Z^3 Array Manipulation Member Functions

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ARRAY FUNCTIONS

A listing of the Array functions are given below:

Every Array Member Function is also globalized with the same name but with Uppercase First Letter. For example, .chunks has a twin Global called Chunks, which take first parameter as an array, and followed with the exact same parameters of the original member function. Hence Chunks(Array,ChunkSize) will work the same. If there is an existing function with a similar name, then the globalized name will have a $x appended to it. For example, .map is also available as Map$x.

Quick Reference: Array.R = Array.reduce Array.M = Array.map Array.F = Array.filter

Function name Parameter

Function Name	Parameters	Notes
$	Function/Array of Functions	Apply functions to each element of array
$$	Function/Array of Functions	Apply functions to each row of array
$$$	Function/Array of Functions	Apply functions to each column of array
$$F	Function/Array of Functions	Append results of functions to each row
$A	Parameter	Get attributes from an array of objects
$C	Column Array to apply, Function/Array of Functions, Optional Parameters	Apply a function with parameters to a column
$CELLS	Row/Column Area indices and width and height to apply (l,t,w,h), Function/Array of Functions, Optional Parameters	Apply a function with parameters to a cell area
$d		Same as Array.$diag
$diag		Apply function to the proper diagonal of an array
$dth		Apply function to dth diagonal of an array
diagonal		Get the nth diagonal of an array
$R	Row Array to apply, Function/Array of Functions, Optional Parameters	Apply a function with parameters to a row
$X	SomeArray	Combines two arrays using an across operation. Reverse is .X$
$x	SomeArray	Same as $X
$_	Mode, Functions, Parameters	Apply a function to the entire array as one aggregate call
__$	Mode, Functions, Parameters	Using a mode (value, valuebyrow, index etc), apply a function to the cells with parameters
ac	ColCount	Add columns
accumulate	Total	Accumulate each element with the next and give a cumulative result. Start from Total if need be.
accumulatewith	CumulateFunction, CurrentResult	Accumulate each element with the next using the function and give a cumulative result. Start from Total if need be.
across	OtherArray, Function	Apply the functions to each combination of cells in the two arrays
add	Thing	Add Thing to Array
addcolumn	NumberOfColumns	Add specified number of columns to the array
addrow	NumberOfRows	Add specified number of rows to the array
addsequence	InFront, StartFrom, OptionalSequenceArray	Add the sequence value to the specified column
adjoint	Array	Adjoint of the matrix
after	(NthOrExpOrFn, BothSides,IsCaseSpecific)	Give elements after a certain index. If Exp or Fn given for first parameter, finds a matching element, and find elements after that. Exclude the element at the index itself.
afterx	(NthOrExpOrFn, BothSides,IsCaseSpecific)	Same as .after, but includes the element at the index.
aggregate	Columns,Function, Params	Apply functions to columns with parameters given
allslices	SliceSize	slices of numbers
any	Count	Get Count elements from the array randomly
appendfunction	Function	Adds a column which the result of this function on the remaining row.
ar		Modify the array row/Column
around	(NthOrExpOrFn, Count, BothSides,IsCaseSpecific)	Give elements before and after a certain index, upto Count. If Exp or Fn given for first parameter, finds a matching element, and find elements around that. Exclude the element at the index itself.
aroundx	(NthOrExpOrFn, BothSides,IsCaseSpecific)	Same as .around, but includes the element at the index.
async	Iterator, CallBack
atindex	List of indices	Indices indicated by the parameters
atnode	Function, SubtractByArray, ScaleByArray, DoNotShowIndices
backward	Function, StartValue	Backwards the given array from the start value
before	(NthOrExpOrFn, BothSides,IsCaseSpecific)	Give elements before a certain index. If Exp or Fn given for first parameter, finds a matching element, and find elements after that. Exclude the element at the index itself.
beforex	(NthOrExpOrFn, BothSides,IsCaseSpecific)	Same as .before, but includes the element at the index.
bindcolumn
branch	fns (default [neg, zero, positive])	Give an array of functions (default one for negative, zero and positive with false/true for each value in the array). Any arbitrary array of functions will generate a similar array as output. -10..10.branch([LT,[EQ,GT]]) .print()
branchvalues	SomeOnlyMatches	Give three arrays (one for negative, zero and positive) with value that matched for each value in the array. SomeOnlyMatches if true, shows only for the items that matched the condition
buckets		An object with key frequency pairs.
bykey		Create an object from the array with array elements bucketed by keys from a column
c	Columns	Extract columns from array
calci		Convert array to calci
head		Head of an array
cartesianproduct	IsWithoutFlatten	Create a cartesian product of the elements of the arrays.
cdr		Tail of an array
cell	Row, Column, Width, Height	Cells with the specified addresses
cells	Row, Column, Width, Height	Cells with the specified addresses. Same as cell
checktype	TypeArray, ForceCheckOnVariables	Check if elements are of the type/typearray mentioned
chunks	ChunkSize, Function	Chunks of size from array. Function is applied to the chunks if provided. pieces gives pieces of size starting with each element which is different.
ci		Apply a function to column indices (same as Array.__$ in "ic" mode)
clean	Expression, ReplaceWith	Remove the items that match Expression and replace with ReplaceWith if provided
clear	FillWith	Clear array and fill with FillWith if provided
clearcopy	FillWith	Clear each element in a copy of the array
clearrepeats
clone		Clone an array
colconcat	AnotherArray	Concat columns
colcount		Column Count
collect		Takes matches at element level
collectasvector		Takes matches at top level
collectwhile		Takes matches at element level while true
collectwhileasvector		Takes matches at top level while true
column	SomeColumns	Extract columns
columnconcat	AnotherArray	Concat two arrays by column
columns	SomeColumns	Extract columns
compare
concatall	LimitArray, IncludeEdges	Concatenates all the elements in an array or table row wise.
converge	Function, NumberOfIterations, Accuracy, Converge
copy		Make a copy of the array
core
count	FirstLevelOnly
crosstab	RowSet, ColSet,PageSet,DataSet	Returns a simple cross tabulation of two or more factors
cube
cumcolumn		Cumulate column(s)
cumcolumns		Cumulate column(s)
cumcolumnswith		Cumulate column(s) with a function
cumcolumnwith		Cumulate column(s) with a function
cumrow		Cumulate row(s)
cumrows		Cumulate row(s)
cumrowswith		Cumulate row(s) with a function
cumrowwith		Cumulate row(s) with a function
cumulate		Cumulate elements with NUMSUM
data
dc	Which	Delete columns specified
deal	Within, ManyInEach	Generates Random Numbers
deepcopy		Deep copy of an array
deletecolumn	Which	Delete a specified or last column
deleterow	Which	Delete a specified or last row
det	Array	Determinant of an array
determinant	Array	Determinant of an array
dim	Dimensions	Create a new array with the dimensions given
div	Thing	Divide Thing to Array
divide	Thing	Integer Divide Thing to Array
dr	Which	Delete a specified or last row
drop
dropwhile		Drops elements that do not match at element level
dropwhileasvector		Drops matches at top level
eighteenth	SomeCount	Pick the SomeCount of items from eighteenth position
eighth	SomeCount	Pick the SomeCount of items from eigth position
eleventh	SomeCount	Pick the SomeCount of items from eleventh position
ends	SomeNth, SomeCount	Pick the SomeCount of items from SomeNth position from both sides of the array
equal	Array, CheckLength, StartFrom	Comparing the each value in the array and gives true/false.
equalvalues	Array, CheckLength, StartFrom	Comparison of set of arrays with its length and values without considering its order
eval		Execute each element of the array as code
except	Indices	Extract the elements at indices mentioned
exec	Parameters	Execute each element of the array as a function with given parameters
explode	StartIndex, By, RecurseTillLevel	Explode each element into a sequence from start Index
extract	column list	Extract specified columns
extractslices	SliceExpression, KeepSplitValue, IgnoreRepeats	Splits array with matches, without split value or repeats of match. Useful to get the array split with a match. Similar to .splices
few	IncludeHeader	Pick a few elements from the array randomly
findx	fn,mode,includefalse	Applies a function and returns matches. Mode can be "INDEX", "ELEMENT", "TRUE"/"TRUTH", "VALUE","INDEXELEMENT","INDEXELEMENTVALUE", etc. includeFalse keeps false matches.
findi	fn,includefalse	Applies a function and returns indices of matches.
finde	fn,includefalse	Applies a function and returns elements that matched.
findie	fn,includefalse	Applies a function and returns index and elements that matched.
findiev	fn,includefalse	Applies a function and returns index, elements that matched and result of the match.
findiv	fn,includefalse	Applies a function and returns index, result of the match.
findv	fn,includefalse	Applies a function and returns result of the match.
findt	fn,includefalse	Applies a function and returns result of the match as true or false.
fifteenth	SomeCount	Pick the SomeCount of items from fifteenth position
fifth	SomeCount	Pick the SomeCount of items from fifth position
fillwith	Numbers	Fill the array with numbers provided. Repeat the numbers if fewer than size specified
filtermatches	MatchIdenticalMatrix, OnlyMatches
filteroncolumn	Condition, ExtractColumns, FilterOnColumn	ExtractColumns are the columns that are extracted, and filters are applied on FilterOnColumn where condition is satisfied
filteroncondition	TakeDropOrAllFlag, Function, Parameter	Apply a function to an array with parameters, and return list that matched/not matched/all
filteronrow	Condition, ExtractRows, FilterOnRow	ExtractRows are the rows that are extracted, and filters are applied on FilterOnRow where condition is satisfied
findcellref	Values
first	SomeCount	Pick the SomeCount of items from first position
firstelement	SomeCount	Pick the element from first position
firsthalf		First half of the array
fixat	Index, Fix
fjoin	HeadLength, JoinString
flatten		Flatten the array to a single dimension
flip	IncludeHeader	Same as transpose
flipparts		Switch first and second half of an array
fold	AtFoldValue, AtReverseFoldValue
foldl	Function, StartSeed	Apply a function cumulatively to left
foldr	Function, StartSeed	Apply a function cumulatively to right
forward	Function, StartValue
fourteenth	SomeCount	Pick the SomeCount of items from fourteenth position
fourth	SomeCount	Pick the SomeCount of items from fourth position
fourths		Split array in four pieces
funcjoin	HeadLength, FindString, FirstString, MidString, LastString
gettype
graph	Mode
graphin
half		Give two halves of the array
halves		Same as half
head		Head of the array (Same as Array.car)
headings
hundredth	SomeCount	Pick the SomeCount of items from hundredth position
i	PreviousArray	Indices in an array, concatenated to the PreviousArray if provided
ic	Functions	Apply functions to the column indices
ids		Get ids of all objects in an array of objects if present
implode	RecurseTillLevel
inc
include
indexwith	ExpressionOrIndex, IsCaseSpecific	finds the first index that matches the expression. String or Regexp can be provided, or a number.
indexanddata	Function, SubtractByArray, ScaleByArray, DoNotShowIndices, RowArray	Returns the result of applying the Function/FunctionSet to each x,y, and index location of the array, then subtracts and scales the results with SubtractByArray and ScaleByArray.
indiceswith	ExpressionOrIndex, IsCaseSpecific	finds all indices that matches the expression. String or Regexp can be provided, or a number.
indices	Function, SubtractByArray, ScaleByArray, DoNotShowIndices, RowArray	Returns the result of applying the Function/FunctionSet to each x,y location of the array, then subtracts and scales the results with SubtractByArray and ScaleByArray.
injoin	JoinWith	A string with all array elements joined starting from second element
inner	InnerSize	Give inner elements.
insert	Value, AfterLastFlag
insertcolumn	Index, NumberOfColumns
insertrow	Index, NumberOfRows
inverse	Array	Calculate the inverse of this array
ir
is	Thing, IsNot
is1d		Check if there is One dimension
is2d		Check if there is Two dimension
isFalse		Check if there is any False
isfalse		Check if there is any False
islikelytype
isnotnull
isnull
isTrue		Check everything is true
istrue		Check everything is true
istype
ith	(Nth, Count, BothSides)	Same as .nth, but gives indices starting with 0, while nth gives numbers starting from 1.
j
joincolumnswith	ArrayOfJoinCharacters, IsRepeat
joinrowswith	ArrayOfJoinCharacters, IsRepeat
joinwith
jq
keep
last	Count	Get Count elements from the Last element
lastelement	Count
list
lookup
make
make1to2d	ReplaceOriginal
makecore
makekeyarray	Recursive
maplist	fun
mapper	Function	Same as $
maprow	Function	Same as $$
maplength	IncludeStringsEtc	Calculate length of each element. IncludeStringsEtc calculates the length if the element is a string also.
mask
match	Expression
matchcolumn	Expression, Column
matchindex	Expression, IndexThenFromMatch
matchrow	Expression, Row
matchvalue	Expression, IndexThenFromMatch
merge	OtherArray, Function
mergecolumns	OtherArray
mergeio
mergerows
mid	From, Count	Pick Count elements from From location onwards
millionth	SomeCount	Pick the SomeCount of items from millionth position
mod	Thing	Mod Thing to Array
multiply	Thing	Multiply Thing to Array
nicejoin	JoinString, EndString, SubArrayString
nineteenth	SomeCount	Pick the SomeCount of items from nineteenth position
nineth	SomeCount	Pick the SomeCount of items from nineth position
nodeindex		Simply gives the indices of the node.
notinclude	Item
notwithinlimits	LimitArray, IncludeEdges
nth	Nth, Count, IsBothSides	Pick the SomeCount of items from nth position. IsBothSides will provide results from both sides of the array.
ntimes	Function, NumberOfIterations, Accuracy, Converge
nullifyobjects	Recursive
numbers	ForceCheckOnVariables
o	List of Items	Same as Array.objects()
objects	List of Items	Returns the array of Objects in the ZSpace DOM with each element being applied with function OBJECT applied to the variable.
of	elements	Elements used to create the array.
op		Op with another number using units (Supported Operators %, <, >, <=, >=, ==, !=,===, FEQ Floating Equals)
otherthan	ArrayWithElementsToExclude	The elements except the specified elements.
outer	OuterSize	Outer 2 elements.
pack		Remove consecutive duplicates and compact the array.
pad	Length, PadString	Pad the array to be of length NewLength, and fill the extra elements added with PadString .
pair	Value, OnRight
pairmatch	AtFoldValue, AtReverseFoldValue, StartFrom	Folds the array for the corresponding SomeAtFoldValue,into subarrays if the value in the array element matches the given fold value
partitiononcondition	TakeDropOrAllFlag, Function, Parameter
parts	NumberOfParts, SpecificPartOrFunction	Divides the array into parts of Part Size. Applies function if provided, or provide the specific requested part such as an element at the index (2nd of 3 parts for example). NumberOfParts can be negative, and it will reverse the array before processing.
pastefolds	MidOnly	Unfold the result of a fold.
pick	PickMaskArray	Pick all elements that matches a true in the array mask.
pieces	Width, Function, Stride	Split the array into pieces of Piece Size. For each piece, a function can be applied. Stride or width can be negative, and will reverse the array before processing. Example: nums = [3,6,9,1]; MAX(nums.pieces(2,MINUS@ABS))
pip	PathIndexArray, Length, PassThroughFunction,UseClone	Push and Insert into subarrays at pathindices given
pipall	ExceptIndexUpto, MarkSliced	Push and Insert for all elements from index provided
pipallwithslice	ExceptIndexUpto, MarkSliced	pipall with slices marked for later unpipping
plot
prefix	Prefix	Add a prefix to every element in an array
primitives		Returns the primitive values of objects in the array
print	Trimmed, TabLevel	Print an array as a text string
printf
r	Array/Parameters	Same as Array.row()
rand	Base,Count	Same as Array.random()
random	Base,Numbers	Fill the array with random numbers
raw		Returns pure array without headers, input, input headers, and data indices information.
remove	List of Elements	Remove the elements from the original array
removeByVal	Value	Removes the value,and changes the original array, unless Return Copy is true.
removeindices
removewith
repeatntimes	Function, NumberOfIterations, Accuracy, Converge
replace	ExpressionArrayOrValues, ReplaceWith
replicate	Count
rest	Start, Count	Remove the part of the array from Start
result
reverse	Function, StartValue	Reverse the given array from the start value along with the original array. (Dropped)
reversecopy		Reverse the given array from the start value along with the copy of an original array.
reverselevel	Level
reversepip	SomeExceptIndexUpto, SomeMarkSliced	Push and Insert for all elements from index provided in reverse
reversesort	Function	Sorting the arrays in the reverse order.
ri		Apply a function to row indices (same as Array.__$ in "ir" mode)
rotate	NumberOfSteps	Rotate an array NumberOfSteps times
rotatecolumns	NumberOfSteps	Rotates columns in an array with the specified number of steps.
rotaterows	NumberOfSteps	Rotates columns in an array with the specified number of steps.
row
rowconcat	OtherArray	Concat two arrays by row
rowcount		Count of rows
rowlengths	Function
rowpush	OtherArray
rows
rslice	Begin, End	Same as Array.slice()
second	SomeCount	Pick the SomeCount of items from second position
secondhalf		Get second half of the array
seq	StartIndex, By	Replaces each element in this array by a number sequence from StartIndex incremented by By
set
setaxis	Axis, ColumnValues
setcolumn	Column, ColumnValues
setheadings	Header List as Parameters	Sets the headings of this array with the parameters given.
setrow	Row, Array
setunit
seventeenth	SomeCount	Pick the SomeCount of items from seventeenth position
seventh	SomeCount	Pick the SomeCount of items from seventh position
shiftlevel	Level, NumberOfTimes
shuffle		shuffle the array randomly.
sixteenth	SomeCount	Pick the SomeCount of items from sixteenth position
sixth	SomeCount	Pick the SomeCount of items from sixth position
size		Give the size of this array for each dimension.
size2d
slices	SliceExpression, KeepSplitValue, IgnoreRepeats	Splits array with matches, keep matches or not in the split array, treat repeat matches as one match or repeats
slides
some	callback[, thisArg	Tests whether some element in the array passes the test implemented by the provided function.
sortrecursively
sortwith
sortbykey		Sorts the array by the specified key.
specialprint	Trimmed,TabLevel
spliteach	SplitExpression, RetainSplitterAlsoInResult	Finds the removes the character/text from the array elements and removes the same.
splitwhile		Same as Array.partitiononcondition()
splitwhileasvector		Same as Array.partitiononcondition()
stringlist		Displays the array elements as strings.
subtract	Thing	Subtract Thing to Array
suchthat		Filter an array with a condition (same as filteroncondition)
suchthatasvector		Filter an array with a condition (same as filteroncondition) at top array level
suffix	Suffix	Add a suffix to every element in an array
stride	SomeWidth, SomeStride, SomeFunction,SomeFullPiecesOnly	Same as Array.pieces, but index steps by strides. stride or width can be negative, and will reverse the array before processing.
t	IncludeHeader	Transpose an array
table		Convert array to an html table
tablelookup	RowValueMatch, ColumnValueMatch
tail
takewhile		Takes matches at every element
takewhileasvector		Takes matches at top level
tenth	SomeCount	Pick the SomeCount of items from tenth position
third	SomeCount	Pick the SomeCount of items from third position
thirds		Split array in three pieces
thirteenth	SomeCount	Pick the SomeCount of items from thirteenth position
thousandth	SomeCount	Pick the SomeCount of items from thousandth position
tofunctions
transpose	IncludeHeader	Transpose an array
truefalse	IsCheckTrueFunctionList, IsCheckFalseFunctionList, DoFlattenFirst
twelfth	SomeCount	Pick the SomeCount of items from twelfth position
twentieth	SomeCount	Pick the SomeCount of items from twentieth position
twod
type
uncrosstab	UptoColumn
unimplode	RecurseTillLevel
unimplodeleaf
unitsof
unwrapleaf
unzip	OtherArray	Split alternate elements into separate array.
value	Function
where	Term
withinlimits	LimitArray, IncludeEdges
withouttail
X$	SomeArray	Combines two arrays using an across operation in reverse. Opposite of .$X
x$	FunctionArray, OffsetArray, ScaleArray, GiveIndicesAlso,DoCentering	Apply a function array to the array, with offsets and scales applied, with indices or centering as requested
xy	Function, OffsetArray, ScaleArray,GiveIndicesAlso,DoCentering	Apply a function array to the array, with offsets and scales applied, with indices
xypanel	FunctionArray, OffsetArray, ScaleArray, GiveIndicesAlso	Apply a function array to the array, with offsets and scales applied, with indices, centered by default at 0. Useful to create contour panels with inputs to apply functions on.
z3
zero	ValueInstead, PreserveStructure	Zero or replace values in an array
zip	OtherArray	Combine two arrays into one zipped array
ZJSON

Combinator Functions

Array.$fns takes an array of functions and creates combinator pipe.

Array.$combinators takes take the name of a combinator and generate a function with that combinator behavior. These are globalized with λ prefix. For example, B Combinator is λB in global space.