# Stack transform ​

The stack transform comes in two orientations: stackY replaces y with y1 and y2 to form vertical↑ stacks grouped on x, while stackX replaces x with x1 and x2 for horizontal→ stacks grouped on y. In effect, stacking transforms a length into lower and upper positions: the upper position of each element equals the lower position of the next element in the stack. Stacking makes it easier to perceive a total while still showing its parts.

For example, below is a stacked area chart of deaths in the Crimean War — predominantly from disease — using Florence Nightingale’s data.

Fork
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``````Plot.plot({
y: {grid: true},
color: {legend: true},
marks: [
Plot.areaY(crimea, {x: "date", y: "deaths", fill: "cause"}),
Plot.ruleY([0])
]
})``````

TIP

The areaY mark applies the stackY transform implicitly if you do not specify either y1 or y2. The same applies to barY and rectY. You can invoke the stack transform explicitly as `Plot.stackY({x: "date", y: "deaths", fill: "cause"})` to produce an identical chart.

The stack transform works with any mark that consumes y1 & y2 or x1 & x2, so you can stack rects, too.

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``````Plot.plot({
y: {grid: true},
marks: [
Plot.rectY(crimea, {x: "date", y: "deaths", interval: "month", fill: "cause"}),
Plot.ruleY([0])
]
})``````

INFO

The interval mark option specifies the periodicity of the data; without it, Plot wouldn’t know how wide to make the rects.

And you can stack bars if you’d prefer to treat x as ordinal.

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``````Plot.plot({
x: {
interval: "month",
tickFormat: (d) => d.toLocaleString("en", {month: "narrow"}),
label: null
},
y: {grid: true},
marks: [
Plot.barY(crimea, {x: "date", y: "deaths", fill: "cause"}),
Plot.ruleY([0])
]
})``````

INFO

The interval scale option specifies the periodicity of the data; without it, any gaps in the data would not be visible since barY implies that x is ordinal.

The stackY transform also outputs y representing the midpoint of y1 and y2, and likewise stackX outputs x representing the midpoint of x1 and x2. This is useful for point-based marks such as text and dot. Below, a single stacked horizontal bar shows the relative frequency of English letters; this form is a compact alternative to a pie 🥧 or donut 🍩 chart.

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``````Plot.plot({
x: {percent: true},
marks: [
Plot.barX(alphabet, Plot.stackX({x: "frequency", fillOpacity: 0.3, inset: 0.5})),
Plot.textX(alphabet, Plot.stackX({x: "frequency", text: "letter", inset: 0.5})),
Plot.ruleX([0, 1])
]
})``````

The order option controls the order in which the layers are stacked. It defaults to null, meaning to respect the input order of the data. The appearance order excels when each series has a prominent peak, as in the chart below of recording industry revenue. Compact disc sales started declining well before the rise of downloads and streaming, suggesting that the industry was slow to provide a convenient digital product and hence lost revenue to piracy.

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``````Plot.plot({
y: {
grid: true,
transform: (d) => d / 1000 // convert millions to billions
},
color: {legend: true},
marks: [
Plot.areaY(riaa, {x: "year", y: "revenue", z: "format", fill: "group", order}),
Plot.ruleY([0])
]
})``````

INFO

In this data, the group field is a supercategory of the format field, which is useful to avoid overwhelming the color encoding with too many categories. For example, the Vinyl group includes both the LP/EP and Vinyl Single formats.

The reverse option reverses the order of layers. In conjunction with the appearance order, now layers enter from the bottom rather than the top.

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js
``````Plot.plot({
y: {
grid: true,
transform: (d) => d / 1000 // convert millions to billions
},
color: {legend: true},
marks: [
Plot.areaY(riaa, Plot.stackY({order: "appearance", reverse}, {x: "year", y: "revenue", z: "format", fill: "group"})),
Plot.ruleY([0])
]
})``````

TIP

The reverse option is also used by the sort transform. To disambiguate, pass the stack options separately using the two-argument form of the stack transform as above.

The value order is worth special mention: it sorts each stack by value independently such that the order of layers can change, emphasizing the changing ranks of layers. This is sometimes called a “ribbon” chart. (In fact, the default null order supports changing order of layers, too! But most often data comes already sorted by series.)

Fork
js
``````Plot.plot({
y: {
grid: true,
transform: (d) => d / 1000 // convert millions to billions
},
marks: [
Plot.areaY(riaa, {x: "year", y: "revenue", z: "format", fill: "group", order: "value"}),
Plot.ruleY([0])
]
})``````

The offset option controls the baseline of stacked layers. It defaults to null for a y = 0 baseline (for stackY, or x = 0 for stackX). The center offset centers each stack independently per Havre et al.; the wiggle offset minimizes apparent movement per Byron & Wattenberg; these two offsets produce “streamgraphs”, so called for their fluid appearance. The wiggle offset changes the default order to inside-out to further minimize movement.

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js
``````Plot.plot({
y: {
grid: true,
transform: (d) => d / 1000
},
marks: [
Plot.areaY(riaa, {x: "year", y: "revenue", z: "format", fill: "group", offset})
]
})``````

CAUTION

When offset is not null, the y axis is harder to use because there is no longer a shared baseline at y = 0, though it is still useful for eyeballing length.

The normalize offset is again worth special mention: it scales stacks to fill the interval [0, 1], thereby showing the relative proportion of each layer. Sales of compact discs accounted for over 90% of revenue in the early 2000’s, but now most revenue comes from streaming.

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``````Plot.plot({
y: {
label: "Annual revenue (%)",
percent: true
},
marks: [
Plot.areaY(riaa, Plot.stackY({offset: "normalize", order: "group", reverse: true}, {x: "year", y: "revenue", z: "format", fill: "group"})),
Plot.ruleY([0, 1])
]
})``````

When the provided length (typically y) is negative, in conjunction with the null offset the stack transform will produce diverging stacks on opposites sides of the zero baseline. The diverging stacked dot plot below shows the age and gender distribution of the U.S. Congress in 2023. This form is also often popular for population pyramids.

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``````Plot.plot({
aspectRatio: 1,
x: {label: "Age (years)"},
y: {
grid: true,
label: "← Women · Men →",
labelAnchor: "center",
tickFormat: Math.abs
},
marks: [
Plot.dot(
congress,
Plot.stackY2({
x: (d) => 2023 - d.birthday.getUTCFullYear(),
y: (d) => d.gender === "M" ? 1 : -1,
fill: "gender",
title: "full_name"
})
),
Plot.ruleY([0])
]
})``````

INFO

The stackY2 transform places each dot at the upper bound of the associated stacked interval, rather than the middle of the interval as when using stackY. Hence, the first male dot is placed at y = 1, and the first female dot is placed at y = -1.

When visualizing Likert scale survey results we may wish to place negative (disagreeing) responses on the left and positive (agreeing) responses on the right, leaving neutral responses in the middle. This is achieved below using a custom offset function.

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``````Plot.plot({
x: {tickFormat: Math.abs},
color: {domain: likert.order, scheme: "RdBu", legend: true},
marks: [
Plot.barX(
survey,
Plot.groupZ({x: "count"}, {fy: "Question", fill: "Response", ...likert})
),
Plot.ruleX([0])
]
})``````

Here `likert` declares which response values are negative (`-1`), which are positive (`1`), and which are neutral (`0`).

js
``````likert = Likert([
["Strongly Disagree", -1],
["Disagree", -1],
["Neutral", 0],
["Agree", 1],
["Strongly Agree", 1]
])``````

And `Likert` implements the order (as an explicit array of ordinal values, such that the ordinal color scale lists in the correct order rather than sorting alphabetically) and offset (as a function that mutates the x1 and x2 channel values) stack options.

js
``````function Likert(responses) {
const map = new Map(responses);
return {
order: Array.from(map.keys()),
offset(I, X1, X2, Z) {
for (const stacks of I) {
for (const stack of stacks) {
const k = d3.sum(stack, (i) => (X2[i] - X1[i]) * (1 - map.get(Z[i]))) / 2;
for (const i of stack) {
X1[i] -= k;
X2[i] -= k;
}
}
}
}
};
}``````

See the Marimekko example for another interesting application of the stack transform.

## Stack options ​

The stackY transform groups on x and transforms y into y1 and y2; the stackX transform groups on y and transforms x into x1 and x2. If y is not specified for stackY, or if x is not specified for stackX, it defaults to the constant one, which is useful for constructing simple isotype charts (e.g., stacked dots).

The supported stack options are:

• offset - the offset (or baseline) method
• order - the order in which stacks are layered
• reverse - true to reverse order

The following order methods are supported:

• null (default) - input order
• value - ascending value order (or descending with reverse)
• x - alias of value; for stackX only
• y - alias of value; for stackY only
• sum - order series by their total value
• appearance - order series by the position of their maximum value
• inside-out (default with wiggle) - order the earliest-appearing series on the inside
• a named field or function of data - order data by priority
• an array of z values

The reverse option reverses the effective order. For the value order, stackY uses the y value while stackX uses the x value. For the appearance order, stackY uses the x position of the maximum y value while stackX uses the y position of the maximum x value. If an array of z values are specified, they should enumerate the z values for all series in the desired order; this array is typically hard-coded or computed with d3.groupSort. Note that the input order (null) and value order can produce crossing paths: they do not guarantee a consistent series order across stacks.

The stack transform supports diverging stacks: negative values are stacked below zero while positive values are stacked above zero. For stackY, the y1 channel contains the value of lesser magnitude (closer to zero) while the y2 channel contains the value of greater magnitude (farther from zero); the difference between the two corresponds to the input y channel value. For stackX, the same is true, except for x1, x2, and x respectively.

After all values have been stacked from zero, an optional offset can be applied to translate or scale the stacks. The following offset methods are supported:

• null (default) - a zero baseline
• normalize - rescale each stack to fill [0, 1]
• center - align the centers of all stacks
• wiggle - translate stacks to minimize apparent movement
• a function to be passed a nested index, and start, end, and z values

If a given stack has zero total value, the normalize offset will not adjust the stack’s position. Both the center and wiggle offsets ensure that the lowest element across stacks starts at zero for better default axes. The wiggle offset is recommended for streamgraphs, and if used, changes the default order to inside-out; see Byron & Wattenberg.

If the offset is specified as a function, it will receive four arguments: an index of stacks nested by facet and then stack, an array of start values, an array of end values, and an array of z values. For stackX, the start and end values correspond to x1 and x2, while for stackY, the start and end values correspond to y1 and y2. The offset function is then responsible for mutating the arrays of start and end values, such as by subtracting a common offset for each of the indices that pertain to the same stack.

In addition to the y1 and y2 output channels, stackY computes a y output channel that represents the midpoint of y1 and y2; stackX does the same for x. This can be used to position a label or a dot in the center of a stacked layer. The x and y output channels are lazy: they are only computed if needed by a downstream mark or transform.

If two arguments are passed to the stack transform functions below, the stack-specific options (offset, order, and reverse) are pulled exclusively from the first options argument, while any channels (e.g., x, y, and z) are pulled from second options argument. Options from the second argument that are not consumed by the stack transform will be passed through. Using two arguments is sometimes necessary is disambiguate the option recipient when chaining transforms.

## stackY(stack, options) ​

js
``Plot.stackY({x: "year", y: "revenue", z: "format", fill: "group"})``

Creates new channels y1 and y2, obtained by stacking the original y channel for data points that share a common x (and possibly z) value. A new y channel is also returned, which lazily computes the middle value of y1 and y2. The input y channel defaults to a constant 1, resulting in a count of the data points. The stack options (offset, order, and reverse) may be specified as part of the options object, if the only argument, or as a separate stack options argument.

## stackY1(stack, options) ​

js
``Plot.stackY1({x: "year", y: "revenue", z: "format", fill: "group"})``

Like stackY, except that the y1 channel is returned as the y channel. This can be used, for example, to draw a line at the bottom of each stacked area.

## stackY2(stack, options) ​

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``Plot.stackY2({x: "year", y: "revenue", z: "format", fill: "group"})``

Like stackY, except that the y2 channel is returned as the y channel. This can be used, for example, to draw a line at the top of each stacked area.

## stackX(stack, options) ​

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``Plot.stackX({y: "year", x: "revenue", z: "format", fill: "group"})``

Like stackY, but with x as the input value channel, y as the stack index, x1, x2 and x as the output channels.

## stackX1(stack, options) ​

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``Plot.stackX1({y: "year", x: "revenue", z: "format", fill: "group"})``

Like stackX, except that the x1 channel is returned as the x channel. This can be used, for example, to draw a line at the left edge of each stacked area.

## stackX2(stack, options) ​

js
``Plot.stackX2({y: "year", x: "revenue", z: "format", fill: "group"})``

Like stackX, except that the x2 channel is returned as the x channel. This can be used, for example, to draw a line at the right edge of each stacked area.

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