stride-align

Faster than rapidfuzz. Faster than parasail. One import away.

Languages: English · 简体中文

stride-align is a SIMD-accelerated Python library for fuzzy string matching, sequence alignment, phonetic encoding, and time-series distance — with first-class Unicode/CJK and a runtime CPU dispatcher that picks the widest SIMD backend your machine supports (x86, ARM, LoongArch, POWER), with a scalar fallback.

It also provides work-alike imports for four popular libraries: import stride_align.rapidfuzz as rapidfuzz replaces rapidfuzz, from stride_align.thefuzz import fuzz, process replaces TheFuzz, import stride_align.parasail as parasail replaces parasail-python, and import stride_align.jellyfish as jellyfish replaces jellyfish — existing code moves to stride-align by changing one import. (New code should prefer the native stride_align API.)

The full feature list, every supported algorithm, and per-backend detail live in the API reference under docs/api/, with LLM-friendly bundles at llms.txt and llms-full.txt.

Instead of giving you a lecture, we're going to learn by doing. Let's dive right into how it works.

Getting Started

pip install stride-align

Loongson / LoongArch64 users: wheels live on GitHub Releases rather than PyPI, and you pick between the old-world and new-world binary worlds — see LoongArch installation further down.

Simple example

First, just a disclaimer: I'm not using religious texts here to push an agenda - for this demo I need multiple largish public domain documents that have the same meaning but are phrased differently. The Bible just happens to fit that demo requirement freakishly well.

Imagine we have two sentences - let's use the first sentence in Genesis for this:

In the American Standard Version we have: "In the beginning God created the heavens and the earth."

In the King James Version we have: "In the beginning God created the heaven and the earth."

We can see with our eyes there's a difference - heavens vs heaven. But how do we quantify this difference? We'd use this little bit of code:

import stride_align as sa

print(sa.smith_waterman_normalized_score(
      "In the beginning God created the heavens and the earth.",
      "In the beginning God created the heaven and the earth."))

When we run this it prints:

0.9907407407407407

Normalized scores are between 0 and 1. A score of 1 means the inputs are an exact match under the default scoring model. Scores near 0 mean the inputs have little in common, though Smith-Waterman may still find small local matches inside otherwise unrelated strings.

Now let's change the text and see what happens to the score.

import stride_align as sa

print(sa.smith_waterman_normalized_score(
      "In the beginning God created the heavens and the earth.",
      "The quick brown fox jumped over the lazy dog."))

and Python prints

0.12222222222222222

Starting to get the idea? The more similar the strings, the higher the score.

Larger example: search

Let's build a bigger example, something that gives us a feel for the library's performance. You'll probably notice that we switch between Smith-Waterman and Needleman-Wunsch and may be wondering which to use when. Use Needleman-Wunsch when you want to compare the whole input against the whole input. Use Smith-Waterman when you want to find the best matching region inside larger inputs.

Okay, let's move on to the demo code. You need requests for this part of the demo:

pip install requests

import os, time, requests
import stride_align as sa

if not os.path.exists("kjv.txt"):
    response = requests.get("https://openbible.com/textfiles/kjv.txt")
    response.raise_for_status()
    response.encoding = "utf-8-sig"
    open("kjv.txt", "w", encoding="utf-8").write(response.text)

lines = [line.strip().lower() for line in open("kjv.txt")][2:]

while True:
    if not (query := input("Enter a snippet to match.  Press enter to end.\n")):
        break
    t = time.perf_counter()
    scores = sa.needleman_wunsch_normalized_scores(query.lower(), lines)
    best = int(scores.argmax())
    print()
    print("Score:", float(scores[best]))
    print(lines[best])
    print("Search time: %0.2fms" % ((time.perf_counter() - t) * 1000))
    print()
    print()

Now how can we use this? Suppose we have a random Bible verse and want to know what chapter and verse it comes from. grep you say? Oh, heavens, no: we made a mistake. The verse we have is from a different translation, say the Catholic Public Domain, and what we have on our computer is the King James Bible. grep's exact string matching won't work here. How do we find the chapter and verse? We search for the "closest" or "most similar" string using stride-align, of course.

In our demo the first part concerns itself with downloading and caching. The good folks at Open Bible put this text where it's HTTP-reachable, but we want to be respectful of their IT budget so we cache what we download. It's just good citizenship.

In the next part we load all of the lines into a list. We remove newlines and make everything lower case because we don't want to get all fiddly about whether we're holding the shift key.

Lastly that while True: loop collects a line of text, presumably the Bible verse from the Catholic version of the Bible we want to look up the chapter and verse for, and matches it against all of the lines in the King James Bible using the batch form of Needleman-Wunsch. It returns an array of scores. We use argmax() to find the best-scoring line and then print the line associated with that index. Let's try it.

I'm going to use Jeremiah 4:28 from the Catholic Bible - it's actually quite different from the same verse in the King James Bible. Let's see what happens ...

$ python3 demo2.py
Enter a snippet to match.  Press enter to end.
The earth will mourn, and the heavens will lament from above. For I have spoken, I have decided, and I have not regretted. Neither will I be turned away from it.

Score: 0.3598901098901099
jeremiah 4:28   for this shall the earth mourn, and the heavens above be black: because i have spoken [it], i have purposed [it], and will not repent, neither will i turn back from it.
Search time: 206.51ms

... and we found it! And pretty quickly too.

Larger example: spell checker

This is a toy spell checker, not a production one. It ignores punctuation, capitalization, word frequency, proper nouns, and context. The point is to show the same one-query-against-many-candidates pattern on a familiar task.

import os, sys
import stride_align as sa

paths = ['/usr/share/dict/words',
         '/usr/dict/words',
         '/var/lib/dict/words',
         '/etc/dictionaries-common/words']

for path in paths:
    if os.path.exists(path):
        break
else:
    print("Sorry, I can't find your dictionary", file=sys.stderr)
    exit(1)


words = [line.strip().lower() for line in open(path)]


for line in sys.stdin:
    new_line = []
    for word in line.split():
        scores = sa.needleman_wunsch_normalized_scores(word.lower(), words)
        word = words[int(scores.argmax())]
        new_line.append(word)
    print(' '.join(new_line), flush=True)

The first thing this script does is try to find our operating system's list of correctly spelled words. Its location can vary from distribution to distribution. Once we've found it, we load it, strip off newlines and start the act of spell checking.

The spell checking looks a lot like the matching we did before. For each candidate word, we match it against all of the words in our list of correctly spelled words, use argmax() to find the highest-scoring candidate, and replace the word with that candidate. We could speed things up with some optimizations, like not searching for a match for correctly spelled words, but this is a demo and that optimization is left as an exercise for the reader.

Let's see how it works!

$ cat - | python3 demo3.py
this is a demonstrtion of a spel checker
it doesn't matter that I can't spell corectly

this is a demonstration of a spell checker
it doesn't matter that i can't spell correctly

Capabilities

The native stride_align API covers, in one library, the surface that's usually split across parasail, rapidfuzz, python-Levenshtein, jellyfish, editdistance, and dtw-python.

Edit distance and similarity scorers. Levenshtein, Damerau-Levenshtein (both OSA and unrestricted variants), Indel, Hamming, Jaro, Jaro-Winkler, longest common subsequence / substring, Ratcliff-Obershelp, Monge-Elkan, character-n-gram Jaccard / Sørensen- Dice / cosine / overlap. Each algorithm exposes a consistent variant family: _score, _normalized_score, _scores (one query × N targets, batched), _normalized_scores, _best, _normalized_best, _top_k. Detail in docs/api/edit-distance.md and docs/api/similarity.md.

Sequence alignment. Smith-Waterman (local) and Needleman-Wunsch (global) DP with linear or affine gaps and substitution matrices. Score-only, normalised, batch-over-targets, top-k, traceback to alignment path, SAM/BAM-style CIGAR (_cigar, _trace_cigar, _trade_cigar). A Farrar score-only fast path uses an interleaved DP layout for the throughput-oriented case. Detail in docs/api/alignment.md.

All-pairs cdist family. cdist, cdist_above_threshold, cdist_top_k, and cdist_top_k_per_query over any built-in scorer (via the Scorer enum) or any Python callable. Multi-threaded SIMD under a released GIL, with closed-form length-difference pruning and per-pair cutoff push-down into the kernel inner loop. Detail in docs/api/cdist.md.

Substitution matrices. Built-in blosum45 / 50 / 62 / 80 / 90 and pam30 / 70 / 250, an NCBI-text loader, and a generic SubstitutionMatrix for custom alphabets (case-sensitive text included). Detail in docs/api/matrices.md.

Phonetic encoders. Soundex, Metaphone (Apache Commons or jellyfish rule families), Double Metaphone (Apache Commons or Python-package bug-compat), NYSIIS, Match Rating Approach, Caverphone 2, Cologne Phonetic (Unicode-aware German), Daitch-Mokotoff Soundex, and Beider-Morse Phonetic Matching. Detail in docs/api/phonetic.md.

Dynamic time warping. dtw_distances for one query against many targets, int16 / float32 / float64, optional Sakoe-Chiba band, choice of local metric. Detail in docs/api/dtw.md.

Compatibility shims. stride_align.rapidfuzz, stride_align.thefuzz, stride_align.parasail, and stride_align.jellyfish are work-alike import replacements for widely used libraries in the space. Detail in docs/api/rapidfuzz-shim.md and docs/api/thefuzz-shim.md, docs/api/parasail-shim.md, and docs/api/jellyfish-shim.md.

The native boundary accepts:

• bytes against bytes
• str against str (UCS-1 / UCS-2 / UCS-4, zero-copy — Chinese, Japanese, Korean, Arabic, emoji all hit the SIMD path without a UTF-8 round-trip)
• sequences of immutable hashable Python objects
• mixed sequence/object inputs where a str or bytes side is treated as a sequence
• NumPy ndarray of integer dtype (8 / 16 / 32 / 64 bit)

Direct bytes versus str pairs raise TypeError.

Score-only functions return numeric scores. The normalised variants return scores between 0 and 1. Path functions return alignment result objects with the score, aligned sequences, operations, and CIGAR-style summaries where available.

Documentation

Both READMEs and every markdown file in the repo are rendered to HTML by tools/md_to_html.py. The long-form English README is published as README.html. The tracked English product homepage is authored directly at html/index.html; the Simplified Chinese homepage and shared assets are authored under website/. The published site lives in html/ and is mirrored at stride-align.com.

Cloudflare Workers hosting

The site is configured as an assets-only Cloudflare Worker. Wrangler uploads the built html/ tree directly; there is no JavaScript Worker entry point or runtime binding.

For Cloudflare Workers Builds, set this build variable in Settings → Build → Build Variables and Secrets. This disables Cloudflare's automatic Python dependency detection, which would otherwise see pyproject.toml and try to compile the stride-align native extension:

SKIP_DEPENDENCY_INSTALL=1

Use these exact build settings:

Build command:  bash tools/cloudflare_build.sh
Deploy command: npx wrangler deploy --assets ./html
Root directory: /

The Cloudflare build script runs npm ci, installs only the pure-Python dependency in requirements-site.txt, and runs the Markdown renderer. It never installs the stride-align package or invokes a C/C++ compiler.

For local development, use Node.js 22 or newer and install the Python Markdown build dependency once:

python3 -m pip install "markdown>=3.5"
npm ci

Then build and preview locally, validate the upload without deploying, or deploy to the configured stride-align Worker. Authenticate once before the first interactive deployment:

npx wrangler login
npm run site:dev
npm run site:check
npm run site:deploy

site:build runs tools/md_to_html.py. That generator preserves the tracked, hand-authored html/index.html and refreshes the localized homepage, documentation, styles, benchmark artifacts, and shared assets around it. Wrangler account selection and any stride-align.com custom domain route remain Cloudflare account configuration, so a dry run cannot change live DNS or routing.

API quick-start

The full reference lives under docs/api/, grouped by surface (edit-distance, similarity, alignment, all-pairs cdist, substitution matrices, DTW, phonetic encoders, and the four compatibility shims). This section is a tour of the most common patterns to get you started.

import stride_align

score = stride_align.needleman_wunsch_score("ACGT", "ACCT")
scores = stride_align.Scores("ACGT", variant="needleman_wunsch").compare(["ACCT", "AGGT"])
result = stride_align.smith_waterman_path("ACCGT", "CCG")
wide_result = stride_align.smith_waterman_path("ACCGT", "CCG", width=64)
object_result = stride_align.needleman_wunsch_path(
    [frozenset({1}), frozenset({2})],
    [frozenset({1}), frozenset({3})],
)

print(score)
print(scores)
print(result.score, result.aligned_query, result.aligned_target, result.operations)
print(wide_result.score)
print(object_result.aligned_query, object_result.aligned_target)

Use Scores(...).compare([...]) or the *_scores() functions for one-query against many-target score workloads. That path prepares the query/profile once and is the preferred performance API for repeated English/Chinese text comparisons.

Traceback outputs preserve the paired fast-path type:

• str inputs return aligned str
• bytes inputs return aligned bytes
• sequence/object inputs return aligned tuple values with None gaps

Pass width=8, 16, 32, or 64 to force the internal token/scoring width instead of using automatic selection.

Some functions expose CIGAR strings, short for "Concise Idiosyncratic Gapped Alignment Report". CIGAR is the compact alignment-operation notation used by SAM/BAM tooling. If you want the full formal version, see the SAM specification.

Substitution matrices (BLOSUM, PAM)

For protein alignment, stride_align.matrices ships the canonical BLOSUM and PAM substitution matrices. Pass any of them via the matrix= kwarg on smith_waterman_score, needleman_wunsch_score, or their _scores batch counterparts:

import stride_align
from stride_align.matrices import blosum62, pam250

# Local alignment, NCBI standard BLOSUM62 with affine gaps (open=-11,
# extend=-1). matrix= is mutually exclusive with match_score / mismatch_score.
stride_align.smith_waterman_score(
    "HEAGAWGHEE", "PAWHEAE",
    matrix=blosum62,
    gap_open_score=-11, gap_extend_score=-1,
)

# Batch (1 query × N targets) with profile reuse — the recommended
# path for "score one query against a library".
stride_align.smith_waterman_scores(
    "HEAGAWGHEE",
    ["PAWHEAE", "HEAGAWGHEE", "MEEPS"],
    matrix=pam250, gap_open_score=-14, gap_extend_score=-2,
)

# Custom matrices: parse any NCBI-format text file
custom = stride_align.matrices.SubstitutionMatrix.from_ncbi_text(
    open("/path/to/BLOSUM62").read(),
    name="BLOSUM62",
    gap_open=-11, gap_extend=-1,
)

Each built-in SubstitutionMatrix exposes its alphabet, matrix data (int8 ndarray), and recommended gap defaults via .gap_score (linear), .gap_open, and .gap_extend. Both linear gaps (gap_score=) and affine gaps (gap_open_score= + gap_extend_score=) are supported on the AVX-512 backend; other SIMD backends currently fall back to the scalar generic kernel for matrix-mode.

The shipped matrix values come from the NCBI BLAST distribution ftp.ncbi.nih.gov/blast/matrices/, which carries the canonical reference scores. The original publications are:

• BLOSUM45 / 50 / 62 / 80 / 90 — Henikoff S., Henikoff J.G. (1992). Amino acid substitution matrices from protein blocks. PNAS 89(22):10915–10919. doi:10.1073/pnas.89.22.10915  ·  PDF (open access)
• PAM30 / 70 / 250 — Dayhoff M.O., Schwartz R.M., Orcutt B.C. (1978). A model of evolutionary change in proteins. In Atlas of Protein Sequence and Structure, vol. 5, supplement 3, pages 345–352. National Biomedical Research Foundation, Washington, D.C. (Book chapter; not available online as an open PDF. A widely cited follow-on derivation appears in Schwartz R.M., Dayhoff M.O. (1978), Matrices for detecting distant relationships, same volume, pages 353–358.)

Keyboard typo matrices (real typing-error data)

stride-align also ships example keyboard confusion matrices built from real human typing errors — the Aalto "136 Million Keystrokes" dataset, used with the authors' permission. Each scores how likely it is that one character was typed when another was meant, so a plausible slip (teh for the) aligns as a near-match instead of a flat mismatch:

import stride_align as sa
from stride_align.matrices import keyboard

sa.smith_waterman_score("teh", "the", matrix=keyboard.qwerty)

Orientation — the query is the misspelled side. Like every stride-align matrix these are m[a][b] with a = query and b = target, and here a is the character actually typed (the mistake) and b is the character that was intended (the correction). So pass the misspelled / user-entered string as the query and the canonical / dictionary string as the target.

Unlike symmetric BLOSUM/PAM, these matrices are asymmetric, so orientation matters. If your pipeline has it the other way round — the query is the correct string — flip the matrix with NumPy's .T (transpose), which swaps the axes to m[intended][misspelled]:

import numpy as np
from stride_align.matrices import SubstitutionMatrix, keyboard

fwd = keyboard.qwerty
rev = SubstitutionMatrix(
    name=fwd.name + ".T", alphabet=fwd.alphabet,
    matrix=np.ascontiguousarray(fwd.matrix.T),   # .T swaps query/target
    gap_score=fwd.gap_score, wildcard=fwd.wildcard,
)

Build your own from a {(typed, intended): count} mapping with keyboard.from_confusion_counts(...). The shipped matrices are derived log-odds artifacts, not the raw keystroke data; see NOTICE and docs/keyboard-matrix-external-sources.md for attribution and the scope of the permission.

rapidfuzz compatibility (drop-in shim)

Replace one import line and most rapidfuzz code keeps working:

# Before:
# import rapidfuzz

# After:
import stride_align.rapidfuzz as rapidfuzz

# fuzz: full token-ratio family, scores in [0, 100]
rapidfuzz.fuzz.ratio("hello", "hallo")                  # 80.0
rapidfuzz.fuzz.WRatio("foo bar baz", "foo bar")         # 90.0
rapidfuzz.fuzz.token_set_ratio("the cat", "cat the")    # 100.0

# distance: classes with distance / normalized / similarity methods,
# plus editops / opcodes for Levenshtein.
rapidfuzz.distance.Levenshtein.distance("kitten", "sitting")          # 3
rapidfuzz.distance.JaroWinkler.normalized_similarity("MARTHA", "MARHTA")
rapidfuzz.distance.Levenshtein.editops("kitten", "sitting")
# -> Editops([Editop(tag='replace', src_pos=0, dest_pos=0), ...], src_len=6, dest_len=7)

# process: extract / extractOne / cdist
rapidfuzz.process.extract("hello", ["hallo", "world", "helo"], limit=2)
# -> [('helo', 88.88, 2), ('hallo', 80.0, 0)]

# utils: default_process (matches upstream bit-exactly, does NOT
# collapse internal whitespace runs)
rapidfuzz.utils.default_process("Hello, World!")        # 'hello  world'

Known divergences: the partial_ratio family inherits stride-align's Phase D.3 conservative-underestimate — never overshoots upstream, but can underestimate by a few points on pairs where rapidfuzz finds a shifted optimal window. Levenshtein.distance does not yet support the weights=(insert, delete, replace) kwarg.

TheFuzz compatibility (work-alike facade)

TheFuzz keeps an older integer-scored API and two-element extraction tuples. The dedicated facade preserves those conventions while using stride-align's native kernels:

# Before:
# from thefuzz import fuzz, process

# After:
from stride_align.thefuzz import fuzz, process

fuzz.ratio("this is a test", "this is a test!")       # 97
fuzz.token_sort_ratio("fuzzy wuzzy was a bear", "wuzzy fuzzy was a bear")
# -> 100
process.extractOne("cowboys", ["New York Jets", "Dallas Cowboys"])
# -> ('Dallas Cowboys', 90)

All ten TheFuzz 0.22.1 scorers, extract*, and dedupe are covered. The direct scorers also accept arbitrary sequences of hashable Python objects through stride-align's shared compact-token encoder. See docs/api/thefuzz-shim.md for exact preprocessing, rounding, result-shape, and custom-scorer behavior. The partial_ratio family inherits the same rare shifted-window conservative underestimate documented for the RapidFuzz shim above.

parasail compatibility (drop-in shim)

Replace one import line and most parasail code keeps working:

# Before:
# import parasail

# After:
import stride_align.parasail as parasail

# Same parasail signature: (s1, s2, open, extend, matrix)
# Gap penalties are positive numbers (BLAST convention:
# cost(N) = open + (N-1)*extend).
r = parasail.sw_trace("HEAGAWGHEE", "PAWHEAE", 11, 1, parasail.blosum62)
print(r.score)               # int
print(r.cigar.decode)        # bytes, e.g. b'2=1X3='
print(r.traceback.query)     # 'HEAGAWGHEE' aligned with gaps
print(r.traceback.ref)       # 'PAWHEAE'    aligned with gaps
print(r.traceback.comp)      # '|.| ||'-style match annotation

# matrix_create + stats
m = parasail.matrix_create("ACGT", 2, -1)
r = parasail.sw_stats("ACGTAC", "ACATAC", 5, 2, m)
print(r.matches, r.similar, r.length)

# The 2000+ kernel-suffix variants (sw_striped_avx2_16, nw_scan_64,
# sw_trace_diag_sat, ...) all alias to the matching core entry —
# stride-align picks the kernel based on score range and hardware.
parasail.sw_striped_avx2_16("ACGT", "ACGT", 5, 2, m)

Known divergences: SW with multiple optimal alignments may pick a different path than upstream parasail (both score-correct); the sg_qb/sg_qe/sg_qb_de style semi-global mode selectors and the dnafull / nuc44 matrices are not yet provided.

Edit-distance scorers

Beyond Smith-Waterman and Needleman-Wunsch, stride-align exposes six unit-cost edit-distance and similarity metrics — each with its own SIMD-batched code path:

import stride_align

# Levenshtein (Myers 1999 bit-parallel) — inserts, deletes, substitutes
stride_align.levenshtein_score("kitten", "sitting")               # -> 3
stride_align.levenshtein_normalized_score("kitten", "sitting")    # -> 0.571...
stride_align.levenshtein_scores("kitten", ["kit", "sitting"])     # -> ndarray[int64]

# Optional `score_cutoff` (rapidfuzz convention): bail early per-target,
# results that exceed the cutoff come back as `cutoff + 1`.
stride_align.levenshtein_scores(query, targets, score_cutoff=3)

# Damerau-Levenshtein (OSA-restricted, Hyyrö 2002) — adds adjacent
# transposition at unit cost. This is what rapidfuzz exposes as
# OSA.distance and is what most callers asking for
# "Damerau-Levenshtein" actually want.
stride_align.damerau_levenshtein_score("ab", "ba")                # -> 1

# True Damerau-Levenshtein — the unrestricted form, where one
# character may participate in more than one edit. Slower (no
# bit-parallel kernel yet) but matches rapidfuzz.distance.DamerauLevenshtein
# exactly. Diverges from OSA on overlapping transpositions, e.g.
# "ca" -> "abc": OSA=3, true-DL=2.
stride_align.true_damerau_levenshtein_score("ca", "abc")          # -> 2

# Indel — Levenshtein restricted to insertions and deletions, no
# substitutions. Equivalent to |a| + |b| - 2 * LCS(a, b). Bit-
# parallel Allison-Dix (1986) inner loop.
stride_align.indel_score("kitten", "sitting")                     # -> 5

# Hamming — count of positions where two equal-length strings differ.
# Cutoff variant bails the byte loop once mismatches exceed the cap.
stride_align.hamming_score("100", "110")                          # -> 1

# Jaro / Jaro-Winkler — similarities in [0, 1]; Winkler adds a
# capped prefix bonus.
stride_align.jaro_similarity("martha", "marhta")                  # -> 0.944...
stride_align.jaro_winkler_similarity("martha", "marhta")          # -> 0.961...

The batch variants (*_scores, *_similarities) pack one target per SIMD lane on every supported backend:

• x86: SSE4.1 / AVX2 / AVX-512 / AVX10-256 / AVX10-512
• ARM: NEON (Linux + macOS), SVE / SVE2
• LoongArch: LSX / LASX
• PowerPC: VSX

For Lev / OSA, patterns up to 64 chars run a single-word Myers; 65–256 chars use the multi-word kernel (W=2/3/4). Indel and OSA fall back to scalar bit-parallel for patterns >64 (multi-word generalization deferred); true-DL is scalar DP only.

Longest Common Subsequence + Substring

Two related but distinct dynamic programs, both shipped:

import stride_align as sa

# Longest Common Subsequence — characters need not be contiguous.
# "ABCBDAB" and "BDCAB" share "BCAB" (length 4).
sa.lcs_length("ABCBDAB", "BDCAB")                    # -> 4

# Closed-form relation to Indel distance: indel = |a| + |b| - 2·LCS.
sa.indel_score("kitten", "sitting") == \
    len("kitten") + len("sitting") - 2 * sa.lcs_length("kitten", "sitting")
# -> True

# Longest Common Substring — characters MUST be contiguous.
sa.lcs_substring_length("ABCBDAB", "BDCAB")          # -> 2
sa.lcs_substring("ABCBDAB", "BDCAB")                 # -> "AB"

# Result type matches inputs: bytes in, bytes out.
sa.lcs_substring(b"hello world", b"world hello")     # -> b"hello"

# Codepoint engine — non-ASCII is first-class.
sa.lcs_substring("Müller", "Mueller")                # -> "ller"

Both DPs are scalar O(m·n) time with two rolling rows for O(min(m,n)) (subsequence) or O(|b|) (substring) space. When multiple substrings tie at the maximum length, the first occurrence in a is returned (matches str.find convention).

Ratcliff-Obershelp similarity

The algorithm Python's difflib.SequenceMatcher().ratio() ships, which rapidfuzz does not — recursive longest-matching-substring split, summed match lengths divided by total length:

import stride_align as sa

sa.ratcliff_obershelp_similarity("kitten", "sitting")
# -> 0.6153846153846154

# Bit-exact with difflib at autojunk=False (we have no junk
# character heuristic):
import difflib
sa.ratcliff_obershelp_similarity("ABCBDAB", "BDCAB") == \
    difflib.SequenceMatcher(None, "ABCBDAB", "BDCAB", autojunk=False).ratio()
# -> True

# Batch form: one query against many targets, returned as
# ndarray[float64].
sa.ratcliff_obershelp_similarities("kitten",
                                    ["sitting", "kitten", "kit"])
# -> array([0.61538462, 1.        , 0.66666667])

Not commutative — the inner longest-common-substring tiebreak (earliest in a, then earliest in b) means the recursion splits leftover ranges differently for (a, b) vs (b, a), and the total match length can differ. Faithful to difflib, which has the same property; sa.ratcliff_obershelp_similarity("ABCBDAB", "BDCAB") gives 0.333… while the reverse gives 0.667…. Pin both directions if your tests need an order-independent metric.

N-gram set similarity

Four metrics over character n-gram multisets (each n-gram counted with multiplicity), keyword-only n= (default 2 — character bigrams):

import stride_align as sa

# Jaccard: |A ∩ B| / |A ∪ B|
sa.jaccard("ABCBDAB", "BDCAB")                  # -> 0.25

# Sørensen-Dice: 2 * |A ∩ B| / (|A| + |B|)
sa.dice("ABCBDAB", "BDCAB")                     # -> 0.4

# Overlap coefficient: |A ∩ B| / min(|A|, |B|)
sa.overlap("ABCBDAB", "BDCAB")                  # -> 0.5

# Cosine over multiset frequency vectors: ⟨A, B⟩ / (‖A‖ · ‖B‖)
sa.cosine("ABCBDAB", "BDCAB")                   # -> ~0.5303

# Trigrams.
sa.jaccard("hello", "help", n=3)                # -> 0.25

# Batch — query multiset built once and reused across targets.
sa.jaccard_similarities("kitten", ["sitting", "kitten", "kit"])
# -> array([0.25, 1.0, 0.111...])

All four metrics are symmetric and bounded in [0, 1]. Identity convention: both inputs empty (or both shorter than n) → 1.0; one empty → 0.0. Dice and Jaccard satisfy the closed-form relation D = 2·J / (1 + J).

Token-ratio family (rapidfuzz fuzz.* parity)

Drop-in replacements for the rapidfuzz.fuzz.* token-ratio API, returning values in [0, 1] (multiply by 100 for rapidfuzz's [0, 100] convention). The base ratio is sa.indel_normalized_score — algebraically identical to rapidfuzz.fuzz.ratio / 100 (both reduce to 2 · LCS / (|a| + |b|)).

import stride_align as sa

# Token sort: split on whitespace, sort, join, compute the ratio.
sa.token_sort_ratio("fuzzy wuzzy bear", "bear wuzzy fuzzy")     # -> 1.0

# Token set: set intersection + per-side differences, max of three
# pairwise ratios.
sa.token_set_ratio("the quick brown fox", "the quick brown dog") # -> ~0.895

# Partial ratio: best match of the shorter string within the longer
# (sliding-window + LCS-substring candidate).
sa.partial_ratio("apple", "an apple a day")                     # -> 1.0
sa.partial_ratio("java language",
                 "python programming language")                 # -> ~0.818

# Token-sort / token-set combined with partial ratio.
sa.partial_token_sort_ratio("apple bear", "an apple and a bear") # -> 1.0
sa.partial_token_set_ratio("the cat",     "a cat sat down")      # -> 1.0

# rapidfuzz's weighted blend.
sa.WRatio("fuzzy wuzzy was a bear", "wuzzy fuzzy was a bear")    # -> 1.0

# Case-insensitive: pass a processor callable.
sa.token_sort_ratio("FOO BAR", "bar foo", processor=str.lower)   # -> 1.0

token_set_ratio and partial_token_set_ratio follow rapidfuzz's convention of returning 0.0 when either side has no tokens after whitespace splitting. The implementations are pure Python on top of stride-align's own kernels — no third-party code is imported into the production path.

Monge-Elkan multi-token similarity

Classic record-linkage hybrid (Monge & Elkan, 1996). For each token in s1, find the best-matching token in s2 under a configurable inner similarity, then average across s1's tokens. Asymmetric by definition — pass symmetric=True to average both directions when an order-independent score is wanted.

import stride_align as sa

# Default inner is Jaro.
sa.monge_elkan("paul johnson", "paul jones")      # -> ~0.94

# Asymmetric: |s1| tokens drive the average.
sa.monge_elkan("paul",         "paul johnson")    # -> 1.0
sa.monge_elkan("paul johnson", "paul")            # -> 0.5

# Symmetric variant.
sa.monge_elkan("paul",         "paul johnson",
               symmetric=True)                    # -> 0.75

# Inner similarity selection.
sa.monge_elkan("hello world", "hallo world",
               inner="jaro_winkler")              # boost common prefixes
sa.monge_elkan("hello world", "hallo world",
               inner="levenshtein_ratio")         # bit-parallel Levenshtein
sa.monge_elkan("a b c", "a c d",
               inner=lambda x, y: 1.0 if x == y else 0.0)  # custom callable

# Preprocessor (e.g. case-insensitive).
sa.monge_elkan("PAUL JOHNSON", "paul Johnson",
               processor=str.lower)               # -> 1.0

Returns 1.0 when both inputs have no tokens after whitespace splitting (vacuously identical); 0.0 when exactly one side has no tokens. The implementation is pure Python on top of stride-align's Jaro / Jaro-Winkler / Levenshtein / Indel kernels — no new C++ kernels and no third-party code in the production path.

Phonetic encoders

For name matching, deduplication, and search-as-you-type, stride-align ships the full standard phonetic-encoder family. Each encoder maps a string to a short code such that names that sound similar share a code, regardless of spelling:

import stride_align as sa

# American Soundex (Russell & Odell, 1918). 4-character code.
sa.soundex("Robert")                                     # -> "R163"
sa.soundex("Rupert")                                     # -> "R163"
sa.soundex_equal("Robert", "Rupert")                     # -> True

# Metaphone (Lawrence Philips, 1990) — two-letter and longer
# spec-correct variants. The published 1990 spec and the popular
# jellyfish library disagree on a handful of edge cases; the variant
# kwarg picks the rule family.
sa.metaphone("Schmidt")                                  # -> "SKMTT"  (PHILIPS, spec)
sa.metaphone("Schmidt", variant=sa.MetaphoneVariant.JELLYFISH)  # -> "SXMTT"
sa.metaphone_equal("Schmidt", "Smith")                   # -> False

# Double Metaphone (Lawrence Philips, 2000) — primary and alternate
# codes; the alternate captures plausible non-English pronunciations.
# COMMONS is the faithful Apache Commons Codec port; PYTHON is bug-
# compat with the metaphone PyPI package.
sa.double_metaphone("Schwartz")                          # -> ("XRTS", "XFRTS")
sa.double_metaphone("Hugh")                              # -> ("H", "")
sa.double_metaphone("Hugh",
    variant=sa.DoubleMetaphoneVariant.PYTHON)            # -> ("HH", "")

# NYSIIS (Taft, 1970). More discriminative than Soundex for English
# names — "Watkins" / "Wilkins" / "Wilkinson" don't collide.
sa.nysiis("Watkins"), sa.nysiis("Wilkins")               # -> ("WATCAN", "WALCAN")

# Match Rating Approach (Moore, Western Airlines, 1977). A codex plus
# a pairwise comparator with length-difference + rating-threshold rules.
sa.match_rating_codex("Christopher")                     # -> "CHRPHR"
sa.match_rating_compare("Robert", "Rupert")              # -> True

# Caverphone 2.0 (Hood, 2004). Fixed-length 10-character code,
# right-padded with '1'. Designed for late-19th-century New Zealand
# electoral rolls but widely applied to general English-language
# name matching.
sa.caverphone("Stevenson")                               # -> "STFNSN1111"

# Cologne Phonetic / Kölner Phonetik (Postel, 1969). German-language
# encoder that maps letters to digits 0-8 with context-sensitive rules
# for C, X, D, T, P. Umlauts and ß preprocess to their Latin-letter
# equivalents so callers don't have to NFKD-fold first.
sa.cologne_phonetic("Müller")                            # -> "657"
sa.cologne_phonetic("Schmidt")                           # -> "862"

# Daitch-Mokotoff Soundex (Daitch & Mokotoff, 1985). Six-digit
# Soundex tuned for Slavic and Yiddish surnames. The leading letter
# is encoded (not preserved verbatim); multi-character clusters like
# 'sch', 'tsch', 'rz' fire before any single-letter rule; several
# rules emit '|'-joined alternative codes via branching.
sa.daitch_mokotoff("LEWINSKY")                           # -> "876450"
sa.daitch_mokotoff("Goldman")                            # -> "583660"
sa.daitch_mokotoff("AUERBACH")                           # -> "097400|097500"
sa.daitch_mokotoff("AUERBACH", branching=False)          # -> "097400"

# Beider-Morse Phonetic Matching (Beider & Morse, 2008). Multi-
# language phonetic encoder returning a '|'-separated set of plausible
# pronunciation codes across European languages, optimised for family
# names. stride-align ships the GENERIC name-type only — the broad
# general-purpose rule set; the Ashkenazi and Sephardic rule sets from
# the upstream Apache Commons Codec distribution are not included.
sa.beider_morse("Renault")
# -> "rinD|rinDlt|rina|rinalt|rino|rinolt|rinu|rinult"
sa.beider_morse("Renault", rule_type=sa.BmpmRuleType.EXACT)
# -> "renau|renault|reno|renolt"
sa.beider_morse("Müller", rule_type=sa.BmpmRuleType.EXACT)
# -> "mQler|muler"
sa.beider_morse("d'ortley", rule_type=sa.BmpmRuleType.EXACT)
# -> "(ortlaj|ortlej)-(dortlaj|dortlej)"   (d' prefix handler)

The first seven encoders are dispatched through the same byte- extraction helper, accept str and bytes inputs interchangeably, and skip non-letter / non-ASCII codepoints before encoding — pre- normalise with unicodedata.normalize("NFKD", s) if you want accent folding. Cologne Phonetic re-encodes str inputs through UTF-8 so its ß / Ä / Ö / Ü preprocessing fires correctly. Beider-Morse ships its GENERIC rule data (the 63 gen_*.txt files from Apache Commons Codec) as package resources loaded once at first call via importlib.resources, runs the language guesser plus a rule-based phonetic engine entirely in C++, and returns a |-separated UTF-8 string of phonetic codes. Cross-checked against the canonical Apache Commons Codec reference data and the jellyfish, metaphone, and doublemetaphone PyPI packages.

Dynamic Time Warping

For aligning numeric sequences whose timing or speed varies — audio signals, gesture / sensor traces, financial time series — stride-align exposes Dynamic Time Warping with optional Sakoe-Chiba band:

import numpy as np
import stride_align as sa

q = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
t = np.array([1.0, 2.0, 2.5, 4.0, 5.0])

# Default distance follows the dtype:
#   float32 / float64 -> L2-squared, (x - y)^2
#   int16             -> L1, |x - y|  (audio convention)
sa.dtw(q, t)                                              # -> 0.25

# Sakoe-Chiba band: int radius or fraction of max(|q|, |t|).
sa.dtw(q, t, window=2)
sa.dtw(q, t, window=0.2)

# Explicit distance.
sa.dtw(q.astype(np.int16), t.astype(np.int16), distance="l1")

# Batch.
sa.dtw_distances(q, [t, t * 2, t + 0.5], window=2)

Inputs must be NumPy ndarray with matching dtype (float32, float64, or int16 — the natural audio dtype). Other dtypes and non-ndarray inputs raise TypeError.

cdist, cdist_above_threshold, cdist_top_k, cdist_top_k_per_query

For all-pairs scoring across two lists of strings, stride-align ships three matrix-style entry points:

qs = ["kitten", "sitting", "kit"]
ts = ["kitten", "kit", "sitting", "biting"]

# Full N×M similarity matrix — ndarray[float64] (similarity scorers)
# or ndarray[int64] (distance scorers).
sa.cdist(qs, ts, scorer=sa.Scorer.JARO)

# Streaming filter — yields only pairs whose similarity exceeds the
# threshold. Workers feed a bounded queue; the caller drains it.
# Length pruning + per-pair cutoff push-down into the kernel skip
# most of the work at high thresholds.
for score, q, t in sa.cdist_above_threshold(
    qs, ts, scorer=sa.Scorer.LEVENSHTEIN_NORMALIZED, threshold=0.7,
):
    ...

# Top-k by score — returns at most k highest-scoring (or lowest, for
# distance scorers) (score, query, target) tuples. Heaps are
# per-thread; a shared atomic global-min bound lets the per-pair
# cutoff push-down lift the prune threshold as work progresses.
sa.cdist_top_k(qs, ts, scorer=sa.Scorer.JARO, k=10)

# Top-k targets PER QUERY, yielded as a generator. Differs from
# cdist_top_k (which returns the k highest pairs globally) by keeping
# a separate top-k heap per query. With pruning=True, the worst-in-
# heap score adapts as scoring progresses and targets whose closed-
# form length-difference upper bound on similarity can't beat it
# are skipped before the kernel runs — a big win on workloads with
# wide length variation.
for query, top in sa.cdist_top_k_per_query(
    qs, ts, scorer=sa.Scorer.LEVENSHTEIN_NORMALIZED, k=5, pruning=True,
):
    # top is [(score, target), ...] sorted descending
    ...

# Smith-Waterman and Needleman-Wunsch on cdist. The SW / NW scorers
# accept the same scoring parameters as the per-pair calls; both
# raw-score and normalised-similarity variants are available. The
# dispatch happens via a Python-level ThreadPoolExecutor over rows
# because the SW / NW per-row kernels release the GIL.
sa.cdist(qs, ts, scorer=sa.Scorer.SMITH_WATERMAN,
         match_score=2, mismatch_score=-1, gap_score=-1)   # int64
sa.cdist(qs, ts, scorer=sa.Scorer.SMITH_WATERMAN_NORMALIZED)  # float64 in [0, 1]
sa.cdist(qs, ts, scorer=sa.Scorer.NEEDLEMAN_WUNSCH,
         gap_open_score=-5, gap_extend_score=-1)            # int64, can be negative
sa.cdist(qs, ts, scorer=sa.Scorer.NEEDLEMAN_WUNSCH_NORMALIZED)

At high thresholds the pruning is dramatic — see the cross-arch table in BENCHMARK (the cdist pruning rows). Loongson LASX in particular flips the expected ranking against Tiger Lake AVX-512 at T=0.99; the comparison report lives at docs/loongson-vs-tiger-lake-cdist-2026-05-24.

See BENCHMARK for full cross-architecture numbers.

Optimizations and Benchmarks

Careful attention has been, and continues to be, paid to stride-align's performance story. The library includes SIMD optimization for a variety of common targets, including x86, Arm, and LoongArch.

Intel AVX-512 versus Parasail (2026-07-18). The current pinned sweep ran on a Granite Rapids Xeon 6975P-C with GCC 16.1 and Parasail 1.3.4. It covers 80 directly comparable combinations: English and Chinese inputs, linear and affine gaps, 16- and 32-bit score widths, 1:1 and 1:many shapes, and seven score/path/CIGAR variants. Ratios are Parasail median runtime divided by stride-align median runtime, so values above 1 mean stride-align is faster.

The strongest variant geomeans are Needleman-Wunsch path at 2.356x, Needleman-Wunsch CIGAR at 2.341x, and Smith-Waterman score at 1.989x. The single losing AVX-512 row is Chinese, linear-gap, 1:1 Needleman-Wunsch score at width 16 (0.874x). The complete methodology, AVX2 comparison, per-variant tables, and five worst rows are in BENCHMARK. The canonical raw data is benchmark.csv, with an immutable dated snapshot.

rapidfuzz shim full-surface bench (v0.5.0). Across 108 workloads covering every public entry point of stride_align.rapidfuzz (10 fuzz methods, 8 distance classes × 4 methods, process.cdist + process.extract with several scorers), the cross-architecture geomeans against upstream rapidfuzz 3.14.5 are:

(Ratio = upstream / shim, > 1.0 means shim is faster.) The Mac M4 Max backend wins or ties 100 of 108 workloads (geomean 1.34x); its 8 losses are the bit-exact partial_token_ratio recipe (kept exact rather than fast), a few tiny-string Hamming cases, and the multithreaded process.cdist / process.extract throughput harnesses. Intel lands just past parity (1.02x) with a wider tail in those same cdist/throughput and token-composite workloads. Loongson is a clean sweep because upstream rapidfuzz ships no LoongArch wheel. Mac and Intel re-measured 2026-06-17; Loongson last measured 2026-06-10 (pre the Jaro and token-ratio work, so unchanged or better today).

Striped Smith-Waterman / Needleman-Wunsch kernel update (2026-07). The score-only local-SW and NW kernels were reworked. Measured throughput of the new kernels against the previous ones (native microbench, 1 query × 8 targets, length 1024, match +8 / mismatch −9), 2026-07-16:

• Affine-gap local SW — a faster prefix lazy-F correction: roughly +30–45% across AVX2, AVX-512, and NEON. (The win narrows at the exact length where the specialized exact-fill path engages; one AVX2 i32 corner there is a small regression — every other config wins.)
• Needleman-Wunsch — unchanged (±1%).
• Linear-gap local SW — a correctness fix. The previous fast path used an unsound early-exit that could silently under-report scores on structured inputs (post-mortem and reproducible counter-examples in docs/known-issue-bounded-lazy-f-scan.md). The replacement is exact everywhere; a deferred correction recovers most of the lost speed where a sound early-exit is impossible. The residual cost is architecture-dependent:

On the narrow-SIMD backends the exact answer is nearly free; on AVX-512 no sound early-exit exists, so deferred and the naive full scan both land at ~12.5 Gcells/s — correctness costs ~20% there, a trade taken deliberately for a library whose scores are meant to be exact.

LoongArch / Loongson. The Loongson optimization story is especially telling: for the checked benchmark case -- English text, 16-bit score width, score-only Smith-Waterman -- the LASX backend is 16x faster than the generic backend and 22.4x faster than Parasail.

If you are a researcher using Loongson servers and benefiting from this speedup, citations, bug reports, benchmark cases, and tiny inexpensive Chinese souvenirs are appreciated. Tea, calligraphy bookmarks, paper-cut ornaments, Chinese knot charms, panda keychains, and small dragon desk objects are all welcome. Please do not send anything expensive or anything that requires customs paperwork.

See complete benchmarks.

Native Microbench

For perf profiling without Python frames or benchmark orchestration, configure a native x86 microbench build:

nanobind_dir="$(.venv/bin/python -m nanobind --cmake_dir)"
cmake -S . -B build/perf \
  -DCMAKE_BUILD_TYPE=RelWithDebInfo \
  -DSTRIDE_ALIGN_BUILD_MICROBENCH=ON \
  -DSTRIDE_ALIGN_PERF_SYMBOLS=ON \
  -DPython_EXECUTABLE=.venv/bin/python \
  -Dnanobind_DIR="$nanobind_dir"
cmake --build build/perf --target stride_align_x86_microbench
build/perf/stride_align_x86_microbench --backend avx2 --shape 1:many --pass english --width 16
python tools/x86_microbench_regression.py \
  --binary build/perf/stride_align_x86_microbench \
  --cpu 2 \
  --backends avx2,avx512bwvl \
  --shapes 1:1,1:many \
  --passes english,chinese \
  --widths 16,32 \
  --write-json /tmp/stride-align-x86-microbench.json
.venv/bin/python tools/pinned_benchmark_sweep.py \
  --output-dir /tmp/stride-align-pinned \
  --cpu 2 \
  --iterations 15 \
  --warmups 3

STRIDE_ALIGN_PERF_SYMBOLS=ON keeps nanobind modules unstripped and adds debug symbols plus frame pointers while preserving -O3.

The checked-in native microbench baseline lives at benchmarks/x86_microbench_baseline.json. Treat it as a local guardrail with a loose threshold, not as a cross-machine SLA.

LoongArch installation

LoongArch wheels are not on PyPI (PyPI doesn't index the linux_loongarch64 platform tag), so they ship through a different channel:

Same wheels on both, pick whichever loads faster from your network. The mirror is convenient when GitHub egress is slow from inside China; GitHub Releases is the canonical home.

Install NumPy from your distro first (loongarch64 NumPy wheels are sparse on PyPI, and the distro one is usually ABI-compatible with the rest of the system):

sudo apt install python3-numpy
PY=$(python3 -c 'import sys; print(f"cp{sys.version_info.major}{sys.version_info.minor}")')

Old-world vs new-world: what to pick

LoongArch hardware runs in one of two mutually incompatible binary worlds. They differ in two things:

1. Which dynamic loader the executable references (this is the filename baked into the ELF header at link time).
2. Which glibc ABI version the binary depends on.

A wheel built for one world will not load on the other — the loader filename doesn't exist on the wrong side, and the symbols would mismatch even if it did. We ship one wheel per world:

Both wheels are statically linked against libstdc++ / libgcc so the only thing separating them is the loader / glibc ABI.

Pick the right one with this one-liner:

test -e /lib64/ld-linux-loongarch-lp64d.so.1 && echo new-world || echo old-world

If you see new-world, the loader is in place — use the new-world wheel. If you see old-world, either install the old-world wheel, or run the one-time sudo symlink below to enter new-world land (safe — it's a new filename, not a replacement, so existing old-world binaries keep working).

Old-world wheel

pip install \
  https://github.com/adamdeprince/stride-align/releases/download/v0.5.0/stride_align-0.5.0-1.oldworld-${PY}-${PY}-linux_loongarch64.whl

Mirror:

pip install \
  https://stride-align.com/wheels/v0.5.0/stride_align-0.5.0-1.oldworld-${PY}-${PY}-linux_loongarch64.whl

New-world wheel

The new-world wheel needs the new loader available at the path the ELF references. One sudo step, once per box, leaves old-world binaries unaffected:

sudo ln -sf /opt/loongson-gcc-16.1.0/sysroot/lib64/ld-linux-loongarch-lp64d.so.1 \
            /lib64/ld-linux-loongarch-lp64d.so.1

(Distro packagers usually drop an equivalent symlink as part of the new-world transition, in which case you can skip this.)

Then:

pip install \
  https://github.com/adamdeprince/stride-align/releases/download/v0.5.0/stride_align-0.5.0-1.newworld-${PY}-${PY}-linux_loongarch64.whl

Mirror:

pip install \
  https://stride-align.com/wheels/v0.5.0/stride_align-0.5.0-1.newworld-${PY}-${PY}-linux_loongarch64.whl

Other notes

Prebuilt LoongArch64 wheels are available for Python 3.12, 3.13, and 3.14 — in both worlds — on both mirrors. The build details (toolchains, RPATH wrapper, static C++ runtime) live in docs/loongson-build. If you're on a different Python or want to build from source, pip install stride-align falls back to the PyPI source distribution and compiles the LSX/LASX kernels locally.

Citations

If you use my software in your research, please cite me.

@software{deprince_stride_align,
  author       = {DePrince, Adam},
  title        = {stride-align: Fast Smith-Waterman and Needleman-Wunsch alignment for Python},
  year         = {2026},
  publisher    = {GitHub},
  url          = {https://github.com/adamdeprince/stride-align},
  note         = {Python/C++ library for sequence and string alignment}
}

References

stride-align's SIMD Smith-Waterman / Needleman-Wunsch kernels take algorithmic ideas from parasail (Jeff Daily's SIMD pairwise-alignment library — the striped-profile layout and lazy-F gap correction). If you use stride-align in published research, please also cite parasail:

@article{daily2016parasail,
  author  = {Daily, Jeff},
  title   = {Parasail: SIMD C library for global, semi-global, and local pairwise sequence alignments},
  journal = {BMC Bioinformatics},
  year    = {2016},
  volume  = {17},
  number  = {1},
  pages   = {1--11},
  doi     = {10.1186/s12859-016-0930-z}
}