C-integrators and specifying systems of eqs.

  • Anonymous - 2013-09-18


    I'm having trouble specifying the systems of eqs. in a separate function and at the same time use Dopri/Radau integrators.
    Using the python/VODE integrator works, but as I would like to get event detection, c-integrators seems to be the way to go.

    I guess the problem at hand is that PyDSTool need the system of eqs. as strings for the generation of c-files.
    But I really like the way of using a function for providing the eqs. Especially in my case, where I need to call a function when setting up the eqs.

    Are there any way around this?

    Regards, Paw
    Ps. Thanks to amanderson for help with the 'custom code calls'

    Sample code:

    import numpy as np
    import matplotlib.pyplot as plt
    import time
    import PyDSTool as pdt
    domain   = np.array([-10, 5, -3, 3])#         % domain boundaries
    gspace   = 20 * 0.05 #                        % grid spacing
    tspan    = np.array([0, 5e2])#                % time span vector for integration
    def vel(x,y):
        r = 1; U = 1; z = x+1j*y
        vel = U*(1-r**2/z**2);
        u = vel.real
        v = -vel.imag
        return u,v
    ## Compute potential flow field
    x     = np.arange(domain[0],domain[1]+gspace,gspace)
    y     = np.arange(domain[2],domain[3]+gspace,gspace)
    [X,Y] = np.meshgrid(x,y)
    [u,v] = vel(X,Y)
    def dfdt(t,up,vp,xp,yp,C):
        # setup df = [dup dvp dxp dyp]
        df = np.zeros(4)
        # flow velocity
        [u,v] = vel(xp,yp)
        df[0] = -(up-u)
        df[1] = -(vp-v)
        df[2:4] = C*np.array([up,vp])
        return df
    udot = 'df[0]';vdot = 'df[1]';xdot = 'df[2]';ydot = 'df[3]'
    ics = {'u':1,'v':0,'x':-32,'y':0.1}
    pars = {'c': 0.3}
    DSargs = pdt.args()
    DSargs.name = 'test'
    DSargs.ics = ics
    DSargs.pars = pars
    DSargs.tdata = tspan
    DSargs.varspecs = {'u':udot,'v':vdot,'x':xdot,'y':ydot}
    DSargs.vfcodeinsert_start = 'df = ds.df(t,u,v,x,y,c)'
    DSargs.ignorespecial = ['df']
    DSargs.algparams = {'init_step': 0.1,'atol':1e-5, 'rtol':1e-5 }
    ode = pdt.Generator.Vode_ODEsystem(DSargs)
    # ode = pdt.Generator.Dopri_ODEsystem(DSargs)
    # attach function to ODE definition
    ode.df = dfdt
    t = time.time()
    result = ode.compute('test')
    print "time for integration: %f" %(time.time() - t)
    pts = result.sample()
    # PLOTS
    fig = plt.figure(1); plt.clf(); plt.hold(True)
    ax = fig.add_subplot(1, 1, 1)
    p = ax.plot(pts['x'],pts['y'],'g:',linewidth=2)
    ax.streamplot(X,Y,u,v, density=[1,0.4],color='cornflowerblue')
    # add a proxy artist, because streamplot doesn't support legend
    p2 = plt.Rectangle((0, 0), 1, 1, fc='cornflowerblue')
    circ = plt.Circle((0, 0), radius=1, color='r')
    ax.legend([p,p2],["particle path, c=%0.1f"%0.3,"Potential flow field"])
    plt.legend(); plt.hold(False); plt.grid(True)
    plt.xlabel('x'); plt.ylabel('y')
    plt.axis('equal'); plt.axis((domain))
    # run matplotlib in interactive mode
    plt.ion(); plt.show()
  • Anonymous - 2013-09-18

    Hmm, I did a poor job posting the code.
    Download it from {here} instead.

  • Anonymous - 2013-09-18

    I forgot to add that I'm running 32 bit linux and test  Dopri_backwards_test.py works fine.

  • Rob Clewley

    Rob Clewley - 2013-09-18


    Correct me if I'm overlooking something, but I think the solution using the C integrators is relatively easy. You do not seem to need the meshgrid functionality in your final simulation. If that's the case, then it should be fairly simple to use some custom C code and a C math library that supports complex numbers and arithmetic. You can generate the C source code for your model, again inserting a call to your C vector field function (that calls your C vel function). Alternatively, you can make a dummy 4D RHS and edit it later (probably easiest unless you want to try to make it more automated).

    In either case, just follow the example in tests/HH_model_Cintegrator.py. Use the nobuild=True option then edit the C source file to include your new functions and the edited vector field function (to redirect to yours). You just have to enter new values into the "return" array (it's call by reference so there's no explicit return). Then add include any header files for other libraries you used in the call to makeLib.

    Let me know if you have more questions.

  • Anonymous - 2013-09-19

    Thanks for the quick answer. Will try it tomorrow.
    In the mean time, I guess there is no way I can do something like

        udot = '-(u-velx(x,y))'
        vdot = '-(v-vely(x,y))'
        xdot = 'c*u'
        ydot = 'c*v'
        aux = {
            'velx': (['x','y'], 'real(1*(1-1**2/(x+1j*y)**2))' ),
            'vely': (['x','y'], '-imag(1*(1-1**2/(x+1j*y)**2))' )
    And then a last question:
    When I call dfdt(t,up,vp,xp,yp,C), can it be done so the call is dfdt(t,f,C) instead, where f = [up,vp,xp,yp]?
    Thanks a lot
  • Rob Clewley

    Rob Clewley - 2013-09-19

    Yes, you can do that provided you have the functions real and imag defined in C. I don't think they are in the default C math library but I'm rusty on what's in there. If necessary, you can add a list of custom libraries to include when you call makeLib, and you could call that right after nobuild=True even if you don't go "outside" to edit anything by hand in between those two steps.

    I'm not sure at which level your question about dfdt refers to. You can't specify a vector argument directly in the PyDSTool spec strings for functions or RHS's. You can make your custom python or C function accept any form of vector argument when you call it from the regular, original RHS vector field function.


  • Anonymous - 2013-09-19

    Got it to work with

    udot = '-(u-velx(x,y))'
    vdot = '-(v-vely(x,y))'
    xdot = 'c*u'
    ydot = 'c*v'
    aux = {
        'velx': (['x','y'], 'creal(1*(1-1**2/( (x+1*I*y)*(x+1*I*y) )))' ),
        'vely': (['x','y'], '-cimag(1*(1-1**2/( (x+1*I*y)*(x+1*I*y) )))' )
    DSargs.ignorespecial = ['cimag','creal','I']

    Note that **2 cannot be used in vel. It compiles to pow() - as expected - and we need cpow().
    It is lightening fast. Especially when you come from an matlab environment.

    Thank you! This is nice :)

    Can you explain what you mean by a you can make a dummy 4D RHS and edit it later (probably easiest unless you want to try to make it more automated).. I do not quite get it.


  • Rob Clewley

    Rob Clewley - 2013-09-22

    The dummy RHS is for the C code situation, where you set each RHS = 0 or something like that. Then you edit the C code for the vector field and insert any function calls you want. I think you've already found the best solution to your problem here.


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