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* yapc's peak calling, as a port (§18.8, §18.9).
*
* *Yet another peak caller* (Jänes et al. 2018, eLife 7:e37344) reads a
* **coverage track** rather than reads, which is what makes it the one caller
* this app can run: a bigWig is all a browser has of an ATAC or a ChIP
* experiment, and yapc was written for exactly that input — "processed signal
* tracks … that show the most compelling peaks by visual inspection". Its idea
* is a shape and not a threshold. The signal is smoothed, differentiated twice,
* and every stretch where the smoothed second derivative is negative — where
* the track **curves down** — is a candidate peak, scored by how sharply it
* curves. A peak is found by its form rather than by its height, so the call
* needs no background model of a signal that has already been normalised, and
* two summits standing on one shoulder are two peaks rather than one wide one.
*
* What a candidate is worth is then a question for **two replicates**: each
* scores every candidate, and IDR (`analysis/idr.ts`) asks how far down the two
* rankings agree. With one track there is no such test, and the run says so.
*
* ## A port, and what that obliges
*
* §18.9's rule for a second caller is that it arrives with a published upstream
* and a golden built from that upstream's own output, and that the port does
* not improve on it. The upstream is yapc 0.1 — the release on bioconda, which
* the paper's methods describe — and every step below is its code, in its order,
* including four things a first reading takes for oversights:
*
* - **The pooled track and the concave regions are read back through a
* bigWig.** yapc writes the mean coverage and its second derivative to disk
* and calls regions on what it reads back, so both are **float32** by the time
* anything is decided on them, and a tie between two positions of equal
* curvature is a tie in float32. The *scores* are computed from each track in
* float64 and never written, so they are not rounded. Both roundings are kept.
* - **`np.convolve(…, mode='same')` centres an even kernel half a base right**,
* and on a sequence shorter than the kernel it centres on the kernel instead
* — after which pyBigWig silently keeps the first `length` values. Both
* alignments are reproduced ({@link convolveSame}).
* - **Flat signal is concave.** The test is `d2 < 1e-10`, and the composite
* kernel sums to a few times −10⁻¹¹ rather than to zero in float64, so a stretch of
* constant non-negative coverage — a run of zeros included — comes out as a
* concave region with a score near zero. It sorts to the bottom of every
* ranking, which is where it does no harm, and it is there.
* - **A sequence whose concave stretches never begin after its first base has
* none.** `find_concave_regions_chrom` returns early when there is no rising
* edge, before it adds the region open at position 0 ({@link ConcaveScan}).
*
* Where yapc does not produce an answer at all, the port has to, and each place
* is named where it is decided: a sequence ending on an open concave stretch
* with no rising edge before it (yapc raises an `IndexError`), a fixed
* half-width reaching past a sequence end (yapc writes a negative BED start),
* and a tie in rank at the truncation cut (yapc's `quicksort` puts it wherever
* numpy's introsort left it; here it is broken by position).
*
* ## Streaming, which yapc does not do
*
* yapc holds a whole chromosome per sample in memory — 2 GB for a human
* chromosome 1 in float64. Nothing here needs more than one window at a time:
* the convolution reaches 228 bases each side, so a window read with that halo
* is computed exactly as the whole sequence would be, and {@link ConcaveScan}
* carries an open region, its summit candidates and its values across the seam.
* The answer is the same function of the same numbers; only the memory is not.
*/
import { numpyMean } from './stats'
// ---------------------------------------------------------------------------
// The kernel
// ---------------------------------------------------------------------------
/** yapc's own defaults, from its `argparse` help. */
export const YAPC_DEFAULTS = {
/** `--smoothing-window-width`: "try … values ranging from 75 to 200". */
width: 150,
/** `--smoothing-times`. */
times: 3,
/** `--min-concave-region-width`. */
minWidth: 75,
/** `--truncate-idr-input`. */
truncate: 100_000,
} as const
/**
* The nine-point central difference for a second derivative, accurate to eighth
* order — the weights yapc cites (Fornberg 1988, *Math. Comp.* 51:699).
*/
export const SECOND_DERIVATIVE_STENCIL: readonly number[] = [
-1.0 / 560,
8.0 / 315,
-1.0 / 5,
8.0 / 5,
-205.0 / 72,
8.0 / 5,
-1.0 / 5,
8.0 / 315,
-1.0 / 560,
]
/**
* yapc's `ADHOC_LARGE_NUMBER`: "scale to have better visualisation of d2smooth
* in IGV". It multiplies every score, so it is part of what the numbers mean
* and is kept, whatever it was for.
*/
export const KERNEL_SCALE = 1e6
/** `find_concave_regions_chrom`'s `tol`: a position is concave below it. */
export const CONCAVE_TOLERANCE = 1e-10
/** The composite kernel, and its running total for the run-wise convolution. */
export interface YapcKernel {
readonly width: number
readonly times: number
/** `prepare_second_derivative_kernel(width, times)`: scaled and reversed. */
readonly values: Float64Array
/** `cumulative[m]` is the sum of `values[0, m)`; one longer than `values`. */
readonly cumulative: Float64Array
}
/**
* `prepare_second_derivative_kernel`: the stencil convolved `times` times with a
* rolling mean of `width`, scaled, and reversed.
*
* One convolution with this is the smoothed second derivative, which is why yapc
* builds it rather than smoothing and then differentiating: the composite is 456
* taps at the defaults and applied once. The reversal is a no-op on a symmetric
* kernel and is kept anyway, because the float64 composite is symmetric only to
* about one part in 10¹⁴ and it is yapc's orientation that the numbers are in.
*/
export function yapcKernel(width: number, times: number): YapcKernel {
let kernel: Float64Array = Float64Array.from(SECOND_DERIVATIVE_STENCIL)
const box = new Float64Array(width).fill(1 / width)
for (let pass = 0; pass < times; pass++) kernel = convolveFull(kernel, box)
const values = new Float64Array(kernel.length)
for (let k = 0; k < kernel.length; k++) values[k] = KERNEL_SCALE * kernel[kernel.length - 1 - k]
const cumulative = new Float64Array(values.length + 1)
for (let k = 0; k < values.length; k++) cumulative[k + 1] = cumulative[k] + values[k]
return { width, times, values, cumulative }
}
/** `np.convolve(a, b)` in its default `'full'` mode. */
function convolveFull(a: Float64Array, b: Float64Array): Float64Array {
const out = new Float64Array(a.length + b.length - 1)
for (let n = 0; n < out.length; n++) {
let total = 0
const from = Math.max(0, n - (b.length - 1))
const to = Math.min(n, a.length - 1)
for (let k = from; k <= to; k++) total += a[k] * b[n - k]
out[n] = total
}
return out
}
/**
* Where output `i` of `np.convolve(x, kernel, mode='same')` is centred: it is
* `full[i + centre]`, so it reads `x[i + centre − (L − 1) … i + centre]`.
*
* numpy swaps its arguments when the kernel is the longer of the two and centres
* the `'same'` window on *that*, so on a sequence shorter than the kernel the
* centre is the sequence's rather than the kernel's. yapc then writes all
* `L` values into a sequence `length` bases long, and pyBigWig keeps the first
* `length` of them — the alignment below.
*/
export function convolutionCentre(kernel: YapcKernel, length: number): number {
return (Math.min(length, kernel.values.length) - 1) >> 1
}
/** How far, each side of a position, the convolution reads. */
export function convolutionReach(kernel: YapcKernel, length: number): { left: number; right: number } {
const centre = convolutionCentre(kernel, length)
return { left: kernel.values.length - 1 - centre, right: centre }
}
// ---------------------------------------------------------------------------
// Runs: a track as it arrives
// ---------------------------------------------------------------------------
/**
* A stretch of one sequence as abutting constant pieces, `NaN` where there is no
* value.
*
* The shape a bigWig *is* — `bedGraph`-like intervals — and the shape the
* convolution below is fastest on. Expanding it to one value per base first
* would cost 12 MB per megabase and change nothing.
*/
export interface Runs {
/** 0-based, half-open, ascending and abutting. */
readonly starts: Int32Array
readonly ends: Int32Array
readonly values: Float64Array
readonly length: number
}
/**
* The pieces of `[from, to)` a track's intervals describe, with every base they
* do not cover as `NaN`.
*
* `NaN` rather than zero because that is what `pyBigWig.values` returns for a
* base with no entry, and yapc never replaces it: the mean over tracks is `NaN`
* wherever one of them is, and the convolution carries it `reach` bases each
* way, where nothing can be concave. A lane with a hole in it has no peaks in
* the hole.
*
* Intervals are clipped to the span and to each other: a bedGraph that repeats a
* base is read for its first interval there, which is what a bigWig built from
* it would hold. Abutting intervals of one value are one piece — a binned bigWig
* stores a run of equal bins bin by bin — so a piece is a stretch of constant
* signal, which is what the flat test in `convolveSame` asks about.
*/
export function runsOver(
starts: ArrayLike<number>,
ends: ArrayLike<number>,
values: ArrayLike<number>,
from: number,
to: number,
): Runs {
const outStarts: number[] = []
const outEnds: number[] = []
const outValues: number[] = []
const piece = (start: number, end: number, value: number): void => {
const last = outValues.length - 1
if (last >= 0 && outEnds[last] === start && sameValue(outValues[last], value)) {
outEnds[last] = end
return
}
outStarts.push(start)
outEnds.push(end)
outValues.push(value)
}
let at = from
for (let i = 0; i < starts.length && at < to; i++) {
const start = Math.max(starts[i], at)
const end = Math.min(ends[i], to)
if (end <= start) continue
if (start > at) piece(at, start, Number.NaN)
piece(start, end, values[i])
at = end
}
if (at < to) piece(at, to, Number.NaN)
return {
starts: Int32Array.from(outStarts),
ends: Int32Array.from(outEnds),
values: Float64Array.from(outValues),
length: outStarts.length,
}
}
/**
* `[from, to)` as one piece of zeros: a track that does not have the sequence.
*
* yapc's `coverage()` reads such a track as zeros — `RuntimeError suggests
* empty chromosome; returning flat signal` — so it pulls the pooled mean down
* rather than blanking it, and its own scores there are `-inf`.
*/
export function zeroRuns(from: number, to: number): Runs {
return {
starts: Int32Array.of(from),
ends: Int32Array.of(to),
values: Float64Array.of(0),
length: 1,
}
}
/**
* The mean of several tracks over `[from, to)`, as yapc's pooled coverage track
* holds it after the round trip through a bigWig.
*
* `np.mean(l_val, axis=0)` adds the tracks in order and divides by their count,
* and `addEntries` then stores it as float32: both are here, in that order, so
* the pooled value is bit for bit the one yapc calls regions on. One track is
* its own mean — and already float32 — so it passes through untouched.
*/
export function pooledRuns(tracks: readonly Runs[], from: number, to: number): Runs {
if (tracks.length === 1) return tracks[0]
const starts: number[] = []
const ends: number[] = []
const values: number[] = []
const cursor = new Int32Array(tracks.length)
let at = from
while (at < to) {
let next = to
let total = 0
for (let t = 0; t < tracks.length; t++) {
const runs = tracks[t]
while (cursor[t] < runs.length && runs.ends[cursor[t]] <= at) cursor[t]++
const r = cursor[t]
// Every track covers the whole span by construction (`runsOver` fills its
// gaps), so a missing piece is a caller's mistake rather than data.
if (r >= runs.length || runs.starts[r] > at) {
throw new Error(`pooledRuns: a track does not cover ${at}`)
}
total += runs.values[r]
if (runs.ends[r] < next) next = runs.ends[r]
}
const value = Math.fround(total / tracks.length)
const last = values.length - 1
if (last >= 0 && sameValue(values[last], value)) ends[last] = next
else {
starts.push(at)
ends.push(next)
values.push(value)
}
at = next
}
return {
starts: Int32Array.from(starts),
ends: Int32Array.from(ends),
values: Float64Array.from(values),
length: starts.length,
}
}
/** Equal as signal: the same number, or both missing. */
function sameValue(a: number, b: number): boolean {
return a === b || (a !== a && b !== b)
}
// ---------------------------------------------------------------------------
// The convolution
// ---------------------------------------------------------------------------
/**
* `np.convolve(x, kernel, mode='same')` at positions `[from, to)` of a sequence
* `length` bases long, with `x` given as {@link Runs}.
*
* `runs` must cover `[from − left, to + right)` inside the sequence, where
* `left` and `right` are {@link convolutionReach}; positions outside the sequence
* are zeros, which is numpy's padding.
*
* **Run by run rather than base by base**, and it is the same sum: a piece of
* constant value `v` over `[s, e)` contributes `v · Σ kernel` over the taps it
* meets, and that sum is a difference of the kernel's running total. A 456-tap
* kernel over a bigWig whose intervals average five bases is ninety pieces per
* position instead of 456 products. What it is *not* is the same float64
* rounding as a dot product, which numpy's own BLAS does not promise either; the
* golden (§18.10) holds the two to where every region, summit and score agrees.
*
* Flat input stays what numpy makes of it: a window inside one piece is `v` times
* the kernel's total, a few times −10⁻¹¹ · `v` in either, and a window of zeros is
* exactly zero.
* Any `NaN` in the window makes the output `NaN`, as it does in a dot product.
*
* **Piece by piece, each position's terms in the order they always were.** A
* position's value is one term per piece its window meets, added from the
* leftmost piece to the rightmost, and that order is what fixes its last place.
* Summed a position at a time, every addition waits on the one before it — a
* chain of a hundred dependent float64 adds per base on an ATAC-seq pair, which
* was most of the time a genome-wide call took (§18.8). So the loop is turned
* inside out: each piece, in order, adds its term to every position whose
* window it meets ({@link addTerms}). Each position still receives its terms in
* the same order, as the same products of the same differences, so the result
* is bit for bit the one a position at a time gives; what changes is that
* neighbouring positions no longer wait on one another.
*/
export function convolveSame(
runs: Runs,
kernel: YapcKernel,
length: number,
from: number,
to: number,
/**
* Set to 1 at each position whose whole window lies inside one constant piece
* of the signal — where the second derivative is the kernel's sum times a
* constant, which is to say flat rather than curved. See {@link ConcaveScan}.
*/
flat?: Uint8Array,
/**
* Where given — 1 or 0 at each position — only the positions marked 1 are
* computed, and the rest are `NaN`. A replicate's own second derivative is
* read only where the pooled one is concave — about half of a genome — so the
* rest is never summed.
*/
only?: Uint8Array,
): Float64Array {
const taps = kernel.values.length
const centre = convolutionCentre(kernel, length)
const out = new Float64Array(Math.max(0, to - from))
if (only === undefined) addTerms(runs, kernel, centre, from, to, out, from)
else {
// Stretch by stretch of 1s, the gaps between them `NaN`.
let at = 0
while (at < out.length) {
const k = only.indexOf(1, at)
const start = k < 0 || k > out.length ? out.length : k
out.fill(Number.NaN, at, start)
if (start === out.length) break
const stop = only.indexOf(0, start)
const end = stop < 0 || stop > out.length ? out.length : stop
addTerms(runs, kernel, centre, from + start, from + end, out, from)
at = end
}
}
if (flat !== undefined) {
// A window `[i + centre − (taps − 1), i + centre + 1)` inside one piece
// `[S, E)`: the positions from `S − centre + taps − 1` to `E − centre − 1`.
for (let r = 0; r < runs.length; r++) {
const first = Math.max(from, runs.starts[r] - centre + taps - 1)
const last = Math.min(to - 1, runs.ends[r] - centre - 1)
if (first <= last) flat.fill(1, first - from, last - from + 1)
}
}
return out
}
/**
* Every piece's term, added to each position of `[p, q)` whose window it meets,
* into `out` — which holds position `from` at index 0 and starts at zero.
*
* Position `i` reads the bases `[low, high)` below its **anchor** `a = i +
* centre + 1`: `low = max(0, a − taps)` and `high = min(length, a)`. A piece
* `[S, E)` meets it where `S < a < E + taps`, over `[max(S, low), min(E, high))`
* — and since a piece lies inside the sequence, the clamps at its two ends never
* decide that overlap: it starts at `S` while `a ≤ S + taps`, at `a − taps` after,
* and ends at `a` while `a < E`, at `E` after. So the anchors a piece reaches
* fall in four stretches, each one formula:
*
* 1. `S < a < E`, `a ≤ S + taps`: the window's right end inside the piece;
* 2. `E ≤ a ≤ S + taps`: the whole piece inside the window;
* 3. `S + taps < a < E`: the whole window inside the piece;
* 4. `a ≥ E`, `a > S + taps`: the window's left end inside the piece.
*
* The term is the one the overlap `[s, e)` always gave: `v · K[a − 1 − s]` for a
* single base, `v · (C[a − s] − C[a − e])` otherwise, with `K` the kernel and `C`
* its running total. One base is one tap, taken as it is: a difference of
* running totals is accurate to their size rather than to the tap's, and a
* bigWig at base resolution is mostly pieces one or two bases long. A single
* base is where stretch 1 begins, where stretch 4 ends, and the whole of
* stretch 2 for a piece one base long.
*/
function addTerms(
runs: Runs,
kernel: YapcKernel,
centre: number,
p: number,
q: number,
out: Float64Array,
from: number,
): void {
const taps = kernel.values.length
const K = kernel.values
const C = kernel.cumulative
const starts = runs.starts
const ends = runs.ends
const level = runs.values
// Anchors `[first, last]`, and where anchor `a` is in `out`: `a + shift`.
const first = p + centre + 1
const last = q + centre
const shift = -(centre + 1) - from
// The first piece that reaches `first`: `E + taps − 1 ≥ first`.
let r = 0
let hi = runs.length
while (r < hi) {
const mid = (r + hi) >>> 1
if (ends[mid] > first - taps) hi = mid
else r = mid + 1
}
const C0 = C[0]
const sum = C[taps]
for (; r < runs.length; r++) {
const S = starts[r]
if (S + 1 > last) break
const E = ends[r]
const v = level[r]
// 1 · `s = S`, `e = a`.
let a0 = S + 1 > first ? S + 1 : first
let a1 = E - 1 < S + taps ? E - 1 : S + taps
if (a1 > last) a1 = last
if (a0 <= a1) {
let a = a0
if (a === S + 1) {
out[shift + a] += v * K[0]
a++
}
for (let o = shift + a, j = a - S, end = shift + a1; o <= end; o++, j++) out[o] += v * (C[j] - C0)
}
// 2 · `s = S`, `e = E`.
a0 = E > first ? E : first
a1 = S + taps < last ? S + taps : last
if (a0 <= a1) {
if (E - S === 1) {
for (let o = shift + a0, j = a0 - 1 - S, end = shift + a1; o <= end; o++, j++) out[o] += v * K[j]
} else {
for (let o = shift + a0, j = a0 - S, k = a0 - E, end = shift + a1; o <= end; o++, j++, k++) {
out[o] += v * (C[j] - C[k])
}
}
}
// 3 · `s = a − taps`, `e = a`: one term throughout.
a0 = S + taps + 1 > first ? S + taps + 1 : first
a1 = E - 1 < last ? E - 1 : last
if (a0 <= a1) {
const term = v * (sum - C0)
for (let o = shift + a0, end = shift + a1; o <= end; o++) out[o] += term
}
// 4 · `s = a − taps`, `e = E`, one base wide at the last anchor.
a0 = E > S + taps + 1 ? E : S + taps + 1
if (a0 < first) a0 = first
const single = E + taps - 1
a1 = single < last ? single : last
if (a0 <= a1) {
const end = shift + (a1 === single ? a1 - 1 : a1)
for (let o = shift + a0, k = a0 - E; o <= end; o++, k++) out[o] += v * (sum - C[k])
if (a1 === single) out[shift + single] += v * K[taps - 1]
}
}
}
// ---------------------------------------------------------------------------
// Concave regions
// ---------------------------------------------------------------------------
/** Every concave region of one sequence, with each track's score for it. */
export interface ConcaveRegions {
readonly contig: string
readonly starts: Int32Array
readonly ends: Int32Array
/** yapc's `mode`: the most concave position, the middle one of a tie. */
readonly modes: Int32Array
/**
* One array per track: `-np.mean(d2)` over the region, in float64 from that
* track's own smoothed second derivative. `-Infinity` for a track that does
* not have the sequence, which is what yapc's `scores()` yields for one.
*/
readonly scores: Float64Array[]
/**
* 1 for a region the pooled signal is **flat** across somewhere inside — a
* position whose whole kernel window is one constant piece. Not yapc's: see
* {@link ConcaveScan}.
*/
readonly flat: Uint8Array
}
/** The most values per track {@link ConcaveScan} keeps room for once a region is closed. */
const HELD_KEPT = 1 << 16
/**
* yapc's test, `d2 < tol`, on the pooled second derivative as its bigWig holds
* it — float32 — and so the one place a position is concave or not.
*/
export function isConcave(d2: number): boolean {
return Math.fround(d2) < CONCAVE_TOLERANCE
}
/**
* 1 at each position {@link isConcave} holds for: the only positions whose
* per-track second derivatives {@link ConcaveScan.feed} reads, and so the only
* ones `convolveSame` need compute them at (its `only`).
*/
export function concaveMask(pooled: Float64Array): Uint8Array {
const out = new Uint8Array(pooled.length)
for (let k = 0; k < pooled.length; k++) if (isConcave(pooled[k])) out[k] = 1
return out
}
/**
* `find_concave_regions_chrom` and `scores()`, fed one window at a time.
*
* yapc finds the rising and falling edges of `d2 < tol` over the whole
* sequence, then patches the two ends: a region open at the first base gains a
* start of 0, and one open at the last base gains an end of `length`. Fed in
* windows, the edges are the same edges; the patches are applied in
* {@link finish}, where it is known how the sequence ended.
*
* **No rising edge, no regions** — the early `return` that precedes both
* patches, so a sequence that is concave from its first base and never becomes
* concave again reports nothing, and nor does one concave throughout. Kept.
* **A rising edge and no falling one** is where yapc stops with an `IndexError`
* (`e[0]` of an empty array); here the one region runs to the end, which is
* what both patches were written to say.
*
* **What is added is a flag, and nothing is removed for it.** A stretch of
* constant signal passes yapc's test — its second derivative is the kernel's
* float64 sum times the constant, zero or −10⁻¹¹ — so a run of explicit zeros
* longer than the kernel is a concave region, scoring whatever the ringing at its
* edges leaves (10⁻⁷, on a plateau of three kilobases). In yapc that is harmless:
* IDR ranks it last in both replicates and drops it. A region is marked `flat`
* where one of its positions had a window inside one constant piece
* (`convolveSame`'s mask), which no peak has, so that a run with one track — which
* yapc has no cut for — can leave it out without a threshold on its score.
*/
export class ConcaveScan {
private readonly tracks: number
private readonly absent: readonly boolean[]
private starts: number[] = []
private ends: number[] = []
private modes: number[] = []
private flats: number[] = []
private readonly scores: number[][]
private previous = false
private rose = false
private open = -1
/** The most concave value so far in the open region, and where it is tied. */
private best = Number.NEGATIVE_INFINITY
private ties: number[] = []
/** Each track's smoothed second derivative over the open region. */
private held: Float64Array[]
private heldLength = 0
private openFlat = 0
private position = 0
constructor(
readonly contig: string,
readonly length: number,
/** One flag per track: `true` for a track that does not have this sequence. */
absent: readonly boolean[],
) {
this.tracks = absent.length
this.absent = absent
this.scores = absent.map(() => [])
this.held = absent.map(() => new Float64Array(1024))
}
/**
* Positions `[from, from + pooled.length)`, which must follow the last ones fed.
*
* `pooled` is the pooled track's smoothed second derivative in float64; it is
* rounded to float32 here, where yapc's round trip through `_d2smooth.bw`
* would round it. `tracks` is each track's own, unrounded, over the same
* positions — the same array as `pooled` when there is one track. `flat` is
* `convolveSame`'s mask for the pooled track, where the caller wants it.
*/
feed(
from: number,
pooled: Float64Array,
tracks: readonly Float64Array[],
flat?: Uint8Array,
): void {
if (from !== this.position) {
throw new Error(`ConcaveScan: fed ${from} after ${this.position}`)
}
for (let k = 0; k < pooled.length; k++) {
const at = from + k
const d2 = Math.fround(pooled[k])
const concave = isConcave(d2)
if (at === 0) {
if (concave) this.begin(0)
} else if (concave && !this.previous) {
this.rose = true
this.begin(at)
} else if (!concave && this.previous) {
this.close(at)
}
if (concave) {
// `nanargmax_median(-d2y[i:j])`: the largest of `-d2` in float32, every
// position that equals it, and the middle one of those at the end.
const value = -d2
if (value > this.best) {
this.best = value
this.ties = [at]
} else if (value === this.best) {
this.ties.push(at)
}
this.hold(tracks, k)
if (flat !== undefined && flat[k] === 1) this.openFlat = 1
}
this.previous = concave
}
this.position = from + pooled.length
}
/** yapc's two end patches, and the early return before them. */
finish(): ConcaveRegions {
if (this.open >= 0) this.close(this.length)
if (!this.rose) {
this.starts = []
this.ends = []
this.modes = []
this.flats = []
for (const list of this.scores) list.length = 0
}
return {
contig: this.contig,
starts: Int32Array.from(this.starts),
ends: Int32Array.from(this.ends),
modes: Int32Array.from(this.modes),
scores: this.scores.map((list) => Float64Array.from(list)),
flat: Uint8Array.from(this.flats),
}
}
private begin(at: number): void {
this.open = at
this.best = Number.NEGATIVE_INFINITY
this.ties = []
this.heldLength = 0
this.openFlat = 0
// A stretch of flat signal megabases long is one region, and grows these to
// fit it — 32 MB a track over a mouse centromere's zeros. Let that go with the
// region rather than hold it to the end of the sequence.
if (this.held[0].length > HELD_KEPT) this.held = this.held.map(() => new Float64Array(1024))
}
private hold(tracks: readonly Float64Array[], k: number): void {
if (this.heldLength === this.held[0].length) {
this.held = this.held.map((values) => {
const grown = new Float64Array(values.length * 2)
grown.set(values)
return grown
})
}
for (let t = 0; t < this.tracks; t++) this.held[t][this.heldLength] = tracks[t][k]
this.heldLength++
}
private close(at: number): void {
this.starts.push(this.open)
this.ends.push(at)
this.flats.push(this.openFlat)
this.modes.push(this.ties.length === 0 ? this.open : this.ties[this.ties.length >> 1])
for (let t = 0; t < this.tracks; t++) {
this.scores[t].push(
this.absent[t] ? Number.NEGATIVE_INFINITY : -numpyMean(this.held[t], 0, this.heldLength),
)
}
this.open = -1
}
}
// ---------------------------------------------------------------------------
// From regions to peaks
// ---------------------------------------------------------------------------
/**
* `df.rank(ascending=False)`: 1 for the highest score, ties sharing the mean of
* the ranks they span (pandas' default `method='average'`).
*/
export function descendingRanks(scores: Float64Array): Float64Array {
const n = scores.length
const order = Array.from({ length: n }, (_, i) => i)
order.sort((a, b) => scores[b] - scores[a] || a - b)
const out = new Float64Array(n)
let i = 0
while (i < n) {
let j = i + 1
while (j < n && scores[order[j]] === scores[order[i]]) j++
const rank = (i + 1 + j) / 2
for (let k = i; k < j; k++) out[order[k]] = rank
i = j
}
return out
}
/**
* The regions yapc hands IDR: every track ranks them, each keeps its best rank,
* and the `limit` best go through (`--truncate-idr-input`).
*
* Returned as indices in **yapc's IDR order** — sorted by sequence name, then
* start, then end — because that is the order `fit_model_and_calc_local_idr`
* adds its likelihoods in, and a port is held to the last place of those sums.
*
* A tie in best rank at the cut is broken by position. yapc sorts with pandas'
* default `quicksort`, which leaves tied rows wherever numpy's introsort put
* them; there is no order of theirs to reproduce, and position is one it could
* have produced.
*/
export function strongestRegions(
contigs: readonly string[],
starts: Int32Array,
ends: Int32Array,
scores: readonly Float64Array[],
limit: number,
): Int32Array {
const n = starts.length
const best = new Float64Array(n).fill(Number.POSITIVE_INFINITY)
for (const column of scores) {
const ranks = descendingRanks(column)
for (let i = 0; i < n; i++) if (ranks[i] < best[i]) best[i] = ranks[i]
}
const byPosition = (a: number, b: number): number =>
contigs[a] < contigs[b] ? -1 : contigs[a] > contigs[b] ? 1 : starts[a] - starts[b] || ends[a] - ends[b]
const order = Array.from({ length: n }, (_, i) => i)
order.sort((a, b) => best[a] - best[b] || byPosition(a, b))
const kept = order.slice(0, Math.max(0, Math.min(n, limit)))
kept.sort(byPosition)
return Int32Array.from(kept)
}
/**
* {@link strongestRegions}, fed one region at a time, holding only the regions
* that can still be among the strongest.
*
* yapc ranks every candidate of the genome in each track before it cuts to the
* strongest `limit`, and this did too, holding every one of them to the end —
* 5.6 million on a mouse ATAC-seq pair, most of a gigabyte (§18.8) — for the
* hundred thousand it kept. Far fewer decide the cut:
*
* - each track's `limit` highest scores, its ties at the cut included, are some
* `m ≥ limit` regions ranked `m` or better, so the best rank `B` of the last
* region kept is at most `m`;
* - a region outside them ranks `m + 1` or worse in that track, whether ranked
* among every region or among those held, since every region above it is held.
*
* So a region with a best rank of `B` or better has it in a track whose top it is
* in, where its rank among those held is its rank among all, and is worse than
* `B` nowhere it ranks lower; and a region whose best rank is worse than `B` is
* worse than `B` among those held too. {@link strongestRegions} over the regions
* held therefore keeps the same regions, in the same order. A region is let go
* when its score in every track is below that track's `limit`-th highest so far,
* a threshold that only rises, so nothing let go could have come back.
*
* **Except past a `NaN` score**, which only a track holding an infinite value can
* give: ranked by a comparison that is false both ways, it leaves an order that
* depends on every region there is, and no subset reproduces it. The first one
* stops the pruning, and {@link finish} says whether anything had been let go
* before it ({@link StrongestRegionsHeld.exact}), in which case the caller has to
* run again holding everything (`prune: false`).
*/
export class StrongestRegions {
private size = 0
private contigs: string[] = []
private starts = new Int32Array(1024)
private ends = new Int32Array(1024)
private modes = new Int32Array(1024)
private flats = new Uint8Array(1024)
private scores: Float64Array[]
/** Each track's `limit`-th highest score so far; −∞ until there are `limit`. */
private readonly floor: Float64Array
private seen = 0
private dropped = 0
private holdAll = false
/** Track 0's score of each region let go, where it is positive and not flat. */
private below: Float64Array | null
private belowSize = 0
constructor(
private readonly tracks: number,
private readonly limit: number,
options: {
/** `false` to hold every region, as {@link strongestRegions} is given them. */
prune?: boolean
/**
* Keep track 0's curvature of each region let go — the one-track figure
* draws every candidate, tested or not.
*/
below?: boolean
} = {},
) {
this.scores = Array.from({ length: tracks }, () => new Float64Array(1024))
this.floor = new Float64Array(tracks).fill(Number.NEGATIVE_INFINITY)
if (options.prune === false) this.holdAll = true
this.below = options.below === true ? new Float64Array(1024) : null
}
/** Region `i` of one sequence's regions. */
add(regions: ConcaveRegions, i: number): void {
this.seen++
let keep = this.holdAll
for (let t = 0; t < this.tracks; t++) {
const score = regions.scores[t][i]
if (score !== score && !this.holdAll) {
this.holdAll = true
keep = true
}
if (score >= this.floor[t]) keep = true
}
if (!keep) {
this.drop(regions.scores[0][i], regions.flat[i])
return
}
if (this.size === this.starts.length) this.grow()
const at = this.size++
this.contigs[at] = regions.contig
this.starts[at] = regions.starts[i]
this.ends[at] = regions.ends[i]
this.modes[at] = regions.modes[i]
this.flats[at] = regions.flat[i]
for (let t = 0; t < this.tracks; t++) this.scores[t][at] = regions.scores[t][i]
if (!this.holdAll && this.size >= 2 * this.tracks * this.limit + 1024) this.prune()
}
/** The regions held, and the strongest `limit` of them in yapc's IDR order. */
finish(): StrongestRegionsHeld {
if (!this.holdAll) this.prune()
const n = this.size
const held = {
contig: this.contigs.slice(0, n),
starts: this.starts.slice(0, n),
ends: this.ends.slice(0, n),
modes: this.modes.slice(0, n),
flat: this.flats.slice(0, n),
scores: this.scores.map((column) => column.slice(0, n)),
}
return {
...held,
tested: strongestRegions(held.contig, held.starts, held.ends, held.scores, this.limit),
below: this.below === null ? new Float64Array(0) : this.below.slice(0, this.belowSize),
exact: !(this.holdAll && this.dropped > 0),
}
}
/** Raise each track's threshold to its `limit`-th highest, and let go what is under all of them. */
private prune(): void {
if (this.seen < this.limit) return
const n = this.size
for (let t = 0; t < this.tracks; t++) {
// Every region at or above the old threshold is held, and the `limit`
// highest of all are among them, so the `limit`-th highest held is theirs.
const sorted = this.scores[t].slice(0, n).sort()
this.floor[t] = sorted[n - this.limit]
}
let kept = 0
for (let i = 0; i < n; i++) {
let keep = false
for (let t = 0; t < this.tracks; t++) if (this.scores[t][i] >= this.floor[t]) keep = true
if (!keep) {
this.drop(this.scores[0][i], this.flats[i])
continue
}
if (kept !== i) {
this.contigs[kept] = this.contigs[i]
this.starts[kept] = this.starts[i]
this.ends[kept] = this.ends[i]
this.modes[kept] = this.modes[i]
this.flats[kept] = this.flats[i]
for (let t = 0; t < this.tracks; t++) this.scores[t][kept] = this.scores[t][i]
}
kept++
}
this.size = kept
this.contigs.length = kept
}
private drop(score: number, flat: number): void {
this.dropped++
if (this.below === null || !(score > 0) || flat === 1) return
if (this.belowSize === this.below.length) {
const grown = new Float64Array(this.below.length * 2)
grown.set(this.below)
this.below = grown
}
this.below[this.belowSize++] = score
}
private grow(): void {
const twice = <T extends Int32Array | Uint8Array | Float64Array>(values: T): T => {
const grown = new (values.constructor as new (n: number) => T)(values.length * 2)
grown.set(values)
return grown
}
this.starts = twice(this.starts)
this.ends = twice(this.ends)
this.modes = twice(this.modes)
this.flats = twice(this.flats)
this.scores = this.scores.map(twice)
}
}
/** What {@link StrongestRegions} held, and what it found among them. */
export interface StrongestRegionsHeld {
readonly contig: string[]
readonly starts: Int32Array
readonly ends: Int32Array
readonly modes: Int32Array
readonly flat: Uint8Array
readonly scores: Float64Array[]
/** {@link strongestRegions} of the regions held: indices into them, in yapc's IDR order. */
readonly tested: Int32Array
/** Track 0's positive curvature of every non-flat region let go, where asked for. */
readonly below: Float64Array
/** `false` where a `NaN` score came after a region was let go: run again, holding everything. */
readonly exact: boolean
}
/**
* yapc's final bounds: the concave region itself, or `halfWidth` bases each side
* of its summit — `mode − h` to `mode + h + 1`.
*
* Clamped to the sequence, which yapc does not do: it writes the negative start
* a summit near position 0 gives, and a BED line that no parser accepts is not a
* peak anybody can use.
*/
export function peakBounds(
start: number,
end: number,
mode: number,
halfWidth: number,
length: number,
): [number, number] {
if (!(halfWidth > 0)) return [start, end]
return [Math.max(0, mode - halfWidth), Math.min(length, mode + halfWidth + 1)]
}
/**
* `-math.log(th, 10)`: the scaled global IDR a peak must reach at threshold `th`.
*
* `math.log(x, 10)` is `log(x) / log(10)`, not `log10(x)`, and at 0.001 the two
* differ in the last place — `2.9999999999999996` against `3` — which decides
* whether a peak whose IDR is exactly 10⁻³ is in or out. yapc's spelling is kept.
*/
export function scaledThreshold(threshold: number): number {
return -(Math.log(threshold) / Math.log(10))
}
/** The IDR thresholds yapc writes a BED at, in its order. */
export const YAPC_IDR_THRESHOLDS: readonly number[] = [0.001, 0.005, 0.01, 0.05, 0.1, 0.2]
|