Press n or j to go to the next uncovered block, b, p or k for the previous block.
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* Aggregate peak analysis: many small squares of the matrix, averaged.
*
* The kernel. What makes it worth its own module is not the averaging — that is
* a running sum — but the three decisions around it, each of which changes what
* the picture means.
*
* **Reads are per window, at the file's own resolution, never a bounding box.**
* This is a deliberate reversal of the obvious optimisation and the reason is
* resolution: a whole-genome or bounding-box read is pooled at `POOLED_CELL_CAP`
* (§7.2), so a pileup taken from one silently inherits a coarser bin than the
* reader asked for, on any genome large enough for it to matter — and nothing in
* the picture would say so. `k` windows inherit nothing. Where windows happen to
* sit near each other they are read together (see `analysis/run/apa.ts`), which
* is an optimisation of the *reads* and not of the resolution.
*
* **The control is distance-matched by default, not observed/expected.** Both
* are offered and both are honest, but they control for different things. O/E
* divides by the expected at each diagonal offset, which removes the distance
* decay and nothing else. A distance-matched control is a pileup of *shifted*
* anchor pairs at the same separations, which removes the distance decay **and**
* whatever local coverage, mappability and compartment background the real
* anchors sit in. On a real loop set the difference is large and in the
* direction that matters: O/E over-reports, because loops sit in active regions
* that are hot for reasons that have nothing to do with the loop.
*
* **The enrichment is a corner ratio, and it is reported.** A pileup always
* looks like something. P2LL — the centre against the lower-left corner — is the
* number that says whether it looks like a dot, and a pileup published without
* one is a picture doing the work a statistic should.
*
* **A domain pileup is a different picture and takes a different corner.** The
* scaled mode piles up *intervals* — TADs between two called boundaries, say —
* with a flank each side and every body resampled onto the same columns
* ({@link scaledLayout}, {@link scaledEdges}), so what comes out is a square with
* the domain in the middle of it rather than a dot in the middle of a window.
* P2LL on that measures the distance decay and nothing else, which is why
* {@link domainScore} exists and why it is the number reported there.
*/
/** A running mean over many equally-shaped windows. */
export class PileupAccumulator {
private readonly sum: Float64Array
private readonly count: Float64Array
/** Windows that contributed at least one cell. */
private windows = 0
constructor(
readonly rows: number,
readonly cols: number,
) {
this.sum = new Float64Array(rows * cols)
this.count = new Float64Array(rows * cols)
}
/**
* Add one window, already extracted and in this pileup's shape.
*
* `NaN` cells are skipped per cell rather than per window, so a window with a
* balancer-dropped row still contributes everything else it has. The count is
* therefore per cell too — which is what makes the mean of a pileup over
* ragged windows the mean of what was actually seen.
*/
add(values: ArrayLike<number>): void {
let any = false
for (let i = 0; i < this.sum.length; i++) {
const value = values[i]
if (!Number.isFinite(value)) continue
this.sum[i] += value
this.count[i] += 1
any = true
}
if (any) this.windows++
}
/** The pileup, with `NaN` where no window had a value. */
finish(): { values: Float32Array; n: number } {
const values = new Float32Array(this.sum.length)
for (let i = 0; i < values.length; i++) {
values[i] = this.count[i] > 0 ? this.sum[i] / this.count[i] : Number.NaN
}
return { values, n: this.windows }
}
}
/**
* One window of a square, resampled to a fixed shape.
*
* `fixed` mode is a straight copy: the window is already the right size, because
* it was asked for that way. `scaled` mode is the one that needs arithmetic —
* every domain is a different number of bins and they all have to land on the
* same grid — and it is area-weighted rather than nearest-neighbour, for the
* reason `render/tracks.ts` gives about pixels: taking whichever input cell an
* output cell starts in makes the picture jump as the input size changes, which
* across a set of differently sized domains is a blur that looks like biology.
*/
export function resampleWindow(
source: ArrayLike<number>,
sourceRows: number,
sourceCols: number,
outRows: number,
outCols: number,
): Float64Array {
const out = new Float64Array(outRows * outCols)
if (sourceRows === outRows && sourceCols === outCols) {
for (let i = 0; i < out.length; i++) out[i] = source[i]
return out
}
const weights = new Float64Array(outRows * outCols)
const rowScale = outRows / sourceRows
const colScale = outCols / sourceCols
for (let r = 0; r < sourceRows; r++) {
const rLo = r * rowScale
const rHi = (r + 1) * rowScale
for (let c = 0; c < sourceCols; c++) {
const value = source[r * sourceCols + c]
if (!Number.isFinite(value)) continue
const cLo = c * colScale
const cHi = (c + 1) * colScale
for (let orow = Math.floor(rLo); orow < Math.min(outRows, Math.ceil(rHi)); orow++) {
const rOverlap = Math.min(rHi, orow + 1) - Math.max(rLo, orow)
if (!(rOverlap > 0)) continue
for (let ocol = Math.floor(cLo); ocol < Math.min(outCols, Math.ceil(cHi)); ocol++) {
const cOverlap = Math.min(cHi, ocol + 1) - Math.max(cLo, ocol)
if (!(cOverlap > 0)) continue
const weight = rOverlap * cOverlap
out[orow * outCols + ocol] += value * weight
weights[orow * outCols + ocol] += weight
}
}
}
}
for (let i = 0; i < out.length; i++) {
out[i] = weights[i] > 0 ? out[i] / weights[i] : Number.NaN
}
return out
}
/**
* One window resampled onto a grid whose **cell edges are given**, rather than
* spread evenly across it.
*
* The difference matters for exactly one picture, and it is the one this exists
* for: a *domain* pileup, where every window is a flank, a body and a flank and
* the bodies are all different lengths. Resampled evenly — the whole window
* stretched onto the grid — a 20 kb domain's left boundary lands on one column
* and a 200 kb domain's lands on another, because `round(L * flank)` is not the
* same fraction of `L(1 + 2f)` for the two of them. Averaging those together
* smears both boundaries over a few columns, and a smeared boundary in an
* aggregate looks exactly like a real one that is soft.
*
* Edges are in **source cells** and may be fractional, so `scaledEdges` can put
* the body's two ends on the same two grid lines for every window whatever its
* length. Area-weighted, `NaN`-skipping and gap-preserving, like
* {@link resampleWindow}, whose uniform case this generalises.
*/
export function resampleWindowTo(
source: ArrayLike<number>,
sourceRows: number,
sourceCols: number,
rowEdges: ArrayLike<number>,
colEdges: ArrayLike<number>,
): Float64Array {
const outRows = rowEdges.length - 1
const outCols = colEdges.length - 1
const out = new Float64Array(outRows * outCols)
for (let orow = 0; orow < outRows; orow++) {
const rLo = rowEdges[orow]
const rHi = rowEdges[orow + 1]
const rFrom = Math.max(0, Math.floor(rLo))
const rTo = Math.min(sourceRows, Math.ceil(rHi))
for (let ocol = 0; ocol < outCols; ocol++) {
const cLo = colEdges[ocol]
const cHi = colEdges[ocol + 1]
const cFrom = Math.max(0, Math.floor(cLo))
const cTo = Math.min(sourceCols, Math.ceil(cHi))
let total = 0
let weight = 0
for (let r = rFrom; r < rTo; r++) {
const rOverlap = Math.min(rHi, r + 1) - Math.max(rLo, r)
if (!(rOverlap > 0)) continue
const at = r * sourceCols
for (let c = cFrom; c < cTo; c++) {
const value = source[at + c]
if (!Number.isFinite(value)) continue
const cOverlap = Math.min(cHi, c + 1) - Math.max(cLo, c)
if (!(cOverlap > 0)) continue
const share = rOverlap * cOverlap
total += value * share
weight += share
}
}
out[orow * outCols + ocol] = weight > 0 ? total / weight : Number.NaN
}
}
return out
}
/**
* One square window stretched evenly onto a `side`-cell grid by **linear
* interpolation**, every grid cell a missing value reaches left a gap.
*
* The resampling a domain pileup over the expected goes through, because that
* is coolpuppy's (`rescale=True`), and with no controls drawn at random it is
* the one scaled pileup two tools can agree on cell for cell. It is cooltools'
* `zoom_array` over scipy's `ndimage.zoom` at order 1, step for step:
*
* - the window is blown up to `side · m` cells a side, `m` the smallest whole
* number that is at least `n / side` (1 where the window is smaller than the
* grid), by linear interpolation at `o · (n − 1) / (side · m − 1)` for output
* cell `o` — and a coordinate that rounds past the last cell is scipy's
* constant edge, 0, not the last cell's value;
* - then averaged back down in blocks of `m × m`;
* - with the gaps set to 0 first and interpolated the same way as a 0/1 mask,
* a grid cell any gap reaches with any weight is a gap.
*
* Unlike {@link resampleWindowTo} this is not area-weighted and it does not
* average round a gap — it is smoothing, and it drops every cell a dropped bin
* or a near diagonal touches. Both are coolpuppy's choices, kept because the
* point of this path is to be its answer, not a better one.
*
* Done as `A · X · Aᵀ / m²`, `A` the interpolation weights already summed over
* each block, so the blown-up square — `n²` cells and more — is never held.
*/
export function zoomWindow(source: ArrayLike<number>, n: number, side: number): Float64Array {
const blocks = side < n ? Math.ceil(n / side) : 1
const fine = side * blocks
// scipy's zoom, `grid_mode=False`: the two end cells of the input land on the
// two end cells of the output.
const step = fine > 1 ? (n - 1) / (fine - 1) : 1
// Each grid cell's weights over the input, summed over its block: at most a
// block and one cells wide, kept as a start and a dense run.
const firsts = new Int32Array(side)
const runs: Float64Array[] = []
for (let a = 0; a < side; a++) {
let lo = Number.POSITIVE_INFINITY
let hi = -1
const pairs: Array<[number, number]> = []
for (let i = a * blocks; i < (a + 1) * blocks; i++) {
const at = i * step
if (at > n - 1) continue
const from = Math.floor(at)
const t = at - from
pairs.push([from, 1 - t])
if (from + 1 < n) pairs.push([from + 1, t])
lo = Math.min(lo, from)
hi = Math.max(hi, from + 1 < n ? from + 1 : from)
}
if (hi < 0) {
firsts[a] = 0
runs.push(new Float64Array(0))
continue
}
const run = new Float64Array(hi - lo + 1)
for (const [index, weight] of pairs) run[index - lo] += weight
firsts[a] = lo
runs.push(run)
}
// Rows of the input against the grid's columns, then the grid's rows against
// those: the data with its gaps as 0, and the gaps as a 0/1 mask beside it.
const half = new Float64Array(n * side)
const halfGaps = new Float64Array(n * side)
for (let p = 0; p < n; p++) {
for (let b = 0; b < side; b++) {
const run = runs[b]
const from = firsts[b]
let total = 0
let gaps = 0
for (let k = 0; k < run.length; k++) {
const value = source[p * n + from + k]
if (Number.isFinite(value)) total += run[k] * value
else gaps += run[k]
}
half[p * side + b] = total
halfGaps[p * side + b] = gaps
}
}
const out = new Float64Array(side * side)
const scale = 1 / (blocks * blocks)
for (let a = 0; a < side; a++) {
const run = runs[a]
const from = firsts[a]
for (let b = 0; b < side; b++) {
let total = 0
let gaps = 0
for (let k = 0; k < run.length; k++) {
total += run[k] * half[(from + k) * side + b]
gaps += run[k] * halfGaps[(from + k) * side + b]
}
out[a * side + b] = gaps > 0 ? Number.NaN : total * scale
}
}
return out
}
/**
* The bins a domain's window covers when it is stretched evenly: the domain
* scaled by `1 + 2f` about its middle, half-open, relative to its sequence's
* first bin.
*
* bioframe's `expand(scale=1 + 2f)`, which is how coolpuppy makes the window:
* each end moved by `f` times the length and **rounded half to even** (numpy's
* `round`), then snapped outwards to whole bins.
*/
export function evenWindow(
start: number,
end: number,
flankFraction: number,
binsize: number,
): { from: number; to: number } {
// In bioframe's own order of operations, so a flank like 0.3 rounds as it does.
const scale = 2 * flankFraction + 1
const pad = 0.5 * (scale - 1) * (end - start)
return {
from: Math.floor(roundHalfEven(start - pad) / binsize),
to: Math.ceil(roundHalfEven(end + pad) / binsize),
}
}
/** numpy's `round`: to the nearest whole number, and a half to the even one. */
export function roundHalfEven(value: number): number {
const floor = Math.floor(value)
const diff = value - floor
if (diff > 0.5) return floor + 1
if (diff < 0.5) return floor
return floor % 2 === 0 ? floor : floor + 1
}
/**
* How a scaled window's grid divides into **flank, body, flank**.
*
* One layout for the whole run, so every window lands its body on the same
* columns. `body` is what is left after the two flanks, which is why the flank
* is rounded first: a reader asks for a flank as a fraction of the feature and
* the body takes the remainder, rather than the other way about, so a run with
* no flank is a grid that is all body and never a grid with one cell missing.
*/
export interface ScaledLayout {
/** Cells a side; `2 * flank + body`. */
side: number
/** Cells each flank occupies. `0` where no flank was asked for. */
flank: number
/** Cells the body occupies — the grid rows and columns `[flank, flank + body)`. */
body: number
}
/** The grid's division, for a flank given as a fraction of the body. */
export function scaledLayout(side: number, flankFraction: number): ScaledLayout {
const grid = Math.max(3, Math.round(side))
const fraction = Math.max(0, flankFraction)
// The body keeps at least one cell however wide the flank was asked for, so a
// flank of 20x is a thin body rather than a picture with no domain in it.
const room = Math.floor((grid - 1) / 2)
const flank = Math.min(room, Math.round((grid * fraction) / (1 + 2 * fraction)))
return { side: grid, flank, body: grid - 2 * flank }
}
/**
* One window's cell edges, in source cells, for {@link resampleWindowTo}.
*
* `bodyFrom`/`bodyTo` and `pad` are relative to the window's own first cell.
* The body's two ends land exactly on grid lines `flank` and `flank + body`,
* by construction and for every window — which is the whole point of taking
* edges rather than a shape.
*/
export function scaledEdges(
layout: ScaledLayout,
bodyFrom: number,
bodyTo: number,
pad: number,
): Float64Array {
const edges = new Float64Array(layout.side + 1)
for (let i = 0; i < layout.flank; i++) {
edges[i] = bodyFrom - pad + (pad * i) / layout.flank
}
for (let j = 0; j <= layout.body; j++) {
edges[layout.flank + j] = bodyFrom + ((bodyTo - bodyFrom) * j) / layout.body
}
for (let k = 1; k <= layout.flank; k++) {
edges[layout.flank + layout.body + k] = bodyTo + (pad * k) / layout.flank
}
return edges
}
/**
* A domain pileup's enrichment: the domain's own corner against the same block
* across its boundary.
*
* P2LL is the wrong statistic here and wrong in a way that flatters: the
* lower-left corner of a *domain* window is the upstream flank against the
* downstream flank — two neighbours of the domain, further apart than anything
* inside it — so a ratio against it is mostly the distance decay and reads well
* above 1 for a set with no domains in it at all.
*
* The corner is the block just inside the domain at its widest separation —
* rows at the domain's start, columns at its end — and the denominator is the
* two blocks immediately outside it: the same columns one boundary up, and the
* same rows one boundary down. Those sit at very nearly the same separation as
* the numerator by construction, so what is left when you divide is whether
* contact **stops at the boundary**. Above 1 is a domain; 1 is a set of
* intervals with no boundaries at their edges.
*
* `NaN` where there is no flank to compare against, which is a run that asked
* for no padding: there is then no outside in the picture, and a ratio against
* a block that was never read is not a large number, it is no number.
*/
export function domainScore(values: ArrayLike<number>, layout: ScaledLayout): number {
const { side, flank, body } = layout
if (flank === 0 || body === 0) return Number.NaN
const q = Math.max(1, Math.round(body / 4))
const p = Math.min(flank, q)
const mean = (r0: number, r1: number, c0: number, c1: number): number => {
let total = 0
let seen = 0
for (let r = Math.max(0, r0); r < Math.min(side, r1); r++) {
for (let c = Math.max(0, c0); c < Math.min(side, c1); c++) {
const value = values[r * side + c]
if (!Number.isFinite(value)) continue
total += value
seen++
}
}
return seen === 0 ? Number.NaN : total / seen
}
const inside = mean(flank, flank + q, flank + body - q, flank + body)
const outside: number[] = []
// Across the upstream boundary: the same columns, rows just above the domain.
const above = mean(flank - p, flank, flank + body - q, flank + body)
if (Number.isFinite(above)) outside.push(above)
// Across the downstream boundary: the same rows, columns just past the domain.
const beyond = mean(flank, flank + q, flank + body, flank + body + p)
if (Number.isFinite(beyond)) outside.push(beyond)
if (!Number.isFinite(inside) || outside.length === 0) return Number.NaN
const background = outside.reduce((sum, value) => sum + value, 0) / outside.length
return background === 0 ? Number.NaN : inside / background
}
/**
* Peak to lower-left: the centre of a pileup against its lower-left corner.
*
* The conventional APA statistic, and the corner is not arbitrary. On an
* off-diagonal pileup the lower-left quadrant is the region *further* from the
* diagonal on one anchor and *nearer* on the other — background at a comparable
* separation, with none of the loop in it. Taking the whole border instead would
* include the two quadrants that a stripe runs through, and a stripe would then
* read as a dot.
*
* `NaN` where either part has nothing in it: a ratio against an empty corner is
* not a large number, it is no number.
*/
export function p2ll(values: ArrayLike<number>, rows: number, cols: number): number {
const quadrant = Math.max(1, Math.floor(Math.min(rows, cols) / 5))
const centreR = Math.floor(rows / 2)
const centreC = Math.floor(cols / 2)
const half = Math.max(0, Math.floor(quadrant / 2))
const mean = (r0: number, r1: number, c0: number, c1: number): number => {
let total = 0
let seen = 0
for (let r = Math.max(0, r0); r < Math.min(rows, r1); r++) {
for (let c = Math.max(0, c0); c < Math.min(cols, c1); c++) {
const value = values[r * cols + c]
if (!Number.isFinite(value)) continue
total += value
seen++
}
}
return seen === 0 ? Number.NaN : total / seen
}
const peak = mean(centreR - half, centreR + half + 1, centreC - half, centreC + half + 1)
const corner = mean(rows - quadrant, rows, 0, quadrant)
if (!Number.isFinite(peak) || !Number.isFinite(corner) || corner === 0) return Number.NaN
return peak / corner
}
/** Divide one pileup by another, cell by cell. */
export function ratioOf(
numerator: ArrayLike<number>,
denominator: ArrayLike<number>,
): Float32Array {
const out = new Float32Array(numerator.length)
for (let i = 0; i < out.length; i++) {
const a = numerator[i]
const b = denominator[i]
// A zero denominator gives no ratio rather than an infinity: an infinity
// cannot be drawn on a diverging scale, cannot be written to a bigWig, and
// would take the colour range of the whole picture with it (§18.7).
out[i] = Number.isFinite(a) && Number.isFinite(b) && b !== 0 ? a / b : Number.NaN
}
return out
}
/** One pair of anchors, in absolute bins. */
export interface AnchorPair {
row: number
col: number
/** Bins between them; `col - row` for an ordered pair. */
separation: number
}
/**
* Controls at the same separations, drawn by shifting both anchors together.
*
* The shift preserves the separation exactly, which is the whole point: a
* control at a different distance would be controlling for the wrong thing, and
* the distance decay would come back as signal. The offset is drawn from a
* seeded generator (§18.4) and is bounded so a control stays on the same
* sequence as the pair it came from — a "control" that lands in trans is
* measuring a different quantity entirely.
*
* Controls that cannot be placed are dropped rather than clamped: clamping would
* pile several controls onto the same cells and give the denominator a spurious
* structure of its own.
*/
export function shiftedControls(
pair: AnchorPair,
bounds: { from: number; to: number },
options: { perPair: number; minShift: number; maxShift: number; rng(): number },
): AnchorPair[] {
const out: AnchorPair[] = []
for (let i = 0; i < options.perPair; i++) {
const magnitude =
options.minShift + Math.floor(options.rng() * (options.maxShift - options.minShift + 1))
const sign = options.rng() < 0.5 ? -1 : 1
const row = pair.row + sign * magnitude
const col = pair.col + sign * magnitude
if (row < bounds.from || col >= bounds.to) continue
out.push({ row, col, separation: pair.separation })
}
return out
}
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