IteratorAlgorithms 0.1.6
A collection of iterator algorithms for Python3.
Requires Python: >=3.6
Keywords: accumulate,adjacent_difference,all_of,any_of,difference,exclusive_scan,fork,generate,generate_n,inclusive_scan,inner_product,intersection,iota,min_max,none_of,partial_sum,partition,product,reduce,star_sum,star_product,symmetric_difference,transform,transform_reduce,transposed_sums,union,zip_transform

# Iterator Algorithms
#### Robert Sharp, Library Author


IA is a collection of iterator algorithms for Python3, inspired by the C++ 
algorithms library.

Many of the algorithms are the same as those found in the standard library, but 
extended in some way. For example: the IA.symmetric_difference function can 
accept an arbitrary number of sets as input. For comparison, the builtin set 
method of the same name can only compare 2 sets. The abstraction is raised from - 
"What's not in both sets." to "What's not in all sets." In both cases the result
is the exact opposite of the intersection of the same sets.

### Quick Installation:
```bash
$ python3 -m pip install IteratorAlgorithms
```

### Run Test Suite:
```bash
$ python3 -m IteratorAlgorithms
# Verbose Test Output
...
102 tests in 32 items.
102 passed and 0 failed.
Test passed.
```
Tests are verbose by default. Tests are only run when the module is executed as a script, as above.

### Standard Import:
```bash
$ python3
>>> import IteratorAlgorithms as ia
# No Test Output. Ready for work!
>>>
```
None of the standard import styles should trigger the tests.

### Help Features
All the features of this module have full help support built in.
```bash
$ python3
>>> from IteratorAlgorithms import fork
>>> help(fork)
```
```
Help on function fork in module IteratorAlgorithms:

fork(array: Iterable, forks: int = 2) -> tuple
    Fork
    Iterator Duplicator. Same as itertools.tee but with a better name.
    
    # DocTest:
    >>> it = iter(range(10))
    >>> a, b, c = fork(it, 3)
    >>> list(c)
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    >>> a == b
    False
    >>> list(a) == list(b)
    True
    
    @param array: Iterable to be forked.
    @param forks: Optional Integer. Default is 2. Represents the number of forks.
    @return: tuple of N Iterators where N is the number of forks.

```

## Table of Contents:
- Generators
    - iota
    - generate
    - generate_n
- Expansions
    - fork
    - exclusive_scan
    - inclusive_scan
- Transforms
    - transform
    - adjacent_difference
    - partial_sum
- Permutations
    - partition
- Reductions
    - reduce
    - accumulate
    - product
    - min_max
- Queries
    - all_of
    - any_of
    - none_of
- Transform & Reduction
    - transform_reduce
    - inner_product
    - matrix_multiply
- Multidimensional Reductions
    - zip_transform
    - transposed_sums
- Multi-Set Operations
    - union
    - intersection
    - difference
    - symmetric_difference

---

## Generators

### `IteratorAlgorithms.iota`
```
Help on function iota in module IteratorAlgorithms:

iota(start, *, stop=None, step=1, stride=0) -> Iterator
    Iota
    Iterator of a given range with grouping size equal to the stride.
    If stride is zero - a single dimensional iterator is returned.
    
    DocTests:
    >>> list(iota(10))
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    >>> list(iota(start=1, stop=11))
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    >>> list(iota(start=2, stop=21, step=2))
    [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]
    >>> list(iota(start=2, stop=21, step=2, stride=2))
    [(2, 4), (6, 8), (10, 12), (14, 16), (18, 20)]
    
    @param start: Beginning. Required.
    @param stop: Ending. Default is None.
    @param step: Stepping. Default is one.
    @param stride: Size of groupings. Default is zero.

```
### `IteratorAlgorithms.generate`
```
Help on function generate in module IteratorAlgorithms:

generate(func: Callable, *args, **kwargs) -> Iterator
    Generate
    Infinite iterator of a callable with arguments.
    
    DocTests:
    >>> counter = itertools.count(1)
    >>> gen = generate(next, counter)
    >>> list(next(gen) for _ in range(10))
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    
    @param func: Callable.
    @param args: Positional arguments for the functor.
    @param kwargs: Keyword arguments for the functor.

```
### `IteratorAlgorithms.generate_n`
```
Help on function generate_n in module IteratorAlgorithms:

generate_n(n: int, func: Callable, *args, **kwargs) -> Iterator
    Generate N
    Abstract generator function. Finite.
    
    DocTests:
    >>> counter = itertools.count(1)
    >>> list(generate_n(10, next, counter))
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    
    @param n: Number of elements to generate.
    @param func: Callable.
    @param args: Positional arguments for the functor.
    @param kwargs: Keyword arguments for the functor.

```

## Expansions

### `IteratorAlgorithms.fork`
```
Help on function fork in module IteratorAlgorithms:

fork(array: Iterable, forks: int = 2) -> Iterator
    Fork
    Iterator Duplicator. Same as itertools.tee but with a better name.
    
    DocTests:
    >>> it = iter(range(10))
    >>> a, b, c = fork(it, 3)
    >>> list(c)
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    >>> a == b
    False
    >>> list(a) == list(b)
    True
    
    @param array: Iterable to be forked.
    @param forks: Optional Integer. Default is 2. Represents the number of forks.
    @return: Tuple of N Iterators where N is the number of forks.

```
### `IteratorAlgorithms.inclusive_scan`
```
Help on function inclusive_scan in module IteratorAlgorithms:

inclusive_scan(array: Iterable, init=None) -> Iterator
    Inclusive Scan -> Adjacent Pairs
    
    DocTests:
    >>> list(inclusive_scan(range(1, 10)))
    [(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)]
    >>> list(inclusive_scan(range(1, 10), 0))
    [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9)]
    
    @param array: Iterable to be scanned.
    @param init: Optional initial value. Default is None.
    @return: Iterator of Pairs.

```
### `IteratorAlgorithms.exclusive_scan`
```
Help on function exclusive_scan in module IteratorAlgorithms:

exclusive_scan(array: Iterable, init=None) -> Iterator
    Exclusive Scan -> Adjacent Pairs
    Like inclusive_scan, but ignores the last value.
    
    DocTests:
    >>> list(exclusive_scan(range(1, 10)))
    [(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8)]
    >>> list(exclusive_scan(range(1, 10), 0))
    [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8)]
    
    @param array: Iterable to be scanned.
    @param init: Initial Value.
    @return: Iterator of Pairs.

```

## Transforms

### `IteratorAlgorithms.transform`
```
Help on function transform in module IteratorAlgorithms:

transform(array: Iterable, func: Callable) -> Iterator
    Transform
    Similar to map but with a reversed signature.
    
    DocTests:
    >>> list(transform(range(10), add_one))
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    >>> list(transform(range(10), square))
    [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
    
    @param array: Iterable of Values.
    @param func: Unary Functor. F(x) -> Value
    @return: Iterator of transformed Values.

```
### `IteratorAlgorithms.adjacent_difference`
```
Help on function adjacent_difference in module IteratorAlgorithms:

adjacent_difference(array: Iterable) -> Iterator
    Adjacent Difference
    Calculates the difference between adjacent pairs.
    This is the opposite of Partial Sum.
    The first iteration compares with zero for proper offset.
    
    DocTests:
    >>> list(adjacent_difference(range(1, 10)))
    [1, 1, 1, 1, 1, 1, 1, 1, 1]
    >>> list(adjacent_difference(partial_sum(range(1, 10))))
    [1, 2, 3, 4, 5, 6, 7, 8, 9]
    >>> list(adjacent_difference(partial_sum(range(-10, 11, 2))))
    [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10]
    
    @param array: Iterable of Numeric Values.
    @return: Iterator of adjacent differences.

```
### `IteratorAlgorithms.partial_sum`
```
Help on function partial_sum in module IteratorAlgorithms:

partial_sum(array: Iterable) -> Iterator
    Partial Sum
    Calculates the sum of adjacent pairs.
    This is the opposite of Adjacent Difference.
    
    DocTests:
    >>> list(partial_sum(range(1, 10)))
    [1, 3, 6, 10, 15, 21, 28, 36, 45]
    >>> list(partial_sum([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))
    [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    
    @param array: Iterable of Numeric Values.
    @return: Iterator of adjacent sums.

```

## Permutations

### `IteratorAlgorithms.partition`
```
Help on function partition in module IteratorAlgorithms:

partition(array: Iterable, predicate: Callable) -> Iterator
    Stable Partition
    Arranges all the elements of a group such that any that return true
        when passed to the predicate will be at the front, and the rest will be
        at the back. The size of the output iterator will be the same as the
        size of the input iterable.
    
    DocTests:
    >>> list(partition(range(1, 10), is_even))
    [2, 4, 6, 8, 1, 3, 5, 7, 9]
    >>> list(partition(range(1, 10), is_odd))
    [1, 3, 5, 7, 9, 2, 4, 6, 8]
    
    @param array: Iterable of values to be partitioned.
    @param predicate: Unary functor. F(x) -> bool
    @return: Partitioned Iterator.

```

## Reductions

### `IteratorAlgorithms.reduce`
```
Help on function reduce in module IteratorAlgorithms:

reduce(array: Iterable, func: Callable, initial=None)
    Reduce from functools
    Similar to accumulate but allows any binary functor and an initial value.
    
    DocTests:
    >>> reduce(range(1, 5), operator.add)
    10
    >>> reduce(range(1, 5), operator.add, 100)
    110
    >>> reduce(range(1, 5), operator.mul)
    24
    >>> reduce(range(1, 5), operator.mul, 0)
    0
    
    @param array: Iterable of Values to be reduced.
    @param func: Binary Functor.
    @param initial: Initial value. Typically, 0 for add or 1 for multiply.
    @return: Reduced Value.

```
### `IteratorAlgorithms.accumulate`
```
Help on function accumulate in module IteratorAlgorithms:

accumulate(array: Iterable, func: Callable = <built-in function add>, initial=None) -> Iterator
    Accumulate from itertools
    Returns the resulting list from appling the functor to pairs of previous
    result and each next value.
    
    DocTests:
    >>> list(accumulate([1, 1, 1]))
    [1, 2, 3]
    >>> list(accumulate([1, 2, 3]))
    [1, 3, 6]
    >>> list(accumulate([1, 1, 1], operator.sub, 10))
    [10, 9, 8, 7]
    
    @param initial: Initial Value. `None` by default.
    @param func: Binary Functor. `operator.add` by default.
    @param array: Iterable of Values
    @return: Iterator of Accumulated Values

```
### `IteratorAlgorithms.product`
```
Help on function product in module IteratorAlgorithms:

product(array: Iterable)
    Product
    Reduce with multiply.
    For counting numbers from 1 to N: returns the factorial of N.
    
    DocTests:
    >>> product(range(1, 5))
    24
    >>> product(range(5, 10))
    15120
    
    @param array: Iterable of Values to be reduced.
    @return: Product of all elements multiplied together.

```
### `IteratorAlgorithms.min_max`
```
Help on function min_max in module IteratorAlgorithms:

min_max(array: Iterable) -> Iterator
    Min & Max Element
    
    DocTests:
    >>> tuple(min_max(range(1, 10)))
    (1, 9)
    >>> tuple(min_max([100, 42, 69, 1]))
    (1, 100)
    
    @param array: Iterable of Numeric Values
    @return: Tuple(Minimum, Maximum)

```
### `IteratorAlgorithms.star_sum`
```
Help on function star_sum in module IteratorAlgorithms:

star_sum(*args)
    Star Sum: Add All Args
    Similar to accumulate, but takes an arbitrary number of arguments.
    
    DocTests:
    >>> star_sum(1)
    1
    >>> star_sum(1, 2)
    3
    >>> star_sum(1, 2, 3)
    6
    >>> star_sum(1, 2, 3, 4)
    10
    
    @param args: Numbers to be summed.
    @return: Sum of all arguments.

```
### `IteratorAlgorithms.star_product`
```
Help on function star_product in module IteratorAlgorithms:

star_product(*args)
    Star Product: Multiply All Args
    Similar to product, but takes an arbitrary number of arguments.
    
    DocTests:
    >>> star_product(0, 42)
    0
    >>> star_product(3, 3, 3)
    27
    >>> star_product(1, 2, 3, 4)
    24
    
    @param args: Numbers to be multiplied.
    @return: Product of all arguments.

```

## Queries

### `IteratorAlgorithms.all_of`
```
Help on function all_of in module IteratorAlgorithms:

all_of(array: Iterable, predicate: Callable) -> bool
    All of These
    
    DocTests:
    >>> all_of([], is_even)
    True
    >>> all_of([2, 4, 6], is_even)
    True
    >>> all_of([1, 4, 6], is_even)
    False
    >>> all_of([1, 3, 5], is_even)
    False
    
    @param array: Iterable to inspect.
    @param predicate: Callable. f(x) -> bool
    @return: Boolean.

```
### `IteratorAlgorithms.any_of`
```
Help on function any_of in module IteratorAlgorithms:

any_of(array: Iterable, predicate: Callable) -> bool
    Any of These
    
    DocTests:
    >>> any_of([], is_even)
    False
    >>> any_of([2, 4, 6], is_even)
    True
    >>> any_of([1, 4, 6], is_even)
    True
    >>> any_of([1, 3, 5], is_even)
    False
    
    @param array: Iterable to inspect.
    @param predicate: Callable. f(x) -> bool
    @return: Boolean.

```
### `IteratorAlgorithms.none_of`
```
Help on function none_of in module IteratorAlgorithms:

none_of(array: Iterable, predicate: Callable) -> bool
    None Of These
    
    DocTests:
    >>> none_of([], is_even)
    True
    >>> none_of([2, 4, 6], is_even)
    False
    >>> none_of([1, 4, 6], is_even)
    False
    >>> none_of([1, 3, 5], is_even)
    True
    
    @param array: Iterable to inspect.
    @param predicate: Callable. f(x) -> bool
    @return: Boolean.

```

## Transform & Reduce

### `IteratorAlgorithms.transform_reduce`
```
Help on function transform_reduce in module IteratorAlgorithms:

transform_reduce(lhs: Iterable, rhs: Iterable, transformer: Callable, reducer: Callable)
    Transform Reduce
    Pairwise transform and then reduction across all results.
    
    DocTests:
    >>> transform_reduce(range(1, 6), range(1, 6), operator.mul, sum)
    55
    >>> transform_reduce(range(1, 6), range(1, 6), operator.add, product)
    3840
    
    @param lhs: Left Iterator
    @param rhs: Right Iterator
    @param transformer: Binary Functor F(x, y) -> Value
    @param reducer: Reduction Functor F(Iterable) -> Value
    @return: Reduced Value

```
### `IteratorAlgorithms.inner_product`
```
Help on function inner_product in module IteratorAlgorithms:

inner_product(lhs: Iterable, rhs: Iterable)
    Inner Product
    Performs pairwise multiplication across the iterables,
        then returns the sum of the products.
    
    DocTests:
    >>> inner_product(range(1, 6), range(1, 6))
    55
    >>> inner_product(range(11), range(11))
    385
    
    @param lhs: Left Iterator
    @param rhs: Right Iterator
    @return: Sum of the products.

```

## Multidimensional Reductions

### `IteratorAlgorithms.zip_transform`
```
Help on function zip_transform in module IteratorAlgorithms:

zip_transform(transducer: Callable, *args: Iterable) -> Iterator
    Zip Transform
    The transducer should take the same number of arguments as the number of
    iterators passed. Each iteration will call the transducer with the ith element
    of each iterable. F(a[i], b[i], c[i]...) ...
    
    DocTests:
    >>> l1 = (0, 1, 2, 3)
    >>> l2 = (8, 7, 6, 5)
    >>> l3 = (1, 1, 1, 1)
    >>> list(zip_transform(star_sum, []))
    []
    >>> list(zip_transform(star_sum, l1))
    [0, 1, 2, 3]
    >>> list(zip_transform(star_sum, l1, l2))
    [8, 8, 8, 8]
    >>> list(zip_transform(star_sum, l1, l2, l3))
    [9, 9, 9, 9]
    
    @param transducer: Callable
    @param args: Any number of iterables.
    @return: Iterator of values from the transducer.

```
### `IteratorAlgorithms.transposed_sums`
```
Help on function transposed_sums in module IteratorAlgorithms:

transposed_sums(*args: Iterable) -> Iterator
    Transposed Sums - Column Sums
    The size of the output iterator will be the same as
        the smallest input iterator.
    
    DocTests:
    >>> l1 = (0, 1, 2, 3)
    >>> l2 = (8, 7, 6, 5)
    >>> l3 = (1, 1, 1, 1)
    >>> list(transposed_sums(l1, l2, l3))
    [9, 9, 9, 9]
    
    @param args: Arbitrary number of Iterators of numeric values.
    @return: Iterator of transposed sums aka column sums.

```

## Multi-Set Operations

### `IteratorAlgorithms.union`
```
Help on function union in module IteratorAlgorithms:

union(*args: set) -> set
    Multiple Set Union
    Includes all elements of every set passed in.
    
    DocTests:
    >>> s1 = {0, 2, 4, 6, 8}
    >>> s2 = {1, 2, 3, 4, 5}
    >>> s3 = {2, 8, 9, 1, 7}
    >>> union(s1, s2, s3)
    {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
    
    @param args: Arbitrary number of sets.
    @return: Unified set

```
### `IteratorAlgorithms.intersection`
```
Help on function intersection in module IteratorAlgorithms:

intersection(*args: set) -> set
    Multiple Set Intersection
    Includes all elements that are common to every set passed in.
    If there is no intersection, it will return the empty set.
    If all sets are the same, it will return the union of all sets.
    Opposite of symmetric_difference.
    
    DocTests:
    >>> s1 = {0, 2, 4, 6, 8}
    >>> s2 = {1, 2, 3, 4, 5}
    >>> s3 = {2, 8, 9, 1, 7}
    >>> intersection(s1, s2, s3)
    {2}
    
    @param args: Arbitrary number of sets.
    @return: Set of common elements

```
### `IteratorAlgorithms.difference`
```
Help on function difference in module IteratorAlgorithms:

difference(*args: set) -> set
    Multiple Set Difference
    Includes every element in the first set that isn't in one of the others.
    If there is no difference, it will return the empty set.
    
    DocTests:
    >>> s1 = {0, 2, 4, 6, 8}
    >>> s2 = {1, 2, 3, 4, 5}
    >>> s3 = {2, 8, 9, 1, 7}
    >>> difference(s1, s2, s3)
    {0, 6}
    
    @param args: Arbitrary number of sets.
    @return: Difference between the first set and the rest.

```
### `IteratorAlgorithms.symmetric_difference`
```
Help on function symmetric_difference in module IteratorAlgorithms:

symmetric_difference(*args: set) -> set
    Multiple Set Symmetric Difference
    Includes all elements that are not common to every set passed in.
    If there is no intersection, it will return the union of all sets.
    If all sets are the same, it will return the empty set.
    Opposite of intersection.
    
    DocTests:
    >>> s1 = {0, 2, 4, 6, 8}
    >>> s2 = {1, 2, 3, 4, 5}
    >>> s3 = {2, 8, 9, 1, 7}
    >>> symmetric_difference(s1, s2, s3)
    {0, 1, 3, 4, 5, 6, 7, 8, 9}
    
    @param args: Arbitrary number of sets.
    @return: Symmetric difference considering all sets.

```


## Test Summary
```
1 items had no tests:
    __main__
32 items passed all tests:
   3 tests in __main__.accumulate
   2 tests in __main__.add_one
   3 tests in __main__.adjacent_difference
   4 tests in __main__.all_of
   4 tests in __main__.any_of
   4 tests in __main__.difference
   2 tests in __main__.exclusive_scan
   5 tests in __main__.fork
   3 tests in __main__.generate
   2 tests in __main__.generate_n
   2 tests in __main__.inclusive_scan
   2 tests in __main__.inner_product
   4 tests in __main__.intersection
   4 tests in __main__.iota
   5 tests in __main__.is_even
   5 tests in __main__.is_odd
   2 tests in __main__.matrix_multiply
   2 tests in __main__.min_max
   4 tests in __main__.none_of
   2 tests in __main__.partial_sum
   2 tests in __main__.partition
   2 tests in __main__.product
   4 tests in __main__.reduce
   3 tests in __main__.square
   3 tests in __main__.star_product
   4 tests in __main__.star_sum
   4 tests in __main__.symmetric_difference
   2 tests in __main__.transform
   2 tests in __main__.transform_reduce
   4 tests in __main__.transposed_sums
   4 tests in __main__.union
   7 tests in __main__.zip_transform
105 tests in 33 items.
105 passed and 0 failed.
Test passed.
```