<div dir="auto">I would use option 3. Keep a work vector and do a vector summation instead of the multiple multiplication by scale and 1/scale. <div dir="auto"><br></div><div dir="auto">I agree with you the docs are a little misleading here. </div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Aug 10, 2023, 11:40 Niclas Götting <<a href="mailto:ngoetting@itp.uni-bremen.de">ngoetting@itp.uni-bremen.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><u></u>
<div>
<p>Thank you both for the very quick answer!</p>
<p>So far, I compiled PETSc with debugging turned on, but I think it
should still be faster than standard scipy in both cases.
Actually, Stefano's answer has got me very far already; now I only
define the RHS of the ODE and no Jacobian (I wonder, why the
documentation suggests otherwise, though). I had the following
four tries at implementing the RHS:</p>
<ol>
<li><font face="monospace">def rhsfunc1(ts, t, u, F):<br>
scale = 0.5 * (5 < t < 10)<br>
(l + scale * pump).mult(u, F)</font></li>
<li><font face="monospace">def rhsfunc2(ts, t, u, F):<br>
l.mult(u, F)<br>
scale = 0.5 * (5 < t < 10)<br>
(scale * pump).multAdd(u, F, F)</font></li>
<li><font face="monospace">def rhsfunc3(ts, t, u, F):<br>
l.mult(u, F)<br>
scale = 0.5 * (5 < t < 10)<br>
if scale != 0:<br>
pump.scale(scale)<br>
pump.multAdd(u, F, F)<br>
pump.scale(1/scale)</font></li>
<li><font face="monospace">def rhsfunc4(ts, t, u, F):<br>
tmp_pump.zeroEntries() # tmp_pump is pump.duplicate()<br>
l.mult(u, F)<br>
scale = 0.5 * (5 < t < 10)<br>
tmp_pump.axpy(scale, pump,
structure=PETSc.Mat.Structure.SAME_NONZERO_PATTERN)<br>
tmp_pump.multAdd(u, F, F)<br>
</font></li>
</ol>
<p>They all yield the same results, but with 50it/s, 800it/,
2300it/s and 1900it/s, respectively, which is a huge performance
boost (almost 7 times as fast as scipy, with PETSc debugging still
turned on). As the scale function will most likely be a gaussian
in the future, I think that option 3 will be become numerically
unstable and I'll have to go with option 4, which is already
faster than I expected. If you think it is possible to speed up
the RHS calculation even more, I'd be happy to hear your
suggestions; the -log_view is attached to this message.</p>
<p>One last point: If I didn't misunderstand the documentation at
<a href="https://petsc.org/release/manual/ts/#special-cases" target="_blank" rel="noreferrer">https://petsc.org/release/manual/ts/#special-cases</a>, should this
maybe be changed?</p>
<p>Best regards<br>
Niclas<br>
</p>
<div>On 09.08.23 17:51, Stefano Zampini
wrote:<br>
</div>
<blockquote type="cite">
<div dir="auto">
<div>TSRK is an explicit solver. Unless you are changing the ts
type from command line, the explicit jacobian should not be
needed. On top of Barry's suggestion, I would suggest you to
write the explicit RHS instead of assembly a throw away matrix
every time that function needs to be sampled.<br>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Wed, Aug 9, 2023, 17:09
Niclas Götting <<a href="mailto:ngoetting@itp.uni-bremen.de" target="_blank" rel="noreferrer">ngoetting@itp.uni-bremen.de</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Hi
all,<br>
<br>
I'm currently trying to convert a quantum simulation from
scipy to <br>
PETSc. The problem itself is extremely simple and of the
form \dot{u}(t) <br>
= (A_const + f(t)*B_const)*u(t), where f(t) in this simple
test case is <br>
a square function. The matrices A_const and B_const are
extremely sparse <br>
and therefore I thought, the problem will be well suited
for PETSc. <br>
Currently, I solve the ODE with the following procedure in
scipy (I can <br>
provide the necessary data files, if needed, but they are
just some <br>
trace-preserving, very sparse matrices):<br>
<br>
import numpy as np<br>
import scipy.sparse<br>
import scipy.integrate<br>
<br>
from tqdm import tqdm<br>
<br>
<br>
l = np.load("../liouvillian.npy")<br>
pump = np.load("../pump_operator.npy")<br>
state = np.load("../initial_state.npy")<br>
<br>
l = scipy.sparse.csr_array(l)<br>
pump = scipy.sparse.csr_array(pump)<br>
<br>
def f(t, y, *args):<br>
return (l + 0.5 * (5 < t < 10) * pump) @ y<br>
#return l @ y # Uncomment for f(t) = 0<br>
<br>
dt = 0.1<br>
NUM_STEPS = 200<br>
res = np.empty((NUM_STEPS, 4096), dtype=np.complex128)<br>
solver = <br>
scipy.integrate.ode(f).set_integrator("zvode").set_initial_value(state)<br>
times = []<br>
for i in tqdm(range(NUM_STEPS)):<br>
res[i, :] = solver.integrate(solver.t + dt)<br>
times.append(solver.t)<br>
<br>
Here, A_const = l, B_const = pump and f(t) = 5 < t <
10. tqdm reports <br>
about 330it/s on my machine. When converting the code to
PETSc, I came <br>
to the following result (according to the chapter <br>
<a href="https://petsc.org/main/manual/ts/#special-cases" rel="noreferrer noreferrer noreferrer" target="_blank">https://petsc.org/main/manual/ts/#special-cases</a>)<br>
<br>
import sys<br>
import petsc4py<br>
petsc4py.init(args=sys.argv)<br>
import numpy as np<br>
import scipy.sparse<br>
<br>
from tqdm import tqdm<br>
from petsc4py import PETSc<br>
<br>
comm = PETSc.COMM_WORLD<br>
<br>
<br>
def mat_to_real(arr):<br>
return np.block([[arr.real, -arr.imag], [arr.imag, <br>
arr.real]]).astype(np.float64)<br>
<br>
def mat_to_petsc_aij(arr):<br>
arr_sc_sp = scipy.sparse.csr_array(arr)<br>
mat = PETSc.Mat().createAIJ(arr.shape[0], comm=comm)<br>
rstart, rend = mat.getOwnershipRange()<br>
print(rstart, rend)<br>
print(arr.shape[0])<br>
print(mat.sizes)<br>
I = arr_sc_sp.indptr[rstart : rend + 1] -
arr_sc_sp.indptr[rstart]<br>
J = arr_sc_sp.indices[arr_sc_sp.indptr[rstart] : <br>
arr_sc_sp.indptr[rend]]<br>
V = arr_sc_sp.data[arr_sc_sp.indptr[rstart] :
arr_sc_sp.indptr[rend]]<br>
<br>
print(I.shape, J.shape, V.shape)<br>
mat.setValuesCSR(I, J, V)<br>
mat.assemble()<br>
return mat<br>
<br>
<br>
l = np.load("../liouvillian.npy")<br>
l = mat_to_real(l)<br>
pump = np.load("../pump_operator.npy")<br>
pump = mat_to_real(pump)<br>
state = np.load("../initial_state.npy")<br>
state = np.hstack([state.real,
state.imag]).astype(np.float64)<br>
<br>
l = mat_to_petsc_aij(l)<br>
pump = mat_to_petsc_aij(pump)<br>
<br>
<br>
jac = l.duplicate()<br>
for i in range(8192):<br>
jac.setValue(i, i, 0)<br>
jac.assemble()<br>
jac += l<br>
<br>
vec = l.createVecRight()<br>
vec.setValues(np.arange(state.shape[0], dtype=np.int32),
state)<br>
vec.assemble()<br>
<br>
<br>
dt = 0.1<br>
<br>
ts = PETSc.TS().create(comm=comm)<br>
ts.setFromOptions()<br>
ts.setProblemType(ts.ProblemType.LINEAR)<br>
ts.setEquationType(ts.EquationType.ODE_EXPLICIT)<br>
ts.setType(ts.Type.RK)<br>
ts.setRKType(ts.RKType.RK3BS)<br>
ts.setTime(0)<br>
print("KSP:", ts.getKSP().getType())<br>
print("KSP PC:",ts.getKSP().getPC().getType())<br>
print("SNES :", ts.getSNES().getType())<br>
<br>
def jacobian(ts, t, u, Amat, Pmat):<br>
Amat.zeroEntries()<br>
Amat.aypx(1, l,
structure=PETSc.Mat.Structure.SUBSET_NONZERO_PATTERN)<br>
Amat.axpy(0.5 * (5 < t < 10), pump, <br>
structure=PETSc.Mat.Structure.SUBSET_NONZERO_PATTERN)<br>
<br>
ts.setRHSFunction(PETSc.TS.computeRHSFunctionLinear)<br>
#ts.setRHSJacobian(PETSc.TS.computeRHSJacobianConstant, l,
l) # <br>
Uncomment for f(t) = 0<br>
ts.setRHSJacobian(jacobian, jac)<br>
<br>
NUM_STEPS = 200<br>
res = np.empty((NUM_STEPS, 8192), dtype=np.float64)<br>
times = []<br>
rstart, rend = vec.getOwnershipRange()<br>
for i in tqdm(range(NUM_STEPS)):<br>
time = ts.getTime()<br>
ts.setMaxTime(time + dt)<br>
ts.solve(vec)<br>
res[i, rstart:rend] = vec.getArray()[:]<br>
times.append(time)<br>
<br>
I decomposed the complex ODE into a larger real ODE, so
that I can <br>
easily switch maybe to GPU computation later on. Now, the
solutions of <br>
both scripts are very much identical, but PETSc runs about
3 times <br>
slower at 120it/s on my machine. I don't use MPI for PETSc
yet.<br>
<br>
I strongly suppose that the problem lies within the
jacobian definition, <br>
as PETSc is about 3 times *faster* than scipy with f(t) =
0 and <br>
therefore a constant jacobian.<br>
<br>
Thank you in advance.<br>
<br>
All the best,<br>
Niclas<br>
<br>
<br>
</blockquote>
</div>
</div>
</div>
</blockquote>
</div>
</blockquote></div>