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# Testing TSAdjoint and matrix-free Jacobian
# Basic usage:
# python vanderpol.py
# Test implicit methods using implicit form:
# python -implicitform
# Test explicit methods:
# python -implicitform 0
# Test IMEX methods:
# python -imexform
# Matrix-free implementations can be enabled with an additional option -mf
import sys
import petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
class VDP:
n = 2
comm = PETSc.COMM_SELF
def __init__(self, mu_=1.0e3, mf_=False, imex_=False):
self.mu_ = mu_
self.mf_ = mf_
self.imex_ = imex_
if self.mf_:
self.Jim_ = PETSc.Mat().createDense([self.n, self.n], comm=self.comm)
self.Jim_.setUp()
self.JimP_ = PETSc.Mat().createDense([self.n, 1], comm=self.comm)
self.JimP_.setUp()
self.Jex_ = PETSc.Mat().createDense([self.n, self.n], comm=self.comm)
self.Jex_.setUp()
self.JexP_ = PETSc.Mat().createDense([self.n, 1], comm=self.comm)
self.JexP_.setUp()
def initialCondition(self, u):
mu = self.mu_
u[0] = 2.0
u[1] = -2.0 / 3.0 + 10.0 / (81.0 * mu) - 292.0 / (2187.0 * mu * mu)
u.assemble()
def evalFunction(self, ts, t, u, f):
mu = self.mu_
f[0] = u[1]
if self.imex_:
f[1] = 0.0
else:
f[1] = mu * ((1.0 - u[0] * u[0]) * u[1] - u[0])
f.assemble()
def evalJacobian(self, ts, t, u, A, B):
if not self.mf_:
J = A
else:
J = self.Jex_
mu = self.mu_
J[0, 0] = 0
J[0, 1] = 1.0
if self.imex_:
J[1, 0] = 0
J[1, 1] = 0
else:
J[1, 0] = -mu * (2.0 * u[1] * u[0] + 1.0)
J[1, 1] = mu * (1.0 - u[0] * u[0])
J.assemble()
if A != B:
B.assemble()
def evalJacobianP(self, ts, t, u, C):
if not self.mf_:
Jp = C
else:
Jp = self.JexP_
if not self.imex_:
Jp[0, 0] = 0
Jp[1, 0] = (1.0 - u[0] * u[0]) * u[1] - u[0]
Jp.assemble()
def evalIFunction(self, ts, t, u, udot, f):
mu = self.mu_
if self.imex_:
f[0] = udot[0]
else:
f[0] = udot[0] - u[1]
f[1] = udot[1] - mu * ((1.0 - u[0] * u[0]) * u[1] - u[0])
f.assemble()
def evalIJacobian(self, ts, t, u, udot, shift, A, B):
if not self.mf_:
J = A
else:
J = self.Jim_
mu = self.mu_
if self.imex_:
J[0, 0] = shift
J[0, 1] = 0.0
else:
J[0, 0] = shift
J[0, 1] = -1.0
J[1, 0] = mu * (2.0 * u[1] * u[0] + 1.0)
J[1, 1] = shift - mu * (1.0 - u[0] * u[0])
J.assemble()
if A != B:
B.assemble()
def evalIJacobianP(self, ts, t, u, udot, shift, C):
if not self.mf_:
Jp = C
else:
Jp = self.JimP_
Jp[0, 0] = 0
Jp[1, 0] = u[0] - (1.0 - u[0] * u[0]) * u[1]
Jp.assemble()
class JacShell:
def __init__(self, ode):
self.ode_ = ode
def mult(self, A, x, y):
"y <- A * x"
self.ode_.Jex_.mult(x, y)
def multTranspose(self, A, x, y):
"y <- A' * x"
self.ode_.Jex_.multTranspose(x, y)
class JacPShell:
def __init__(self, ode):
self.ode_ = ode
def multTranspose(self, A, x, y):
"y <- A' * x"
self.ode_.JexP_.multTranspose(x, y)
class IJacShell:
def __init__(self, ode):
self.ode_ = ode
def mult(self, A, x, y):
"y <- A * x"
self.ode_.Jim_.mult(x, y)
def multTranspose(self, A, x, y):
"y <- A' * x"
self.ode_.Jim_.multTranspose(x, y)
class IJacPShell:
def __init__(self, ode):
self.ode_ = ode
def multTranspose(self, A, x, y):
"y <- A' * x"
self.ode_.JimP_.multTranspose(x, y)
OptDB = PETSc.Options()
mu_ = OptDB.getScalar('mu', 1.0e3)
mf_ = OptDB.getBool('mf', False)
implicitform_ = OptDB.getBool('implicitform', False)
imexform_ = OptDB.getBool('imexform', False)
ode = VDP(mu_, mf_, imexform_)
if not mf_:
Jim = PETSc.Mat().createDense([ode.n, ode.n], comm=ode.comm)
Jim.setUp()
JimP = PETSc.Mat().createDense([ode.n, 1], comm=ode.comm)
JimP.setUp()
Jex = PETSc.Mat().createDense([ode.n, ode.n], comm=ode.comm)
Jex.setUp()
JexP = PETSc.Mat().createDense([ode.n, 1], comm=ode.comm)
JexP.setUp()
else:
Jim = PETSc.Mat().create()
Jim.setSizes([ode.n, ode.n])
Jim.setType('python')
shell = IJacShell(ode)
Jim.setPythonContext(shell)
Jim.setUp()
Jim.assemble()
JimP = PETSc.Mat().create()
JimP.setSizes([ode.n, 1])
JimP.setType('python')
shell = IJacPShell(ode)
JimP.setPythonContext(shell)
JimP.setUp()
JimP.assemble()
Jex = PETSc.Mat().create()
Jex.setSizes([ode.n, ode.n])
Jex.setType('python')
shell = JacShell(ode)
Jex.setPythonContext(shell)
Jex.setUp()
Jex.assemble()
JexP = PETSc.Mat().create()
JexP.setSizes([ode.n, 1])
JexP.setType('python')
shell = JacPShell(ode)
JexP.setPythonContext(shell)
JexP.setUp()
JexP.zeroEntries()
JexP.assemble()
u = PETSc.Vec().createSeq(ode.n, comm=ode.comm)
f = u.duplicate()
adj_u = []
adj_u.append(PETSc.Vec().createSeq(ode.n, comm=ode.comm))
adj_u.append(PETSc.Vec().createSeq(ode.n, comm=ode.comm))
adj_p = []
adj_p.append(PETSc.Vec().createSeq(1, comm=ode.comm))
adj_p.append(PETSc.Vec().createSeq(1, comm=ode.comm))
ts = PETSc.TS().create(comm=ode.comm)
ts.setProblemType(ts.ProblemType.NONLINEAR)
if imexform_:
ts.setType(ts.Type.ARKIMEX)
ts.setIFunction(ode.evalIFunction, f)
ts.setIJacobian(ode.evalIJacobian, Jim)
ts.setIJacobianP(ode.evalIJacobianP, JimP)
ts.setRHSFunction(ode.evalFunction, f)
ts.setRHSJacobian(ode.evalJacobian, Jex)
ts.setRHSJacobianP(ode.evalJacobianP, JexP)
else:
if implicitform_:
ts.setType(ts.Type.CN)
ts.setIFunction(ode.evalIFunction, f)
ts.setIJacobian(ode.evalIJacobian, Jim)
ts.setIJacobianP(ode.evalIJacobianP, JimP)
else:
ts.setType(ts.Type.RK)
ts.setRHSFunction(ode.evalFunction, f)
ts.setRHSJacobian(ode.evalJacobian, Jex)
ts.setRHSJacobianP(ode.evalJacobianP, JexP)
ts.setSaveTrajectory()
ts.setTime(0.0)
ts.setTimeStep(0.001)
ts.setMaxTime(0.5)
ts.setMaxSteps(1000)
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.MATCHSTEP)
ts.setFromOptions()
ode.initialCondition(u)
ts.solve(u)
adj_u[0][0] = 1
adj_u[0][1] = 0
adj_u[0].assemble()
adj_u[1][0] = 0
adj_u[1][1] = 1
adj_u[1].assemble()
adj_p[0][0] = 0
adj_p[0].assemble()
adj_p[1][0] = 0
adj_p[1].assemble()
ts.setCostGradients(adj_u, adj_p)
ts.adjointSolve()
adj_u[0].view()
adj_u[1].view()
adj_p[0].view()
adj_p[1].view()
def compute_derp(du, dp):
print(
du[1] * (-10.0 / (81.0 * mu_ * mu_) + 2.0 * 292.0 / (2187.0 * mu_ * mu_ * mu_))
+ dp[0]
)
compute_derp(adj_u[0], adj_p[0])
compute_derp(adj_u[1], adj_p[1])
del ode, Jim, JimP, Jex, JexP, u, f, ts, adj_u, adj_p
|
