d3-array

d3-array

Data in JavaScript is often represented by an array, and so one tends to manipulate arrays when visualizing or analyzing data. Some common forms of manipulation include taking a contiguous slice (subset) of an array, filtering an array using a predicate function, and mapping an array to a parallel set of values using a transform function. Before looking at the set of utilities that this module provides, familiarize yourself with the powerful array methods built-in 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 left-to-right).
• array.reduceRight - Apply a function to reduce the array to a single value (from right-to-left).

Installing

If you use NPM, npm install d3-array. Otherwise, download the latest release. The released bundle supports AMD, CommonJS, and vanilla environments. Create a custom build using Rollup or your preferred bundler. You can also load directly from d3js.org:

<script src="https://d3js.org/d3-array.v0.6.min.js"></script>

In a vanilla environment, a d3_array global is exported. Try d3-array in your browser.

API Reference

• Statistics
• Transformations
• Search
• Objects
• Maps
• Sets
• Nests
• Histograms
• Histogram Thresholds

Statistics

Methods for computing basic summary statistics.

# d3_array.min(array[, accessor])

Returns the minimum value in the given array using natural order. If the array is empty, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the minimum value.

Unlike the built-in 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 ["20", "3"] is "20", while the minimum of [20, 3] is 3.

See also scan and extent.

# d3_array.max(array[, accessor])

Returns the maximum value in the given array using natural order. If the array is empty, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the maximum value.

Unlike the built-in 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 ["20", "3"] is "3", while the maximum of [20, 3] is 20.

See also scan and extent.

# d3_array.extent(array[, accessor])

Returns the minimum and maximum value in the given array using natural order. If the array is empty, returns [undefined, undefined]. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the extent.

# d3_array.sum(array[, accessor])

Returns the sum of the given array. If the array is empty, returns 0. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the sum. This method ignores undefined and NaN values; this is useful for ignoring missing data.

# d3_array.mean(array[, accessor])

Returns the mean of the given array. If the array is empty, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the mean. This method ignores undefined and NaN values; this is useful for ignoring missing data.

# d3_array.median(array[, accessor])

Returns the median of the given array using the R-7 method. If the array is empty, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the median. This method ignores undefined and NaN values; this is useful for ignoring missing data.

# d3_array.quantile(array, p[, accessor])

Returns the p-quantile of the given sorted array of elements, 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 R-7 method, which is the default for the R programming language and Excel. For example:

var a = [0, 10, 30];
d3_array.quantile(a, 0); // 0
d3_array.quantile(a, 0.5); // 10
d3_array.quantile(a, 1); // 30
d3_array.quantile(a, 0.25); // 5
d3_array.quantile(a, 0.75); // 20
d3_array.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_array.variance(array[, accessor])

Returns an unbiased estimator of the population variance of the given array of numbers. If the array has fewer than two values, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the variance. This method ignores undefined and NaN values; this is useful for ignoring missing data.

# d3_array.deviation(array[, accessor])

Returns the standard deviation, defined as the square root of the bias-corrected variance, of the given array of numbers. If the array has fewer than two values, returns undefined. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before computing the standard deviation. This method ignores undefined and NaN values; this is useful for ignoring missing data.

Transformations

Methods for transforming arrays and for generating new arrays.

# d3_array.merge(arrays)

Merges the specified arrays into a single array. This method is similar to the built-in array concat method; the only difference is that it is more convenient when you have an array of arrays.

d3_array.merge([[1], [2, 3]]); // returns [1, 2, 3]

# d3_array.pairs(array)

For each adjacent pair of elements in the specified array, returns a new array of tuples of element i and element i - 1. For example:

d3_array.pairs([1, 2, 3, 4]); // returns [[1, 2], [2, 3], [3, 4]]

If the specified array has fewer than two elements, returns the empty array.

# d3_array.permute(array, indexes)

Returns a permutation of the specified array using the specified array of indexes. The returned array contains the corresponding element in array for each index in indexes, in order. For example, permute(["a", "b", "c"], [1, 2, 0]) returns ["b", "c", "a"]. It is acceptable for the array of indexes to be a different length from the array of elements, and for indexes 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:

var object = {yield: 27, variety: "Manchuria", year: 1931, site: "University Farm"},
    fields = ["site", "variety", "yield"];

d3_array.permute(object, fields); // returns ["University Farm", "Manchuria", 27]

# d3_array.shuffle(array[, lo[, hi]])

Randomizes the order of the specified array using the Fisher–Yates shuffle.

# d3_array.ticks(start, stop, count)

Returns an array of approximately count + 1 uniformly-spaced, nicely-rounded values between start and stop (inclusive). Each value is a power of ten multiplied by 1, 2 or 5. See also tickStep and linear.ticks. Note that due to the limited precision of IEEE 754 floating point, the returned values may not be exact decimals; use d3-format to format numbers for human consumption.

# d3_array.tickStep(start, stop, count)

Returns the difference between adjacent tick values if the same arguments were passed to ticks: a nicely-rounded 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 d3-format to format numbers for human consumption.

# d3_array.range([start, ]stop[, step])

Returns an array containing an arithmetic progression, similar to the Python built-in range. This method is often used to iterate over a sequence of uniformly-spaced numeric values, such as the indexes of an array or the ticks of a linear scale. (See also ticks for nicely-rounded 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_array.range(0, 1, 0.2) // [0, 0.2, 0.4, 0.6000000000000001, 0.8]

This unexpected behavior is due to IEEE 754 double-precision floating point, which defines 0.2 * 3 = 0.6000000000000001. Use d3-format to format numbers for human consumption with appropriate rounding; see also linear.tickFormat in d3-scale.

Likewise, if the returned array should have a specific length, consider using array.map on an integer range. For example:

d3_array.range(0, 1, 1 / 49); // BAD: returns 50 elements!
d3_array.range(49).map(function(d) { return d / 49; }); // GOOD: returns 49 elements.

# d3_array.transpose(matrix)

Uses the zip operator as a two-dimensional matrix transpose.

# d3_array.zip(arrays…)

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 one-element arrays. With no arguments, the returned array is empty.

d3_array.zip([1, 2], [3, 4]); // returns [[1, 3], [2, 4]]

Search

Methods for searching arrays for a specific element.

# d3_array.scan(array[, comparator])

Performs a linear scan of the specified array, returning the index of the least element according to the specified comparator. If the given array 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:

var array = [{foo: 42}, {foo: 91}];
d3_array.scan(array, function(a, b) { return a.foo - b.foo; }); // 0
d3_array.scan(array, function(a, b) { return b.foo - a.foo; }); // 1

This function is similar to min, except it allows the use of a comparator rather than an accessor and it returns the index instead of the accessed value. See also bisect.

# d3_array.bisectLeft(array, x[, lo[, hi]])

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_array.bisect(array, x[, lo[, hi]])
# d3_array.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_array.bisector(accessor)
# d3_array.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_array.bisector(function(d) { return d.date; }).right;

This is equivalent to specifying a comparator:

var bisectDate = d3_array.bisector(function(d, x) { return d.date - x; }).right;

And then applied as bisect(data, new Date(2011, 1, 2)), 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]])

Equivalent to bisectLeft, but uses this bisector’s associated comparator.

# bisector.right(array, x[, lo[, hi]])

Equivalent to bisectRight, but uses this bisector’s associated comparator.

# d3_array.ascending(a, b)

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 built-in array.sort method to arrange elements in ascending order. It is implemented as:

function ascending(a, b) {
  return a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN;
}

Note that if no comparator function is specified to the built-in sort method, the default order is lexicographic (alphabetical), not natural! This can lead to surprising behavior when sorting an array of numbers.

# d3_array.descending(a, b)

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 built-in array sort method to arrange elements in descending order. It is implemented as:

function descending(a, b) {
  return b < a ? -1 : b > a ? 1 : b >= a ? 0 : NaN;
}

Note that if no comparator function is specified to the built-in sort method, the default order is lexicographic (alphabetical), not natural! This can lead to surprising behavior when sorting an array of numbers.

Objects

A common data type in JavaScript is the associative array, or more simply the object, which has a set of named properties. The standard mechanism for iterating over the keys (or property names) in an associative array is the for…in loop. However, note that the iteration order is undefined. D3 provides several methods for converting associative arrays to standard arrays with numeric indexes.

A word of caution: it is tempting to use plain objects as maps, but this causes unexpected behavior when built-in property names are used as keys, such as object["__proto__"] = 42 and "hasOwnProperty" in object. If you cannot guarantee that map keys and set values will be safe, use maps and sets (or their ES6 equivalents) instead of plain objects.

# d3_array.keys(object)

Returns an array containing the property names of the specified object (an associative array). The order of the returned array is undefined.

# d3_array.values(object)

Returns an array containing the property values of the specified object (an associative array). The order of the returned array is undefined.

# d3_array.entries(object)

Returns an array containing the property keys and values of the specified object (an associative array). Each entry is an object with a key and value attribute, such as {key: "foo", value: 42}. The order of the returned array is undefined.

d3_array.entries({foo: 42, bar: true}); // [{key: "foo", value: 42}, {key: "bar", value: true}]

Maps

Like ES6 Maps, but with a few differences:

• Keys are coerced to strings.
• map.each, not map.forEach. (Also, no thisArg.)
• map.remove, not map.delete.
• map.entries returns an array of {key, value} objects, not an iterator of [key, value].
• map.size is a method, not a property; also, there’s map.empty.

# d3_array.map([object[, key]])

Constructs a new map. If object is specified, copies all enumerable properties from the specified object into this map. The specified object may also be an array or another map. An optional key function may be specified to compute the key for each value in the array. For example:

var map = d3_array.map([{name: "foo"}, {name: "bar"}], function(d) { return d.name; });
map.get("foo"); // {"name": "foo"}
map.get("bar"); // {"name": "bar"}
map.get("baz"); // undefined

See also nests.

# map.has(key)

Returns true if and only if this map has an entry for the specified key string. Note: the value may be null or undefined.

# map.get(key)

Returns the value for the specified key string. If the map does not have an entry for the specified key, returns undefined.

# map.set(key, value)

Sets the value for the specified key string. If the map previously had an entry for the same key string, the old entry is replaced with the new value. Returns the map, allowing chaining. For example:

var map = d3_array.map()
    .set("foo", 1)
    .set("bar", 2)
    .set("baz", 3);

map.get("foo"); // 1

# map.remove(key)

If the map has an entry for the specified key string, removes the entry and returns true. Otherwise, this method does nothing and returns false.

# map.clear()

Removes all entries from this map.

# map.keys()

Returns an array of string keys for every entry in this map. The order of the returned keys is arbitrary.

# map.values()

Returns an array of values for every entry in this map. The order of the returned values is arbitrary.

# map.entries()

Returns an array of key-value objects for each entry in this map. The order of the returned entries is arbitrary. Each entry’s key is a string, but the value has arbitrary type.

# map.each(function)

Calls the specified function for each entry in this map, passing the entry’s value and key as arguments, followed by the map itself. Returns undefined. The iteration order is arbitrary.

# map.empty()

Returns true if and only if this map has zero entries.

# map.size()

Returns the number of entries in this map.

Sets

Like ES6 Sets, but with a few differences:

• Values are coerced to strings.
• set.each, not set.forEach. (Also, no thisArg.)
• set.remove, not set.delete.
• set.size is a method, not a property; also, there’s set.empty.

# d3_array.set([array[, accessor]])

Constructs a new set. If array is specified, adds the given array of string values to the returned set. The specified array may also be another set. An optional accessor function may be specified, which is equivalent to calling array.map(accessor) before constructing the set.

# set.has(value)

Returns true if and only if this set has an entry for the specified value string.

# set.add(value)

Adds the specified value string to this set. Returns the set, allowing chaining. For example:

var set = d3_array.set()
    .add("foo")
    .add("bar")
    .add("baz");

set.has("foo"); // true

# set.remove(value)

If the set contains the specified value string, removes it and returns true. Otherwise, this method does nothing and returns false.

# set.clear()

Removes all values from this set.

# set.values()

Returns an array of the string values in this set. The order of the returned values is arbitrary. Can be used as a convenient way of computing the unique values for a set of strings. For example:

d3_array.set(["foo", "bar", "foo", "baz"]).values(); // "foo", "bar", "baz"

# set.each(function)

Calls the specified function for each value in this set, passing the value as the first two arguments (for symmetry with map.each), followed by the set itself. Returns undefined. The iteration order is arbitrary.

# set.empty()

Returns true if and only if this set has zero values.

# set.size()

Returns the number of values in this set.

Nests

Nesting allows elements in an array to be grouped into a hierarchical tree structure; think of it like the GROUP BY operator in SQL, except you can have multiple levels of grouping, and the resulting output is a tree rather than a flat table. The levels in the tree are specified by key functions. The leaf nodes of the tree can be sorted by value, while the internal nodes can be sorted by key. An optional rollup function will collapse the elements in each leaf node using a summary function. The nest operator (the object returned by nest) is reusable, and does not retain any references to the data that is nested.

For example, consider the following tabular data structure of Barley yields, from various sites in Minnesota during 1931-2:

var yields = [
  {yield: 27.00, variety: "Manchuria", year: 1931, site: "University Farm"},
  {yield: 48.87, variety: "Manchuria", year: 1931, site: "Waseca"},
  {yield: 27.43, variety: "Manchuria", year: 1931, site: "Morris"},
  ...
];

To facilitate visualization, it may be useful to nest the elements first by year, and then by variety, as follows:

var entries = d3_array.nest()
    .key(function(d) { return d.year; })
    .key(function(d) { return d.variety; })
    .entries(yields);

This returns a nested array. Each element of the outer array is a key-values pair, listing the values for each distinct key:

[{key: "1931", values: [
   {key: "Manchuria", values: [
     {yield: 27.00, variety: "Manchuria", year: 1931, site: "University Farm"},
     {yield: 48.87, variety: "Manchuria", year: 1931, site: "Waseca"},
     {yield: 27.43, variety: "Manchuria", year: 1931, site: "Morris"}, ...]},
   {key: "Glabron", values: [
     {yield: 43.07, variety: "Glabron", year: 1931, site: "University Farm"},
     {yield: 55.20, variety: "Glabron", year: 1931, site: "Waseca"}, ...]}, ...]},
 {key: "1932", values: ...}]

The nested form allows easy iteration and generation of hierarchical structures in SVG or HTML.

For a longer introduction to nesting, see:

• Phoebe Bright’s D3 Nest Tutorial and examples
• Shan Carter’s Mister Nester

# d3_array.nest()

Creates a new nest operator. The set of keys is initially empty. If the map or entries operator is invoked before any key functions are registered, the nest operator simply returns the input array.

# nest.key(function)

Registers a new key function. The key function will be invoked for each element in the input array, and must return a string identifier that is used to assign the element to its group. Most often, the function is implemented as a simple accessor, such as the year and variety accessors in the example above. The function is not passed the input array index. Each time a key is registered, it is pushed onto the end of an internal keys array, and the resulting map or entries will have an additional hierarchy level. There is not currently a facility to remove or query the registered keys. The most-recently registered key is referred to as the current key in subsequent methods.

# nest.sortKeys(comparator)

Sorts key values for the current key using the specified comparator, such as descending. If no comparator is specified for the current key, the order in which keys will be returned is undefined. Note that this only affects the result of the entries operator; the order of keys returned by the map operator is always undefined, regardless of comparator.

var entries = d3_array.nest()
    .key(function(d) { return d.year; })
    .sortKeys(ascending)
    .entries(yields);

# nest.sortValues(comparator)

Sorts leaf elements using the specified comparator, such as descending. This is roughly equivalent to sorting the input array before applying the nest operator; however it is typically more efficient as the size of each group is smaller. If no value comparator is specified, elements will be returned in the order they appeared in the input array. This applies to both the map and entries operators.

# nest.rollup(function)

Specifies a rollup function to be applied on each group of leaf elements. The return value of the rollup function will replace the array of leaf values in either the associative array returned by the map operator, or the values attribute of each entry returned by the entries operator.

# nest.map(array)

Applies the nest operator to the specified array, returning a nested map. Each entry in the returned map corresponds to a distinct key value returned by the first key function. The entry value depends on the number of registered key functions: if there is an additional key, the value is another map; otherwise, the value is the array of elements filtered from the input array that have the given key value.

# nest.object(array)

Applies the nest operator to the specified array, returning a nested object. Each entry in the returned associative array corresponds to a distinct key value returned by the first key function. The entry value depends on the number of registered key functions: if there is an additional key, the value is another associative array; otherwise, the value is the array of elements filtered from the input array that have the given key value.

Note: this method is unsafe if any of the keys conflict with built-in JavaScript properties, such as __proto__. If you cannot guarantee that the keys will be safe, you should use nest.map instead.

# nest.entries(array)

Applies the nest operator to the specified array, returning an array of key-values entries. Conceptually, this is similar to applying entries to the associative array returned by map, but it applies to every level of the hierarchy rather than just the first (outermost) level. Each entry in the returned array corresponds to a distinct key value returned by the first key function. The entry value depends on the number of registered key functions: if there is an additional key, the value is another nested array of entries; otherwise, the value is the array of elements filtered from the input array that have the given key value.

Histograms

Histograms bin many discrete samples into a smaller number of consecutive, non-overlapping intervals. They are often used to visualize the distribution of numerical data.

# d3_array.histogram()

Constructs a new histogram generator with the default settings.

# histogram(data)

Computes the histogram for the given array 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).

# histogram.value([value])

If value is specified, sets the value accessor to the specified function or number and returns this histogram generator. If value is not specified, returns the current value accessor, which defaults to the identity function.

When a histogram is 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 numbers, or that they are coercible to numbers using valueOf. If your data are not simply numbers, then you should specify an accessor that returns the corresponding numeric value for a given datum.

This is similar to mapping your data to values before invoking the histogram 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.

# histogram.domain([domain])

If domain is specified, sets the domain accessor to the specified function or array and returns this histogram generator. If domain is not specified, returns the current domain accessor, which defaults to extent. The histogram 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 histogram is generated.

For example, if you are using the the histogram in conjunction with a linear scale x, you might say:

var histogram = d3_array.histogram()
    .domain(x.domain())
    .thresholds(x.ticks(20));

You can then compute the bins from an array of numbers like so:

var bins = histogram(numbers);

Note that the domain accessor is invoked on the materialized array of values, not on the input data array.

# histogram.thresholds([count])
# histogram.thresholds([thresholds])

If thresholds is specified, sets the threshold generator to the specified function or array and returns this histogram generator. If thresholds is not specified, returns the current threshold generator, which by default implements Sturges’ formula. Thresholds are defined as an array of numbers [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 histogram will have thresholds.length + 1 bins. See histogram thresholds for more information.

If a count is specified instead of an array of thresholds, then the domain will be uniformly divided into approximately count bins; see ticks.

Histogram Thresholds

These functions are typically not used directly; instead, pass them to histogram.thresholds. 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.

# d3_array.thresholdFreedmanDiaconis(values, min, max)

Returns the number of bins according to the Freedman–Diaconis rule.

# d3_array.thresholdScott(values, min, max)

Returns the number of bins according to Scott’s normal reference rule.

# d3_array.thresholdSturges(values)

Returns the number of bins according to Sturges’ formula.

Changes from D3 3.x:

• Array accessor functions now take the array as the third argument, rather than setting it as the this context.
• The range method now returns the empty array for infinite ranges, rather than throwing an error.
• The nest.map method now always returns a map; use nest.object to return a plain object instead.