() - int_energy)/int_energy << std::endl;
//std::cout << std::setprecision(16) << mass_sum - 1 << std::endl;
delete GasMixture;
"""))
code = stepper.generate()
# Implicit solve thingy
from leap.implicit import replace_AssignImplicit
code = replace_AssignImplicit(code, {"solve": solver_hook})
codegen = cxx.CodeGenerator(
'LeapIMEX',
user_type_map={
component_id: cxx.ArrayType(
(10, ),
cxx.BuiltinType('double'),
),
},
function_registry=freg,
emit_instrumentation=True,
timing_function="clock",
header_preamble="\n#include \"mechanism.hpp\"\n#include " +
"\"species_rates.hpp\"\n#include " +
"\"jacobian.hpp\"\n#include \"memcpy_2d.hpp" +
"\"\n#include \"lapack_kernels.H\"\n#include " +
"\"cantera/IdealGasMix.h\"\n#include " +
"\"cantera/thermo.h\"\n#include " +
"\"cantera/kinetics.h\"\n#include " + "\"cantera/transport.h\"")
import sys
# Write out Leap/Dagrt code:
with open(sys.argv[1], "a") as outf:
code_str = codegen(code)
print(code_str, file=outf)