In the VegasFlow repository you can find several examples of integrands which can hopefully help you to quickstart your project.

In this page we explain in more detail some of these examples. You can find the full code in the repository alongside more complicated versions.

Basic Integral

The most general usage of Vegasflow is the integration of a tensorflow-based integrand.

from vegasflow import vegas_wrapper
import tensorflow as tf

def my_integrand(xarr, **kwargs):
  return tf.reduce_sum(xarr, axis=1)

n_dim = 10
n_events = int(1e6)
n_iter = 5
result = vegas_wrapper(my_integrand, n_dim, n_iter, n_events)

You can find a runnable example of such a basic example in the repository.

Using VegasFlow as a clever Random Number Generator

A possible use case for VegasFlow is to have an function that we don’t necessarily want to integrate, but that we want to sample from. In general, sampling from a function can be very complicated and instead we just want to approximately sample from it. For that we can use the vegasflow package which instantly give access to all integrator algorithms as function approximators.

In the example below we use importance sampling, from VegasFlow to approximate the function and sample from it, but the same code will work for any of the other implemented integrators.

from vegasflow import VegasFlow, run_eager
import tensorflow as tf


def my_complicated_fun(xarr, **kwargs):
  return tf.reduce_sum(xarr, axis=1)

n_dim = 10
n_events = int(1e5)
sampler = VegasFlow(n_dim, n_events, verbose=False)

# Now let's train the integrator for 10 iterations
_ = sampler.run_integration(10)

# Now we can use sampler to generate random numbers
rnds, _, px = sampler.generate_random_array(100)

The first object returned by generate_random_array are the random points, in the case in the example an array of shape (100, 10), i.e., the first axis is the number of requested events and the second axis the number of dimensions.

The second object, ignored in this example, is whatever information the algorithm need to train. Since we are just generating random numbers and not training anymore we can ignore that.

Finally, generate_random_array returns also the probability distribution of the random points (i.e., the weight they carry).

For convenience we include sampler wrappers which directly return a trained reference to the generate_random_array method:

from vegasflow import vegas_sampler

sampler = vegas_sampler(my_complicated_fun, n_dim, n_events)
rnds, _, px = sampler(100)

It is possible to change the number of training steps (default 5) or to retrieve a reference to the sampler class instead to the sampler method by using keyword arguments.

sampler_class = vegas_sampler(my_complicated_fun, n_dim, n_events, training_steps=1, return_class=True)
rnds, _, px = sampler_class.generate_random_array(100)

Integrating a numpy function

VegasFlow admits also the integration of non-tensorflow python-based integrands. In this case, however, it is necessary to activate eager-mode, see Eager Vs Graph-mode.

import numpy as np
from vegasflow import vegas_wrapper, run_eager

def my_integrand(xarr, **kwargs):
  return np.sum(xarr)

n_dim = 10
n_events = int(1e6)
n_iter = 5
result = vegas_wrapper(my_integrand, n_dim, n_iter, n_events)

Note, however, that in this case the integrand will always be run on CPU, while the internal steps of the integration will be run on GPU by VegasFlow. In order to run the integration exclusively on GPU the environment variable CUDA_VISIBLE_DEVICES should be set to '':


Interfacing C code: CFFI

A popular way of interfacing python and C code is to use the CFFI library.

Imagine you have a C-file with some integrand:

// integrand.c
void integrand(double *xarr, int ndim, int nevents, double *out) {
    for (int i = 0; i < nevents; i++) {
        out[i] = 0.0;
        for (int j = 0; j < ndim; j++) {
            out[i] += 2.0*xarr[j+i*ndim];

You can compile this code and integrate it (no pun intended) with vegasflow by using the CFFI library as you can see in this example.

from vegasflow.configflow import DTYPE
import numpy as np
from vegasflow import vegas_wrapper

from cffi import FFI
ffibuilder = FFI()

ffibuilder.cdef("void integrand(double*, int, int, double*);")

with open("integrand.c", "r") as f:
    ffibuilder.set_source("_integrand_cffi", f.read())


# Now you can read up the compiled C code as a python library
from _integrand_cffi import ffi, lib

def integrand(xarr, **kwargs):
    n_dim = xarr.shape[-1]
    result = np.empty(n_events, dtype=DTYPE.as_numpy_dtype)
    x_flat = xarr.numpy().flatten()

    p_input = ffi.cast("double*", ffi.from_buffer(x_flat))
    p_output = ffi.cast("double*", ffi.from_buffer(result))

    lib.integrand(p_input, n_dim, xarr.shape[0], p_output)
    return result

vegas_wrapper(integrand, 5, 10, int(1e5), compilable=False)

Note the usage of the compilable=False flag. This signals VegasFlow that the integrand is not pure tensorflow and that a graph of the full computation cannot be compiled.

Create your own TF-compilable operators

Tensorflow tries to do its best to compile your integrand to something that can quickly be evaluated on GPU. It has no information, however, about specific situations that would allow for non trivial optimizations.

In these cases one could want to write its own C++ or Cuda code while still allowing for Tensorflow to create a full graph of the computation.

Creating new operations in TF are an advance feature and, when possible, it is recommended to create your integrand as a composition of TF operators. If you still want to go ahead we have prepared a simple example in the repository that can be used as a template for C++ or Cuda custom operators.

The example includes a makefile that you might need to modify for your particular needs.

Note that in order to run the code in both GPUs and CPU you will need to provide a GPU and CPU capable kernels.