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* Contig and genome roll-up of an **already-loaded** matrix (spec §4, M2.5).
*
* This is the free operation in the cost table: a genome's matrix is already
* in memory (§2), so the contig-level view of it is arithmetic, not I/O. No
* function in this file touches the handle.
*
* Three constraints shape it:
*
* - **bin → contig comes from `chrom_offset`**, by binary search, not from
* `/bins/chrom`. `/bins` is never read (§3.3), and the index already encodes
* the same mapping exactly.
* - **accumulation is `Float64Array`.** The on-disk format widens counts to
* int64 precisely because summation overflows int32 (a genome pair can
* exceed 2^31 contacts on real metagenomic data); a `Float32Array`
* accumulator would start losing whole contacts above 2^24.
* - **an on-diagonal block must be folded before it is summed.** The loaded
* block carries *both* triangles of an upper-triangular store, so a stored
* pixel `(i, j)` with `i < j` appears at both `(i, j)` and `(j, i)`. Summing
* the block naively therefore counts every within-group off-diagonal pixel
* twice, inflating exactly the diagonal of the result — which is where a
* contig- or genome-level heatmap has its largest values, so the error is
* invisible as an artefact and simply reads as "the diagonal is strong".
* `_aggregate_sparse` maps stored pixels once and only then symmetrises
* (`agg + agg.T - diag(agg)`), and {@link aggregateDense} reproduces that.
*/
import type { DenseMatrix, Extent } from '../types'
import type { Coords } from './coords'
import { IDENTITY_PLAN, partitionAxis } from './pooling'
import type { PlacementMode } from './matrix'
/** Aggregation level, matching `ops/aggregate.py`. */
export type AggregationLevel = 'contig' | 'genome'
/**
* A rolled-up block. Deliberately not a {@link DenseMatrix}: the values are
* `Float64Array`, and each axis carries the ids it aggregated to so the UI can
* label rows without re-deriving them.
*/
export interface AggregatedMatrix {
nrows: number
ncols: number
/** Row-major sums, `nrows * ncols` long. */
values: Float64Array
/** Contig or genome id of each output row, in output order. */
rowIds: Int32Array
/** Contig or genome id of each output column, in output order. */
colIds: Int32Array
level: AggregationLevel
}
/** What {@link pixelAccumulator} hands back: a place to put pixels, and the block. */
export interface PixelAccumulator<V extends Float64Array | Float32Array> {
place(bin1: number, bin2: number, value: number): void
finish(): Omit<AggregatedMatrix, 'level' | 'values'> & { values: V }
}
/** A grouping of an axis: which output slot each input row falls into. */
export interface AxisGrouping {
/** Output slot of every input row/column. */
slot: Int32Array
/** The group id occupying each output slot, in first-appearance order. */
ids: Int32Array
}
/**
* Collapse a vector of group ids into output slots, preserving the order in
* which each id is first seen.
*
* First-appearance order is the right rule even though bins arrive sorted by
* contig (and contigs by genome, under the accepted ordering): it makes the
* function total, so a caller that hands it an arbitrary permutation gets a
* sensible answer instead of a silently wrong one.
*/
export function groupRuns(ids: Int32Array): AxisGrouping {
const slot = new Int32Array(ids.length)
const seen = new Map<number, number>()
const order: number[] = []
for (let i = 0; i < ids.length; i++) {
const id = ids[i]
let index = seen.get(id)
if (index === undefined) {
index = order.length
seen.set(id, index)
order.push(id)
}
slot[i] = index
}
return { slot, ids: Int32Array.from(order) }
}
/**
* Sum a dense block into the groups its axes belong to.
*
* @param m The loaded block; `m.values` is read, never modified.
* @param rows Grouping of `m`'s rows (`slot.length === m.nrows`).
* @param cols Grouping of `m`'s columns (`slot.length === m.ncols`).
* @param level What the group ids mean, carried through to the result.
* @param symmetrised `true` when the block covers one bin range on both axes
* and was mirrored out of an upper-triangular store — i.e. the block is
* symmetric and each stored pixel off the diagonal is present twice. Then
* only the upper triangle is summed and the result is mirrored, which is
* `_aggregate_sparse`'s `agg + agg.T - diag(agg)` and the only way to match
* `metacooler aggregate` / `metacooler show --level contig`. Requires a
* square block; a rectangular one (a genome *pair*) holds each stored pixel
* once and must be summed directly.
*/
export function aggregateDense(
m: DenseMatrix,
rows: AxisGrouping,
cols: AxisGrouping,
level: AggregationLevel,
symmetrised = false,
): AggregatedMatrix {
const nrows = rows.ids.length
const ncols = cols.ids.length
const values = new Float64Array(nrows * ncols)
const fold = symmetrised && m.nrows === m.ncols
for (let r = 0; r < m.nrows; r++) {
const a = rows.slot[r]
const inRow = r * m.ncols
// `c = r` keeps the diagonal, drops the mirror. On a square block the two
// axes index the same bins, so `c >= r` is exactly `bin1_id <= bin2_id`.
for (let c = fold ? r : 0; c < m.ncols; c++) {
const b = cols.slot[c]
// The output slot is upper-triangular too, mirroring `to_upper_triangle`
// on the *group* ids. Under the accepted ordering `a <= b` already holds
// whenever `r <= c`; the swap keeps the function total for a caller that
// hands in an arbitrary permutation.
const out = fold && a > b ? b * ncols + a : a * ncols + b
const value = m.values[inRow + c]
// A NaN is a bin the balancer dropped, not a value. It contributes
// nothing rather than turning its whole contig NaN — one filtered bin
// among 4,000 would otherwise blank the chromosome it sits in, and a
// balanced contig-level view of a real file would be empty.
if (!Number.isNaN(value)) values[out] += value
}
}
if (fold) {
for (let a = 0; a < nrows; a++) {
for (let b = a + 1; b < ncols; b++) values[b * ncols + a] = values[a * ncols + b]
}
}
return { nrows, ncols, values, rowIds: rows.ids, colIds: cols.ids, level }
}
/**
* Contig id of every bin in `[lo, hi)`, derived from `chrom_offset`.
*
* The substitute for `/bins/chrom`, which `_bin_to_level_mapping` reads and
* this viewer must not.
*/
export function contigGrouping(coords: Coords, lo: number, hi: number): AxisGrouping {
return groupRuns(coords.contigsOfBins(lo, hi))
}
/**
* Genome id of every bin in `[lo, hi)`: the same `chrom_offset` walk, then one
* lookup per bin into `contigs/genome_id` — the file's own mapping, used as
* written.
*/
export function genomeGrouping(
coords: Coords,
contigGenomeIds: Int32Array,
lo: number,
hi: number,
): AxisGrouping {
const contigs = coords.contigsOfBins(lo, hi)
const genomes = new Int32Array(contigs.length)
for (let i = 0; i < contigs.length; i++) genomes[i] = contigGenomeIds[contigs[i]]
return groupRuns(genomes)
}
/**
* The same grouping, with its output slots collapsed until there are at most
* `cap` of them.
*
* A contig-level roll-up allocates one cell per contig on each axis and nothing
* bounded it: a genome of 4,882 contigs is a 190 MB accumulator for a picture
* 4,096 pixels wide, and the renderer then pooled it two cells to a pixel — flat,
* blind to which contig was which, so the pointer resolved one sequence and the
* pixel held the largest of the four pairs under it. That is the straddling the
* bin path was fixed for, reached through a different door.
*
* So the axis is coarsened where it is built, by the same {@link partitionAxis}
* the bin grid uses, over the *groups* rather than over the bins. A cell is then
* a run of whole contigs — kept inside one genome, since that is the distinction
* the picture exists to draw — and it is named after the first of them, which is
* what a run of them was already named after.
*
* @param groupOf Coarser structure over the groups, if there is one: the genome
* each contig belongs to. Absent at genome level, where there is nothing above.
*/
export function coarsenGrouping(
grouping: AxisGrouping,
cap: number,
groupOf?: (id: number) => number,
): { grouping: AxisGrouping; perCell: number } {
const n = grouping.ids.length
if (n <= cap) return { grouping, perCell: 1 }
const starts = Int32Array.from({ length: n }, (_, i) => i)
const groups = groupOf === undefined ? undefined : Int32Array.from(grouping.ids, groupOf)
const part = partitionAxis(n, starts, cap, IDENTITY_PLAN, groups)
const slot = new Int32Array(grouping.slot.length)
for (let i = 0; i < slot.length; i++) {
const was = grouping.slot[i]
slot[i] = was < 0 ? -1 : part.slot[was]
}
const ids = new Int32Array(part.cells)
for (let c = 0; c < part.cells; c++) ids[c] = grouping.ids[part.cellStart[c]]
return { grouping: { slot, ids }, perCell: part.plan.contigsPerCell }
}
/**
* The roll-up, from the **stored pixels** rather than from a dense block.
*
* {@link aggregateMatrix} needs the block materialised first, and that is the wrong
* way round for a selection whose output is small and whose input is not: a
* whole yeast genome at 500 bp is 2,366 MB of `Float32Array` and 295 million
* loop iterations to produce a 17 × 17 answer — 2,046,919 dense cells per output
* cell — and its cost does not move with the file's sparsity, because it walks
* cells rather than pixels. Measured on that shape: 2,090 ms against 139 ms for
* this, with identical output.
*
* It also means the roll-up no longer passes through the dense guard. A
* contig-level whole-genome view was being refused for the size of a block it
* only ever wanted to collapse — the one escape hatch the refusal offered, and
* it did not work.
*
* The accumulation is `_aggregate_sparse`'s: map each stored pixel once into its
* pair of groups, then symmetrise on the diagonal. That is exactly what
* {@link aggregateDense}'s `fold` reproduces from the mirrored dense block, so
* the two agree cell for cell.
*
* @param place Called once per stored pixel with its two bin ids and value;
* the caller drives the read, so this module still performs no I/O.
*/
export function sparseAggregator(
rows: Extent,
cols: Extent,
coords: Coords,
contigGenomeIds: Int32Array,
level: AggregationLevel,
plan: PlacementMode,
upperTriangular = true,
cap = Number.POSITIVE_INFINITY,
): {
place(bin1: number, bin2: number, value: number): void
finish(): AggregatedMatrix
perCell: number
} {
const build = (extent: Extent): AxisGrouping =>
level === 'contig'
? contigGrouping(coords, extent[0], extent[1])
: genomeGrouping(coords, contigGenomeIds, extent[0], extent[1])
const onDiagonal = rows[0] === cols[0] && rows[1] === cols[1]
// Only a contig axis has a coarser structure to stay inside; at genome level
// the group already *is* the genome.
const groupOf =
level === 'contig' && contigGenomeIds.length > 0
? (id: number): number => contigGenomeIds[id] ?? -1
: undefined
const rowCoarse = coarsenGrouping(build(rows), cap, groupOf)
const colCoarse = onDiagonal ? rowCoarse : coarsenGrouping(build(cols), cap, groupOf)
const acc = pixelAccumulator(
rows,
cols,
rowCoarse.grouping,
colCoarse.grouping,
plan,
upperTriangular,
)
return {
place: acc.place,
finish: () => ({ ...acc.finish(), level }),
perCell: Math.max(rowCoarse.perCell, colCoarse.perCell),
}
}
/**
* The accumulation itself, over groupings the caller chose.
*
* Split out from {@link sparseAggregator} because the *arithmetic* — map each
* stored pixel into a pair of output slots, fold the diagonal once — has nothing
* to do with what the slots are. Contigs and genomes are two answers (above);
* runs of `stride` consecutive bins are a third, which is how a block is read at
* a coarser bin size than the file stores (`metacooler/pooling.ts`).
*
* On-diagonal is decided from the extents rather than passed, for the same
* reason it is there: identical extents mean the block carries both triangles of
* an upper-triangular store, and summing it without folding double-counts every
* off-diagonal pixel into the diagonal of the result — where a coarsened map has
* its largest values, so the error reads as "the diagonal is strong".
*/
export function pixelAccumulator(
rows: Extent,
cols: Extent,
rowGroups: AxisGrouping,
colGroups: AxisGrouping,
plan: PlacementMode,
upperTriangular?: boolean,
): PixelAccumulator<Float64Array>
/**
* …and the **narrowing** form, for a block whose next stop is the wire.
*
* On a folded diagonal — one square axis, one stored triangle — it keeps only
* the upper triangle, in `Float64`, and finishes straight into the `Float32`
* square the worker would have narrowed it to anyway. The full-square `Float64`
* and its `Float32` copy were both alive at the end of a whole-file read:
* 12 B a cell, 200 MB at the raster's 4,096², which is the allocation a browser
* refuses first. This is 8 B a cell at the peak — what the contig and genome
* levels have always cost (`worker/overview.ts`) — so the level that is the
* default no longer needs more memory than the two beside it.
*
* Off the diagonal, or over a square store, nothing is folded and the ordinary
* `Float64` square comes back, exactly as the other form.
*/
export function pixelAccumulator(
rows: Extent,
cols: Extent,
rowGroups: AxisGrouping,
colGroups: AxisGrouping,
plan: PlacementMode,
upperTriangular: boolean,
narrow: true,
): PixelAccumulator<Float64Array | Float32Array>
export function pixelAccumulator(
rows: Extent,
cols: Extent,
rowGroups: AxisGrouping,
colGroups: AxisGrouping,
plan: PlacementMode,
upperTriangular = true,
narrow = false,
): PixelAccumulator<Float64Array | Float32Array> {
const onDiagonal = rows[0] === cols[0] && rows[1] === cols[1]
const fold = onDiagonal && upperTriangular
const nrows = rowGroups.ids.length
const ncols = colGroups.ids.length
// The triangle, where the fold makes the lower half a copy of the upper.
const triangle = narrow && fold && nrows === ncols
const values = new Float64Array(triangle ? (nrows * (nrows + 1)) / 2 : nrows * ncols)
const [r0, r1] = rows
const [c0, c1] = cols
const placeDirect = plan !== 'transpose'
// Not simply `plan !== 'direct'`. The flipped placement is what builds the
// *mirrored dense block*, and on an on-diagonal selection the fold below is
// what mirrors instead — `aggregateDense` reads only `c >= r` there for
// exactly this reason. Placing both and folding as well counts every pixel
// twice, which lands on the diagonal of the result, where a contig-level
// heatmap has its largest values and an inflated one reads as normal.
//
// A *partially* overlapping selection is `symmetric` but not folded, and there
// both placements are correct, because the dense path sums every cell.
const placeFlipped = plan !== 'direct' && !fold
const skipDiagonal = plan === 'symmetric'
const add = (row: number, col: number, value: number): void => {
const a = rowGroups.slot[row]
const b = colGroups.slot[col]
// A negative slot is a bin the grouping left out — the case a *selection*
// makes, where most of the file is not on either axis (`selectionPooling`).
// Dropped here rather than filtered by the caller, so that every grouping
// this accumulator accepts is one it can be handed pixels for.
if (a < 0 || b < 0) return
// Upper-triangular in *group* space too, mirroring `to_upper_triangle`, so
// the fold below has one triangle to mirror rather than two half-filled ones.
if (triangle) {
const lo = a < b ? a : b
const hi = a < b ? b : a
values[lo * nrows - (lo * (lo - 1)) / 2 + (hi - lo)] += value
return
}
values[fold && a > b ? b * ncols + a : a * ncols + b] += value
}
return {
place(bin1: number, bin2: number, value: number): void {
// A NaN is a bin the balancer dropped, not a value; it contributes
// nothing rather than turning its whole contig NaN.
if (Number.isNaN(value)) return
if (placeDirect && bin1 >= r0 && bin1 < r1 && bin2 >= c0 && bin2 < c1) {
add(bin1 - r0, bin2 - c0, value)
}
if (
placeFlipped &&
!(skipDiagonal && bin1 === bin2) &&
bin2 >= r0 &&
bin2 < r1 &&
bin1 >= c0 &&
bin1 < c1
) {
add(bin2 - r0, bin1 - c0, value)
}
},
finish() {
if (triangle) {
// Row by row through the triangle, which is the order it is stored in,
// so the one strided write is the mirror and the reads are sequential.
const square = new Float32Array(nrows * nrows)
let at = 0
for (let a = 0; a < nrows; a++) {
for (let b = a; b < nrows; b++, at++) {
const v = values[at]
square[a * nrows + b] = v
square[b * nrows + a] = v
}
}
return { nrows, ncols, values: square, rowIds: rowGroups.ids, colIds: colGroups.ids }
}
if (fold) {
for (let a = 0; a < nrows; a++) {
for (let b = a + 1; b < ncols; b++) values[b * ncols + a] = values[a * ncols + b]
}
}
return { nrows, ncols, values, rowIds: rowGroups.ids, colIds: colGroups.ids }
},
}
}
/**
* Roll a loaded block up to contig or genome level in one call.
*
* The block's own `rowExtent` / `colExtent` say which bins it covers, so the
* grouping is derived from the matrix itself and cannot drift out of step with
* the data it describes — and it is also what decides whether the block needs
* folding: identical extents mean an on-diagonal block, which carries both
* triangles of the store and would otherwise double-count its own diagonal.
*
* @param upperTriangular `true` for a `symmetric-upper` file (every one
* metacooler writes). Under `square` storage both triangles are stored
* independently, each dense cell is a value in its own right, and the direct
* sum is the correct one.
*
* A block whose extents *partially* overlap is neither case: it is mirrored
* inside the overlap only. No view produces one — genome views are
* on-diagonal and pair views disjoint — so it is summed directly, and the
* overlap would be double-counted if a caller ever built one.
*/
export function aggregateMatrix(
m: DenseMatrix,
coords: Coords,
contigGenomeIds: Int32Array,
level: AggregationLevel,
upperTriangular = true,
): AggregatedMatrix {
const build = (extent: readonly [number, number]): AxisGrouping =>
level === 'contig'
? contigGrouping(coords, extent[0], extent[1])
: genomeGrouping(coords, contigGenomeIds, extent[0], extent[1])
const onDiagonal = m.rowExtent[0] === m.colExtent[0] && m.rowExtent[1] === m.colExtent[1]
const rows = build(m.rowExtent)
// Reused, not rebuilt: on-diagonal the two axes *are* the same bins, and
// sharing the object makes that identity visible rather than incidental.
const cols = onDiagonal ? rows : build(m.colExtent)
return aggregateDense(m, rows, cols, level, onDiagonal && upperTriangular)
}
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