Python Reduce Product
Python Product reduction. In relational database theory, the join operation between tables can be viewed as a Cartesian product with a filter condition. In an SQL statement, if the SELECT statement is not followed by a WHERE clause, the result returned is the Cartesian product of the records in the tables. In other words, the product operation without a filter condition is a poor algorithm. Enumerating all possible combinations and then filtering to retain those that meet the conditions can be achieved using the product() function in the itertools module.
The following function can be used to define a join operation between two iterable collections or generators.
JT_ = TypeVar("JT_")
def join(
t1: Iterable[JT_],
t2: Iterable[JT_],
where: Callable[[Tuple[JT_, JT_]], bool]
) -> Iterable[Tuple[JT_, JT_]]:
return filter(where, product(t1, t2))
All combinations of iterable objects t1 and t2 are included in the calculation. The filter() function uses the given where() function to determine whether to accept or reject pairs of Tuple[JT_, JT_]. The where() function type is Callable[[Tuple [JT_, JT_]], bool], indicating that the return value is a Boolean. When there are no available indexes or sequence markers in the database, SQL queries can only operate inefficiently in this less-than-ideal scenario.
While this algorithm implementation works, it is very inefficient. Careful analysis of the problem and data is generally required to find a more efficient algorithm.
First, let’s abstract the problem a bit and replace a simple Boolean match with a problem of finding the maximum/minimum distance between multiple data items. The comparison result is a real number.
Suppose the following dataset consists of Color objects:
from typing import NamedTuple
class Color(NamedTuple):
rgb: Tuple[int, int, int]
name: str
[Color(rgb=(239, 222, 205), name='Almond'),
Color(rgb=(255, 255, 153), name='Canary'),
Color(rgb=(28, 172, 120), name='Green'),...
Color(rgb=(255, 174, 66), name='Yellow Orange')]
For more information, see
An image consisting of a set of pixels can be represented as follows:
pixels = [(r, g, b), (r, g, b), (r, g, b), ...]
As a widely used library, PIL (Python Image Library) provides various pixel representation methods, including converting coordinate values of the form (x, y) into RGB triplets. For more information about this library, see the Pillow project documentation.
For a given PIL Image object, you can use the following script to iterate over each element:
from PIL import Image
from typing import Iterator, Tuple
Point = Tuple[int, int]
RGB = Tuple[int, int, int]
Pixel = Tuple[Point, RGB]
def pixel_iter(img: Image) -> Iterator[Pixel]:
w, h = img.size
return (
(c, img.getpixel(c))
for c in product(range(w), range(h))
)
Using the image size to determine the coordinate range, use product(range(w), range(h)) to obtain all possible pixel coordinate combinations. This is actually equivalent to two nested for loops.
The advantage of this processing method is that each pixel has its own coordinate position, so processing pixels in any order can restore the entire image. This allows the computational load to be distributed across multiple cores or processors using multi-processing or multi-threading techniques. Python’s concurrent.futures module supports distributed computing based on multiple cores (processors).