d3array
Data in JavaScript is often represented by an iterable (such as an array, set or generator), and so iterable manipulation is a common task when analyzing or visualizing data. For example, you might take a contiguous slice (subset) of an array, filter an array using a predicate function, or map an array to a parallel set of values using a transform function. Before looking at the methods that d3array provides, familiarize yourself with the powerful array methods builtin to JavaScript.
JavaScript includes mutation methods that modify the array:
 array.pop  Remove the last element from the array.
 array.push  Add one or more elements to the end of the array.
 array.reverse  Reverse the order of the elements of the array.
 array.shift  Remove the first element from the array.
 array.sort  Sort the elements of the array.
 array.splice  Add or remove elements from the array.
 array.unshift  Add one or more elements to the front of the array.
There are also access methods that return some representation of the array:
 array.concat  Join the array with other array(s) or value(s).
 array.join  Join all elements of the array into a string.
 array.slice  Extract a section of the array.
 array.indexOf  Find the first occurrence of a value within the array.
 array.lastIndexOf  Find the last occurrence of a value within the array.
And finally iteration methods that apply functions to elements in the array:
 array.filter  Create a new array with only the elements for which a predicate is true.
 array.forEach  Call a function for each element in the array.
 array.every  See if every element in the array satisfies a predicate.
 array.map  Create a new array with the result of calling a function on every element in the array.
 array.some  See if at least one element in the array satisfies a predicate.
 array.reduce  Apply a function to reduce the array to a single value (from lefttoright).
 array.reduceRight  Apply a function to reduce the array to a single value (from righttoleft).
Installing
If you use npm, npm install d3array
. You can also download the latest release on GitHub. For vanilla HTML in modern browsers, import d3array from Skypack:
<script type="module">
import {min} from "https://cdn.skypack.dev/d3array@3";
const m = min(array);
</script>
For legacy environments, you can load d3array’s UMD bundle from an npmbased CDN such as jsDelivr; a d3
global is exported:
<script src="https://cdn.jsdelivr.net/npm/d3array@3"></script>
<script>
const m = d3.min(array);
</script>
API Reference
Statistics
Methods for computing basic summary statistics.
# d3.min(iterable[, accessor]) · Source, Examples
Returns the minimum value in the given iterable using natural order. If the iterable contains no comparable values, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the minimum value.
Unlike the builtin Math.min, this method ignores undefined, null and NaN values; this is useful for ignoring missing data. In addition, elements are compared using natural order rather than numeric order. For example, the minimum of the strings [“20”, “3”] is “20”, while the minimum of the numbers [20, 3] is 3.
See also extent.
# d3.minIndex(iterable[, accessor]) · Source, Examples
Returns the index of the minimum value in the given iterable using natural order. If the iterable contains no comparable values, returns 1. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the minimum value.
Unlike the builtin Math.min, this method ignores undefined, null and NaN values; this is useful for ignoring missing data. In addition, elements are compared using natural order rather than numeric order. For example, the minimum of the strings [“20”, “3”] is “20”, while the minimum of the numbers [20, 3] is 3.
# d3.max(iterable[, accessor]) · Source, Examples
Returns the maximum value in the given iterable using natural order. If the iterable contains no comparable values, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the maximum value.
Unlike the builtin Math.max, this method ignores undefined values; this is useful for ignoring missing data. In addition, elements are compared using natural order rather than numeric order. For example, the maximum of the strings [“20”, “3”] is “3”, while the maximum of the numbers [20, 3] is 20.
See also extent.
# d3.maxIndex(iterable[, accessor]) · Source, Examples
Returns the index of the maximum value in the given iterable using natural order. If the iterable contains no comparable values, returns 1. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the maximum value.
Unlike the builtin Math.max, this method ignores undefined values; this is useful for ignoring missing data. In addition, elements are compared using natural order rather than numeric order. For example, the maximum of the strings [“20”, “3”] is “3”, while the maximum of the numbers [20, 3] is 20.
# d3.extent(iterable[, accessor]) · Source, Examples
Returns the minimum and maximum value in the given iterable using natural order. If the iterable contains no comparable values, returns [undefined, undefined]. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the extent.
# d3.mode(iterable[, accessor]) · Source, Examples
Returns the mode of the given iterable, i.e. the value which appears the most often. In case of equality, returns the first of the relevant values. If the iterable contains no comparable values, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the mode. This method ignores undefined, null and NaN values; this is useful for ignoring missing data.
# d3.sum(iterable[, accessor]) · Source, Examples
Returns the sum of the given iterable of numbers. If the iterable contains no numbers, returns 0. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the sum. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.mean(iterable[, accessor]) · Source, Examples
Returns the mean of the given iterable of numbers. If the iterable contains no numbers, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the mean. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.median(iterable[, accessor]) · Source, Examples
Returns the median of the given iterable of numbers using the R7 method. If the iterable contains no numbers, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the median. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.medianIndex(array[, accessor]) · Source
Similar to median, but returns the index of the element to the left of the median.
# d3.cumsum(iterable[, accessor]) · Source, Examples
Returns the cumulative sum of the given iterable of numbers, as a Float64Array of the same length. If the iterable contains no numbers, returns zeros. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the cumulative sum. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.quantile(iterable, p[, accessor]) · Source, Examples
Returns the pquantile of the given iterable of numbers, where p is a number in the range [0, 1]. For example, the median can be computed using p = 0.5, the first quartile at p = 0.25, and the third quartile at p = 0.75. This particular implementation uses the R7 method, which is the default for the R programming language and Excel. For example:
var a = [0, 10, 30];
d3.quantile(a, 0); // 0
d3.quantile(a, 0.5); // 10
d3.quantile(a, 1); // 30
d3.quantile(a, 0.25); // 5
d3.quantile(a, 0.75); // 20
d3.quantile(a, 0.1); // 2
An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the quantile.
# d3.quantileIndex(array, p[, accessor]) Source
Similar to quantile, but returns the index to the left of p.
# d3.quantileSorted(array, p[, accessor]) · Source, Examples
Similar to quantile, but expects the input to be a sorted array of values. In contrast with quantile, the accessor is only called on the elements needed to compute the quantile.
# d3.rank(iterable[, comparator]) · Source, Examples
# d3.rank(iterable[, accessor])
Returns an array with the rank of each value in the iterable, i.e. the zerobased index of the value when the iterable is sorted. Nullish values are sorted to the end and ranked NaN. An optional comparator or accessor function may be specified; the latter is equivalent to calling array.map(accessor) before computing the ranks. If comparator is not specified, it defaults to ascending. Ties (equivalent values) all get the same rank, defined as the first time the value is found.
d3.rank([{x: 1}, {}, {x: 2}, {x: 0}], d => d.x); // [1, NaN, 2, 0]
d3.rank(["b", "c", "b", "a"]); // [1, 3, 1, 0]
d3.rank([1, 2, 3], d3.descending); // [2, 1, 0]
# d3.variance(iterable[, accessor]) · Source, Examples
Returns an unbiased estimator of the population variance of the given iterable of numbers using Welford’s algorithm. If the iterable has fewer than two numbers, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the variance. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.deviation(iterable[, accessor]) · Source, Examples
Returns the standard deviation, defined as the square root of the biascorrected variance, of the given iterable of numbers. If the iterable has fewer than two numbers, returns undefined. An optional accessor function may be specified, which is equivalent to calling Array.from before computing the standard deviation. This method ignores undefined and NaN values; this is useful for ignoring missing data.
# d3.fsum([values][, accessor]) · Source, Examples
Returns a full precision summation of the given values.
d3.fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]); // 1
d3.sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1]); // 0.9999999999999999
Although slower, d3.fsum can replace d3.sum wherever greater precision is needed. Uses d3.Adder.
# d3.fcumsum([values][, accessor]) · Source, Examples
Returns a full precision cumulative sum of the given values.
d3.fcumsum([1, 1e14, 1]); // [1, 1.00000000000001, 1e14]
d3.cumsum([1, 1e14, 1]); // [1, 1.00000000000001, 9.992e15]
Although slower, d3.fcumsum can replace d3.cumsum when greater precision is needed. Uses d3.Adder.
# new d3.Adder()
Creates a full precision adder for IEEE 754 floating point numbers, setting its initial value to 0.
# adder.add(number)
Adds the specified number to the adder’s current value and returns the adder.
# adder.valueOf()
Returns the IEEE 754 double precision representation of the adder’s current value. Most useful as the shorthand notation +adder
.
Search
Methods for searching arrays for a specific element.
# d3.least(iterable[, comparator]) · Source, Examples
# d3.least(iterable[, accessor])
Returns the least element of the specified iterable according to the specified comparator or accessor. If the given iterable contains no comparable elements (i.e., the comparator returns NaN when comparing each element to itself), returns undefined. If comparator is not specified, it defaults to ascending. For example:
const array = [{foo: 42}, {foo: 91}];
d3.least(array, (a, b) => a.foo  b.foo); // {foo: 42}
d3.least(array, (a, b) => b.foo  a.foo); // {foo: 91}
d3.least(array, a => a.foo); // {foo: 42}
This function is similar to min, except it allows the use of a comparator rather than an accessor.
# d3.leastIndex(iterable[, comparator]) · Source, Examples
# d3.leastIndex(iterable[, accessor])
Returns the index of the least element of the specified iterable according to the specified comparator or accessor. If the given iterable contains no comparable elements (i.e., the comparator returns NaN when comparing each element to itself), returns 1. If comparator is not specified, it defaults to ascending. For example:
const array = [{foo: 42}, {foo: 91}];
d3.leastIndex(array, (a, b) => a.foo  b.foo); // 0
d3.leastIndex(array, (a, b) => b.foo  a.foo); // 1
d3.leastIndex(array, a => a.foo); // 0
This function is similar to minIndex, except it allows the use of a comparator rather than an accessor.
# d3.greatest(iterable[, comparator]) · Source, Examples
# d3.greatest(iterable[, accessor])
Returns the greatest element of the specified iterable according to the specified comparator or accessor. If the given iterable contains no comparable elements (i.e., the comparator returns NaN when comparing each element to itself), returns undefined. If comparator is not specified, it defaults to ascending. For example:
const array = [{foo: 42}, {foo: 91}];
d3.greatest(array, (a, b) => a.foo  b.foo); // {foo: 91}
d3.greatest(array, (a, b) => b.foo  a.foo); // {foo: 42}
d3.greatest(array, a => a.foo); // {foo: 91}
This function is similar to max, except it allows the use of a comparator rather than an accessor.
# d3.greatestIndex(iterable[, comparator]) · Source, Examples
# d3.greatestIndex(iterable[, accessor])
Returns the index of the greatest element of the specified iterable according to the specified comparator or accessor. If the given iterable contains no comparable elements (i.e., the comparator returns NaN when comparing each element to itself), returns 1. If comparator is not specified, it defaults to ascending. For example:
const array = [{foo: 42}, {foo: 91}];
d3.greatestIndex(array, (a, b) => a.foo  b.foo); // 1
d3.greatestIndex(array, (a, b) => b.foo  a.foo); // 0
d3.greatestIndex(array, a => a.foo); // 1
This function is similar to maxIndex, except it allows the use of a comparator rather than an accessor.
# d3.bisectLeft(array, x[, lo[, hi]]) · Source
Returns the insertion point for x in array to maintain sorted order. The arguments lo and hi may be used to specify a subset of the array which should be considered; by default the entire array is used. If x is already present in array, the insertion point will be before (to the left of) any existing entries. The return value is suitable for use as the first argument to splice assuming that array is already sorted. The returned insertion point i partitions the array into two halves so that all v < x for v in array.slice(lo, i) for the left side and all v >= x for v in array.slice(i, hi) for the right side.
# d3.bisect(array, x[, lo[, hi]]) · Source, Examples
# d3.bisectRight(array, x[, lo[, hi]])
Similar to bisectLeft, but returns an insertion point which comes after (to the right of) any existing entries of x in array. The returned insertion point i partitions the array into two halves so that all v <= x for v in array.slice(lo, i) for the left side and all v > x for v in array.slice(i, hi) for the right side.
# d3.bisectCenter(array, x[, lo[, hi]]) · Source, Examples
Returns the index of the value closest to x in the given array of numbers. The arguments lo (inclusive) and hi (exclusive) may be used to specify a subset of the array which should be considered; by default the entire array is used.
See bisector.center.
# d3.bisector(accessor) · Source
# d3.bisector(comparator)
Returns a new bisector using the specified accessor or comparator function. This method can be used to bisect arrays of objects instead of being limited to simple arrays of primitives. For example, given the following array of objects:
var data = [
{date: new Date(2011, 1, 1), value: 0.5},
{date: new Date(2011, 2, 1), value: 0.6},
{date: new Date(2011, 3, 1), value: 0.7},
{date: new Date(2011, 4, 1), value: 0.8}
];
A suitable bisect function could be constructed as:
var bisectDate = d3.bisector(function(d) { return d.date; }).right;
This is equivalent to specifying a comparator:
var bisectDate = d3.bisector(function(d, x) { return d.date  x; }).right;
And then applied as bisectDate(array, date), returning an index. Note that the comparator is always passed the search value x as the second argument. Use a comparator rather than an accessor if you want values to be sorted in an order different than natural order, such as in descending rather than ascending order.
# bisector.left(array, x[, lo[, hi]]) · Source
Equivalent to bisectLeft, but uses this bisector’s associated comparator.
# bisector.right(array, x[, lo[, hi]]) · Source
Equivalent to bisectRight, but uses this bisector’s associated comparator.
# bisector.center(array, x[, lo[, hi]]) · Source
Returns the index of the closest value to x in the given sorted array. This expects that the bisector’s associated accessor returns a quantitative value, or that the bisector’s associated comparator returns a signed distance; otherwise, this method is equivalent to bisector.left.
# d3.quickselect(array, k, left = 0, right = array.length  1, compare = ascending) · Source, Examples
See mourner/quickselect.
# d3.ascending(a, b) · Source, Examples
Returns 1 if a is less than b, or 1 if a is greater than b, or 0. This is the comparator function for natural order, and can be used in conjunction with the builtin array.sort method to arrange elements in ascending order. It is implemented as:
function ascending(a, b) {
return a == null  b == null ? NaN : a < b ? 1 : a > b ? 1 : a >= b ? 0 : NaN;
}
Note that if no comparator function is specified to the builtin sort method, the default order is lexicographic (alphabetical), not natural! This can lead to surprising behavior when sorting an array of numbers.
# d3.descending(a, b) · Source, Examples
Returns 1 if a is greater than b, or 1 if a is less than b, or 0. This is the comparator function for reverse natural order, and can be used in conjunction with the builtin array sort method to arrange elements in descending order. It is implemented as:
function descending(a, b) {
return a == null  b == null ? NaN : b < a ? 1 : b > a ? 1 : b >= a ? 0 : NaN;
}
Note that if no comparator function is specified to the builtin sort method, the default order is lexicographic (alphabetical), not natural! This can lead to surprising behavior when sorting an array of numbers.
Transformations
Methods for transforming arrays and for generating new arrays.
# d3.group(iterable, ...keys) · Source, Examples
Groups the specified iterable of values into an InternMap from key to array of value. For example, given some data:
data = [
{name: "jim", amount: "34.0", date: "11/12/2015"},
{name: "carl", amount: "120.11", date: "11/12/2015"},
{name: "stacy", amount: "12.01", date: "01/04/2016"},
{name: "stacy", amount: "34.05", date: "01/04/2016"}
]
To group the data by name:
d3.group(data, d => d.name)
This produces:
Map(3) {
"jim" => Array(1)
"carl" => Array(1)
"stacy" => Array(2)
}
If more than one key is specified, a nested InternMap is returned. For example:
d3.group(data, d => d.name, d => d.date)
This produces:
Map(3) {
"jim" => Map(1) {
"11/12/2015" => Array(1)
}
"carl" => Map(1) {
"11/12/2015" => Array(1)
}
"stacy" => Map(1) {
"01/04/2016" => Array(2)
}
}
To convert a Map to an Array, use Array.from. For example:
Array.from(d3.group(data, d => d.name))
This produces:
[
["jim", Array(1)],
["carl", Array(1)],
["stacy", Array(2)]
]
You can also simultaneously convert the [key, value] to some other representation by passing a map function to Array.from:
Array.from(d3.group(data, d => d.name), ([key, value]) => ({key, value}))
This produces:
[
{key: "jim", value: Array(1)},
{key: "carl", value: Array(1)},
{key: "stacy", value: Array(2)}
]
selection.data accepts iterables directly, meaning that you can use a Map (or Set or other iterable) to perform a data join without first needing to convert to an array.
# d3.groups(iterable, ...keys) · Source, Examples
Equivalent to group, but returns nested arrays instead of nested maps.
# d3.flatGroup(iterable, ...keys) · Source, Examples
Equivalent to group, but returns a flat array of [key0, key1, …, values] instead of nested maps.
# d3.index(iterable, ...keys) · Source, Examples
Equivalent to group but returns a unique value per compound key instead of an array, throwing if the key is not unique.
For example, given the data defined above,
d3.index(data, d => d.amount)
returns
Map(4) {
"34.0" => Object {name: "jim", amount: "34.0", date: "11/12/2015"}
"120.11" => Object {name: "carl", amount: "120.11", date: "11/12/2015"}
"12.01" => Object {name: "stacy", amount: "12.01", date: "01/04/2016"}
"34.05" => Object {name: "stacy", amount: "34.05", date: "01/04/2016"}
}
On the other hand,
d3.index(data, d => d.name)
throws an error because two objects share the same name.
# d3.indexes(iterable, ...keys) · Source, Examples
Equivalent to index, but returns nested arrays instead of nested maps.
# d3.rollup(iterable, reduce, ...keys) · Source, Examples
Groups and reduces the specified iterable of values into an InternMap from key to value. For example, given some data:
data = [
{name: "jim", amount: "34.0", date: "11/12/2015"},
{name: "carl", amount: "120.11", date: "11/12/2015"},
{name: "stacy", amount: "12.01", date: "01/04/2016"},
{name: "stacy", amount: "34.05", date: "01/04/2016"}
]
To count the number of elements by name:
d3.rollup(data, v => v.length, d => d.name)
This produces:
Map(3) {
"jim" => 1
"carl" => 1
"stacy" => 2
}
If more than one key is specified, a nested Map is returned. For example:
d3.rollup(data, v => v.length, d => d.name, d => d.date)
This produces:
Map(3) {
"jim" => Map(1) {
"11/12/2015" => 1
}
"carl" => Map(1) {
"11/12/2015" => 1
}
"stacy" => Map(1) {
"01/04/2016" => 2
}
}
To convert a Map to an Array, use Array.from. See d3.group for examples.
# d3.rollups(iterable, reduce, ...keys) · Source, Examples
Equivalent to rollup, but returns nested arrays instead of nested maps.
# d3.flatRollup(iterable, reduce, ...keys) · Source, Examples
Equivalent to rollup, but returns a flat array of [key0, key1, …, value] instead of nested maps.
# d3.groupSort(iterable, comparator, key) · Source, Examples
# d3.groupSort(iterable, accessor, key)
Groups the specified iterable of elements according to the specified key function, sorts the groups according to the specified comparator, and then returns an array of keys in sorted order. For example, if you had a table of barley yields for different varieties, sites, and years, to sort the barley varieties by ascending median yield:
d3.groupSort(barley, g => d3.median(g, d => d.yield), d => d.variety)
For descending order, negate the group value:
d3.groupSort(barley, g => d3.median(g, d => d.yield), d => d.variety)
If a comparator is passed instead of an accessor (i.e., if the second argument is a function that takes exactly two arguments), it will be asked to compare two groups a and b and should return a negative value if a should be before b, a positive value if a should be after b, or zero for a partial ordering.
# d3.count(iterable[, accessor]) · Source, Examples
Returns the number of valid number values (i.e., not null, NaN, or undefined) in the specified iterable; accepts an accessor.
For example:
d3.count([{n: "Alice", age: NaN}, {n: "Bob", age: 18}, {n: "Other"}], d => d.age) // 1
# d3.cross(...iterables[, reducer]) · Source, Examples
Returns the Cartesian product of the specified iterables. For example, if two iterables a and b are specified, for each element i in the iterable a and each element j in the iterable b, in order, invokes the specified reducer function passing the element i and element j. If a reducer is not specified, it defaults to a function which creates a twoelement array for each pair:
function pair(a, b) {
return [a, b];
}
For example:
d3.cross([1, 2], ["x", "y"]); // returns [[1, "x"], [1, "y"], [2, "x"], [2, "y"]]
d3.cross([1, 2], ["x", "y"], (a, b) => a + b); // returns ["1x", "1y", "2x", "2y"]
# d3.merge(iterables) · Source, Examples
Merges the specified iterable of iterables into a single array. This method is similar to the builtin array concat method; the only difference is that it is more convenient when you have an array of arrays.
d3.merge([[1], [2, 3]]); // returns [1, 2, 3]
# d3.pairs(iterable[, reducer]) · Source, Examples
For each adjacent pair of elements in the specified iterable, in order, invokes the specified reducer function passing the element i and element i  1. If a reducer is not specified, it defaults to a function which creates a twoelement array for each pair:
function pair(a, b) {
return [a, b];
}
For example:
d3.pairs([1, 2, 3, 4]); // returns [[1, 2], [2, 3], [3, 4]]
d3.pairs([1, 2, 3, 4], (a, b) => b  a); // returns [1, 1, 1];
If the specified iterable has fewer than two elements, returns the empty array.
# d3.permute(source, keys) · Source, Examples
Returns a permutation of the specified source object (or array) using the specified iterable of keys. The returned array contains the corresponding property of the source object for each key in keys, in order. For example:
permute(["a", "b", "c"], [1, 2, 0]); // returns ["b", "c", "a"]
It is acceptable to have more keys than source elements, and for keys to be duplicated or omitted.
This method can also be used to extract the values from an object into an array with a stable order. Extracting keyed values in order can be useful for generating data arrays in nested selections. For example:
let object = {yield: 27, variety: "Manchuria", year: 1931, site: "University Farm"};
let fields = ["site", "variety", "yield"];
d3.permute(object, fields); // returns ["University Farm", "Manchuria", 27]
# d3.shuffle(array[, start[, stop]]) · Source, Examples
Randomizes the order of the specified array inplace using the Fisher–Yates shuffle and returns the array. If start is specified, it is the starting index (inclusive) of the array to shuffle; if start is not specified, it defaults to zero. If stop is specified, it is the ending index (exclusive) of the array to shuffle; if stop is not specified, it defaults to array.length. For example, to shuffle the first ten elements of the array: shuffle(array, 0, 10).
# d3.shuffler(random) · Source
Returns a shuffle function given the specified random source. For example, using d3.randomLcg:
const random = d3.randomLcg(0.9051667019185816);
const shuffle = d3.shuffler(random);
shuffle([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]); // returns [7, 4, 5, 3, 9, 0, 6, 1, 2, 8]
# d3.ticks(start, stop, count) · Source, Examples
Returns an array of approximately count + 1 uniformlyspaced, nicelyrounded values between start and stop (inclusive). Each value is a power of ten multiplied by 1, 2 or 5. See also d3.tickIncrement, d3.tickStep and linear.ticks.
Ticks are inclusive in the sense that they may include the specified start and stop values if (and only if) they are exact, nicelyrounded values consistent with the inferred step. More formally, each returned tick t satisfies start ≤ t and t ≤ stop.
# d3.tickIncrement(start, stop, count) · Source, Examples
Like d3.tickStep, except requires that start is always less than or equal to stop, and if the tick step for the given start, stop and count would be less than one, returns the negative inverse tick step instead. This method is always guaranteed to return an integer, and is used by d3.ticks to guarantee that the returned tick values are represented as precisely as possible in IEEE 754 floating point.
# d3.tickStep(start, stop, count) · Source, Examples
Returns the difference between adjacent tick values if the same arguments were passed to d3.ticks: a nicelyrounded value that is a power of ten multiplied by 1, 2 or 5. Note that due to the limited precision of IEEE 754 floating point, the returned value may not be exact decimals; use d3format to format numbers for human consumption.
# d3.nice(start, stop, count) · Source
Returns a new interval [niceStart, niceStop] covering the given interval [start, stop] and where niceStart and niceStop are guaranteed to align with the corresponding tick step. Like d3.tickIncrement, this requires that start is less than or equal to stop.
# d3.range([start, ]stop[, step]) · Source, Examples
Returns an array containing an arithmetic progression, similar to the Python builtin range. This method is often used to iterate over a sequence of uniformlyspaced numeric values, such as the indexes of an array or the ticks of a linear scale. (See also d3.ticks for nicelyrounded values.)
If step is omitted, it defaults to 1. If start is omitted, it defaults to 0. The stop value is exclusive; it is not included in the result. If step is positive, the last element is the largest start + i * step less than stop; if step is negative, the last element is the smallest start + i * step greater than stop. If the returned array would contain an infinite number of values, an empty range is returned.
The arguments are not required to be integers; however, the results are more predictable if they are. The values in the returned array are defined as start + i * step, where i is an integer from zero to one minus the total number of elements in the returned array. For example:
d3.range(0, 1, 0.2) // [0, 0.2, 0.4, 0.6000000000000001, 0.8]
This unexpected behavior is due to IEEE 754 doubleprecision floating point, which defines 0.2 * 3 = 0.6000000000000001. Use d3format to format numbers for human consumption with appropriate rounding; see also linear.tickFormat in d3scale.
Likewise, if the returned array should have a specific length, consider using array.map on an integer range. For example:
d3.range(0, 1, 1 / 49); // BAD: returns 50 elements!
d3.range(49).map(function(d) { return d / 49; }); // GOOD: returns 49 elements.
# d3.transpose(matrix) · Source, Examples
Uses the zip operator as a twodimensional matrix transpose.
# d3.zip(arrays…) · Source, Examples
Returns an array of arrays, where the ith array contains the ith element from each of the argument arrays. The returned array is truncated in length to the shortest array in arrays. If arrays contains only a single array, the returned array contains oneelement arrays. With no arguments, the returned array is empty.
d3.zip([1, 2], [3, 4]); // returns [[1, 3], [2, 4]]
Blur
# d3.blur(data, radius) · Source, Examples
Blurs an array of data inplace by applying three iterations of a moving average transform, for a fast approximation of a gaussian kernel of the given radius, a nonnegative number, and returns the array.
const randomWalk = d3.cumsum({length: 1000}, () => Math.random()  0.5);
blur(randomWalk, 5);
Copy the data if you don’t want to smooth it inplace:
const smoothed = blur(randomWalk.slice(), 5);
# d3.blur2({data, width[, height]}, rx[, ry]) · Source, Examples
Blurs a matrix of the given width and height inplace, by applying an horizontal blur of radius rx and a vertical blur or radius ry (which defaults to rx). The matrix data is stored in a flat array, used to determine the height if it is not specified. Returns the blurred {data, width, height}.
data = [
1, 0, 0,
0, 0, 0,
0, 0, 1
];
blur2({data, width: 3}, 1);
# d3.blurImage(imageData, rx[, ry]) · Source, Examples
Blurs an ImageData structure inplace, blurring each of the RGBA layers independently by applying an horizontal blur of radius rx and a vertical blur or radius ry (which defaults to rx). Returns the blurred ImageData.
const imData = context.getImageData(0, 0, width, height);
blurImage(imData, 5);
Iterables
These are equivalent to builtin array methods, but work with any iterable including Map, Set, and Generator.
# d3.every(iterable, test) · Source
Returns true if the given test function returns true for every value in the given iterable. This method returns as soon as test returns a nontruthy value or all values are iterated over. Equivalent to array.every:
d3.every(new Set([1, 3, 5, 7]), x => x & 1) // true
# d3.some(iterable, test) · Source
Returns true if the given test function returns true for any value in the given iterable. This method returns as soon as test returns a truthy value or all values are iterated over. Equivalent to array.some:
d3.some(new Set([0, 2, 3, 4]), x => x & 1) // true
# d3.filter(iterable, test) · Source
Returns a new array containing the values from iterable, in order, for which the given test function returns true. Equivalent to array.filter:
d3.filter(new Set([0, 2, 3, 4]), x => x & 1) // [3]
# d3.map(iterable, mapper) · Source
Returns a new array containing the mapped values from iterable, in order, as defined by given mapper function. Equivalent to array.map and Array.from:
d3.map(new Set([0, 2, 3, 4]), x => x & 1) // [0, 0, 1, 0]
# d3.reduce(iterable, reducer[, initialValue]) · Source
Returns the reduced value defined by given reducer function, which is repeatedly invoked for each value in iterable, being passed the current reduced value and the next value. Equivalent to array.reduce:
d3.reduce(new Set([0, 2, 3, 4]), (p, v) => p + v, 0) // 9
# d3.reverse(iterable) · Source
Returns an array containing the values in the given iterable in reverse order. Equivalent to array.reverse, except that it does not mutate the given iterable:
d3.reverse(new Set([0, 2, 3, 1])) // [1, 3, 2, 0]
# d3.sort(iterable, comparator = d3.ascending) · Source
# d3.sort(iterable, ...accessors)
Returns an array containing the values in the given iterable in the sorted order defined by the given comparator or accessor function. If comparator is not specified, it defaults to d3.ascending. Equivalent to array.sort, except that it does not mutate the given iterable, and the comparator defaults to natural order instead of lexicographic order:
d3.sort(new Set([0, 2, 3, 1])) // [0, 1, 2, 3]
If an accessor (a function that does not take exactly two arguments) is specified,
d3.sort(data, d => d.value)
it is equivalent to a comparator using natural order:
d3.sort(data, (a, b) => d3.ascending(a.value, b.value))
The accessor is only invoked once per element, and thus the returned sorted order is consistent even if the accessor is nondeterministic.
Multiple accessors may be specified to break ties:
d3.sort(points, ({x}) => x, ({y}) => y)
This is equivalent to:
d3.sort(data, (a, b) => d3.ascending(a.x, b.x)  d3.ascending(a.y, b.y))
Sets
This methods implement basic set operations for any iterable.
# d3.difference(iterable, ...others) · Source
Returns a new InternSet containing every value in iterable that is not in any of the others iterables.
d3.difference([0, 1, 2, 0], [1]) // Set {0, 2}
# d3.union(...iterables) · Source
Returns a new InternSet containing every (distinct) value that appears in any of the given iterables. The order of values in the returned set is based on their first occurrence in the given iterables.
d3.union([0, 2, 1, 0], [1, 3]) // Set {0, 2, 1, 3}
# d3.intersection(...iterables) · Source
Returns a new InternSet containing every (distinct) value that appears in all of the given iterables. The order of values in the returned set is based on their first occurrence in the given iterables.
d3.intersection([0, 2, 1, 0], [1, 3]) // Set {1}
Returns true if a is a superset of b: if every value in the given iterable b is also in the given iterable a.
d3.superset([0, 2, 1, 3, 0], [1, 3]) // true
Returns true if a is a subset of b: if every value in the given iterable a is also in the given iterable b.
d3.subset([1, 3], [0, 2, 1, 3, 0]) // true
Returns true if a and b are disjoint: if a and b contain no shared value.
d3.disjoint([1, 3], [2, 4]) // true
Bins
Binning groups discrete samples into a smaller number of consecutive, nonoverlapping intervals. They are often used to visualize the distribution of numerical data as histograms.
Constructs a new bin generator with the default settings.
# bin(data) · Source, Examples
Bins the given iterable of data samples. Returns an array of bins, where each bin is an array containing the associated elements from the input data. Thus, the length
of the bin is the number of elements in that bin. Each bin has two additional attributes:

x0
 the lower bound of the bin (inclusive). 
x1
 the upper bound of the bin (exclusive, except for the last bin).
Any null or noncomparable values in the given data, or those outside the domain, are ignored.
# bin.value([value]) · Source, Examples
If value is specified, sets the value accessor to the specified function or constant and returns this bin generator. If value is not specified, returns the current value accessor, which defaults to the identity function.
When bins are generated, the value accessor will be invoked for each element in the input data array, being passed the element d
, the index i
, and the array data
as three arguments. The default value accessor assumes that the input data are orderable (comparable), such as numbers or dates. If your data are not, then you should specify an accessor that returns the corresponding orderable value for a given datum.
This is similar to mapping your data to values before invoking the bin generator, but has the benefit that the input data remains associated with the returned bins, thereby making it easier to access other fields of the data.
# bin.domain([domain]) · Source, Examples
If domain is specified, sets the domain accessor to the specified function or array and returns this bin generator. If domain is not specified, returns the current domain accessor, which defaults to extent. The bin domain is defined as an array [min, max], where min is the minimum observable value and max is the maximum observable value; both values are inclusive. Any value outside of this domain will be ignored when the bins are generated.
For example, if you are using the bin generator in conjunction with a linear scale x
, you might say:
var bin = d3.bin()
.domain(x.domain())
.thresholds(x.ticks(20));
You can then compute the bins from an array of numbers like so:
var bins = bin(numbers);
If the default extent domain is used and the thresholds are specified as a count (rather than explicit values), then the computed domain will be niced such that all bins are uniform width.
Note that the domain accessor is invoked on the materialized array of values, not on the input data array.
# bin.thresholds([count]) · Source, Examples
# bin.thresholds([thresholds])
If thresholds is specified, sets the threshold generator to the specified function or array and returns this bin generator. If thresholds is not specified, returns the current threshold generator, which by default implements Sturges’ formula. (Thus by default, the values to be binned must be numbers!) Thresholds are defined as an array of values [x0, x1, …]. Any value less than x0 will be placed in the first bin; any value greater than or equal to x0 but less than x1 will be placed in the second bin; and so on. Thus, the generated bins will have thresholds.length + 1 bins. See bin thresholds for more information.
Any threshold values outside the domain are ignored. The first bin.x0 is always equal to the minimum domain value, and the last bin.x1 is always equal to the maximum domain value.
If a count is specified instead of an array of thresholds, then the domain will be uniformly divided into approximately count bins; see ticks.
Bin Thresholds
These functions are typically not used directly; instead, pass them to bin.thresholds.
# d3.thresholdFreedmanDiaconis(values, min, max) · Source, Examples
Returns the number of bins according to the Freedman–Diaconis rule; the input values must be numbers.
# d3.thresholdScott(values, min, max) · Source, Examples
Returns the number of bins according to Scott’s normal reference rule; the input values must be numbers.
# d3.thresholdSturges(values) · Source, Examples
Returns the number of bins according to Sturges’ formula; the input values must be numbers.
You may also implement your own threshold generator taking three arguments: the array of input values derived from the data, and the observable domain represented as min and max. The generator may then return either the array of numeric thresholds or the count of bins; in the latter case the domain is divided uniformly into approximately count bins; see ticks.
For instance, when binning date values, you might want to use the ticks from a time scale (Example).
Interning
# new d3.InternMap([iterable][, key]) · Source, Examples
# new d3.InternSet([iterable][, key]) · Source, Examples
The InternMap and InternSet classes extend the native JavaScript Map and Set classes, respectively, allowing Dates and other nonprimitive keys by bypassing the SameValueZero algorithm when determining key equality. d3.group, d3.rollup and d3.index use an InternMap rather than a native Map. These two classes are exported for convenience.