I am numerically solving a differential equation that depends on parameters. I am not really interested on the solutions but on their behaviour depending on the value of the parameters. Since I want a very precise description I must use a very fine array of parameters' values resulting in a lot of ODE solving processes. So I want to know if it would be possible to "parallelize" such a program. The idea is that maybe each processor of my computer can solve the ODE for a distinct pair of parameters. A kind of example is the following:
import matplotlib.pyplot as plt from scipy.integrate import ode import numpy as np # - ODE - # def sys(t,x,p1,p2): #p1 and p2 are the parameters dx=np.zeros(2) dx[0] = x[1] dx[1] = (p1+p2*cos(t))*x[0] return dx t0=0; tEnd=10; dt=0.01 r = ode(sys).set_integrator('dopri5', nsteps=10,max_step=dt) Y=[];S=[];T=[] ic=[.1,0] # - parameters range - # P1=np.linspace(0,1,100) P2=np.linspace(0,1,100) # -------------------- # for p1 in P1: for p2 in P2: r.set_initial_value(ic, t0).set_f_params(p1,p2) flag='No' while r.successful() and r.t +dt < tEnd: r.integrate(r.t+dt) Y.append(r.y) T.append(r.t) #-This is what we want to know. if r.y[0]>2*ic[0]: flag='Yes' break if flag=='Yes': plt.scatter(p1,p2,s=1, c='k', marker='.') # ------------------------------------ # plt.show() Note that each for loop is independent so: Is it possible to make those for loops in a parallel way? So I would imagine that it is possible that each of my 8 processors do one double for loop at a time and then probably make the computations roughly 8 times faster? Or at least faster?
