# Universal Functions¶

With NumbaPro, universal functions (ufuncs) can be created by applying the vectorize decorator on to simple scalar functions. A ufunc can operates on scalars or NumPy arrays. When used on arrays, the ufunc apply the core scalar function to every group of elements from each arguments in an element-wise fashion. NumPy Broadcasting is applied to every argument with mismatching dimensions.

## Example: Basic¶

Here is a simple example to perform element-wise addition:

import numpy
from numbapro import vectorize

# Create a ufunc
@vectorize(['float32(float32, float32)',
'float64(float64, float64)'])
def sum(a, b):
return a + b

# Use the ufunc
a = numpy.arange(10)
b = numpy.arange(10)
result = sum(a, b)      # call the ufunc

print("a = %s" % a)
print("b = %s" % b)
print("sum = %s" % result)

The ufunc is compiled to operate on float32 and float64 arrays. It is used to compute element-wise addition of array a and b which are arrays of numpy.float64 with 10 elements. The output

a = [0 1 2 3 4 5 6 7 8 9]
b = [0 1 2 3 4 5 6 7 8 9]
sum = [  0.   2.   4.   6.   8.  10.  12.  14.  16.  18.]

## Usage¶

A generalization of the usage of the vectorize decorator is described in this section.

vectorize(type_signatures[, target='cpu'])

Returns a vectorizer object to be applied to python functions.

Parameters: type_signatures – an iterable of type signatures, which are either function type object or a string describing the function type. target – a string for hardware target; e.g. “cpu”, “parallel”, “gpu”. a vectorizers object.

To use multithreaded version, change the target to “parallel”:

from numbapro import vectorize

@vectorize(['float32(float32, float32)'], target='parallel')
def sum(a, b):
return a + b

For CUDA target, use “gpu” for target:

from numbapro import vectorize

@vectorize(['float32(float32, float32)'], target='gpu')
def sum(a, b):
return a + b

## Performance Guideline¶

A general guideline is to choose different targets for different data sizes and algorithms. The “cpu” target works well for small data sizes (approx. less than 1KB) and low compute intensity algorithms. It has the least amount of overhead. The “parallel” target works well for medium data sizes (approx. less than 1MB). Threading adds a small delay. The “gpu” target works well for big data sizes (approx. greater than 1MB) and high compute intensity algorithms. Transfering memory to and from the GPU adds significant overhead.

## Universal Function Targets¶

There are several vectorizer versions available. The different options are listed below:

Target Description
parallel Multi-core CPU
stream

Optimize for CPU cache

Note

Experimental. Computation speeds may vary.

gpu

CUDA GPU

Note

This creates an ufunc-like object. See documentation for CUDA ufunc for detail.