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Using Transforms

The boost-histogram library provides a powerful transform system on Regular axes that allows you to provide a functional form for the conversion between a regular spacing and the actual bin edges. The following transforms are built in:

  • bh.axis.transform.sqrt: A square root transform

  • bh.axis.transform.log: A logarithmic transform

  • bh.axis.transform.Pow(power) Raise to a specified power (power=0.5 is identical to sqrt)

There is also a flexible bh.axis.transform.Function, which allows you to specify arbitrary conversion functions (detailed below).

Simple custom transforms

The Function transform takes two ctypes double(double) function pointers, a forward transform and a inverse transform. An object that provides a ctypes function pointer through a .ctypes attribute is supported, as well. As an example, let’s look at how one would recreate the log transform using several different methods:

Pure Python

You can directly cast a python callable to a ctypes pointer, and use that. However, you will call Python every time you interact with the transformed axis, and this will be 15-90 times slower than a compiled method, like bh.axis.transform.log. In most cases, a Variable axis will be faster.

import ctypes

ftype = ctypes.CFUNCTYPE(ctypes.c_double, ctypes.c_double)

# Pure Python (15x slower)
bh.axis.Regular(
    10, 1, 4, transform=bh.axis.transform.Function(ftype(math.log), ftype(math.exp))
)

# Pure Python: NumPy (90x slower)
bh.axis.Regular(
    10, 1, 4, transform=bh.axis.transform.Function(ftype(np.log), ftype(np.exp))
)

You can create a Variable axis from the edges of this axis; often that will be faster.

You can also use transform=ftype and just directly provide the functions; this provides nicer reprs, but is still not picklable because ftype is a generated and not picklable; see below for a way to make this picklable. You can also specify name="..." to customize the repr explicitly.

Using Numba

If you have the numba library installed, and your transform is reasonably simple, you can use the @numba.cfunc decorator to create a callable that will run directly through the C interface. This is just as fast as the compiled version provided!

import numba


@numba.cfunc(numba.float64(numba.float64))
def exp(x):
    return math.exp(x)


@numba.cfunc(numba.float64(numba.float64))
def log(x):
    return math.log(x)


bh.axis.Regular(10, 1, 4, transform=bh.axis.transform.Function(log, exp))

Manual compilation

You can also get a ctypes pointer from the usual place: a library. Let’s say you have the following mylib.c file:

#include <math.h>

double my_log(double value) {
    return log(value);
}

double my_exp(double value) {
    return exp(value);
}

And you compile it with:

gcc mylib.c -shared -o mylib.so

You can now use it like this:

import ctypes

ftype = ctypes.CFUNCTYPE(ctypes.c_double, ctypes.c_double)

mylib = ctypes.CDLL("mylib.so")

my_log = ctypes.cast(mylib.my_log, ftype)
my_exp = ctypes.cast(mylib.my_exp, ftype)

bh.axis.Regular(10, 1, 4, transform=bh.axis.transform.Function(my_log, my_exp))

Note that you do actually have to cast it to the correct function type; just setting argtypes and restype does not work.

Picklable custom transforms

The above examples to not support pickling, since ctypes pointers (or pointers in general) are not picklable. However, the Function transform supports a convert= keyword argument that takes the two provided objects and converts them to ctypes pointers. So if you can supply a pair of picklable objects and a conversion function, you can make a fully picklable transform. A few common cases are given below.

Pure Python

This is the easiest example; as long as your Python function is picklable, all you need to do is move the ctypes call into the convert function. You need a little wrapper function to make it picklable:

import ctypes, math

# We need a little wrapper function only because `ftype` is not directly picklable
def convert_python(func):
    ftype = ctypes.CFUNCTYPE(ctypes.c_double, ctypes.c_double)
    return ftype(func)


bh.axis.Regular(
    10,
    1,
    4,
    transform=bh.axis.transform.Function(math.log, math.exp, convert=convert_python),
)

That’s it.

Using Numba

The same procedure works for numba decorators. NumPy only supports functions, not builtins like math.log, so if you want to pass those, you’ll need to wrap them in a lambda function or add a bit of logic to the convert function. Here are your options:

import numba, math


def convert_numba(func):
    return numba.cfunc(numba.double(numba.double))(func)


# Built-ins and ufuncs need to be wrapped (numba can't read a signature)
# User functions would not need the lambda
bh.axis.Regular(
    10,
    1,
    4,
    transform=bh.axis.transform.Function(
        lambda x: math.log(x), lambda x: math.exp(x), convert=convert_numba
    ),
)

Note that numba.cfunc does not work on its own builtins, but requires a user function. Since with the exception of the simple example I’m showing here that is already available directly in boost-histogram, you will probably be composing your own functions out of more than one builtin operation, you generally will not need the lambda here.

Manual compilation

You can use strings to look up functions in the shared library:

def lookup(name):
    mylib = ctypes.CDLL("mylib.so")
    function = getattr(mylib, name)
    return ctypes.cast(function, ftype)


bh.axis.Regular(
    10, 1, 4, transform=bh.axis.transform.Function("my_log", "my_exp", convert=lookup)
)
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