Error from wrapping GSL in Cython: Cannot convert Python object to 'double (*)(double, void *) nogil'

Question

First of all, please do excuse my poor use of programming terminology and bad (or even completely wrong) programming practices; i am still trying to find my feet :-)

In summary, i am trying to write a version of the multidimensional integration routine in Numerical Recipes, 3rd Edition, pgs. 198 - 199. in Cython, using the GSL numerical integration library. I have reproduced the relevant snippet from NR book below:

struct NRf3 {
double xsav, ysav;
double (*func3d)(const double, const double, const double);
double operator()(const double z)
{
    return func3d(xsav, ysav, z);
}
    }

struct NRf2 {
    NRf3 f3;
    double (*z1)(double, double);
    double (*z2)(double, double);
    NRf2(double zz1(double, double), double zz2(double, double)):    z1(zz1), z2(zz2)} {}
    double operator()(const double y)
    {
        f3.ysav = y;
        return qgaus(f3, z1(f3.xsav, y), z2(f3.xsav, y));
    }
}

struct NRf1 {
    double (*y1)(double);
    double (*y2)(double);
    NRf2 f2;
    NRf1(double yy1(double), yy2(double), z1(double, double), z2(double,  double)) : y1(yy1), y2(yy2), f2(z1, z2) {}
    double operator()(const double x){
        f2.f3.xsav = x;
        return qgaus(f2, y1(x), y2(x));
    }
}

template <class T>
double quad3d(T &func, const double x1, const double x2, double     y1(double), double y2(double), double z1(double, double), double z2(double, double))
{
    NRf1 f1(y1, y2, z1, z2);
    f1.f2.f3.func3d = func;
    return qgaus(f1, x1, x2)
}

This script does applies a previously written integration routine qgaus (which I will later substitute with a routine from GSL) which takes a double function and two doubles representing the integration limits as input parameters.

Mathematically, the code performs the integration as displayed in Eq. (4.6.2) of this link. The integration limits y[i] and z[i] have (x) and (x,y) dependencies, respectively, because the integration runs over a predefined region in the (x,y) plane (see see Fig. 4.6.1 of the same link above).

My own attempt in Cython is below (note my problem has, i think, nothing to do with interfacing to GSL, but is still at the level of correct Cythoning):

from cython_gsl cimport *
from numpy import *

ctypedef double * double_ptr
ctypedef void * void_ptr

cdef double sigma = 0.045
cdef double mu = 0.37

## Test : a test function in x, y, z
    cdef double gauss(double x, double y, double z, void * params) nogil:
    cdef double mu = (<double_ptr> params)[0]
    cdef double sigma = (<double_ptr> params)[1]
    return mu * x + sigma * y + z

cdef class NRf3:
    cdef double xsav, ysav
    cdef double (*func3d)(double x, double y, double z, void * params)

    def __init__(self, xsav, ysav):
        self.xsav = xsav
        self.ysav = ysav

    def func(self, double z):
        xsav = self.xsav
        ysav = self.ysav
        return func3d(xsav, ysav, z, void * params)

## Calling the gsl integrator qags
## Function: int gsl_integration_qags (const gsl_function * f, double a,     double b, double epsabs, double epsrel, size_t limit,     gsl_integration_workspace * workspace, double * result, double * abserr)

cdef class NRf2:
    cdef NRf3 f3
    cdef double z1
    cdef double z2
    cdef double paramsf2[1]
    cdef size_t nevalf2

    def __init__(self, double z1, double z2):
        self.z1 = z1
        self.z2 = z2

    def __call__(self, double y):
        cdef double resultf2, errorf2
        cdef gsl_integration_workspace * W
        W = gsl_integration_workspace_alloc(1000)
        cdef gsl_function F2
        z1 = self.z1
        z2 = self.z2

        f3.ysav = y
        f3_temp = f3(f3.xsav, y)
        F2.function = f3_temp
        F2.params = self.paramsf2
        gsl_integration_qags(&F2, z1, z2, 1e-2, 1e-2, 1000, W, &resultf2, &errorf2) # this line calls the GSL routine
        gsl_integration_workspace_free(W) 
        return resultf2

cdef class NRf1:
    cdef NRf2 f2
    cdef double y1
    cdef double y2
    cdef double paramsf1[1]
    cdef size_t nevalf1

    def __init__(self, double yy1, double yy2, double z1, double z2):
        self.y1 = yy1
        self.y2 = yy2
        self.z1 = z1
        self.z2 = z2
        self.f2 = f2(self.z1, self.z2)

    def __call__(self, func, double x):
        cdef double result, error
        cdef gsl_integration_workspace * W
        W = gsl_integration_workspace_alloc(1000)
        cdef gsl_function F1
        f2 = self.f2

        f2.f3.func3d = func
        f2.f3.xsav = x
        y1 = self.y1
        y2 = self.y2
        F1.function = f2
        F1.params = self.paramsf1
        gsl_integration_qags(&F1, y1, y2, 1e-2, 1e-2, 1000, W, &result, &error)
        gsl_integration_workspace_free(W)
        return result

Compiling this script with the usual

python min_example.py build_ext --inplace

as found on the Cython website gives the following errors:

Error compiling Cython file:
------------------------------------------------------------ ...

        z1 = self.z1
        z2 = self.z2

        f3.ysav = y
        f3_temp = f3(f3.xsav, y)
        F2.function = f3_temp
                            ^
------------------------------------------------------------

min_example.pyx:61:29: Cannot convert Python object to 'double
(*)(double, void *) nogil'

Error compiling Cython file:
------------------------------------------------------------ ...

        f2.f3.func3d = func
        f2.f3.xsav = x
        y1 = self.y1
        y2 = self.y2
        F1.function = f2
                       ^
------------------------------------------------------------

min_example.pyx:92:24: Cannot convert Python object to 'double
(*)(double, void *) nogil'

Errors refer to the lines F2.function = f3_temp and F1.function = f2 respectively. In this example gsl_integration_qags is a library from gsl, but for the purposes of this problem the correctness of the interfacing does not matter as (I think) the problem lies with the incorrect Cython syntax I have used.

My intuition tells me that this is a very trivial novice error, but I have been unable to find the reason. Any input (on the problem, on my code in general) would be very welcome.

Edit 1 : to reflect actual error messages

Edit 2 : Edited title to reflect nature of error messages

Edit 3 : I should say that i understand that the error comes from me trying to assign a Python instance object, i.e., in the lines F2.function = f3_temp and F1.function = f2, to a struct member that is a function taking two arguments. As this seems like a fairly trivial porting of code from C to Cython, and assuming that one sticks closely to the original C implementation, i am just wondering how would one write those lines correctly.

Edit 4: A bit of searching turns up this thread. I think my confusion can be distilled in the same way: How do I pass a Python class member (which if i have instantiated it correctly) to a C function ?