Set stride to 0 for any dimension with shape 1. Given a flat layout L = (s_1,...,s_m):(d_1,...,d_m), sets d_i = 0 if s_i = 1.

Return connectors upward; junction y = weighted avg of descendant leaves.

Generate a pair of nested tuple morphisms with disjoint images. :return: Pair of morphisms with disjoint images :rtype: Tuple[Nest_m

Generate a pair of composable nested tuple morphisms. :param min_length: Minimum length :type min_length: int :param max_length:

Generate a pair of composable tuple morphisms. :param min_length: Minimum length :type min_length: int :param max_length: Maximu

Generate a pair of nested tuple morphisms where one divides the other. :param min_length: Minimum length :type min_length: int :

Generate a pair of nested tuple morphisms admissible for product. :param min_length: Minimum length :type min_length: int :param

Restrict morphism to a subtuple of its domain. :param subtuple: Indices to restrict to (1-based) :type subtuple: tup

Sort a flat layout and return the permutation used. :param flat_layout: Input flat layout :type flat_layout: cute.Layout :return

Compute the sum α ⊕ β: <m+p>_* → <n+q>_*. :param beta: Second morphism in sum :type beta: Fin_morphism :retu

Convert to nested tuple morphism. :return: Equivalent Nest_morphism :rtype: Nest_morphism

Generate TikZ representation of the morphism. :return: TikZ code :rtype: str

String representation of the morphism. :return: String representation :rtype: str

Check if morphisms are composable. :param g: Second morphism :type g: Tuple_morphism :return: True if compos

Check if morphisms are composable. :param g: Second morphism :type g: Nest_morphism :return: True if composa

Compute weak coalescence of the morphism. :return: Weakly coalesced morphism :rtype: Tuple_morphism

Compute weak coalescence with equivalence classes. :return: Tuple of (coalesced morphism, codomain equivalence classes)

Compute the complement of a flat layout with respect to size N. :param flat_layout: Input flat layout :type flat_layout: cute.Layout

Flatten only the codomain. :return: Morphism with flattened codomain :rtype: Nest_morphism

Check if morphism is complementary to other morphism. :param other: Other morphism :type other: Tuple_morphism

Check if two NestedTuples have the same profile. :param other: Other NestedTuple to compare :type other: NestedTuple

Check if self is refined by other. :param other: NestedTuple to check :type other: NestedTuple :return: True

Create a Nest_morphism. :param domain: Domain nested tuple data :type domain: tuple :param codomain: Codomain nested tuple data

Generate a TikZ diagram illustrating the mutual refinement of two nested tuples. :param nestedtuple1: First nested tuple :type neste

Nullify strides for dimensions with shape 1 in nested layouts. :param layout: Input layout :type layout: cute.Layout :return: La

Generate a random complementable morphism in Fin_*. :param domain: Domain size (optional) :type domain: int or None :param codom

Generate a pair of weakly composable nested tuple morphisms. :return: Pair of weakly composable morphisms :rtype: Tuple[Nest_morphis

Compute relative flattening with respect to another NestedTuple. :param other: Reference NestedTuple :type other: Ne

Replace all empty tuples with 1. :return: New NestedTuple with replacements :rtype: NestedTuple

Replace all empty tuples with 0. :return: New NestedTuple with replacements :rtype: NestedTuple

Product of domain entries. :return: Size :rtype: int

Compute strong coalescence of the morphism. :return: Strongly coalesced morphism :rtype: Tuple_morphism

Compute sum f ⊕ g. :param g: Second morphism :type g: Tuple_morphism :return: Sum of morphisms :rtyp

Test that nested tuple morphism complement agrees with layout complement. :param iteration: Test iteration number for seedin

Test that complement of a complementable nested morphism is valid. :param iteration: Test iteration number for seeding

Test that nested morphism composition agrees with layout. :param iteration: Test iteration number for seeding :type

Test that nested morphism concatenation agrees with layout. :param iteration: Test iteration number for seeding :typ

Test that morphism coalescence agrees with layout coalescence. :param iteration: Test iteration number for seeding :

Test that coalescing a tuple morphism produces a coalesced morphism. :param iteration: Test iteration number for seeding

Test that morphism complement agrees with layout complement. :param iteration: Test iteration number for seeding :ty

Test that complement is an involution, up to sorting.

Test that complement of a complementable morphism is valid. :param iteration: Test iteration number for seeding :typ

Test a complex chain of compositions.

Test that morphism composition agrees with layout composition. :param iteration: Test iteration number for seeding :

Test that weak composition algorithm is correct. :param iteration: Test iteration number for seeding :type iteration

Test that morphism composition is associative.

Test that morphism concatenation agrees with layout concatenation. :param iteration: Test iteration number for seeding

Test morphisms with empty domain or codomain.

Test that flat division agrees between morphisms and layouts. :param iteration: Test iteration number for seeding :t

Test that flat product agrees between morphisms and layouts. :param iteration: Test iteration number for seeding :ty

Test that identity morphism behaves correctly.

Test morphisms with large values.

Test edge cases for nested tuples.

Test morphisms with single elements.

Test that sorting a tuple morphism produces a sorted morphism. :param iteration: Test iteration number for seeding :

Test sorting followed by coalescing.

Compute underlying map for refinement. :param other: Reference NestedTuple :type other: NestedTuple :return:

Update codomain according to equivalence relation. :param equivalence_relation: List of equivalence classes :type eq

Compute weak composition of nested tuple morphisms. Computes composition through mutual refinement when domains/codomains don't matc