Different ways to optimize with GPU PyOpenCL a python code : extern function inside kernel GPU/PyOpenCL

I have used the following command to profile my Python code :

python2.7 -m cProfile -o X2_non_flat_multiprocessing_dummy.prof X2_non_flat.py

Then, I can visualize globally the repartition of different greedy functions :

As you can see, a lot of time is spent into Pobs_C and interpolate routine which corresponds to the following code snippet :

def Pobs_C(z, zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T, R_T, DG_T_fid, DG_T, WGT_T, WT_T, WIAT_T, cl, P_dd_spec, RT500):
    cc = 0
    P_dd_ok = np.zeros(len(z_pk))
    while cc < len(z_pk):
        if ((cl+0.5)/RT500[cc] < 35 and (cl+0.5)/RT500[cc] > 0.0005):
            P_dd_ok[cc] = P_dd_spec[cc]((cl+0.5)/RT500[cc])
        cc=cc+1

    P_dd_ok = CubicSpline(z_pk, P_dd_ok)
    if paramo == 8:
        P_dd_ok = P_dd_ok(z)*(DG_T(z)/DG_T_fid(z))**2
    else:
        P_dd_ok = P_dd_ok(z)

    if paramo != 9 or paramo != 10 or paramo != 11:
        C_gg = c/(100.*h_p)*0.5*delta_zpm*np.sum((F_dd_GG(z[1:], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, E_T(z[1:]), R_T(z[1:]), WGT_T[aa][1:], WGT_T[bb][1:], DG_T(z[1:]), P_dd_ok[1:]) + F_dd_GG(z[:-1], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, E_T(z[:-1]), R_T(z[:-1]), WGT_T[aa][:-1], WGT_T[bb][:-1], DG_T(z[:-1]), P_dd_ok[:-1]))) + P_shot_GC(zi, zj)
    else:
        C_gg = 0.
    if paramo < 12:
        C_ee = c/(100.*h_p)*0.5*delta_zpm*(np.sum(F_dd_LL(z[1:], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, E_T(z[1:]), R_T(z[1:]), WT_T[aa][1:], WT_T[bb][1:], DG_T(z[1:]), P_dd_ok[1:]) + F_dd_LL(z[:-1], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, E_T(z[:-1]), R_T(z[:-1]), WT_T[aa][:-1], WT_T[bb][:-1], DG_T(z[:-1]), P_dd_ok[:-1])) + np.sum(F_IA_d(z[1:], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[1:]), R_T(z[1:]), DG_T(z[1:]), WT_T[aa][1:], WT_T[bb][1:], WIAT_T[aa][1:], WIAT_T[bb][1:], P_dd_ok[1:]) + F_IA_d(z[:-1], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[:-1]), R_T(z[:-1]), DG_T(z[:-1]), WT_T[aa][:-1], WT_T[bb][:-1], WIAT_T[aa][:-1], WIAT_T[bb][:-1], P_dd_ok[:-1])) + np.sum(F_IAIA(z[1:], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[1:]), R_T(z[1:]), DG_T(z[1:]), WIAT_T[aa][1:], WIAT_T[bb][1:], P_dd_ok[1:]) + F_IAIA(z[:-1], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[:-1]), R_T(z[:-1]), DG_T(z[:-1]), WIAT_T[aa][:-1], WIAT_T[bb][:-1], P_dd_ok[:-1]))) + P_shot_WL(zi, zj)
    else:
        C_ee = 0.
    C_gl = c/(100.*h_p)*0.5*delta_zpm*np.sum((F_dd_GL(z[1:], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[1:]), R_T(z[1:]), DG_T(z[1:]), WGT_T[aa][1:], WT_T[bb][1:], WIAT_T[bb][1:], P_dd_ok[1:]) + F_dd_GL(z[:-1], zi, zj, h_p, wm_p, wDE_p, w0_p, wa_p, C_IAp, A_IAp, n_IAp, B_IAp, E_T(z[:-1]), R_T(z[:-1]), DG_T(z[:-1]), WGT_T[aa][:-1], WT_T[bb][:-1], WIAT_T[bb][:-1], P_dd_ok[:-1])))
    return C_gg, C_ee, C_gl

1) MAIN QUESTION : Is there a way to implement a GPU/OpenCL layer in this routine, especially for CubicSpline or the whole Pobs_C function. What are the alternatives that would allow me to reduce the time passed into Pobs_C and its inner function CubicSpline ?

I have few notions with OpenCL (not PyOpenCL) like for example the map-reduce method or solving Heat 2D equation with classical kernel.

2) PREVIOUS FEEDBACK :

I know that we can't have optimization by thinking naively that calling an extern function inside a kernel brings a higher speedup since GPU can achieve a lot of calls. Instead, I should rather put all the content of the different functions allow to get optimization : Do you agree with that and confirm it ? So, can I declare inside the kernel code a call to an extern function (I mean a function not inside kernel, i.e the classical part code (called Host code ?) ?

3) OPTIONAL QUESTION : Maybe can I declare this extern function inside the kernel : is it possible by doing explicitely this declaration inside ? Indeed, that could avoid to copy all the content of all functions potentially GPU-parallilzed.

Any idea/remark/advice would be great, Regards.

PS: Sorry if this is a general topic but it will allow me to see clearer about the available ways to include GPU/OpenCL in my code above and then optimize it.

from Different ways to optimize with GPU PyOpenCL a python code : extern function inside kernel GPU/PyOpenCL