Multiple scipy.integrate.ode instances

问题:

I would like to use scipy.integrate.ode (or scipy.integrate.odeint) instances in multiple threads (one for each CPU core) in order to solve multiple IVPs at a time. However the documentation says: "This integrator is not re-entrant. You cannot have two ode instances using the “vode” integrator at the same time."

(Also odeint causes internal errors if instantiated multiple times although the documentation does not say so.)

Any idea what can be done?

回答1:

One option is to use multiprocessing (i.e. use processes instead of threads). Here's an example that uses the map function of the multiprocessing.Pool class.

The function solve takes a set of initial conditions and returns a solution generated by odeint. The "serial" version of the code in the main section calls solve repeatedly, once for each set of initial conditions in ics. The "multiprocessing" version uses the map function of a multiprocessing.Pool instance to run several processes simultaneously, each calling solve. The map function takes care of doling out the arguments to solve.

My computer has four cores, and as I increase num_processes, the speedup maxes out at about 3.6.

from __future__ import division, print_function

import sys
import time
import multiprocessing as mp
import numpy as np
from scipy.integrate import odeint



def lorenz(q, t, sigma, rho, beta):
    x, y, z = q
    return [sigma*(y - x), x*(rho - z) - y, x*y - beta*z]


def solve(ic):
    t = np.linspace(0, 200, 801)
    sigma = 10.0
    rho = 28.0
    beta = 8/3
    sol = odeint(lorenz, ic, t, args=(sigma, rho, beta), rtol=1e-10, atol=1e-12)
    return sol


if __name__ == "__main__":
    ics = np.random.randn(100, 3)

    print("multiprocessing:", end='')
    tstart = time.time()
    num_processes = 5
    p = mp.Pool(num_processes)
    mp_solutions = p.map(solve, ics)
    tend = time.time()
    tmp = tend - tstart
    print(" %8.3f seconds" % tmp)

    print("serial:         ", end='')
    sys.stdout.flush()
    tstart = time.time()
    serial_solutions = [solve(ic) for ic in ics]
    tend = time.time()
    tserial = tend - tstart
    print(" %8.3f seconds" % tserial)

    print("num_processes = %i, speedup = %.2f" % (num_processes, tserial/tmp))

    check = [(sol1 == sol2).all()
             for sol1, sol2 in zip(serial_solutions, mp_solutions)]
    if not all(check):
        print("There was at least one discrepancy in the solutions.")

On my computer, the output is:

multiprocessing:    6.904 seconds
serial:            24.756 seconds
num_processes = 5, speedup = 3.59

回答2:

SciPy.integrate.ode appears to use the LLNL SUNDIALS solvers, although SciPy doesn't say so explicitly, but they should, in my opinion.

The current version of the CVODE ode solver, 3.2.2, is re-entrant, which means that it can be used to solve multiple problems concurrently. The relevant information appears in User Documentation for CVODE v3.2.0 (SUNDIALS v3.2.0).

All state information used by cvode to solve a given problem is saved in a structure, and a pointer to that structure is returned to the user. There is no global data in the cvode package, and so, in this respect, it is reentrant. State information specific to the linear solver is saved in a separate structure, a pointer to which resides in the cvode memory structure. The reentrancy of cvode was motivated by the anticipated multicomputer extension, but is also essential in a uniprocessor setting where two or more problems are solved by intermixed calls to the package from within a single user program.

But I don't know whether SciPy.integrate.ode, or other ode solvers like scikits.odes.ode, support this concurrency.