Stretchy Python Module

The stretchy module contains one- and multi-dimensional containers that can grow in any direction (including the negative one). To grow a container, simply add a value to an element that is not yet used and it will be created. Containers are non-sparse containers, meaning that if you give an element a value without skipping several positions, the intermediate values will also take up space. The default value specified during initialization will be placed in these cells (by default None). If data is read from a cell that is not yet used, the default value will be returned there as well.

E.g.

import stretchy
array = stretchy.empty(default='.')
for i in range(2,8,2):
  array[-i] = '#'
  array[i] = '#'
print(f'{array:s}')

Results in

#.#.#...#.#.#

It's also important to note that array storage starts at 0. So if you only put a value in cell 2, cells 0 and 1 will be created anyway. If you place an element in cell -2, then 0 is not created, just -1. In this way, array[2] = 42 and array[-2] = 42 result in the followings (respectively):

| -2 |  -1  |   0  |   1  |  2 |
|----|------|------|------|----|
|    |      | None | None | 42 |
| 42 | None |      |      |    |

This property affects related features (such as offset, len, etc.), too.

Also important to mention, that one- and multi-dimensional stretchy arrays' functionality (properties, methods) are slightly different. For more information, see below.

stretchy functions

array

def array(
        content: Sequence|Iterable|None = None,
        *,
        default: Any = None,
        offset: tuple[int, ...]|list[int]|int = 0,
        dim: int|None = None
        ) -> Array1D|ArrayND

• content: Array-like object (E.g. list, tuple...). In one-dimensional case this can be any iterable object (e.g. itertools-generated ones, or a generator), but in multi-dimensional cases it can be only Sequence of Sequences (e.g. list of lists).
• offset: lower boundaries of the array in all dimensions. In one-dimensional case it must be an int, and in multi-dimensional ones it is a tuple of as much values as much the number of dimensions the arrays has. The value of offset can be int in the multi-dimensional case, in which case it is equivalent to having the same offset value in all dimensions.
• default: Default value for non-specified cells. If this parameter is not specified, the default value of default is None
• dim: Number of imensions in the array. If not specified and no content is provided the result will be an empty one-dimensional stretchy array.

This function can be used to create stretchy arrays. If an array-like object is given as the input (content) to the function, the stretchy array is filled with the contents of the object. In this case the number of dimensions is determined automatically by the function, but in ambiguous cases you can specify it manually (using dim).

In some cases, the determination of dimensions can be ambiguous. This is the case when the input array contains strings. By default, the strings are kept together by the function (except if the content itself is a str), but if you want the string to be interpreted as a character sequence, specify the appropriate dimension number. So,

stretchy.array(['abc','def','ghi'])

is handled as

['abc', 'def', 'ghi']

but

stretchy.array(['abc','def','ghi'], dim=2)

is

[['a', 'b', 'c'],
 ['d', 'e', 'f'],
 ['g', 'h', 'i']]

If the input content is a string, it will be split up, because dim=0 is pointless.

stretchy.array('abcdef')

results in a one-dimensional array of characters:

['a', 'b', 'c', 'd', 'e', 'f']

content's embedded arrays are not reused, so repeating the "same arrays" does not have any side-effects. To define a three-dimensional array with an initial set of 10x10x10 '.' values, you can use:

array = stretchy.array([[['.']*10]*10]*10)

A more complex example:

import stretchy

tic_tac_toe = stretchy.array(['___'] * 3, dim=2)
steps = ((1,0,'X'), (0,1,'O'), (0,0,'X'), (2,0,'O'), (1,1,'X'), \
                                                  (1,2,'O'), (2,2,'X'))
for i,(x,y,c) in enumerate(steps, 1):
  print('Round', i)
  tic_tac_toe[y,x] = c
  print(f'{tic_tac_toe:b }')

The output of the program is:

Round 1
  _ X _
  _ _ _
  _ _ _
Round 2
...
Round 7
  X X O
  O X _
  _ O X

empty

def empty(dim: int = 1, default: Any = None) -> Array1D|ArrayND

Although you can also use the array function to create an empty stretchy array, this is a lightweight option.

• dim: Dimension of the array. If not specified, the array will be one-dimensional.
• default: Default value for non-specified cells. If this parameter is not specifoed, the default value of default is None.

Example:

import stretchy

array = stretchy.empty(3, 0)
array[1,2,0] = 42
array[1,1,2] = 137
array[0,2,2] = 69
print(f'{array:s, ai}')

results in

Index 0:
  0,   0,   0
  0,   0,   0
  0,   0,  69
Index 1:
  0,   0,   0
  0,   0, 137
 42,   0,   0

Array object properties

The properties can be used to get important information about the array. There are also properties that are writable. For one-dimensional and multi-dimensional arrays, propertys work somewhat differently. These are discussed in the description of propertys.

dim (read only)

Type: int

Use the dim property to get the dimension number of the array.

boundaries (read only)

Type:

• One-dimensional arrays: tuple[int, int]
• Multi-dimensional arrays: tuple[tuple[int, int], ...]

The boundaries property can be used to get the lower and upper bounds of the array in each dimension. While in the multi-dimensional case it is a tuple of tuples that gives the boundaries in all dimensions, in the one-dimensional case it is just a tuple of the two boundaries. Following the pythonic way, the lower limit is the smallest index on which there is a cell, while the upper limit is the largest index plus 1.

E.g.

import stretchy

array = stretchy.array([[1,0,1],[],[1,0,1]], offset=(-1,-1))
print(f'{array.boundaries=}')
print(f'{array!r}')

Results in

array.boundaries=((-1, 2), (-1, 2))
ArrayND(dim=2, default=None, offset=(-1, -1), content=
[[   1,    0,    1],
 [None, None, None],
 [   1,    0,    1]])

offset (read only)

Type:

• One-dimensional arrays: int
• Multi-dimensional arrays: tuple[int, ...]

This property is used to get the lower bounds of the array. See also boundaries.

shape (read only)

Type (only for multi-dimensional arrays): tuple[int, ...]

This property is used to get the size of the array in all directions. In one-dimensional case, use len(array) instead.

index_format (read & write)

In case of dim >= 3, two-dimensional planes are separated by different number of empty lines, or by showing the indices of the plane (See also Formatting). By default this latter looks as follows (5D array, f'{array:s,i}'):

...
1,6,2
8,3,6
Index 2,-5,3:
5,7,2
9,5,3
...

The index text can be changed by setting the index_format. The default value is 'Index {}:' and the {} will be replaced by the index values separated by commas.

Array operations

Length of array (len)

length: int = len(array)

The function call gives the size of the highest dimension of the array. This is the length of the array in the one-dimensional case, and the number of sub-planes (alse the first element of the shape property) in the case of multi-dimensional arrays.

Check array content

if not array:
    print("Array is empty!")

Casting array to bool works similarly to python sequences, i.e. if array is empty, it is converted to False, otherwise to True. The result is True also if array contains exclusively default values. In this case, after trimming, the result of the conversion will be False.

Getting values or subplanes

By indexing a stretchy array, you can perform several tasks depending on the type of index.

value = array[5,-7,-2]
subplane = array[3]
subplane_iterator = array[-10:10:2]

To get the value of a cell, use a tuple in which the values are the indices of all dimensions. If a non-existent cell is indexed, the default value of the array is returned.

You can also get a subplane of the array (indexed by an int) on which you can perform further read or write operations. In this way, we also affect the whole array. In the case of a one-dimensional array, we do not get a plane, but directly the value of the addressed cell. It is important to note that if you request a plane that does not yet exist, the plane is automatically created (for the sake of write operations), as well as all the planes between the current boundary and the new plane.

If you use slice as an index, unlike the traditional python approach, you don't get a stretchy array, but an iterator to iterate through the selected subplanes, or in the one-dimensional case, the cell values. The note mentioned in the previous point, that new planes are created when indexing beyond the boundaries, is true also for this case.

In all of the above cases, it is true that negative values and values beyond the current boundaries are also valid index values.

Changing cell values

To write the contents of the cells, the cells must be indexed in the same way as for rrading:

array[5,-7,-2] = 42

For one-dimensional arrays, slice indexing can also be used, but unlike it usually is in python, in this case all selected elements of the array receive the passed value:

import stretchy

array = stretchy.array('_'*31)
array[::3] = 'O'
print(f'{array:s}')

results in

O__O__O__O__O__O__O__O__O__O__O

To replace the entire contents of the array, you can use the array's replace_content method:

One-dimensional arrays:

replace_content(self, content: Iterable, offset: int = 0) -> None

Multi-dimensional arrays:

replace_content(self, content: Sequence,
                      offset: tuple[int,...]|list[int]|int = 0) -> None

Note, that content has been called array in a previous version, but it has been deprecated by now. It will be removed in a later version.

Changing array size

Thera are three methods, which can be used to resize/reshape the array:

• trim
• shrink_by
• crop_to

These are described below.

trim

def trim(self) -> None

The method can be used to cut off redundant parts, i.e. those where default values are not followed by others. In such a case, after trim, the array returns the same values at all positions as before (of course, other properties, such as boundary, may change).

shrink_by

def shrink_by(self, by: int) -> None
# dim >= 2:
def shrink_by(self, by: tuple[int, ...]) -> None
def shrink_by(self, by: tuple[tuple[int, int], ...]) -> None
# dim = 1:
def shrink_by(self, by: tuple[int, int]) -> None

The method can be used to reduce the size of the array in all directions. This can lose significant data, but if there are only default values within the specified amount in each directions, only those values will be deleted and the array will not change in content. Of course, in all cases the the boundary's values will be reduced by the amount(s) of by (they will not exceed 0).

If by is of type int, the array is reduced by the same amount in each direction. If the type is a tuple, then the amount of reduction along each axis in each direction must be given. In all cases the amount must be greater than or equal to zero.

crop_to

# dim >= 2:
def crop_to(self, by: tuple[tuple[int, int], ...]) -> None
# dim = 1:
def crop_to(self, by: tuple[int, int]) -> None

The method can be used to cut the array to any size in either direction in either dimension. Subject, of course, to the restriction that the two boundaries cannot extend past the zero point, i.e. the lower boundary cannot be positive and the upper boundary cannot be negative.

Iterating over the array

Stretchy arrays are iterable. This means, that you can use it as follows:

import stretchy

array = stretchy.array([[0]*5]*5, offset=-2)
for index, subplane in enumerate(array, array.offset[0]):
    subplane[0] = index
print(f'{array:a}')

And the output is:

 0  0 -2  0  0
 0  0 -1  0  0
 0  0  0  0  0
 0  0  1  0  0
 0  0  2  0  0

Formatting

Stretchy arrays come with a set of formatting options:

s1 = f'{array:s;}'
s2 = '{:b|e|s|a}'.format(array)
...

Grammar of formatting options can be described as:

Format  ← Option*
Option  ← Command Param?
Command ← [a-zA-Z]
Param   ← (Char & !Command)+
Char    ← any single unicode character

This means, that options follow each other without any separator characters. The ascii letters indicate which option to set, the characters after them are their optional parameters. Letters cannot be parameters.

Formatting options

• s: cell separator. The character string after this option will separate values in a row. Default: ' '
• r: row ending. This value separates rows (i.e. separator in the second or higher dimensions). Default: ''
• b: beginning of block. Each dimension is represented by a single block. Default: ''
• e: ending of block. Default: ''
• a: arrange in columns. int and float values are aligned to the right, others to the left. a turns on arrangement, no parameters are allowed.
• i: show indices. If this option is turned on, the higher-order indices (>2) are displayed between the two-dimensional blocks. Otherwise, it uses line breaks to indicate which block follows (1 empty line: level 3, 2 empty lines: level 4...). No parameters are allowed.
• l: literal format. If this option is turned on, the repr format of the cell content is used. Note, that otherwise, None value is represented by an empty string. No parameters are allowed.

With examples that build on each other:

import stretchy

array = stretchy.empty(3)
array[-1,0,-1] = '#'
array[-1,0,1] = '@'
array[-1,1,0] = '%'
array[0,0,-1] = '$'
array[0,1,1] = '&'
print(f'{array}')
##  @
# %
#
# $
#   &
print(f'{array:s,}')
##,,@
#,%,
#
#$,,
#,,&
print(f'{array:s,b|e|}')
#|||#,,@|
#  |,%,||
#
# ||$,,|
#  |,,&|||
print(f'{array:s,r;b|e|}')
#|||#,,@|;
#  |,%,||;
#
# ||$,,|;
#  |,,&|||
print(f'{array:s,r;b|e|a}')
#|||#, ,@|;
#  | ,%, ||;
#
# ||$, , |;
#  | , ,&|||
print(f'{array:s,r;b|e|al}')
#|||'#' ,None,'@' |;
#  |None,'%' ,None||;
#
# ||'$' ,None,None|;
#  |None,None,'&' |||
print(f'{array:s,r;b|e|ali}')
#Index -1:
#|||'#' ,None,'@' |;
#  |None,'%' ,None||;
#Index 0:
# ||'$' ,None,None|;
#  |None,None,'&' |||

str()

Converting the array to str is equivalent to the following formatting options: b[e]a. This also means, that while str(array) == f'{array:b[e]a}', print(array) differs from print(f'{array}').

So, let us consider the following sniplet:

import stretchy

array = stretchy.array([[['ab', 'cd'], ['ef', 'gh']], \
                                  [['ij', 'kl'], ['mn', 'op']]], dim=4)
print(array)
print(repr(array))

The output of it is:

[[[[a b]
   [c d]]

  [[e f]
   [g h]]]


 [[[i j]
   [k l]]

  [[m n]
   [o p]]]]

repr()

You can use this function to print more information about the array. When representing arrays, other data in the array are also displayed, e.g:

ArrayND(dim=2, default='.', offset=(0, 0), content=[])

The content part is displayed with the format equivalent to the following formatting options: s, r,b[e]al.

So the same code as above but with the following printout:

print(repr(array)) # or print(f'{array!r}')

results in

ArrayND(dim=4, default=None, offset=(0, 0, 0, 0), content=
[[[['a', 'b'],
   ['c', 'd']],

  [['e', 'f'],
   ['g', 'h']]],


 [[['i', 'j'],
   ['k', 'l']],

  [['m', 'n'],
   ['o', 'p']]]])

Complex examples

Langton's ant

import stretchy

array = stretchy.empty(2, '.')
pos = (0, 0)
dir = 2
for _ in range(11000):
    if array[pos] == '#':
        dir = (dir + 1) % 4
    else:
        dir = (dir - 1) % 4
    array[pos] = '.' if array[pos] == '#' else '#'
    if dir == 0:
        pos = (pos[0], pos[1] + 1)
    elif dir == 1:
        pos = (pos[0] - 1, pos[1])
    elif dir == 2:
        pos = (pos[0], pos[1] - 1)
    elif dir == 3:
        pos = (pos[0] + 1, pos[1])
print(f'{array:s}')

Future plans

There are some ideas for future development:

• offset shifting: Offset an existing array without changing the contents. Also, offset to center.
• non-zero centric operation: Do not require storage starting from 0 if all elements are in the positive or negative range.
• sub-sub-planes: with partial indexing you can get plane from any levels. E.g. in a 4-dimensional array, array[2,5] returns a 2-dimensional one
• comparison operators
• ellipsis: in case of large arrays, represent values with ellipsis (str or repr)