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* One track made out of two: a ratio or a difference.
*
* The map got the same thing at the same time (`render/compare.ts`) and for the
* same reason, which is worth saying once here rather than twice: two coverage
* profiles drawn as two lanes are read by eye, one against the other, and the
* eye is bad at it. Small consistent differences are invisible under the large
* shared shape, and a reader comparing a treatment against its control ends up
* measuring with a finger on the screen. Drawing the comparison *itself* makes
* the difference the only thing in the lane.
*
* **The common refinement, not a resampling.** Both operands are piecewise
* constant — a bigWig is intervals with values — and two files' intervals do not
* line up: different zoom levels, different bin sizes, different base-resolution
* runs. The temptation is to lay down a uniform grid and evaluate both onto it,
* which is one line and wrong in a way nobody would see: every boundary that
* falls inside a grid cell is smeared across it, so a sharp edge in a control
* track becomes a ramp, and the ratio against it develops a spike at exactly the
* position that mattered. Cutting at *every* boundary of *either* input instead
* is exact — the combination of two step functions is a step function whose
* breakpoints are the union of theirs — and it costs at most `|a| + |b|`
* intervals, which is the same order the inputs already are.
*
* Nothing here fetches. Both operands arrive as ordinary sampled tracks, cached
* and windowed by `annotations/samples.ts` exactly as any other lane's are, so a
* derived track costs no reads of its own and inherits the pan-and-zoom-free
* rule (§8.4) from the two it is made of.
*/
import type { TrackSampleSet, TrackSamples } from './types'
/**
* What two tracks are reduced to.
*
* **There were three, and the third was a scale wearing an operation's clothes.**
* `log2ratio` computed the ratio and then took its logarithm, which put the same
* finding in two rows and left only one of them exportable as the quantity it
* measured: a bigWig of log₂ ratios is a file of a *picture*, and anything
* downstream that wanted the ratio had to undo it. The reason it existed is
* real — a ratio on a linear axis puts "half" in the bottom half-unit and
* "double" a whole unit above the middle, the same finding at two very different
* sizes, with depletion squashed into a sliver against the floor — and it is now
* answered where it belongs, on the lane's own axis (`AnnotationStyle.scale`).
* One row, one quantity, and log₂ a dropdown beside the drawing style.
*/
export type TrackOp = 'ratio' | 'difference'
/** Every operation, in the order the picker offers them. */
export const TRACK_OPS: readonly TrackOp[] = ['ratio', 'difference']
export function isTrackOp(value: string): value is TrackOp {
return (TRACK_OPS as readonly string[]).includes(value)
}
/** What each is called on screen, and in the label of the lane it makes. */
export const TRACK_OP_LABELS: Record<TrackOp, string> = {
ratio: 'ratio',
difference: 'difference',
}
/** How a derived lane names itself, before the reader renames it. */
export function derivedTrackLabel(a: string, b: string, op: TrackOp): string {
return op === 'difference' ? `${a} − ${b}` : `${a} / ${b}`
}
/** Which value the lane sits around — the line a reader reads departures from. */
export function neutralOf(op: TrackOp): number {
return op === 'ratio' ? 1 : 0
}
/**
* Combine two sampled tracks, region by region.
*
* Regions are matched by contig and by the window they cover, because that is
* what they are: both operands were asked for the same windows at the same
* resolution by the same cache, so a region of one has exactly one counterpart.
* A region with no counterpart is dropped rather than passed through — half a
* comparison drawn as though it were a whole one is the failure this is for.
*
* `null` when either operand has not arrived. The lane then draws whatever it
* had, which is `samples.ts`'s rule for every track: a lane that blanks while it
* waits is worse than a lane one frame behind.
*/
export function combineSamples(
a: TrackSampleSet | null,
b: TrackSampleSet | null,
op: TrackOp,
/**
* What becomes of a reading that ran off the end — see {@link clampInfinities}.
*
* `clamp` is the lane, and the default, because a pixel has to go somewhere.
* `drop` is a **file**, and it is the same answer {@link combineVectors} has
* always given for the same reason: `x / 0` says the denominator had nothing
* there, which is exactly what a gap says, and BBI cannot carry an infinity
* without taking the total summary and every zoom record over it with it
* (`write/bigwig.ts`). Two roads to a file, one rule about infinities.
*/
infinities: 'clamp' | 'drop' = 'clamp',
): TrackSampleSet | null {
if (a === null || b === null) return null
const regions: TrackSamples[] = []
let min = Number.POSITIVE_INFINITY
let max = Number.NEGATIVE_INFINITY
for (const left of a.regions) {
const right = b.regions.find(
(other) => other.contig === left.contig && other.start === left.start && other.end === left.end,
)
if (right === undefined) continue
const merged = refine(left, right, op)
if (merged.starts.length === 0) continue
for (const value of merged.values) {
if (!Number.isFinite(value)) continue
if (value < min) min = value
if (value > max) max = value
}
regions.push(merged)
}
// A lane whose every reading is an infinity has no measured scale to pin them
// to — one track covers a region the other does not, anywhere the two overlap
// at all. A unit span about the operation's own neutral is the same fallback
// `render/scale.ts` uses for a constant block, and for the same reason: the
// picture is "all of it, in one direction", and that needs an axis to be drawn
// against even though the data chose none.
if (infinities === 'drop') {
// No axis to pin anything to, and none wanted: what a file says about an
// interval it cannot express is nothing at all, and every writer downstream
// already omits a value that is not finite.
for (const merged of regions) dropInfinities(merged.values)
return { basesPerPixel: a.basesPerPixel, regions, extent: min <= max ? { min, max } : null }
}
const measured = min <= max
const extent = measured
? { min, max }
: hasInfinity(regions)
? { min: neutralOf(op) - 1, max: neutralOf(op) + 1 }
: null
if (extent !== null) for (const merged of regions) clampInfinities(merged.values, extent)
return { basesPerPixel: a.basesPerPixel, regions, extent }
}
/**
* `±Infinity` becomes *no reading*, which is what a file says about one.
*
* A `NaN` is already that everywhere in this viewer, so this is one substitution
* and no second state for the writers to learn: they omit a value that is not
* finite, and after this there are none.
*/
function dropInfinities(values: Float32Array): void {
for (let i = 0; i < values.length; i++) {
if (!Number.isFinite(values[i])) values[i] = Number.NaN
}
}
/** Whether any reading ran off the end in either direction. */
function hasInfinity(regions: readonly TrackSamples[]): boolean {
for (const region of regions) {
for (const value of region.values) {
if (!Number.isFinite(value) && !Number.isNaN(value)) return true
}
}
return false
}
/**
* Bring `±Infinity` back onto the axis, at the far end of what was measured.
*
* An interval where the numerator is empty and the denominator is not is a real
* and often important finding — "none of this here" — and under `log2` it is
* `-Infinity`, which no lane can draw and no autoscale can bound. Dropping those
* intervals would delete the finding; giving them a constant floor would invent
* a number whose size depends on units nobody declared.
*
* So they are pinned to the most extreme value the same lane actually reached,
* which says exactly what is true — this is off the end in that direction — in
* the units the lane is already drawn in, and moves the axis not at all. The
* extent was measured over the finite values alone, so this cannot widen it.
*/
function clampInfinities(values: Float32Array, extent: { min: number; max: number }): void {
for (let i = 0; i < values.length; i++) {
const value = values[i]
if (Number.isFinite(value) || Number.isNaN(value)) continue
values[i] = value > 0 ? extent.max : extent.min
}
}
/**
* Two step functions over one window, cut at every breakpoint of either.
*
* The two cursors only ever move forward, so this is one pass over each input
* however many boundaries interleave. A cell no interval of one side covers gets
* `NaN` from that side, which the arithmetic below carries through to mean "no
* comparison here" — the same thing a `NaN` means everywhere else in this
* viewer, and drawn as a gap rather than as a zero.
*/
function refine(left: TrackSamples, right: TrackSamples, op: TrackOp): TrackSamples {
const edges = boundaries(left, right)
const count = Math.max(0, edges.length - 1)
const starts = new Int32Array(count)
const ends = new Int32Array(count)
const values = new Float32Array(count)
let ai = 0
let bi = 0
let kept = 0
for (let i = 0; i < count; i++) {
const start = edges[i]
const end = edges[i + 1]
if (end <= start) continue
while (ai < left.ends.length && left.ends[ai] <= start) ai++
while (bi < right.ends.length && right.ends[bi] <= start) bi++
const lv = ai < left.starts.length && left.starts[ai] <= start ? left.values[ai] : Number.NaN
const rv = bi < right.starts.length && right.starts[bi] <= start ? right.values[bi] : Number.NaN
// Both absent is not a reading, and emitting it would draw a flat run of
// NaN across every gap the two tracks share.
if (Number.isNaN(lv) && Number.isNaN(rv)) continue
starts[kept] = start
ends[kept] = end
values[kept] = apply(lv, rv, op)
kept++
}
return {
contig: left.contig,
start: left.start,
end: left.end,
starts: starts.subarray(0, kept),
ends: ends.subarray(0, kept),
values: values.subarray(0, kept),
// A min/max band does not compose: the ratio of two maxima is not the
// maximum of the ratios, and drawing it as though it were would put a
// confidence band around a number it is not a band for. A derived lane is
// its line and nothing else.
min: null,
max: null,
variant: null,
summary: left.summary || right.summary,
}
}
/** Every interval boundary of either input, ascending, without duplicates. */
function boundaries(left: TrackSamples, right: TrackSamples): Int32Array {
const all = new Int32Array(
left.starts.length + left.ends.length + right.starts.length + right.ends.length,
)
let at = 0
for (const value of left.starts) all[at++] = value
for (const value of left.ends) all[at++] = value
for (const value of right.starts) all[at++] = value
for (const value of right.ends) all[at++] = value
all.sort()
const unique = new Int32Array(at)
let kept = 0
for (let i = 0; i < at; i++) {
if (kept === 0 || all[i] !== unique[kept - 1]) unique[kept++] = all[i]
}
return unique.subarray(0, kept)
}
/**
* The arithmetic, with the same three readings `render/compare.ts` relies on:
* `x / 0` is `Infinity` — present in one and absent in the other — `0 / 0` is
* `NaN`, and a `NaN` from either side carries through.
*
* An infinity produced here is brought back onto the axis by
* {@link clampInfinities}, once the lane's extent is known — which is why this
* function is free to produce one rather than having to invent a floor without
* knowing what the lane's numbers look like.
*/
function apply(left: number, right: number, op: TrackOp): number {
return op === 'difference' ? left - right : left / right
}
/**
* The same arithmetic over two per-bin vectors, for a file rather than a lane.
*
* One difference, and it is the difference between drawing and writing. A lane
* brings an infinity back onto its own axis ({@link clampInfinities}) because a
* pixel has to go somewhere; a file says **no value**, because an infinity
* cannot be written to a bigWig, would take the range of whatever read it back,
* and is not a measurement — `x / 0` says the denominator had nothing there,
* which is exactly what a gap says.
*/
export function combineVectors(
a: ArrayLike<number>,
b: ArrayLike<number>,
op: TrackOp,
): Float32Array {
const out = new Float32Array(Math.min(a.length, b.length))
for (let i = 0; i < out.length; i++) {
const value = apply(a[i], b[i], op)
out[i] = Number.isFinite(value) ? value : Number.NaN
}
return out
}
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