# 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))
```