Miscellaneous functions/classes¶

Partition: describes an unordered partition of the integers \(\{1,...,n\}\),
Sequence: describes a lazily evaluated sequence of elements, with 1-based vpi (big integer) indices
msg: Prints a diagnostic message

Partition¶

class replab.Partition(blockIndex, blocks)¶

Bases: replab.Str

Represents an unordered partition of the set {1..n} into disjoint subsets

The subsets, or blocks, are represented by sorted integer row vectors. The subsets themselves are sorted by their minimal element.

Class members list

Properties

blockIndex – Index of the block for each element
blocks – List of blocks
n – Domain size

Prettyprinting

additionalFields – Returns the name/value pairs corresponding to additional fields to be printed
disp – Standard MATLAB/Octave display method
headerStr – Tiny single line description of the current object type
hiddenFields – Returns the names of the fields that are not printed as a row vector
longStr – Multi-line description of the current object
shortStr – Single line text description of the current object

General

Partition – Constructs a Partition from blockIndex and list of blocks
check – Verifies the sanity of this partition
finest – Constructs the partition of n singleton blocks
fromApproximateVector – Returns the partition that groups approximately equal coefficients of a vector
fromBlocks – Constructs a partition from disjoint blocks
fromVector – Returns the partition that groups equal coefficients of a vector
permutationsOrbits – Returns the partition of the domain 1...N into orbits
restrictedToBlocks – Returns the partition containing only the given blocks
singletons – Returns a set of all points that are singletons of this partition
trivial – Constructs the trivial partition with a single block of given cardinality

Properties

block – Returns the i-th subset in this partition
blockSize – Returns the size of the i-th block
blockSizes – Returns the sizes of blocks
nBlocks – Returns the number of subsets/blocks in this partition

Comparison

eq – Checks if this partition is equal to another partition
ge – Returns whether the given partition is finer than this partition
gt – Returns whether the given partition is strictly finer than this partition
join – Returns the finest common coarsening of two partitions
le – Returns whether the given partition is coarser than this partition
lt – Returns whether the given partition is strictly coarser than this partition
meet – Returns the common refinement of two partitions
ne – Checks if this partition differs to another partition

Inherited elements

additionalFields(self)¶: Documentation in replab.Str.additionalFields()

disp(self)¶: Documentation in replab.Str.disp()

headerStr(self)¶: Documentation in replab.Str.headerStr()

hiddenFields(self)¶: Documentation in replab.Str.hiddenFields()

longStr(self, maxRows, maxColumns)¶: Documentation in replab.Str.longStr()

shortStr(self, maxColumns)¶: Documentation in replab.Str.shortStr()

Own members

blockIndex¶

Index of the block for each element

Type: integer(1, n)

blocks¶

List of blocks

Type: cell(1,*) of integer(1,*)

n¶

Domain size

Type: integer

Partition(blockIndex, blocks)¶

Constructs a Partition from blockIndex and list of blocks

Do not use this function direclty, rather use another constructor such as .fromBlocks.

Parameters

blockIndex –
blocks (cell(1,*) of integer(1,*)) – Disjoint blocks

Returns

The partition

Return type

Partition

See also

fromBlocks check

block(self, i)¶

Returns the i-th subset in this partition

Parameters: i (integer) – Block index
Returns: Subset
Return type: integer(1,*)

blockSize(self, i)¶

Returns the size of the i-th block

Parameters: i (integer) – Block index
Returns: Size of the i-th block in this partition
Return type: integer

blockSizes(self)¶

Returns the sizes of blocks

Returns: block sizes
Return type: integer(1,*)

check(self)¶: Verifies the sanity of this partition

eq(self, rhs)¶

Checks if this partition is equal to another partition

Parameters: rhs (Partition) – Another partition
Returns: True is both partitions are equal
Return type: logical

static finest(n)¶

Constructs the partition of n singleton blocks

Parameters: n (integer) – Size of the partition and number of blocks
Returns: Partition
Return type: Partition

static fromApproximateVector(vec, tol)¶

Returns the partition that groups approximately equal coefficients of a vector

Example

>>> replab.Partition.fromApproximateVector([0.1 0.2 0.9 1 0.3], 0.11)
  Partition '125|34'
  blockIndex: [1, 1, 2, 2, 1]
      blocks: {[1, 2, 5], [3, 4]}
           n: 5

Parameters

vec (double(1,*), real) – Vector to group the coefficients of
tol (double) – Tolerance

Returns

Partition of blocks with approximately equal coefficients

Return type

Partition

static fromBlocks(blocks)¶

Constructs a partition from disjoint blocks

The blocks will be sorted and reorganized.

Example

>>> replab.Partition.fromBlocks({[1 2 5] [3 4]})
  Partition '125|34'
  blockIndex: [1, 1, 2, 2, 1]
      blocks: {[1, 2, 5], [3, 4]}
           n: 5

Parameters: blocks (cell(1,*) of integer(1,*)) – Disjoint blocks
Returns: Constructed partition
Return type: replab.Partition

static fromVector(vec)¶

Returns the partition that groups equal coefficients of a vector

Example

>>> replab.Partition.fromVector([0 0 1 1 0])
  Partition '125|34'
  blockIndex: [1, 1, 2, 2, 1]
      blocks: {[1, 2, 5], [3, 4]}
           n: 5

Parameters: vec (double(1,*)) – Vector to group the coefficients of
Returns: Partition of blocks with equal coefficients
Return type: Partition

ge(self, rhs)¶

Returns whether the given partition is finer than this partition

Parameters: rhs (Partition) – Partition to compare this one with
Returns: True if every block of the given partition is a subset of a block of this partition
Return type: logical

gt(self, rhs)¶

Returns whether the given partition is strictly finer than this partition

Parameters: rhs (Partition) – Partition to compare this one with
Returns: True if self >= rhs and self ~= rhs
Return type: logical

join(lhs, rhs)¶

Returns the finest common coarsening of two partitions

Parameters: rhs (Partition) – Other partition
Returns: The coarsening of the two partitions
Return type: Partition

le(self, rhs)¶

Returns whether the given partition is coarser than this partition

Parameters: rhs (Partition) – Partition to compare this one with
Returns: True if every block of this partition is a subset of a block of the given partition
Return type: logical

lt(self, rhs)¶

Returns whether the given partition is strictly coarser than this partition

This is a strict version of le

Parameters: rhs (Partition) – Partition to compare this one with
Returns: True if self <= rhs and self ~= rhs
Return type: logical

meet(self, rhs)¶

Returns the common refinement of two partitions

Parameters: rhs (Partition) – Other partition
Returns: The refinement of both partitions
Return type: Partition

nBlocks(self)¶

Returns the number of subsets/blocks in this partition

Returns: Number of blocks
Return type: integer

ne(self, rhs)¶

Checks if this partition differs to another partition

Parameters: rhs (Partition) – Another partition
Returns: True is both partitions differ
Return type: logical

static permutationsOrbits(permutations)¶

Returns the partition of the domain 1...N into orbits

Parameters: permutations (integer(nG, d)) – Permutations given as rows in a matrix
Returns: Partition containing the orbits
Return type: Partition

restrictedToBlocks(self, selBlocks)¶

Returns the partition containing only the given blocks

The selected blocks are ordered

singletons(self)¶

Returns a set of all points that are singletons of this partition

The singletons are the blocks of size 1.

Returns: Set of points
Return type: integer(1,*)

static trivial(n)¶

Constructs the trivial partition with a single block of given cardinality

Parameters: n (integer) – Size of the partition and single block
Returns: Trivial partition
Return type: Partition

Sequence¶

class replab.Sequence(nElements)¶

Bases: replab.Domain

Describes a sequence of elements

See https://en.wikipedia.org/wiki/Sequence .

Our indices are (bounded) integers, represented by vpi instances.

The sequence supports element indexing and searching for elements.

Class members list

Properties

nElements – Number of elements contained in this enumerator

Prettyprinting

additionalFields – Returns the name/value pairs corresponding to additional fields to be printed
disp – Standard MATLAB/Octave display method
headerStr – Tiny single line description of the current object type
hiddenFields – Returns the names of the fields that are not printed as a row vector
longStr – Multi-line description of the current object
shortStr – Single line text description of the current object

Property cache

cache – Sets the value of the designated property in the cache
cached – Returns the cached property if it exists, computing it if necessary
cachedOrDefault – Returns the cached property if it exists, or the provided default value if it is unknown yet
cachedOrEmpty – Returns the cached property if it exists, or [] if it is unknown yet
inCache – Returns whether the value of the given property has already been computed

Laws

check – Checks the consistency of this object
checkAndContinue – Checks the consistency of this object
laws – Returns the laws that this object obeys

Unique ID

eq – Equality test
id – Returns the unique ID of this object (deprecated)
isequal – Equality test
ne – Non-equality test

Test helpers

assertEqv – Compares two elements for equality
assertNotEqv – Compares two elements for inequality

Sampling and equality test

eqv – Tests domain elements for equality/equivalence
sample – Samples an element from this set

Domain construction

lambda – Constructs an indexed family from function handles

General

Sequence –
at – Retrieves a element by position
find – Returns the index of a given element
imap –
toCell – Returns a row cell array containing all elements of this family

Inherited elements

Sequence()¶: No documentation

additionalFields(self)¶: Documentation in replab.Str.additionalFields()

assertEqv(self, x, y, context)¶: Documentation in replab.Domain.assertEqv()

assertNotEqv(self, x, y, context)¶: Documentation in replab.Domain.assertNotEqv()

cache(self, name, value, handleExisting)¶: Documentation in replab.Obj.cache()

cached(self, name, fun)¶: Documentation in replab.Obj.cached()

cachedOrDefault(self, name, defaultValue)¶: Documentation in replab.Obj.cachedOrDefault()

cachedOrEmpty(self, name)¶: Documentation in replab.Obj.cachedOrEmpty()

check(self)¶: Documentation in replab.Obj.check()

checkAndContinue(self)¶: Documentation in replab.Obj.checkAndContinue()

disp(self)¶: Documentation in replab.Str.disp()

eq(self, rhs)¶: Documentation in replab.Obj.eq()

eqv(self, t, u)¶: Documentation in replab.Domain.eqv()

headerStr(self)¶: Documentation in replab.Str.headerStr()

hiddenFields(self)¶: Documentation in replab.Str.hiddenFields()

id(self)¶: Documentation in replab.Obj.id()

imap()¶: No documentation

inCache(self, name)¶: Documentation in replab.Obj.inCache()

isequal(lhs, rhs)¶: Documentation in replab.Obj.isequal()

laws(self)¶: Documentation in replab.Obj.laws()

longStr(self, maxRows, maxColumns)¶: Documentation in replab.Str.longStr()

ne(self, rhs)¶: Documentation in replab.Obj.ne()

sample(self)¶: Documentation in replab.Domain.sample()

shortStr(self, maxColumns)¶: Documentation in replab.Str.shortStr()

Own members

nElements¶

Number of elements contained in this enumerator

Type: vpi

at(self, ind)¶

Retrieves a element by position

Normally, RepLAB encodes big integers using the vpi type. As a user convenience (esp. on the command line), this method must also accept string and double arguments.

Parameters: ind (vpi or double or string) – Index of element to be retrieved, 1 <= ind <= self.nElements
Returns: The element at the “ind” position

find(self, obj)¶

Returns the index of a given element

If the element is not part of the family, this returns vpi(0).

Parameters: obj – Element to retrieve
Returns: 1-based index of the given element
Return type: vpi

static lambda(nElements, atFun, findFun)¶

Constructs an indexed family from function handles

Parameters

nElements (vpi) – Size of the indexed family, so that the index set is 1..``nElements``
atFun (function_handle) – Handle that implements the at method To simplify implementation, it is guaranteed that atFun will receive an argument of type vpi.
findFun (function_handle) – Handle that implements the find method

Returns

The constructed indexed family

Return type

Sequence

toCell(self)¶

Returns a row cell array containing all elements of this family

Returns: A cell array C such that C{i} = self.at(i)
Return type: row cell array of elements
Raises: An error if the enumerator is too big and the elements cannot fit in a cell array. –

msg¶

replab.msg(level, message, varargin)¶

Displays a diagnostic message on the console output

Additional arguments can be function handles, to be evaluated only when the message is actually displayed.

Parameters

level (integer) – Verbosity level beginning at which to show the message (see replab.globals.verbosity)
message (charstring) – Message to display, can include sprintf-style formatting directives