From 8a4ab71c4b7962b51ee8a46f3843458e1f3d16d4 Mon Sep 17 00:00:00 2001
From: Marcello Perathoner <marcello@perathoner.de>
Date: Sat, 23 Sep 2023 17:53:43 +0200
Subject: [PATCH] Better debugging and more docs.

---
 .github/workflows/python-package.yml          |   6 +-
 Makefile                                      |  43 +-
 README.rst                                    |   6 +-
 docs/_build/.buildinfo                        |   2 +-
 docs/_build/_sources/algorithm.rst.txt        |  93 ++
 docs/_build/_sources/examples.rst.txt         |   2 +-
 docs/_build/_sources/index.rst.txt            |   1 +
 docs/_build/_sources/references.rst.txt       |   9 +-
 .../_sphinx_javascript_frameworks_compat.js   | 123 +++
 docs/_build/_static/basic.css                 |  73 +-
 docs/_build/_static/css/badge_only.css        |   2 +-
 docs/_build/_static/css/theme.css             |   4 +-
 docs/_build/_static/custom.css                |  48 +
 docs/_build/_static/doctools.js               | 420 +++------
 docs/_build/_static/documentation_options.js  |   7 +-
 docs/_build/_static/jquery.js                 |   4 +-
 docs/_build/_static/language_data.js          | 102 +--
 docs/_build/_static/pygments.css              |   1 +
 docs/_build/_static/searchtools.js            | 831 ++++++++++--------
 docs/_build/_static/sphinx_highlight.js       | 154 ++++
 .../_build/_static/super-collator-phase1.html |  13 +
 .../_build/_static/super-collator-phase2.html |  13 +
 .../_build/_static/super-collator-result.html |   4 +
 docs/_build/algorithm.html                    | 246 ++++++
 docs/_build/aligner.html                      | 185 ++--
 docs/_build/doctrees/algorithm.doctree        | Bin 0 -> 53507 bytes
 docs/_build/doctrees/aligner.doctree          | Bin 62424 -> 76423 bytes
 docs/_build/doctrees/environment.pickle       | Bin 18755 -> 230692 bytes
 docs/_build/doctrees/examples.doctree         | Bin 9591 -> 9662 bytes
 docs/_build/doctrees/index.doctree            | Bin 4774 -> 4826 bytes
 docs/_build/doctrees/ngrams.doctree           | Bin 15731 -> 15671 bytes
 docs/_build/doctrees/references.doctree       | Bin 3919 -> 4697 bytes
 docs/_build/examples.html                     | 107 ++-
 docs/_build/genindex.html                     |  97 +-
 docs/_build/index.html                        |  94 +-
 docs/_build/ngrams.html                       |  87 +-
 docs/_build/objects.inv                       | Bin 515 -> 557 bytes
 docs/_build/py-modindex.html                  |  71 +-
 docs/_build/references.html                   |  98 ++-
 docs/_build/search.html                       |  71 +-
 docs/_build/searchindex.js                    |   2 +-
 docs/_images/tox-py.svg                       |   1 -
 docs/_images/tox-py312.svg                    |   1 +
 .../{tox-pypy38.svg => tox-pypy39.svg}        |   2 +-
 docs/_static/custom.css                       |  48 +
 docs/_static/super-collator-phase1.html       |  13 +
 docs/_static/super-collator-phase2.html       |  13 +
 docs/_static/super-collator-result.html       |   4 +
 docs/algorithm.rst                            |  93 ++
 docs/conf.py                                  |   4 +-
 docs/index.rst                                |   1 +
 docs/make_badges.py                           |  11 +-
 docs/references.rst                           |   9 +-
 pyproject.toml                                |   2 +-
 requirements-dev.txt                          |   2 +
 scripts/cli.py                                | 127 ++-
 src/super_collator/aligner.py                 | 255 +++---
 src/super_collator/ngrams.py                  |   6 +-
 src/super_collator/super_collator.py          | 113 ++-
 tests/unit/test_aligner.py                    |  33 +-
 60 files changed, 2535 insertions(+), 1222 deletions(-)
 create mode 100644 docs/_build/_sources/algorithm.rst.txt
 create mode 100644 docs/_build/_static/_sphinx_javascript_frameworks_compat.js
 create mode 100644 docs/_build/_static/sphinx_highlight.js
 create mode 100644 docs/_build/_static/super-collator-phase1.html
 create mode 100644 docs/_build/_static/super-collator-phase2.html
 create mode 100644 docs/_build/_static/super-collator-result.html
 create mode 100644 docs/_build/algorithm.html
 create mode 100644 docs/_build/doctrees/algorithm.doctree
 delete mode 100644 docs/_images/tox-py.svg
 create mode 100644 docs/_images/tox-py312.svg
 rename docs/_images/{tox-pypy38.svg => tox-pypy39.svg} (83%)
 create mode 100644 docs/_static/super-collator-phase1.html
 create mode 100644 docs/_static/super-collator-phase2.html
 create mode 100644 docs/_static/super-collator-result.html
 create mode 100644 docs/algorithm.rst

diff --git a/.github/workflows/python-package.yml b/.github/workflows/python-package.yml
index f273a40..80ebc7e 100644
--- a/.github/workflows/python-package.yml
+++ b/.github/workflows/python-package.yml
@@ -15,12 +15,12 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        python-version: ["pypy3.8", "pypy3.9", "3.9", "3.10", "3.11"]
+        python-version: ["pypy3.9", "3.9", "3.10", "3.11", "3.12"]
 
     steps:
     - uses: actions/checkout@v3
     - name: Set up Python ${{ matrix.python-version }}
-      uses: actions/setup-python@v3
+      uses: actions/setup-python@v4
       with:
         python-version: ${{ matrix.python-version }}
     - name: Install dependencies
@@ -30,5 +30,3 @@ jobs:
     - name: Run tox
       run: |
         tox -e py
-
-#
\ No newline at end of file
diff --git a/Makefile b/Makefile
index 42f6cac..a3ed7cf 100644
--- a/Makefile
+++ b/Makefile
@@ -1,5 +1,6 @@
 .PHONY: lint test dist upload docs
 
+BIN=.venv/bin
 DIRS=src/ tests/unit/ docs/ scripts/ # tests/performance/
 BROWSER=firefox
 PYTEST=pytest --doctest-modules --doctest-glob="*.rst" --doctest-ignore-import-errors
@@ -7,64 +8,64 @@ PYTEST=pytest --doctest-modules --doctest-glob="*.rst" --doctest-ignore-import-e
 all: lint test
 
 black:
-	-black $(DIRS)
+	-$(BIN)/black $(DIRS)
 
 blackdoc:
-	-blackdoc $(DIRS)
+	-$(BIN)/blackdoc $(DIRS)
 
 pylint:
-	-pylint src/
+	-$(BIN)/pylint src/
 
 mypy:
-	-mypy $(DIRS)
+	-$(BIN)/mypy $(DIRS)
 
 doc8:
 	-doc8 README.rst
 
 pydocstyle:
-	pydocstyle src/
+	$(BIN)/pydocstyle src/
 
 lint: black blackdoc pylint mypy pydocstyle
 
 test:
-	python3 -m $(PYTEST) src/ tests/ docs/ README.rst
+	$(BIN)/python3 -m $(PYTEST) src/ tests/ docs/ README.rst
 
 test-performance:
-	python3 -m $(PYTEST) --performance tests/performance/
+	$(BIN)/python3 -m $(PYTEST) --performance tests/performance/
 
 coverage:
-	coverage erase
-	coverage run --branch --source=src -m $(PYTEST) tests/
-	coverage run --append --branch --source=src -m $(PYTEST) --debug-mode tests/
-	coverage report
-	coverage html
+	$(BIN)/coverage erase
+	$(BIN)/coverage run --branch --source=src -m $(PYTEST) tests/
+	$(BIN)/coverage run --append --branch --source=src -m $(PYTEST) --debug-mode tests/
+	$(BIN)/coverage report
+	$(BIN)/coverage html
 	$(BROWSER) htmlcov/index.html
 
 profile:
-	python3 -O -m scripts.profile
+	$(BIN)/python3 -O -m scripts.profile
 
 docs:
 	cd docs; make html
 
 badges: coverage
-	python docs/make_badges.py
+	$(BIN)/python docs/make_badges.py
 
 tox:
-	tox
+	$(BIN)/tox
 
 dist: clean test coverage badges
-	python3 -m build
-	twine check dist/*
+	$(BIN)/python3 -m build
+	$(BIN)/twine check dist/*
 
 upload: dist
-	twine check dist/*
-	twine upload dist/*
+	$(BIN)/twine check dist/*
+	$(BIN)/twine upload dist/*
 
 install:
-	pip3 install --force-reinstall -e .
+	$(BIN)/pip3 install --force-reinstall -e .
 
 uninstall:
-	pip3 uninstall super_collator
+	$(BIN)/pip3 uninstall super_collator
 
 clean:
 	-rm -rf dist build *.egg-info
diff --git a/README.rst b/README.rst
index 1228e78..e2c46b9 100644
--- a/README.rst
+++ b/README.rst
@@ -8,11 +8,13 @@ Super Collator
 
 .. |py311| image:: docs/_images/tox-py311.svg
 
-.. |pypy38| image:: docs/_images/tox-pypy38.svg
+.. |py312| image:: docs/_images/tox-py312.svg
+
+.. |pypy39| image:: docs/_images/tox-pypy39.svg
 
 .. |coverage| image:: docs/_images/coverage.svg
 
-|py39| |py310| |py311| |pypy38| |coverage|
+|py39| |py310| |py311| |py312| |pypy39| |coverage|
 
 Collates textual sources with relaxed spelling.  Uses Gotoh's variant of the
 Needleman-Wunsch sequence alignment algorithm.
diff --git a/docs/_build/.buildinfo b/docs/_build/.buildinfo
index c5afa9e..2358a96 100644
--- a/docs/_build/.buildinfo
+++ b/docs/_build/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: f33361227c63b5df6ab434ec7e4ac92e
+config: 7ae0d97b33a5ecf92644856b784e478b
 tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/docs/_build/_sources/algorithm.rst.txt b/docs/_build/_sources/algorithm.rst.txt
new file mode 100644
index 0000000..6e527c4
--- /dev/null
+++ b/docs/_build/_sources/algorithm.rst.txt
@@ -0,0 +1,93 @@
+Collation Algorithm
+~~~~~~~~~~~~~~~~~~~
+
+The library uses an enhancement of the Needleman-Wunsch algorithm by Gotoh [Gotoh1982]_.
+This section provides a very high level overview of the algorithm.
+
+
+Phase 1 - Build Table
+---------------------
+
+In phase 1 the algorithm builds a table.  For example this is the table built for the
+two strings: *the quick brown fox jumps over the lazy dog* and *sick fox is crazy.*
+
+.. raw:: html
+   :file: _static/super-collator-phase1.html
+
+Every cell in the table contains three values: `D`, `P`, and `Q`, and an arrow, like this:
+
+.. raw:: html
+    :align: center
+
+   <table class='super-collator super-collator-debug-matrix' style="margin-left: auto; margin-right: auto">
+   <tr><td class='outer'>
+   <table>
+     <tr><td class='d inner'>D</td><td class='p inner'>P</td></tr>
+     <tr><td class='q inner'>Q</td><td class='inner arrow'>↖</td></tr>
+   </table>
+   </td>
+   </tr>
+   </table>
+
+We define the score `S` for each cell as:
+
+.. math::
+
+    S = \max(D, P, Q)
+
+The grayed cells in the first row and first column are initialized using the *gap start*
+and *gap extension* penalties.  The numbers for each remaining cell are calculated using
+only values from the three cells, to the top-left, the top, and the left, of the current
+cell:
+
+.. math::
+
+   D = S_↖ + \mbox{similarity}(word_←, word_↑)
+
+.. math::
+
+   P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)
+
+.. math::
+
+   Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)
+
+Finally the arrow in the current cell is set to point to that cell which yielded the
+highest of the current cell's `D`, `P`, and `Q` values.
+
+
+Phase 2 - Backtrack
+-------------------
+
+When the table is thus completed, two empty sequences are created.  Then the algorithm
+starts backtracking from the last (bottom-right) cell following the arrows until it
+reaches the first (top-left) cell.  If the arrow points:
+
+↑
+   the word in the row header is added to the first sequence, a hyphen is added to the
+   second sequence,
+↖
+   the word in the row header is added to the first sequence, the word in the column
+   header is added to the second sequence,
+←
+   a hyphen is added to the first sequence, the word in the column header is added to the
+   second sequence.
+
+.. raw:: html
+   :file: _static/super-collator-phase2.html
+
+Finally the two sequences are reversed and printed.
+
+.. raw:: html
+   :file: _static/super-collator-result.html
+
+
+Parameters
+----------
+
+The algorithm can be customized by setting:
+
+- a word comparison (similarity) function,
+- the starting gap penalty,
+- the gap opening penalty,
+- and the gap extension penalty.
diff --git a/docs/_build/_sources/examples.rst.txt b/docs/_build/_sources/examples.rst.txt
index 333d0d5..11f6978 100644
--- a/docs/_build/_sources/examples.rst.txt
+++ b/docs/_build/_sources/examples.rst.txt
@@ -8,7 +8,7 @@ Install:
    $ pip install super-collator
 
 
-Align with relaxed spelling:
+Align two strings with relaxed spelling using N-Grams:
 
 .. code-block:: python
 
diff --git a/docs/_build/_sources/index.rst.txt b/docs/_build/_sources/index.rst.txt
index e0c3e2e..7b4883e 100644
--- a/docs/_build/_sources/index.rst.txt
+++ b/docs/_build/_sources/index.rst.txt
@@ -10,6 +10,7 @@ Needleman-Wunsch sequence alignment algorithm.
    :caption: Contents:
 
    examples
+   algorithm
    aligner
    ngrams
    references
diff --git a/docs/_build/_sources/references.rst.txt b/docs/_build/_sources/references.rst.txt
index f4cb5b2..2f5f9cc 100644
--- a/docs/_build/_sources/references.rst.txt
+++ b/docs/_build/_sources/references.rst.txt
@@ -1,9 +1,10 @@
 References
 ==========
 
-.. [Gotoh1982] Gotoh, O.  An Improved Algorithm for Matching Biological Sequences.
-               1982.  J. Mol. Biol. 162, 705-708
+.. [Gotoh1982] Gotoh, O. 1982.  *An Improved Algorithm for Matching Biological
+               Sequences.*  J. Mol. Biol. 162, 705-708
+               http://jaligner.sourceforge.net/references/gotoh1982.pdf
 
-.. [NeedlemanWunsch1970] Needleman, S.  Wunsch, C.  A General Method Applicable to the
+.. [NeedlemanWunsch1970] Needleman, S.  Wunsch, C.  1970.  *A General Method Applicable to the
                          Search for Similarities in the Amino Acid Sequence of Two
-                         Proteins.  1970.  J. Mol. Biol. 48, 443-453
+                         Proteins.*  J. Mol. Biol. 48, 443-453
diff --git a/docs/_build/_static/_sphinx_javascript_frameworks_compat.js b/docs/_build/_static/_sphinx_javascript_frameworks_compat.js
new file mode 100644
index 0000000..8141580
--- /dev/null
+++ b/docs/_build/_static/_sphinx_javascript_frameworks_compat.js
@@ -0,0 +1,123 @@
+/* Compatability shim for jQuery and underscores.js.
+ *
+ * Copyright Sphinx contributors
+ * Released under the two clause BSD licence
+ */
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+    if (!x) {
+        return x
+    }
+    return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+    if (typeof s === 'undefined')
+        s = document.location.search;
+    var parts = s.substr(s.indexOf('?') + 1).split('&');
+    var result = {};
+    for (var i = 0; i < parts.length; i++) {
+        var tmp = parts[i].split('=', 2);
+        var key = jQuery.urldecode(tmp[0]);
+        var value = jQuery.urldecode(tmp[1]);
+        if (key in result)
+            result[key].push(value);
+        else
+            result[key] = [value];
+    }
+    return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+    function highlight(node, addItems) {
+        if (node.nodeType === 3) {
+            var val = node.nodeValue;
+            var pos = val.toLowerCase().indexOf(text);
+            if (pos >= 0 &&
+                !jQuery(node.parentNode).hasClass(className) &&
+                !jQuery(node.parentNode).hasClass("nohighlight")) {
+                var span;
+                var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+                if (isInSVG) {
+                    span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+                } else {
+                    span = document.createElement("span");
+                    span.className = className;
+                }
+                span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+                node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+                    document.createTextNode(val.substr(pos + text.length)),
+                    node.nextSibling));
+                node.nodeValue = val.substr(0, pos);
+                if (isInSVG) {
+                    var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+                    var bbox = node.parentElement.getBBox();
+                    rect.x.baseVal.value = bbox.x;
+                    rect.y.baseVal.value = bbox.y;
+                    rect.width.baseVal.value = bbox.width;
+                    rect.height.baseVal.value = bbox.height;
+                    rect.setAttribute('class', className);
+                    addItems.push({
+                        "parent": node.parentNode,
+                        "target": rect});
+                }
+            }
+        }
+        else if (!jQuery(node).is("button, select, textarea")) {
+            jQuery.each(node.childNodes, function() {
+                highlight(this, addItems);
+            });
+        }
+    }
+    var addItems = [];
+    var result = this.each(function() {
+        highlight(this, addItems);
+    });
+    for (var i = 0; i < addItems.length; ++i) {
+        jQuery(addItems[i].parent).before(addItems[i].target);
+    }
+    return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+    jQuery.uaMatch = function(ua) {
+        ua = ua.toLowerCase();
+
+        var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+            /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+            /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+            /(msie) ([\w.]+)/.exec(ua) ||
+            ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+            [];
+
+        return {
+            browser: match[ 1 ] || "",
+            version: match[ 2 ] || "0"
+        };
+    };
+    jQuery.browser = {};
+    jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
diff --git a/docs/_build/_static/basic.css b/docs/_build/_static/basic.css
index bf18350..30fee9d 100644
--- a/docs/_build/_static/basic.css
+++ b/docs/_build/_static/basic.css
@@ -4,7 +4,7 @@
  *
  * Sphinx stylesheet -- basic theme.
  *
- * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -222,7 +222,7 @@ table.modindextable td {
 /* -- general body styles --------------------------------------------------- */
 
 div.body {
-    min-width: 450px;
+    min-width: 360px;
     max-width: 800px;
 }
 
@@ -237,14 +237,8 @@ a.headerlink {
     visibility: hidden;
 }
 
-a.brackets:before,
-span.brackets > a:before{
-    content: "[";
-}
-
-a.brackets:after,
-span.brackets > a:after {
-    content: "]";
+a:visited {
+    color: #551A8B;
 }
 
 h1:hover > a.headerlink,
@@ -335,12 +329,16 @@ p.sidebar-title {
     font-weight: bold;
 }
 
+nav.contents,
+aside.topic,
 div.admonition, div.topic, blockquote {
     clear: left;
 }
 
 /* -- topics ---------------------------------------------------------------- */
 
+nav.contents,
+aside.topic,
 div.topic {
     border: 1px solid #ccc;
     padding: 7px;
@@ -379,6 +377,8 @@ div.body p.centered {
 
 div.sidebar > :last-child,
 aside.sidebar > :last-child,
+nav.contents > :last-child,
+aside.topic > :last-child,
 div.topic > :last-child,
 div.admonition > :last-child {
     margin-bottom: 0;
@@ -386,6 +386,8 @@ div.admonition > :last-child {
 
 div.sidebar::after,
 aside.sidebar::after,
+nav.contents::after,
+aside.topic::after,
 div.topic::after,
 div.admonition::after,
 blockquote::after {
@@ -428,10 +430,6 @@ table.docutils td, table.docutils th {
     border-bottom: 1px solid #aaa;
 }
 
-table.footnote td, table.footnote th {
-    border: 0 !important;
-}
-
 th {
     text-align: left;
     padding-right: 5px;
@@ -615,19 +613,26 @@ ul.simple p {
     margin-bottom: 0;
 }
 
-dl.footnote > dt,
-dl.citation > dt {
+aside.footnote > span,
+div.citation > span {
     float: left;
-    margin-right: 0.5em;
 }
-
-dl.footnote > dd,
-dl.citation > dd {
+aside.footnote > span:last-of-type,
+div.citation > span:last-of-type {
+  padding-right: 0.5em;
+}
+aside.footnote > p {
+  margin-left: 2em;
+}
+div.citation > p {
+  margin-left: 4em;
+}
+aside.footnote > p:last-of-type,
+div.citation > p:last-of-type {
     margin-bottom: 0em;
 }
-
-dl.footnote > dd:after,
-dl.citation > dd:after {
+aside.footnote > p:last-of-type:after,
+div.citation > p:last-of-type:after {
     content: "";
     clear: both;
 }
@@ -644,10 +649,6 @@ dl.field-list > dt {
     padding-right: 5px;
 }
 
-dl.field-list > dt:after {
-    content: ":";
-}
-
 dl.field-list > dd {
     padding-left: 0.5em;
     margin-top: 0em;
@@ -673,6 +674,16 @@ dd {
     margin-left: 30px;
 }
 
+.sig dd {
+    margin-top: 0px;
+    margin-bottom: 0px;
+}
+
+.sig dl {
+    margin-top: 0px;
+    margin-bottom: 0px;
+}
+
 dl > dd:last-child,
 dl > dd:last-child > :last-child {
     margin-bottom: 0;
@@ -741,6 +752,14 @@ abbr, acronym {
     cursor: help;
 }
 
+.translated {
+    background-color: rgba(207, 255, 207, 0.2)
+}
+
+.untranslated {
+    background-color: rgba(255, 207, 207, 0.2)
+}
+
 /* -- code displays --------------------------------------------------------- */
 
 pre {
diff --git a/docs/_build/_static/css/badge_only.css b/docs/_build/_static/css/badge_only.css
index e380325..c718cee 100644
--- a/docs/_build/_static/css/badge_only.css
+++ b/docs/_build/_static/css/badge_only.css
@@ -1 +1 @@
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dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.citation):not(.glossary):not(.simple) .k{font-style:italic}html.writer-html4 .rst-content dl:not(.docutils) .descclassname,html.writer-html4 .rst-content dl:not(.docutils) .descname,html.writer-html4 .rst-content dl:not(.docutils) .sig-name,html.writer-html5 .rst-content dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.citation):not(.glossary):not(.simple) .descclassname,html.writer-html5 .rst-content dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.citation):not(.glossary):not(.simple) .descname,html.writer-html5 .rst-content dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.citation):not(.glossary):not(.simple) .sig-name{font-family:SFMono-Regular,Menlo,Monaco,Consolas,Liberation Mono,Courier New,Courier,monospace;color:#000}.rst-content .viewcode-back,.rst-content .viewcode-link{display:inline-block;color:#27ae60;font-size:80%;padding-left:24px}.rst-content .viewcode-back{display:block;float:right}.rst-content p.rubric{margin-bottom:12px;font-weight:700}.rst-content code.download,.rst-content tt.download{background:inherit;padding:inherit;font-weight:400;font-family:inherit;font-size:inherit;color:inherit;border:inherit;white-space:inherit}.rst-content code.download span:first-child,.rst-content tt.download span:first-child{-webkit-font-smoothing:subpixel-antialiased}.rst-content code.download span:first-child:before,.rst-content tt.download span:first-child:before{margin-right:4px}.rst-content .guilabel,.rst-content .menuselection{font-size:80%;font-weight:700;border-radius:4px;padding:2.4px 6px;margin:auto 2px}.rst-content .guilabel,.rst-content .menuselection{border:1px solid #7fbbe3;background:#e7f2fa}.rst-content :not(dl.option-list)>:not(dt):not(kbd):not(.kbd)>.kbd,.rst-content :not(dl.option-list)>:not(dt):not(kbd):not(.kbd)>kbd{color:inherit;font-size:80%;background-color:#fff;border:1px solid #a6a6a6;border-radius:4px;box-shadow:0 2px grey;padding:2.4px 6px;margin:auto 0}.rst-content .versionmodified{font-style:italic}@media screen and (max-width:480px){.rst-content .sidebar{width:100%}}span[id*=MathJax-Span]{color:#404040}.math{text-align:center}@font-face{font-family:Lato;src:url(fonts/lato-normal.woff2?bd03a2cc277bbbc338d464e679fe9942) format("woff2"),url(fonts/lato-normal.woff?27bd77b9162d388cb8d4c4217c7c5e2a) format("woff");font-weight:400;font-style:normal;font-display:block}@font-face{font-family:Lato;src:url(fonts/lato-bold.woff2?cccb897485813c7c256901dbca54ecf2) format("woff2"),url(fonts/lato-bold.woff?d878b6c29b10beca227e9eef4246111b) format("woff");font-weight:700;font-style:normal;font-display:block}@font-face{font-family:Lato;src:url(fonts/lato-bold-italic.woff2?0b6bb6725576b072c5d0b02ecdd1900d) format("woff2"),url(fonts/lato-bold-italic.woff?9c7e4e9eb485b4a121c760e61bc3707c) format("woff");font-weight:700;font-style:italic;font-display:block}@font-face{font-family:Lato;src:url(fonts/lato-normal-italic.woff2?4eb103b4d12be57cb1d040ed5e162e9d) format("woff2"),url(fonts/lato-normal-italic.woff?f28f2d6482446544ef1ea1ccc6dd5892) format("woff");font-weight:400;font-style:italic;font-display:block}@font-face{font-family:Roboto Slab;font-style:normal;font-weight:400;src:url(fonts/Roboto-Slab-Regular.woff2?7abf5b8d04d26a2cafea937019bca958) format("woff2"),url(fonts/Roboto-Slab-Regular.woff?c1be9284088d487c5e3ff0a10a92e58c) format("woff");font-display:block}@font-face{font-family:Roboto Slab;font-style:normal;font-weight:700;src:url(fonts/Roboto-Slab-Bold.woff2?9984f4a9bda09be08e83f2506954adbe) format("woff2"),url(fonts/Roboto-Slab-Bold.woff?bed5564a116b05148e3b3bea6fb1162a) format("woff");font-display:block}
\ No newline at end of file
diff --git a/docs/_build/_static/custom.css b/docs/_build/_static/custom.css
index 18ba401..1f3cb65 100644
--- a/docs/_build/_static/custom.css
+++ b/docs/_build/_static/custom.css
@@ -1 +1,49 @@
 .wy-side-nav-search a.icon.icon-home img.logo { width: 72px; }
+
+.rst-content img.sauml {
+    display: block;
+    margin-top: 12px;
+    margin-bottom: 12px;
+}
+
+.rst-content .std-term {
+    font-style: italic;
+}
+
+.rst-content .pic {
+    margin-bottom: 1em;
+}
+
+.rst-content .pic table {
+    min-width: 100%;
+}
+
+.rst-content .pic table th,
+.rst-content .pic table td {
+    border: 1px solid black;
+    padding: 0.2em;
+    text-align: left;
+}
+
+table.super-collator              { border-collapse: collapse }
+table.super-collator th,
+table.super-collator td.outer     { border: 1px solid black }
+table.super-collator td.inner     { width: 50%; padding: 0 0.5ex; text-align: right }
+table.super-collator td.prefilled { background-color: #eee }
+table.super-collator td.em        { font-weight: bold }
+table.super-collator th           { padding: 0 0.5ex; text-align: right }
+table.super-collator table        { width: 100% }
+table.super-collator-result td    { border: 1px solid black; padding: 0 1ex }
+
+table.super-collator {
+    margin-bottom: 1em;
+}
+
+#super-collator-phase2 td.outer.bt {
+    background-color: #fefece;
+    border: 1.5pt solid #a80136;
+}
+
+#super-collator-phase2 td.outer.bt .arrow {
+    color: #a80136;
+}
diff --git a/docs/_build/_static/doctools.js b/docs/_build/_static/doctools.js
index e1bfd70..d06a71d 100644
--- a/docs/_build/_static/doctools.js
+++ b/docs/_build/_static/doctools.js
@@ -2,357 +2,155 @@
  * doctools.js
  * ~~~~~~~~~~~
  *
- * Sphinx JavaScript utilities for all documentation.
+ * Base JavaScript utilities for all Sphinx HTML documentation.
  *
- * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
-
-/**
- * select a different prefix for underscore
- */
-$u = _.noConflict();
-
-/**
- * make the code below compatible with browsers without
- * an installed firebug like debugger
-if (!window.console || !console.firebug) {
-  var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
-    "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
-    "profile", "profileEnd"];
-  window.console = {};
-  for (var i = 0; i < names.length; ++i)
-    window.console[names[i]] = function() {};
-}
- */
-
-/**
- * small helper function to urldecode strings
- *
- * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
- */
-jQuery.urldecode = function(x) {
-  if (!x) {
-    return x
-  }
-  return decodeURIComponent(x.replace(/\+/g, ' '));
-};
-
-/**
- * small helper function to urlencode strings
- */
-jQuery.urlencode = encodeURIComponent;
-
-/**
- * This function returns the parsed url parameters of the
- * current request. Multiple values per key are supported,
- * it will always return arrays of strings for the value parts.
- */
-jQuery.getQueryParameters = function(s) {
-  if (typeof s === 'undefined')
-    s = document.location.search;
-  var parts = s.substr(s.indexOf('?') + 1).split('&');
-  var result = {};
-  for (var i = 0; i < parts.length; i++) {
-    var tmp = parts[i].split('=', 2);
-    var key = jQuery.urldecode(tmp[0]);
-    var value = jQuery.urldecode(tmp[1]);
-    if (key in result)
-      result[key].push(value);
-    else
-      result[key] = [value];
-  }
-  return result;
-};
-
-/**
- * highlight a given string on a jquery object by wrapping it in
- * span elements with the given class name.
- */
-jQuery.fn.highlightText = function(text, className) {
-  function highlight(node, addItems) {
-    if (node.nodeType === 3) {
-      var val = node.nodeValue;
-      var pos = val.toLowerCase().indexOf(text);
-      if (pos >= 0 &&
-          !jQuery(node.parentNode).hasClass(className) &&
-          !jQuery(node.parentNode).hasClass("nohighlight")) {
-        var span;
-        var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
-        if (isInSVG) {
-          span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
-        } else {
-          span = document.createElement("span");
-          span.className = className;
-        }
-        span.appendChild(document.createTextNode(val.substr(pos, text.length)));
-        node.parentNode.insertBefore(span, node.parentNode.insertBefore(
-          document.createTextNode(val.substr(pos + text.length)),
-          node.nextSibling));
-        node.nodeValue = val.substr(0, pos);
-        if (isInSVG) {
-          var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
-          var bbox = node.parentElement.getBBox();
-          rect.x.baseVal.value = bbox.x;
-          rect.y.baseVal.value = bbox.y;
-          rect.width.baseVal.value = bbox.width;
-          rect.height.baseVal.value = bbox.height;
-          rect.setAttribute('class', className);
-          addItems.push({
-              "parent": node.parentNode,
-              "target": rect});
-        }
-      }
-    }
-    else if (!jQuery(node).is("button, select, textarea")) {
-      jQuery.each(node.childNodes, function() {
-        highlight(this, addItems);
-      });
-    }
-  }
-  var addItems = [];
-  var result = this.each(function() {
-    highlight(this, addItems);
-  });
-  for (var i = 0; i < addItems.length; ++i) {
-    jQuery(addItems[i].parent).before(addItems[i].target);
+"use strict";
+
+const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
+  "TEXTAREA",
+  "INPUT",
+  "SELECT",
+  "BUTTON",
+]);
+
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
   }
-  return result;
 };
 
-/*
- * backward compatibility for jQuery.browser
- * This will be supported until firefox bug is fixed.
- */
-if (!jQuery.browser) {
-  jQuery.uaMatch = function(ua) {
-    ua = ua.toLowerCase();
-
-    var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
-      /(webkit)[ \/]([\w.]+)/.exec(ua) ||
-      /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
-      /(msie) ([\w.]+)/.exec(ua) ||
-      ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
-      [];
-
-    return {
-      browser: match[ 1 ] || "",
-      version: match[ 2 ] || "0"
-    };
-  };
-  jQuery.browser = {};
-  jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
-}
-
 /**
  * Small JavaScript module for the documentation.
  */
-var Documentation = {
-
-  init : function() {
-    this.fixFirefoxAnchorBug();
-    this.highlightSearchWords();
-    this.initIndexTable();
-    this.initOnKeyListeners();
+const Documentation = {
+  init: () => {
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
   },
 
   /**
    * i18n support
    */
-  TRANSLATIONS : {},
-  PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
-  LOCALE : 'unknown',
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
 
   // gettext and ngettext don't access this so that the functions
   // can safely bound to a different name (_ = Documentation.gettext)
-  gettext : function(string) {
-    var translated = Documentation.TRANSLATIONS[string];
-    if (typeof translated === 'undefined')
-      return string;
-    return (typeof translated === 'string') ? translated : translated[0];
-  },
-
-  ngettext : function(singular, plural, n) {
-    var translated = Documentation.TRANSLATIONS[singular];
-    if (typeof translated === 'undefined')
-      return (n == 1) ? singular : plural;
-    return translated[Documentation.PLURALEXPR(n)];
-  },
-
-  addTranslations : function(catalog) {
-    for (var key in catalog.messages)
-      this.TRANSLATIONS[key] = catalog.messages[key];
-    this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
-    this.LOCALE = catalog.locale;
-  },
-
-  /**
-   * add context elements like header anchor links
-   */
-  addContextElements : function() {
-    $('div[id] > :header:first').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this headline')).
-      appendTo(this);
-    });
-    $('dt[id]').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this definition')).
-      appendTo(this);
-    });
-  },
-
-  /**
-   * workaround a firefox stupidity
-   * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
-   */
-  fixFirefoxAnchorBug : function() {
-    if (document.location.hash && $.browser.mozilla)
-      window.setTimeout(function() {
-        document.location.href += '';
-      }, 10);
-  },
-
-  /**
-   * highlight the search words provided in the url in the text
-   */
-  highlightSearchWords : function() {
-    var params = $.getQueryParameters();
-    var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
-    if (terms.length) {
-      var body = $('div.body');
-      if (!body.length) {
-        body = $('body');
-      }
-      window.setTimeout(function() {
-        $.each(terms, function() {
-          body.highlightText(this.toLowerCase(), 'highlighted');
-        });
-      }, 10);
-      $('<p class="highlight-link"><a href="javascript:Documentation.' +
-        'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
-          .appendTo($('#searchbox'));
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
     }
   },
 
-  /**
-   * init the domain index toggle buttons
-   */
-  initIndexTable : function() {
-    var togglers = $('img.toggler').click(function() {
-      var src = $(this).attr('src');
-      var idnum = $(this).attr('id').substr(7);
-      $('tr.cg-' + idnum).toggle();
-      if (src.substr(-9) === 'minus.png')
-        $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
-      else
-        $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
-    }).css('display', '');
-    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
-        togglers.click();
-    }
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
   },
 
-  /**
-   * helper function to hide the search marks again
-   */
-  hideSearchWords : function() {
-    $('#searchbox .highlight-link').fadeOut(300);
-    $('span.highlighted').removeClass('highlighted');
-    var url = new URL(window.location);
-    url.searchParams.delete('highlight');
-    window.history.replaceState({}, '', url);
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
   },
 
-   /**
+  /**
    * helper function to focus on search bar
    */
-  focusSearchBar : function() {
-    $('input[name=q]').first().focus();
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
   },
 
   /**
-   * make the url absolute
+   * Initialise the domain index toggle buttons
    */
-  makeURL : function(relativeURL) {
-    return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
-  },
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
+      }
+    };
 
-  /**
-   * get the current relative url
-   */
-  getCurrentURL : function() {
-    var path = document.location.pathname;
-    var parts = path.split(/\//);
-    $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
-      if (this === '..')
-        parts.pop();
-    });
-    var url = parts.join('/');
-    return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
   },
 
-  initOnKeyListeners: function() {
+  initOnKeyListeners: () => {
     // only install a listener if it is really needed
-    if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
-        !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
-        return;
-
-    $(document).keydown(function(event) {
-      var activeElementType = document.activeElement.tagName;
-      // don't navigate when in search box, textarea, dropdown or button
-      if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
-          && activeElementType !== 'BUTTON') {
-        if (event.altKey || event.ctrlKey || event.metaKey)
-          return;
-
-          if (!event.shiftKey) {
-            switch (event.key) {
-              case 'ArrowLeft':
-                if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS)
-                  break;
-                var prevHref = $('link[rel="prev"]').prop('href');
-                if (prevHref) {
-                  window.location.href = prevHref;
-                  return false;
-                }
-                break;
-              case 'ArrowRight':
-                if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS)
-                  break;
-                var nextHref = $('link[rel="next"]').prop('href');
-                if (nextHref) {
-                  window.location.href = nextHref;
-                  return false;
-                }
-                break;
-              case 'Escape':
-                if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
-                  break;
-                Documentation.hideSearchWords();
-                return false;
-          }
-        }
-
-        // some keyboard layouts may need Shift to get /
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.altKey || event.ctrlKey || event.metaKey) return;
+
+      if (!event.shiftKey) {
         switch (event.key) {
-          case '/':
-            if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS)
-              break;
-            Documentation.focusSearchBar();
-            return false;
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
+            }
+            break;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
+            }
+            break;
         }
       }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
     });
-  }
+  },
 };
 
 // quick alias for translations
-_ = Documentation.gettext;
+const _ = Documentation.gettext;
 
-$(document).ready(function() {
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diff --git a/docs/_build/_static/documentation_options.js b/docs/_build/_static/documentation_options.js
index 620885d..74029b8 100644
--- a/docs/_build/_static/documentation_options.js
+++ b/docs/_build/_static/documentation_options.js
@@ -1,7 +1,6 @@
-var DOCUMENTATION_OPTIONS = {
-    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
-    VERSION: '0.0.2',
-    LANGUAGE: 'None',
+const DOCUMENTATION_OPTIONS = {
+    VERSION: '0.0.3',
+    LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',
     FILE_SUFFIX: '.html',
diff --git a/docs/_build/_static/jquery.js b/docs/_build/_static/jquery.js
index b061403..c4c6022 100644
--- a/docs/_build/_static/jquery.js
+++ b/docs/_build/_static/jquery.js
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diff --git a/docs/_build/_static/language_data.js b/docs/_build/_static/language_data.js
index ebe2f03..250f566 100644
--- a/docs/_build/_static/language_data.js
+++ b/docs/_build/_static/language_data.js
@@ -5,12 +5,12 @@
  * This script contains the language-specific data used by searchtools.js,
  * namely the list of stopwords, stemmer, scorer and splitter.
  *
- * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
 
-var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
 
 
 /* Non-minified version is copied as a separate JS file, is available */
@@ -197,101 +197,3 @@ var Stemmer = function() {
   }
 }
 
-
-
-
-var splitChars = (function() {
-    var result = {};
-    var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
-         1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
-         2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
-         2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
-         3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
-         3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
-         4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
-         8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
-         11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
-         43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
-    var i, j, start, end;
-    for (i = 0; i < singles.length; i++) {
-        result[singles[i]] = true;
-    }
-    var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
-         [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
-         [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
-         [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
-         [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
-         [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
-         [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
-         [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
-         [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
-         [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
-         [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
-         [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
-         [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
-         [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
-         [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
-         [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
-         [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
-         [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
-         [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
-         [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
-         [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
-         [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
-         [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
-         [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
-         [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
-         [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
-         [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
-         [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
-         [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
-         [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
-         [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
-         [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
-         [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
-         [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
-         [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
-         [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
-         [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
-         [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
-         [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
-         [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
-         [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
-         [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
-         [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
-         [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
-         [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
-         [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
-         [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
-         [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
-         [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
-    for (i = 0; i < ranges.length; i++) {
-        start = ranges[i][0];
-        end = ranges[i][1];
-        for (j = start; j <= end; j++) {
-            result[j] = true;
-        }
-    }
-    return result;
-})();
-
-function splitQuery(query) {
-    var result = [];
-    var start = -1;
-    for (var i = 0; i < query.length; i++) {
-        if (splitChars[query.charCodeAt(i)]) {
-            if (start !== -1) {
-                result.push(query.slice(start, i));
-                start = -1;
-            }
-        } else if (start === -1) {
-            start = i;
-        }
-    }
-    if (start !== -1) {
-        result.push(query.slice(start));
-    }
-    return result;
-}
-
-
diff --git a/docs/_build/_static/pygments.css b/docs/_build/_static/pygments.css
index 08bec68..84ab303 100644
--- a/docs/_build/_static/pygments.css
+++ b/docs/_build/_static/pygments.css
@@ -17,6 +17,7 @@ span.linenos.special { color: #000000; background-color: #ffffc0; padding-left:
 .highlight .cs { color: #3D7B7B; font-style: italic } /* Comment.Special */
 .highlight .gd { color: #A00000 } /* Generic.Deleted */
 .highlight .ge { font-style: italic } /* Generic.Emph */
+.highlight .ges { font-weight: bold; font-style: italic } /* Generic.EmphStrong */
 .highlight .gr { color: #E40000 } /* Generic.Error */
 .highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
 .highlight .gi { color: #008400 } /* Generic.Inserted */
diff --git a/docs/_build/_static/searchtools.js b/docs/_build/_static/searchtools.js
index 0a44e85..7918c3f 100644
--- a/docs/_build/_static/searchtools.js
+++ b/docs/_build/_static/searchtools.js
@@ -4,22 +4,24 @@
  *
  * Sphinx JavaScript utilities for the full-text search.
  *
- * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
+"use strict";
 
-if (!Scorer) {
-  /**
-   * Simple result scoring code.
-   */
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
   var Scorer = {
     // Implement the following function to further tweak the score for each result
-    // The function takes a result array [filename, title, anchor, descr, score]
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
     // and returns the new score.
     /*
-    score: function(result) {
-      return result[4];
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
     },
     */
 
@@ -28,9 +30,11 @@ if (!Scorer) {
     // or matches in the last dotted part of the object name
     objPartialMatch: 6,
     // Additive scores depending on the priority of the object
-    objPrio: {0:  15,   // used to be importantResults
-              1:  5,   // used to be objectResults
-              2: -5},  // used to be unimportantResults
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
     //  Used when the priority is not in the mapping.
     objPrioDefault: 0,
 
@@ -39,452 +43,503 @@ if (!Scorer) {
     partialTitle: 7,
     // query found in terms
     term: 5,
-    partialTerm: 2
+    partialTerm: 2,
   };
 }
 
-if (!splitQuery) {
-  function splitQuery(query) {
-    return query.split(/\s+/);
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, searchTerms, highlightTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+  const contentRoot = document.documentElement.dataset.content_root;
+
+  const [docName, title, anchor, descr, score, _filename] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = contentRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = contentRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
   }
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + anchor;
+  linkEl.dataset.score = score;
+  linkEl.innerHTML = title;
+  if (descr) {
+    listItem.appendChild(document.createElement("span")).innerHTML =
+      " (" + descr + ")";
+    // highlight search terms in the description
+    if (SPHINX_HIGHLIGHT_ENABLED)  // set in sphinx_highlight.js
+      highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
+  }
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms)
+          );
+        // highlight search terms in the summary
+        if (SPHINX_HIGHLIGHT_ENABLED)  // set in sphinx_highlight.js
+          highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted"));
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  searchTerms,
+  highlightTerms,
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), searchTerms, highlightTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, searchTerms, highlightTerms),
+      5
+    );
+  }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
 }
 
 /**
  * Search Module
  */
-var Search = {
-
-  _index : null,
-  _queued_query : null,
-  _pulse_status : -1,
-
-  htmlToText : function(htmlString) {
-      var virtualDocument = document.implementation.createHTMLDocument('virtual');
-      var htmlElement = $(htmlString, virtualDocument);
-      htmlElement.find('.headerlink').remove();
-      docContent = htmlElement.find('[role=main]')[0];
-      if(docContent === undefined) {
-          console.warn("Content block not found. Sphinx search tries to obtain it " +
-                       "via '[role=main]'. Could you check your theme or template.");
-          return "";
-      }
-      return docContent.textContent || docContent.innerText;
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
+
+  htmlToText: (htmlString) => {
+    const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
+    htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() });
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
   },
 
-  init : function() {
-      var params = $.getQueryParameters();
-      if (params.q) {
-          var query = params.q[0];
-          $('input[name="q"]')[0].value = query;
-          this.performSearch(query);
-      }
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
   },
 
-  loadIndex : function(url) {
-    $.ajax({type: "GET", url: url, data: null,
-            dataType: "script", cache: true,
-            complete: function(jqxhr, textstatus) {
-              if (textstatus != "success") {
-                document.getElementById("searchindexloader").src = url;
-              }
-            }});
-  },
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
 
-  setIndex : function(index) {
-    var q;
-    this._index = index;
-    if ((q = this._queued_query) !== null) {
-      this._queued_query = null;
-      Search.query(q);
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
     }
   },
 
-  hasIndex : function() {
-      return this._index !== null;
-  },
+  hasIndex: () => Search._index !== null,
 
-  deferQuery : function(query) {
-      this._queued_query = query;
-  },
+  deferQuery: (query) => (Search._queued_query = query),
 
-  stopPulse : function() {
-      this._pulse_status = 0;
-  },
+  stopPulse: () => (Search._pulse_status = -1),
 
-  startPulse : function() {
-    if (this._pulse_status >= 0)
-        return;
-    function pulse() {
-      var i;
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
       Search._pulse_status = (Search._pulse_status + 1) % 4;
-      var dotString = '';
-      for (i = 0; i < Search._pulse_status; i++)
-        dotString += '.';
-      Search.dots.text(dotString);
-      if (Search._pulse_status > -1)
-        window.setTimeout(pulse, 500);
-    }
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
     pulse();
   },
 
   /**
    * perform a search for something (or wait until index is loaded)
    */
-  performSearch : function(query) {
+  performSearch: (query) => {
     // create the required interface elements
-    this.out = $('#search-results');
-    this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
-    this.dots = $('<span></span>').appendTo(this.title);
-    this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
-    this.output = $('<ul class="search"/>').appendTo(this.out);
-
-    $('#search-progress').text(_('Preparing search...'));
-    this.startPulse();
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
+
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
 
     // index already loaded, the browser was quick!
-    if (this.hasIndex())
-      this.query(query);
-    else
-      this.deferQuery(query);
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
   },
 
   /**
    * execute search (requires search index to be loaded)
    */
-  query : function(query) {
-    var i;
-
-    // stem the searchterms and add them to the correct list
-    var stemmer = new Stemmer();
-    var searchterms = [];
-    var excluded = [];
-    var hlterms = [];
-    var tmp = splitQuery(query);
-    var objectterms = [];
-    for (i = 0; i < tmp.length; i++) {
-      if (tmp[i] !== "") {
-          objectterms.push(tmp[i].toLowerCase());
-      }
+  query: (query) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+    const allTitles = Search._index.alltitles;
+    const indexEntries = Search._index.indexentries;
+
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
+
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
 
-      if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") {
-        // skip this "word"
-        continue;
-      }
       // stem the word
-      var word = stemmer.stemWord(tmp[i].toLowerCase());
-      var toAppend;
+      let word = stemmer.stemWord(queryTermLower);
       // select the correct list
-      if (word[0] == '-') {
-        toAppend = excluded;
-        word = word.substr(1);
-      }
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
       else {
-        toAppend = searchterms;
-        hlterms.push(tmp[i].toLowerCase());
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
       }
-      // only add if not already in the list
-      if (!$u.contains(toAppend, word))
-        toAppend.push(word);
-    }
-    var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+    });
 
-    // console.debug('SEARCH: searching for:');
-    // console.info('required: ', searchterms);
-    // console.info('excluded: ', excluded);
+    if (SPHINX_HIGHLIGHT_ENABLED) {  // set in sphinx_highlight.js
+      localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+    }
 
-    // prepare search
-    var terms = this._index.terms;
-    var titleterms = this._index.titleterms;
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
+
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
+
+    const queryLower = query.toLowerCase();
+    for (const [title, foundTitles] of Object.entries(allTitles)) {
+      if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) {
+        for (const [file, id] of foundTitles) {
+          let score = Math.round(100 * queryLower.length / title.length)
+          results.push([
+            docNames[file],
+            titles[file] !== title ? `${titles[file]} > ${title}` : title,
+            id !== null ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
 
-    // array of [filename, title, anchor, descr, score]
-    var results = [];
-    $('#search-progress').empty();
+    // search for explicit entries in index directives
+    for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+      if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+        for (const [file, id] of foundEntries) {
+          let score = Math.round(100 * queryLower.length / entry.length)
+          results.push([
+            docNames[file],
+            titles[file],
+            id ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
 
     // lookup as object
-    for (i = 0; i < objectterms.length; i++) {
-      var others = [].concat(objectterms.slice(0, i),
-                             objectterms.slice(i+1, objectterms.length));
-      results = results.concat(this.performObjectSearch(objectterms[i], others));
-    }
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
 
     // lookup as search terms in fulltext
-    results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
 
     // let the scorer override scores with a custom scoring function
-    if (Scorer.score) {
-      for (i = 0; i < results.length; i++)
-        results[i][4] = Scorer.score(results[i]);
-    }
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
 
     // now sort the results by score (in opposite order of appearance, since the
     // display function below uses pop() to retrieve items) and then
     // alphabetically
-    results.sort(function(a, b) {
-      var left = a[4];
-      var right = b[4];
-      if (left > right) {
-        return 1;
-      } else if (left < right) {
-        return -1;
-      } else {
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
         // same score: sort alphabetically
-        left = a[1].toLowerCase();
-        right = b[1].toLowerCase();
-        return (left > right) ? -1 : ((left < right) ? 1 : 0);
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
       }
+      return leftScore > rightScore ? 1 : -1;
     });
 
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
     // for debugging
     //Search.lastresults = results.slice();  // a copy
-    //console.info('search results:', Search.lastresults);
+    // console.info("search results:", Search.lastresults);
 
     // print the results
-    var resultCount = results.length;
-    function displayNextItem() {
-      // results left, load the summary and display it
-      if (results.length) {
-        var item = results.pop();
-        var listItem = $('<li></li>');
-        var requestUrl = "";
-        var linkUrl = "";
-        if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
-          // dirhtml builder
-          var dirname = item[0] + '/';
-          if (dirname.match(/\/index\/$/)) {
-            dirname = dirname.substring(0, dirname.length-6);
-          } else if (dirname == 'index/') {
-            dirname = '';
-          }
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
-          linkUrl = requestUrl;
-
-        } else {
-          // normal html builders
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
-          linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
-        }
-        listItem.append($('<a/>').attr('href',
-            linkUrl +
-            highlightstring + item[2]).html(item[1]));
-        if (item[3]) {
-          listItem.append($('<span> (' + item[3] + ')</span>'));
-          Search.output.append(listItem);
-          setTimeout(function() {
-            displayNextItem();
-          }, 5);
-        } else if (DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY) {
-          $.ajax({url: requestUrl,
-                  dataType: "text",
-                  complete: function(jqxhr, textstatus) {
-                    var data = jqxhr.responseText;
-                    if (data !== '' && data !== undefined) {
-                      var summary = Search.makeSearchSummary(data, searchterms, hlterms);
-                      if (summary) {
-                        listItem.append(summary);
-                      }
-                    }
-                    Search.output.append(listItem);
-                    setTimeout(function() {
-                      displayNextItem();
-                    }, 5);
-                  }});
-        } else {
-          // just display title
-          Search.output.append(listItem);
-          setTimeout(function() {
-            displayNextItem();
-          }, 5);
-        }
-      }
-      // search finished, update title and status message
-      else {
-        Search.stopPulse();
-        Search.title.text(_('Search Results'));
-        if (!resultCount)
-          Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
-        else
-            Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
-        Search.status.fadeIn(500);
-      }
-    }
-    displayNextItem();
+    _displayNextItem(results, results.length, searchTerms, highlightTerms);
   },
 
   /**
    * search for object names
    */
-  performObjectSearch : function(object, otherterms) {
-    var filenames = this._index.filenames;
-    var docnames = this._index.docnames;
-    var objects = this._index.objects;
-    var objnames = this._index.objnames;
-    var titles = this._index.titles;
-
-    var i;
-    var results = [];
-
-    for (var prefix in objects) {
-      for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) {
-        var match = objects[prefix][iMatch];
-        var name = match[4];
-        var fullname = (prefix ? prefix + '.' : '') + name;
-        var fullnameLower = fullname.toLowerCase()
-        if (fullnameLower.indexOf(object) > -1) {
-          var score = 0;
-          var parts = fullnameLower.split('.');
-          // check for different match types: exact matches of full name or
-          // "last name" (i.e. last dotted part)
-          if (fullnameLower == object || parts[parts.length - 1] == object) {
-            score += Scorer.objNameMatch;
-          // matches in last name
-          } else if (parts[parts.length - 1].indexOf(object) > -1) {
-            score += Scorer.objPartialMatch;
-          }
-          var objname = objnames[match[1]][2];
-          var title = titles[match[0]];
-          // If more than one term searched for, we require other words to be
-          // found in the name/title/description
-          if (otherterms.length > 0) {
-            var haystack = (prefix + ' ' + name + ' ' +
-                            objname + ' ' + title).toLowerCase();
-            var allfound = true;
-            for (i = 0; i < otherterms.length; i++) {
-              if (haystack.indexOf(otherterms[i]) == -1) {
-                allfound = false;
-                break;
-              }
-            }
-            if (!allfound) {
-              continue;
-            }
-          }
-          var descr = objname + _(', in ') + title;
-
-          var anchor = match[3];
-          if (anchor === '')
-            anchor = fullname;
-          else if (anchor == '-')
-            anchor = objnames[match[1]][1] + '-' + fullname;
-          // add custom score for some objects according to scorer
-          if (Scorer.objPrio.hasOwnProperty(match[2])) {
-            score += Scorer.objPrio[match[2]];
-          } else {
-            score += Scorer.objPrioDefault;
-          }
-          results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
-        }
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
+
+    const results = [];
+
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
+
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
       }
-    }
 
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
     return results;
   },
 
-  /**
-   * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
-   */
-  escapeRegExp : function(string) {
-    return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
-  },
-
   /**
    * search for full-text terms in the index
    */
-  performTermsSearch : function(searchterms, excluded, terms, titleterms) {
-    var docnames = this._index.docnames;
-    var filenames = this._index.filenames;
-    var titles = this._index.titles;
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
 
-    var i, j, file;
-    var fileMap = {};
-    var scoreMap = {};
-    var results = [];
+    const scoreMap = new Map();
+    const fileMap = new Map();
 
     // perform the search on the required terms
-    for (i = 0; i < searchterms.length; i++) {
-      var word = searchterms[i];
-      var files = [];
-      var _o = [
-        {files: terms[word], score: Scorer.term},
-        {files: titleterms[word], score: Scorer.title}
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
       ];
       // add support for partial matches
       if (word.length > 2) {
-        var word_regex = this.escapeRegExp(word);
-        for (var w in terms) {
-          if (w.match(word_regex) && !terms[word]) {
-            _o.push({files: terms[w], score: Scorer.partialTerm})
-          }
-        }
-        for (var w in titleterms) {
-          if (w.match(word_regex) && !titleterms[word]) {
-              _o.push({files: titleterms[w], score: Scorer.partialTitle})
-          }
-        }
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
       }
 
       // no match but word was a required one
-      if ($u.every(_o, function(o){return o.files === undefined;})) {
-        break;
-      }
+      if (arr.every((record) => record.files === undefined)) return;
+
       // found search word in contents
-      $u.each(_o, function(o) {
-        var _files = o.files;
-        if (_files === undefined)
-          return
-
-        if (_files.length === undefined)
-          _files = [_files];
-        files = files.concat(_files);
-
-        // set score for the word in each file to Scorer.term
-        for (j = 0; j < _files.length; j++) {
-          file = _files[j];
-          if (!(file in scoreMap))
-            scoreMap[file] = {};
-          scoreMap[file][word] = o.score;
-        }
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
+
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
+
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
       });
 
       // create the mapping
-      for (j = 0; j < files.length; j++) {
-        file = files[j];
-        if (file in fileMap && fileMap[file].indexOf(word) === -1)
-          fileMap[file].push(word);
-        else
-          fileMap[file] = [word];
-      }
-    }
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
 
     // now check if the files don't contain excluded terms
-    for (file in fileMap) {
-      var valid = true;
-
+    const results = [];
+    for (const [file, wordList] of fileMap) {
       // check if all requirements are matched
-      var filteredTermCount = // as search terms with length < 3 are discarded: ignore
-        searchterms.filter(function(term){return term.length > 2}).length
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
       if (
-        fileMap[file].length != searchterms.length &&
-        fileMap[file].length != filteredTermCount
-      ) continue;
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
 
       // ensure that none of the excluded terms is in the search result
-      for (i = 0; i < excluded.length; i++) {
-        if (terms[excluded[i]] == file ||
-            titleterms[excluded[i]] == file ||
-            $u.contains(terms[excluded[i]] || [], file) ||
-            $u.contains(titleterms[excluded[i]] || [], file)) {
-          valid = false;
-          break;
-        }
-      }
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
 
-      // if we have still a valid result we can add it to the result list
-      if (valid) {
-        // select one (max) score for the file.
-        // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
-        var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
-        results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
-      }
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
     }
     return results;
   },
@@ -492,34 +547,28 @@ var Search = {
   /**
    * helper function to return a node containing the
    * search summary for a given text. keywords is a list
-   * of stemmed words, hlwords is the list of normal, unstemmed
-   * words. the first one is used to find the occurrence, the
-   * latter for highlighting it.
+   * of stemmed words.
    */
-  makeSearchSummary : function(htmlText, keywords, hlwords) {
-    var text = Search.htmlToText(htmlText);
-    if (text == "") {
-      return null;
-    }
-    var textLower = text.toLowerCase();
-    var start = 0;
-    $.each(keywords, function() {
-      var i = textLower.indexOf(this.toLowerCase());
-      if (i > -1)
-        start = i;
-    });
-    start = Math.max(start - 120, 0);
-    var excerpt = ((start > 0) ? '...' : '') +
-      $.trim(text.substr(start, 240)) +
-      ((start + 240 - text.length) ? '...' : '');
-    var rv = $('<p class="context"></p>').text(excerpt);
-    $.each(hlwords, function() {
-      rv = rv.highlightText(this, 'highlighted');
-    });
-    return rv;
-  }
+  makeSearchSummary: (htmlText, keywords) => {
+    const text = Search.htmlToText(htmlText);
+    if (text === "") return null;
+
+    const textLower = text.toLowerCase();
+    const actualStartPosition = [...keywords]
+      .map((k) => textLower.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("p");
+    summary.classList.add("context");
+    summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
+
+    return summary;
+  },
 };
 
-$(document).ready(function() {
-  Search.init();
-});
+_ready(Search.init);
diff --git a/docs/_build/_static/sphinx_highlight.js b/docs/_build/_static/sphinx_highlight.js
new file mode 100644
index 0000000..8a96c69
--- /dev/null
+++ b/docs/_build/_static/sphinx_highlight.js
@@ -0,0 +1,154 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      const rest = document.createTextNode(val.substr(pos + text.length));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
+          rest,
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+      /* There may be more occurrences of search term in this node. So call this
+       * function recursively on the remaining fragment.
+       */
+      _highlight(rest, addItems, text, className);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
+      }
+    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+  }
+};
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const SphinxHighlight = {
+
+  /**
+   * highlight the search words provided in localstorage in the text
+   */
+  highlightSearchWords: () => {
+    if (!SPHINX_HIGHLIGHT_ENABLED) return;  // bail if no highlight
+
+    // get and clear terms from localstorage
+    const url = new URL(window.location);
+    const highlight =
+        localStorage.getItem("sphinx_highlight_terms")
+        || url.searchParams.get("highlight")
+        || "";
+    localStorage.removeItem("sphinx_highlight_terms")
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
+
+    // get individual terms from highlight string
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
+
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '<p class="highlight-link">' +
+            '<a href="javascript:SphinxHighlight.hideSearchWords()">' +
+            _("Hide Search Matches") +
+            "</a></p>"
+        )
+    );
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    localStorage.removeItem("sphinx_highlight_terms")
+  },
+
+  initEscapeListener: () => {
+    // only install a listener if it is really needed
+    if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return;
+      if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) {
+        SphinxHighlight.hideSearchWords();
+        event.preventDefault();
+      }
+    });
+  },
+};
+
+_ready(() => {
+  /* Do not call highlightSearchWords() when we are on the search page.
+   * It will highlight words from the *previous* search query.
+   */
+  if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords();
+  SphinxHighlight.initEscapeListener();
+});
diff --git a/docs/_build/_static/super-collator-phase1.html b/docs/_build/_static/super-collator-phase1.html
new file mode 100644
index 0000000..546ed9c
--- /dev/null
+++ b/docs/_build/_static/super-collator-phase1.html
@@ -0,0 +1,13 @@
+<table class='super-collator super-collator-debug-matrix' id=super-collator-phase1><tr><th/><th class='top'></th><th class='top'>sick</th><th class='top'>fox</th><th class='top'>is</th><th class='top'>crazy</th></tr>
+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled bt'><table><tr><td class='d inner'>-0.50</td><td class='p inner em'>-0.50</td></tr><tr><td class='q inner'>-0.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-1.30</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>quick</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.40</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>brown</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.90</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.54</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-1.04</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>fox</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-1.10</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.74</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.46</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-1.24</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.04</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.24</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>jumps</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.30</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-0.94</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.74</td><td class='p inner em'>-0.04</td></tr><tr><td class='q inner'>-1.44</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>0.14</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>over</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.50</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.14</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.94</td><td class='p inner em'>-0.24</td></tr><tr><td class='q inner'>-1.64</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.04</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.74</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.36</td></tr><tr><td class='q inner'>-0.36</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.70</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.34</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.14</td><td class='p inner em'>-0.44</td></tr><tr><td class='q inner'>-1.84</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.24</td><td class='p inner em'>-0.06</td></tr><tr><td class='q inner'>-0.94</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>0.14</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.56</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+</table>
+
diff --git a/docs/_build/_static/super-collator-phase2.html b/docs/_build/_static/super-collator-phase2.html
new file mode 100644
index 0000000..6ca182e
--- /dev/null
+++ b/docs/_build/_static/super-collator-phase2.html
@@ -0,0 +1,13 @@
+<table class='super-collator super-collator-debug-matrix' id=super-collator-phase2><tr><th/><th class='top'></th><th class='top'>sick</th><th class='top'>fox</th><th class='top'>is</th><th class='top'>crazy</th></tr>
+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled bt'><table><tr><td class='d inner'>-0.50</td><td class='p inner em'>-0.50</td></tr><tr><td class='q inner'>-0.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-1.30</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>quick</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.40</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>brown</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.90</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.54</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-1.04</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>fox</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-1.10</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.74</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.46</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-1.24</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.04</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.24</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>jumps</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.30</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-0.94</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.74</td><td class='p inner em'>-0.04</td></tr><tr><td class='q inner'>-1.44</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>0.14</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>over</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.50</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.14</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.94</td><td class='p inner em'>-0.24</td></tr><tr><td class='q inner'>-1.64</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.04</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.74</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.36</td></tr><tr><td class='q inner'>-0.36</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.70</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.34</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.14</td><td class='p inner em'>-0.44</td></tr><tr><td class='q inner'>-1.84</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.24</td><td class='p inner em'>-0.06</td></tr><tr><td class='q inner'>-0.94</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>0.14</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.56</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+</table>
+
diff --git a/docs/_build/_static/super-collator-result.html b/docs/_build/_static/super-collator-result.html
new file mode 100644
index 0000000..070559f
--- /dev/null
+++ b/docs/_build/_static/super-collator-result.html
@@ -0,0 +1,4 @@
+<table class='super-collator super-collator-result' id=super-collator-result><tr><td>the</td><td>quick</td><td>brown</td><td>fox</td><td>jumps</td><td>over</td><td>the</td><td>lazy</td><td>dog</td></tr>
+<tr><td>-</td><td>sick</td><td>-</td><td>fox</td><td>is</td><td>-</td><td>-</td><td>crazy</td><td>-</td></tr>
+</table>
+
diff --git a/docs/_build/algorithm.html b/docs/_build/algorithm.html
new file mode 100644
index 0000000..4632944
--- /dev/null
+++ b/docs/_build/algorithm.html
@@ -0,0 +1,246 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
+
+  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+  <title>Collation Algorithm &mdash; super-collator 0.0.3 documentation</title>
+      <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
+      <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
+      <link rel="stylesheet" href="_static/custom.css" type="text/css" />
+    <link rel="shortcut icon" href="_static/favicon-cceh-blue.png"/>
+  <!--[if lt IE 9]>
+    <script src="_static/js/html5shiv.min.js"></script>
+  <![endif]-->
+  
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
+        <script>window.MathJax = {"tex": {"macros": {"bs": ["\\boldsymbol"]}}}</script>
+        <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
+    <script src="_static/js/theme.js"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" />
+    <link rel="next" title="Aligner" href="aligner.html" />
+    <link rel="prev" title="Examples" href="examples.html" /> 
+</head>
+
+<body class="wy-body-for-nav"> 
+  <div class="wy-grid-for-nav">
+    <nav data-toggle="wy-nav-shift" class="wy-nav-side">
+      <div class="wy-side-scroll">
+        <div class="wy-side-nav-search" >
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+          </a>
+<div role="search">
+  <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
+    <input type="hidden" name="check_keywords" value="yes" />
+    <input type="hidden" name="area" value="default" />
+  </form>
+</div>
+        </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
+              <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
+</ul>
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+  <section id="collation-algorithm">
+<h1>Collation Algorithm<a class="headerlink" href="#collation-algorithm" title="Link to this heading"></a></h1>
+<p>The library uses an enhancement of the Needleman-Wunsch algorithm by Gotoh <a class="reference internal" href="references.html#gotoh1982" id="id1"><span>[Gotoh1982]</span></a>.
+This section provides a very high level overview of the algorithm.</p>
+<section id="phase-1-build-table">
+<h2>Phase 1 - Build Table<a class="headerlink" href="#phase-1-build-table" title="Link to this heading"></a></h2>
+<p>In phase 1 the algorithm builds a table.  For example this is the table built for the
+two strings: <em>the quick brown fox jumps over the lazy dog</em> and <em>sick fox is crazy.</em></p>
+<table class='super-collator super-collator-debug-matrix' id=super-collator-phase1><tr><th/><th class='top'></th><th class='top'>sick</th><th class='top'>fox</th><th class='top'>is</th><th class='top'>crazy</th></tr>
+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled bt'><table><tr><td class='d inner'>-0.50</td><td class='p inner em'>-0.50</td></tr><tr><td class='q inner'>-0.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-1.30</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>quick</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.40</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>brown</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.90</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.54</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-1.04</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>fox</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-1.10</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.74</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.46</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-1.24</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.04</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.24</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>jumps</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.30</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-0.94</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.74</td><td class='p inner em'>-0.04</td></tr><tr><td class='q inner'>-1.44</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>0.14</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>over</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.50</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.14</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.94</td><td class='p inner em'>-0.24</td></tr><tr><td class='q inner'>-1.64</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.04</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.74</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.36</td></tr><tr><td class='q inner'>-0.36</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.70</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.34</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.14</td><td class='p inner em'>-0.44</td></tr><tr><td class='q inner'>-1.84</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.24</td><td class='p inner em'>-0.06</td></tr><tr><td class='q inner'>-0.94</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>0.14</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.56</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+</table>
+
+<p>Every cell in the table contains three values: <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(P\)</span>, and <span class="math notranslate nohighlight">\(Q\)</span>, and an arrow, like this:</p>
+<table class='super-collator super-collator-debug-matrix' style="margin-left: auto; margin-right: auto">
+<tr><td class='outer'>
+<table>
+  <tr><td class='d inner'>D</td><td class='p inner'>P</td></tr>
+  <tr><td class='q inner'>Q</td><td class='inner arrow'>↖</td></tr>
+</table>
+</td>
+</tr>
+</table><p>We define the score <span class="math notranslate nohighlight">\(S\)</span> for each cell as:</p>
+<div class="math notranslate nohighlight">
+\[S = \max(D, P, Q)\]</div>
+<p>The grayed cells in the first row and first column are initialized using the <em>gap start</em>
+and <em>gap extension</em> penalties.  The numbers for each remaining cell are calculated using
+only values from the three cells, to the top-left, the top, and the left, of the current
+cell:</p>
+<div class="math notranslate nohighlight">
+\[D = S_↖ + \mbox{similarity}(word_←, word_↑)\]</div>
+<div class="math notranslate nohighlight">
+\[P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)\]</div>
+<div class="math notranslate nohighlight">
+\[Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)\]</div>
+<p>Finally the arrow in the current cell is set to point to that cell which yielded the
+highest of the current cell’s <span class="math notranslate nohighlight">\(D\)</span>, <span class="math notranslate nohighlight">\(P\)</span>, and <span class="math notranslate nohighlight">\(Q\)</span> values.</p>
+</section>
+<section id="phase-2-backtrack">
+<h2>Phase 2 - Backtrack<a class="headerlink" href="#phase-2-backtrack" title="Link to this heading"></a></h2>
+<p>When the table is thus completed, two empty sequences are created.  Then the algorithm
+starts backtracking from the last (bottom-right) cell following the arrows until it
+reaches the first (top-left) cell.  If the arrow points:</p>
+<dl class="simple">
+<dt>↑</dt><dd><p>the word in the row header is added to the first sequence, a hyphen is added to the
+second sequence,</p>
+</dd>
+<dt>↖</dt><dd><p>the word in the row header is added to the first sequence, the word in the column
+header is added to the second sequence,</p>
+</dd>
+<dt>←</dt><dd><p>a hyphen is added to the first sequence, the word in the column header is added to the
+second sequence.</p>
+</dd>
+</dl>
+<table class='super-collator super-collator-debug-matrix' id=super-collator-phase2><tr><th/><th class='top'></th><th class='top'>sick</th><th class='top'>fox</th><th class='top'>is</th><th class='top'>crazy</th></tr>
+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled bt'><table><tr><td class='d inner'>-0.50</td><td class='p inner em'>-0.50</td></tr><tr><td class='q inner'>-0.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-1.30</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>quick</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.40</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>brown</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.90</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.54</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-1.04</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>fox</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-1.10</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.74</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.46</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-1.24</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.04</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.24</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>jumps</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.30</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-0.94</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.74</td><td class='p inner em'>-0.04</td></tr><tr><td class='q inner'>-1.44</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>0.14</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>over</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.50</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.14</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.94</td><td class='p inner em'>-0.24</td></tr><tr><td class='q inner'>-1.64</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.04</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.74</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.36</td></tr><tr><td class='q inner'>-0.36</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.70</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.34</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.14</td><td class='p inner em'>-0.44</td></tr><tr><td class='q inner'>-1.84</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.24</td><td class='p inner em'>-0.06</td></tr><tr><td class='q inner'>-0.94</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>0.14</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.56</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+</table>
+
+<p>Finally the two sequences are reversed and printed.</p>
+<table class='super-collator super-collator-result' id=super-collator-result><tr><td>the</td><td>quick</td><td>brown</td><td>fox</td><td>jumps</td><td>over</td><td>the</td><td>lazy</td><td>dog</td></tr>
+<tr><td>-</td><td>sick</td><td>-</td><td>fox</td><td>is</td><td>-</td><td>-</td><td>crazy</td><td>-</td></tr>
+</table>
+
+</section>
+<section id="parameters">
+<h2>Parameters<a class="headerlink" href="#parameters" title="Link to this heading"></a></h2>
+<p>The algorithm can be customized by setting:</p>
+<ul class="simple">
+<li><p>a word comparison (similarity) function,</p></li>
+<li><p>the starting gap penalty,</p></li>
+<li><p>the gap opening penalty,</p></li>
+<li><p>and the gap extension penalty.</p></li>
+</ul>
+</section>
+</section>
+
+
+           </div>
+          </div>
+          <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+        <a href="examples.html" class="btn btn-neutral float-left" title="Examples" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
+        <a href="aligner.html" class="btn btn-neutral float-right" title="Aligner" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
+    </div>
+
+  <hr/>
+
+  <div role="contentinfo">
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
+  </div>
+
+  Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+    <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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+  </div>
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+      jQuery(function () {
+          SphinxRtdTheme.Navigation.enable(true);
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+  </script> 
+
+</body>
+</html>
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diff --git a/docs/_build/aligner.html b/docs/_build/aligner.html
index 78d2c85..0ebdc24 100644
--- a/docs/_build/aligner.html
+++ b/docs/_build/aligner.html
@@ -1,10 +1,10 @@
 <!DOCTYPE html>
 <html class="writer-html5" lang="en" >
 <head>
-  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Aligner &mdash; super-collator 0.0.2 documentation</title>
+  <title>Aligner &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,17 +13,18 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
         <script>window.MathJax = {"tex": {"macros": {"bs": ["\\boldsymbol"]}}}</script>
         <script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="NGrams" href="ngrams.html" />
-    <link rel="prev" title="Examples" href="examples.html" /> 
+    <link rel="prev" title="Overview of the Collation Algorithm" href="algorithm.html" /> 
 </head>
 
 <body class="wy-body-for-nav"> 
@@ -31,12 +32,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -45,8 +50,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1 current"><a class="current reference internal" href="#">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Overview of the Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -63,8 +108,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>Aligner</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">Aligner</li>
       <li class="wy-breadcrumbs-aside">
             <a href="_sources/aligner.rst.txt" rel="nofollow"> View page source</a>
       </li>
@@ -75,52 +120,82 @@
            <div itemprop="articleBody">
              
   <section id="module-super_collator.aligner">
-<span id="aligner"></span><h1>Aligner<a class="headerlink" href="#module-super_collator.aligner" title="Permalink to this headline"></a></h1>
+<span id="aligner"></span><h1>Aligner<a class="headerlink" href="#module-super_collator.aligner" title="Link to this heading"></a></h1>
 <p>This module implements the aligner.</p>
 <dl class="py class">
 <dt class="sig sig-object py" id="super_collator.aligner.Data">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Data</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data" title="Permalink to this definition"></a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Data</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data" title="Link to this definition"></a></dt>
 <dd><p>Private data class for the Needleman-Wunsch+Gotoh sequence aligner.</p>
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.aligner.Data.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data.__init__" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data.__init__" title="Link to this definition"></a></dt>
 <dd></dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Data.score">
-<span class="sig-name descname"><span class="pre">score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.score" title="Permalink to this definition"></a></dt>
-<dd><p>The current score.</p>
+<span class="sig-name descname"><span class="pre">score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.score" title="Link to this definition"></a></dt>
+<dd><p>The cumulative score up to this square.</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="super_collator.aligner.Data.m">
+<span class="sig-name descname"><span class="pre">m</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.m" title="Link to this definition"></a></dt>
+<dd><p>The score for this alignment as match.</p>
 </dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Data.p">
-<span class="sig-name descname"><span class="pre">p</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.p" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">p</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.p" title="Link to this definition"></a></dt>
 <dd><p><span class="math notranslate nohighlight">\(P_{m,n}\)</span> in <a class="reference internal" href="references.html#gotoh1982" id="id1"><span>[Gotoh1982]</span></a>.</p>
 </dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Data.q">
-<span class="sig-name descname"><span class="pre">q</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.q" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">q</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Data.q" title="Link to this definition"></a></dt>
 <dd><p><span class="math notranslate nohighlight">\(Q_{m,n}\)</span> in <a class="reference internal" href="references.html#gotoh1982" id="id2"><span>[Gotoh1982]</span></a>.</p>
 </dd></dl>
 
 <dl class="py attribute">
-<dt class="sig sig-object py" id="super_collator.aligner.Data.pSize">
-<span class="sig-name descname"><span class="pre">pSize</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">int</span></em><a class="headerlink" href="#super_collator.aligner.Data.pSize" title="Permalink to this definition"></a></dt>
-<dd><p>The size of the p gap. <span class="math notranslate nohighlight">\(k\)</span> in <a class="reference internal" href="references.html#gotoh1982" id="id3"><span>[Gotoh1982]</span></a>.</p>
+<dt class="sig sig-object py" id="super_collator.aligner.Data.backtrack">
+<span class="sig-name descname"><span class="pre">backtrack</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">int</span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></em><a class="headerlink" href="#super_collator.aligner.Data.backtrack" title="Link to this definition"></a></dt>
+<dd><p>A copy of the backtracking matrix entry for debugging.</p>
 </dd></dl>
 
 <dl class="py attribute">
-<dt class="sig sig-object py" id="super_collator.aligner.Data.qSize">
-<span class="sig-name descname"><span class="pre">qSize</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">int</span></em><a class="headerlink" href="#super_collator.aligner.Data.qSize" title="Permalink to this definition"></a></dt>
-<dd><p>The size of the q gap. <span class="math notranslate nohighlight">\(k\)</span> in <a class="reference internal" href="references.html#gotoh1982" id="id4"><span>[Gotoh1982]</span></a>.</p>
+<dt class="sig sig-object py" id="super_collator.aligner.Data.prefilled">
+<span class="sig-name descname"><span class="pre">prefilled</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">bool</span></em><a class="headerlink" href="#super_collator.aligner.Data.prefilled" title="Link to this definition"></a></dt>
+<dd><p>True if this cell was prefilled.</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="super_collator.aligner.Data.backtracked">
+<span class="sig-name descname"><span class="pre">backtracked</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">bool</span></em><a class="headerlink" href="#super_collator.aligner.Data.backtracked" title="Link to this definition"></a></dt>
+<dd><p>True if we actually backtracked through this entry.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="super_collator.aligner.Data.arrow">
+<span class="sig-name descname"><span class="pre">arrow</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="headerlink" href="#super_collator.aligner.Data.arrow" title="Link to this definition"></a></dt>
+<dd><p>Returns the appropriate arrow form.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="super_collator.aligner.Data.__str__">
+<span class="sig-name descname"><span class="pre">__str__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data.__str__" title="Link to this definition"></a></dt>
+<dd><p>Return str(self).</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="super_collator.aligner.Data.str_size">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">str_size</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Data.str_size" title="Link to this definition"></a></dt>
+<dd><p>The size of the string returned by __str__.</p>
 </dd></dl>
 
 </dd></dl>
 
 <dl class="py class">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Aligner</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">open_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">extend_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">0.5</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Aligner" title="Permalink to this definition"></a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Aligner</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">open_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">extend_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-0.5</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Aligner" title="Link to this definition"></a></dt>
 <dd><p>A generic Needleman-Wunsch+Gotoh sequence aligner.</p>
 <p>This implementation uses Gotoh’s improvements to get <span class="math notranslate nohighlight">\(\mathcal{O}(mn)\)</span> running time
 and reduce memory requirements to essentially the backtracking matrix only.  In
@@ -140,86 +215,90 @@
 the word and the POS-tag.</p>
 <div class="admonition seealso">
 <p class="admonition-title">See also</p>
-<p><a class="reference internal" href="references.html#needlemanwunsch1970" id="id5"><span>[NeedlemanWunsch1970]</span></a></p>
-<p><a class="reference internal" href="references.html#gotoh1982" id="id6"><span>[Gotoh1982]</span></a></p>
+<p><a class="reference internal" href="references.html#needlemanwunsch1970" id="id3"><span>[NeedlemanWunsch1970]</span></a></p>
+<p><a class="reference internal" href="references.html#gotoh1982" id="id4"><span>[Gotoh1982]</span></a></p>
 </div>
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">open_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">extend_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-</span> <span class="pre">0.5</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Aligner.__init__" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">open_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-1.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">extend_score</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">-0.5</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.aligner.Aligner.__init__" title="Link to this definition"></a></dt>
 <dd></dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner.start_score">
-<span class="sig-name descname"><span class="pre">start_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.start_score" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">start_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.start_score" title="Link to this definition"></a></dt>
 <dd><p>The gap opening score at the start of the string.
 Set this to 0 to find local alignments.</p>
 </dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner.open_score">
-<span class="sig-name descname"><span class="pre">open_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.open_score" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">open_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.open_score" title="Link to this definition"></a></dt>
 <dd><p>The gap opening score <span class="math notranslate nohighlight">\(v\)</span>.</p>
 </dd></dl>
 
 <dl class="py attribute">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner.extend_score">
-<span class="sig-name descname"><span class="pre">extend_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.extend_score" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">extend_score</span></span><em class="property"><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="pre">float</span></em><a class="headerlink" href="#super_collator.aligner.Aligner.extend_score" title="Link to this definition"></a></dt>
 <dd><p>The gap extension score <span class="math notranslate nohighlight">\(u\)</span>.</p>
 </dd></dl>
 
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.aligner.Aligner.align">
-<span class="sig-name descname"><span class="pre">align</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">seq_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seq_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">similarity</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Optional</span><span class="p"><span class="pre">[</span></span><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#super_collator.aligner.Aligner.align" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">align</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">seq_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seq_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">similarity</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#super_collator.aligner.Aligner.align" title="Link to this definition"></a></dt>
 <dd><p>Align two sequences.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>similarity</strong> – a callable that returns the similarity of two objects</p></li>
+<li><p><strong>seq_a</strong> – the first sequence to align</p></li>
+<li><p><strong>seq_b</strong> – the second sequence to align</p></li>
+<li><p><strong>similarity</strong> – a callable that returns the similarity of two members of seq_a and seq_b</p></li>
 <li><p><strong>gap_a</strong> – insert gap_a() for a gap in sequence a. None inserts None.</p></li>
 <li><p><strong>gap_b</strong> – insert gap_b() for a gap in sequence b. None inserts gap_a().</p></li>
 </ul>
 </dd>
-<dt class="field-even">Returns</dt>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
 <dd class="field-even"><p>the aligned sequences and the score</p>
 </dd>
 </dl>
 </dd></dl>
 
-</dd></dl>
-
-<dl class="py function">
-<dt class="sig sig-object py" id="super_collator.aligner.build_debug_matrix">
-<span class="sig-name descname"><span class="pre">build_debug_matrix</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">matrix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="#super_collator.aligner.Data" title="super_collator.aligner.Data"><span class="pre">super_collator.aligner.Data</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">len_matrix</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">int</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ts_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ts_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="headerlink" href="#super_collator.aligner.build_debug_matrix" title="Permalink to this definition"></a></dt>
-<dd><p>Build a human-readable debug matrix.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="super_collator.aligner.Aligner.align_debug">
+<span class="sig-name descname"><span class="pre">align_debug</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">seq_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seq_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">similarity</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">Callable</span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">[</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="w"> </span><span class="p"><span class="pre">|</span></span><span class="w"> </span><span class="pre">None</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">debug</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">Tuple</span><span class="p"><span class="pre">[</span></span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">Sequence</span><span class="p"><span class="pre">[</span></span><span class="pre">object</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">float</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">List</span><span class="p"><span class="pre">[</span></span><span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="#super_collator.aligner.Data" title="super_collator.aligner.Data"><span class="pre">Data</span></a><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></span><a class="headerlink" href="#super_collator.aligner.Aligner.align_debug" title="Link to this definition"></a></dt>
+<dd><p>Align two sequences and return debug information.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
-<li><p><strong>matrix</strong> – the full scoring matrix</p></li>
-<li><p><strong>len_matrix</strong> – the backtracking matrix</p></li>
-<li><p><strong>ts_a</strong> – the first aligned string</p></li>
-<li><p><strong>ts_b</strong> – the second aligned string</p></li>
+<li><p><strong>seq_a</strong> – the first sequence to align</p></li>
+<li><p><strong>seq_b</strong> – the second sequence to align</p></li>
+<li><p><strong>similarity</strong> – a callable that returns the similarity of two members of seq_a and seq_b</p></li>
+<li><p><strong>gap_a</strong> – insert gap_a() for a gap in sequence a. None inserts None.</p></li>
+<li><p><strong>gap_b</strong> – insert gap_b() for a gap in sequence b. None inserts gap_a().</p></li>
+<li><p><strong>debug</strong> – calculate debug information if True, debug info wastes memory</p></li>
 </ul>
 </dd>
-<dt class="field-even">Return str</dt>
-<dd class="field-even"><p>the debug matrix as human readable string</p>
+<dt class="field-even">Returns<span class="colon">:</span></dt>
+<dd class="field-even"><p>the aligned sequences, the score, and the debug matrix</p>
 </dd>
 </dl>
 </dd></dl>
 
+</dd></dl>
+
 </section>
 
 
            </div>
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   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
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diff --git a/docs/_build/doctrees/examples.doctree b/docs/_build/doctrees/examples.doctree
index c525c0d683f563b8f45c968d1e3ef5bcc3be899d..c472733708b0156c9b7f8c0a2987866b435dff08 100644
GIT binary patch
delta 330
zcmezFwa=TSfpzNUi7Z<-?vY|-md?<h9M5btnV+eUHA6bXzIbwjsPyEeOd0iNjyaj>
zc?u=v`3l7)MVWc&#R}z_B^e4usX2)isVNG@1*thXKw*W_Vi4)4>t2+YTWmEYgFSXi
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xY$f-Jk@4<kT?HOyG2YDF#PrnooczQTpzo&iumHW9J!P_o@+HR3&C)6{i~!dxc_9D*

delta 224
zcmdnz{oRYDfpu!mM3yZq8LSz?8+S-CGP7nFPQJ*voKpiR!j>VOVLy2xm(1iDOc`u4
zjyaj>d6NT~#rUnJWU$9h$q?&7i1AuYX`RwIrFIHPW7y_8W?nY98A)I>Hi#-sKFfKW
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elbV~9ni8Lxo0y(jJf(ATzw#wUzs*T1F^m8n@k+b^

diff --git a/docs/_build/doctrees/index.doctree b/docs/_build/doctrees/index.doctree
index 822670540296e37daac2ffa279f3be0e36d36fd4..33338ba90e051cdfaa5ce567644ab07f1449c020 100644
GIT binary patch
delta 680
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I3kEX+03EdE6951J

delta 685
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diff --git a/docs/_build/examples.html b/docs/_build/examples.html
index ba06722..9544ee5 100644
--- a/docs/_build/examples.html
+++ b/docs/_build/examples.html
@@ -1,10 +1,10 @@
 <!DOCTYPE html>
 <html class="writer-html5" lang="en" >
 <head>
-  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Examples &mdash; super-collator 0.0.2 documentation</title>
+  <title>Examples &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,14 +13,15 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
-    <link rel="next" title="Aligner" href="aligner.html" />
+    <link rel="next" title="Overview of the Collation Algorithm" href="algorithm.html" />
     <link rel="prev" title="Super Collator" href="index.html" /> 
 </head>
 
@@ -29,12 +30,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -43,8 +48,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul class="current">
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Overview of the Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -61,8 +106,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>Examples</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">Examples</li>
       <li class="wy-breadcrumbs-aside">
             <a href="_sources/examples.rst.txt" rel="nofollow"> View page source</a>
       </li>
@@ -73,12 +118,12 @@
            <div itemprop="articleBody">
              
   <section id="examples">
-<h1>Examples<a class="headerlink" href="#examples" title="Permalink to this headline"></a></h1>
+<h1>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h1>
 <p>Install:</p>
-<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$ pip install super-collator
+<div class="highlight-shell notranslate"><div class="highlight"><pre><span></span>$<span class="w"> </span>pip<span class="w"> </span>install<span class="w"> </span>super-collator
 </pre></div>
 </div>
-<p>Align with relaxed spelling:</p>
+<p>Align two strings with relaxed spelling using N-Grams:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.aligner</span> <span class="kn">import</span> <span class="n">Aligner</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.ngrams</span> <span class="kn">import</span> <span class="n">NGrams</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.super_collator</span> <span class="kn">import</span> <span class="n">to_table</span>
@@ -86,10 +131,10 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 <span class="gp">&gt;&gt;&gt; </span><span class="n">aligner</span> <span class="o">=</span> <span class="n">Aligner</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="s2">&quot;Lorem ipsum dollar amat adipiscing elit&quot;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="s2">&quot;qui dolorem ipsum quia dolor sit amet consectetur adipisci velit&quot;</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">a</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">b</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">aligner</span><span class="o">.</span><span class="n">align</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">NGrams</span><span class="o">.</span><span class="n">similarity</span><span class="p">,</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">NGrams</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">))</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">to_table</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">a</span><span class="p">)),</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">b</span><span class="p">))))</span>  
 <span class="go">-   Lorem   ipsum -    dollar -   amat -           adipiscing elit</span>
@@ -100,7 +145,7 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.aligner</span> <span class="kn">import</span> <span class="n">Aligner</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.ngrams</span> <span class="kn">import</span> <span class="n">NGrams</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.super_collator</span> <span class="kn">import</span> <span class="n">to_table</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">similarity</span><span class="p">(</span><span class="n">aa</span><span class="p">,</span> <span class="n">bb</span><span class="p">):</span>
 <span class="gp">... </span>    <span class="n">sim</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">&quot;-inf&quot;</span><span class="p">)</span>
 <span class="gp">... </span>    <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="n">aa</span><span class="p">:</span>
@@ -109,24 +154,24 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 <span class="gp">... </span>            <span class="k">if</span> <span class="n">score</span> <span class="o">&gt;</span> <span class="n">sim</span><span class="p">:</span>
 <span class="gp">... </span>                <span class="n">sim</span> <span class="o">=</span> <span class="n">score</span>
 <span class="gp">... </span>    <span class="k">return</span> <span class="n">sim</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">merge</span><span class="p">(</span><span class="n">aa</span><span class="p">,</span> <span class="n">bb</span><span class="p">):</span>
 <span class="gp">... </span>    <span class="k">return</span> <span class="p">[</span><span class="n">a</span> <span class="o">+</span> <span class="n">b</span> <span class="k">for</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">aa</span><span class="p">,</span> <span class="n">bb</span><span class="p">)]</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">aligner</span> <span class="o">=</span> <span class="n">Aligner</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="s2">&quot;qui dolorem ipsum quia dolor sit amet consectetur adipisci velit&quot;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="s2">&quot;Lorem ipsum adipiscing&quot;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span> <span class="o">=</span> <span class="s2">&quot;Lorem dollar amat elit&quot;</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[[</span><span class="n">NGrams</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">a</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="p">[[</span><span class="n">NGrams</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">b</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span> <span class="o">=</span> <span class="p">[[</span><span class="n">NGrams</span><span class="p">(</span><span class="n">s</span><span class="p">)</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">2</span><span class="p">)]</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">c</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="p">,</span>  <span class="n">b</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">aligner</span><span class="o">.</span><span class="n">align</span><span class="p">(</span><span class="n">a</span><span class="p">,</span>  <span class="n">b</span><span class="p">,</span> <span class="n">similarity</span><span class="p">,</span> <span class="k">lambda</span><span class="p">:</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">)],</span> <span class="k">lambda</span><span class="p">:</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">)])</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">ab</span> <span class="o">=</span> <span class="n">merge</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">ab</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">aligner</span><span class="o">.</span><span class="n">align</span><span class="p">(</span><span class="n">ab</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">similarity</span><span class="p">,</span> <span class="k">lambda</span><span class="p">:</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">)]</span> <span class="o">*</span> <span class="mi">2</span><span class="p">,</span> <span class="k">lambda</span><span class="p">:</span> <span class="p">[</span><span class="n">NGrams</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">)])</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">abc</span> <span class="o">=</span> <span class="n">merge</span><span class="p">(</span><span class="n">ab</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">to_table</span><span class="p">(</span><span class="o">*</span><span class="nb">zip</span><span class="p">(</span><span class="o">*</span><span class="p">[[</span><span class="n">t</span><span class="o">.</span><span class="n">user_data</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">nn</span><span class="p">]</span> <span class="k">for</span> <span class="n">nn</span> <span class="ow">in</span> <span class="n">abc</span><span class="p">])))</span>  
 <span class="go">qui dolorem ipsum quia dolor  sit amet consectetur adipisci   velit</span>
 <span class="go">-   Lorem   ipsum -    -      -   -    -           adipiscing -</span>
@@ -136,7 +181,7 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 <p>Align two sentences using their part-of-speech tags only:</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.aligner</span> <span class="kn">import</span> <span class="n">Aligner</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">super_collator.super_collator</span> <span class="kn">import</span> <span class="n">to_table</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="k">class</span> <span class="nc">PosToken</span><span class="p">:</span>
 <span class="gp">... </span>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">pos</span><span class="p">):</span>
 <span class="gp">... </span>        <span class="bp">self</span><span class="o">.</span><span class="n">s</span> <span class="o">=</span> <span class="n">s</span>
@@ -148,14 +193,14 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
 <span class="gp">... </span>    <span class="nd">@staticmethod</span>
 <span class="gp">... </span>    <span class="k">def</span> <span class="nf">similarity</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
 <span class="gp">... </span>        <span class="k">return</span> <span class="mf">1.0</span> <span class="k">if</span> <span class="n">a</span><span class="o">.</span><span class="n">pos</span> <span class="o">==</span> <span class="n">b</span><span class="o">.</span><span class="n">pos</span> <span class="k">else</span> <span class="mf">0.0</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">aligner</span> <span class="o">=</span> <span class="n">Aligner</span><span class="p">()</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="s2">&quot;it/PRP was/VBD a/DT dark/JJ and/CC stormy/JJ night/NN&quot;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="s2">&quot;it/PRP is/VBZ a/DT fine/JJ day/NN&quot;</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="n">PosToken</span><span class="p">(</span><span class="o">*</span><span class="n">s</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s2">&quot;/&quot;</span><span class="p">))</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">a</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="n">PosToken</span><span class="p">(</span><span class="o">*</span><span class="n">s</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s2">&quot;/&quot;</span><span class="p">))</span> <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">b</span><span class="o">.</span><span class="n">split</span><span class="p">()]</span>
-<span class="go">&gt;&gt;&gt;</span>
+<span class="gp">&gt;&gt;&gt;</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="n">c</span><span class="p">,</span> <span class="n">d</span><span class="p">,</span> <span class="n">score</span> <span class="o">=</span> <span class="n">aligner</span><span class="o">.</span><span class="n">align</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">PosToken</span><span class="o">.</span><span class="n">similarity</span><span class="p">,</span> <span class="k">lambda</span><span class="p">:</span> <span class="n">PosToken</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="p">,</span> <span class="s2">&quot;&quot;</span><span class="p">))</span>
 <span class="gp">&gt;&gt;&gt; </span><span class="nb">print</span><span class="p">(</span><span class="n">to_table</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">c</span><span class="p">)),</span> <span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">d</span><span class="p">))))</span>  
 <span class="go">it was a dark and stormy night</span>
@@ -169,13 +214,13 @@ <h1>Examples<a class="headerlink" href="#examples" title="Permalink to this head
           </div>
           <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
         <a href="index.html" class="btn btn-neutral float-left" title="Super Collator" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
-        <a href="aligner.html" class="btn btn-neutral float-right" title="Aligner" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
+        <a href="algorithm.html" class="btn btn-neutral float-right" title="Overview of the Collation Algorithm" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
     </div>
 
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/_build/genindex.html b/docs/_build/genindex.html
index 5a9a3f5..9ebe251 100644
--- a/docs/_build/genindex.html
+++ b/docs/_build/genindex.html
@@ -3,7 +3,7 @@
 <head>
   <meta charset="utf-8" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Index &mdash; super-collator 0.0.2 documentation</title>
+  <title>Index &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -12,10 +12,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="#" />
     <link rel="search" title="Search" href="search.html" /> 
@@ -26,12 +27,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -40,8 +45,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -58,8 +103,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>Index</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">Index</li>
       <li class="wy-breadcrumbs-aside">
       </li>
   </ul>
@@ -99,8 +144,12 @@ <h2 id="_">_</h2>
       </ul></li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="ngrams.html#super_collator.ngrams.NGrams.__str__">__str__() (NGrams method)</a>
+      <li><a href="aligner.html#super_collator.aligner.Data.__str__">__str__() (Data method)</a>
+
+      <ul>
+        <li><a href="ngrams.html#super_collator.ngrams.NGrams.__str__">(NGrams method)</a>
 </li>
+      </ul></li>
   </ul></td>
 </tr></table>
 
@@ -108,10 +157,14 @@ <h2 id="A">A</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="aligner.html#super_collator.aligner.Aligner.align">align() (Aligner method)</a>
+</li>
+      <li><a href="aligner.html#super_collator.aligner.Aligner.align_debug">align_debug() (Aligner method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="aligner.html#super_collator.aligner.Aligner">Aligner (class in super_collator.aligner)</a>
+</li>
+      <li><a href="aligner.html#super_collator.aligner.Data.arrow">arrow() (Data method)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -119,7 +172,11 @@ <h2 id="A">A</h2>
 <h2 id="B">B</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="aligner.html#super_collator.aligner.build_debug_matrix">build_debug_matrix() (in module super_collator.aligner)</a>
+      <li><a href="aligner.html#super_collator.aligner.Data.backtrack">backtrack (Data attribute)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="aligner.html#super_collator.aligner.Data.backtracked">backtracked (Data attribute)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -151,6 +208,8 @@ <h2 id="L">L</h2>
 <h2 id="M">M</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="aligner.html#super_collator.aligner.Data.m">m (Data attribute)</a>
+</li>
       <li>
     module
 
@@ -186,7 +245,7 @@ <h2 id="P">P</h2>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="aligner.html#super_collator.aligner.Data.pSize">pSize (Data attribute)</a>
+      <li><a href="aligner.html#super_collator.aligner.Data.prefilled">prefilled (Data attribute)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -195,10 +254,6 @@ <h2 id="Q">Q</h2>
 <table style="width: 100%" class="indextable genindextable"><tr>
   <td style="width: 33%; vertical-align: top;"><ul>
       <li><a href="aligner.html#super_collator.aligner.Data.q">q (Data attribute)</a>
-</li>
-  </ul></td>
-  <td style="width: 33%; vertical-align: top;"><ul>
-      <li><a href="aligner.html#super_collator.aligner.Data.qSize">qSize (Data attribute)</a>
 </li>
   </ul></td>
 </tr></table>
@@ -211,6 +266,8 @@ <h2 id="S">S</h2>
       <li><a href="ngrams.html#super_collator.ngrams.NGrams.similarity">similarity() (NGrams static method)</a>
 </li>
       <li><a href="aligner.html#super_collator.aligner.Aligner.start_score">start_score (Aligner attribute)</a>
+</li>
+      <li><a href="aligner.html#super_collator.aligner.Data.str_size">str_size() (Data static method)</a>
 </li>
   </ul></td>
   <td style="width: 33%; vertical-align: top;"><ul>
@@ -240,7 +297,7 @@ <h2 id="S">S</h2>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/_build/index.html b/docs/_build/index.html
index 5e03512..a604b21 100644
--- a/docs/_build/index.html
+++ b/docs/_build/index.html
@@ -1,10 +1,10 @@
 <!DOCTYPE html>
 <html class="writer-html5" lang="en" >
 <head>
-  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Super Collator &mdash; super-collator 0.0.2 documentation</title>
+  <title>Super Collator &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,10 +13,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
@@ -28,12 +29,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="#" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="#" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -42,8 +47,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -60,8 +105,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="#" class="icon icon-home"></a> &raquo;</li>
-      <li>Super Collator</li>
+      <li><a href="#" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">Super Collator</li>
       <li class="wy-breadcrumbs-aside">
             <a href="_sources/index.rst.txt" rel="nofollow"> View page source</a>
       </li>
@@ -72,20 +117,33 @@
            <div itemprop="articleBody">
              
   <section id="super-collator">
-<h1>Super Collator<a class="headerlink" href="#super-collator" title="Permalink to this headline"></a></h1>
+<h1>Super Collator<a class="headerlink" href="#super-collator" title="Link to this heading"></a></h1>
 <p>Collates textual sources with relaxed spelling.  Uses Gotoh’s variant of the
 Needleman-Wunsch sequence alignment algorithm.</p>
 <div class="toctree-wrapper compound">
 <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a></li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a></li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 </div>
 <section id="indices-and-tables">
-<h2>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this headline"></a></h2>
+<h2>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Link to this heading"></a></h2>
 <ul class="simple">
 <li><p><a class="reference internal" href="genindex.html"><span class="std std-ref">Index</span></a></p></li>
 <li><p><a class="reference internal" href="py-modindex.html"><span class="std std-ref">Module Index</span></a></p></li>
@@ -104,7 +162,7 @@ <h2>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Pe
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/_build/ngrams.html b/docs/_build/ngrams.html
index 472df89..43b5085 100644
--- a/docs/_build/ngrams.html
+++ b/docs/_build/ngrams.html
@@ -1,10 +1,10 @@
 <!DOCTYPE html>
 <html class="writer-html5" lang="en" >
 <head>
-  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>NGrams &mdash; super-collator 0.0.2 documentation</title>
+  <title>NGrams &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,10 +13,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
@@ -29,12 +30,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -43,8 +48,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1 current"><a class="current reference internal" href="#">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Overview of the Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -61,8 +106,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>NGrams</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">NGrams</li>
       <li class="wy-breadcrumbs-aside">
             <a href="_sources/ngrams.rst.txt" rel="nofollow"> View page source</a>
       </li>
@@ -73,23 +118,23 @@
            <div itemprop="articleBody">
              
   <section id="module-super_collator.ngrams">
-<span id="ngrams"></span><h1>NGrams<a class="headerlink" href="#module-super_collator.ngrams" title="Permalink to this headline"></a></h1>
+<span id="ngrams"></span><h1>NGrams<a class="headerlink" href="#module-super_collator.ngrams" title="Link to this heading"></a></h1>
 <p>This module implements the NGrams class.</p>
 <dl class="py class">
 <dt class="sig sig-object py" id="super_collator.ngrams.NGrams">
-<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NGrams</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">user_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.ngrams.NGrams" title="Permalink to this definition"></a></dt>
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NGrams</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">user_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.ngrams.NGrams" title="Link to this definition"></a></dt>
 <dd><p>A class that compares two strings using N-Grams.</p>
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.ngrams.NGrams.__init__">
-<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">user_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.ngrams.NGrams.__init__" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">user_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#super_collator.ngrams.NGrams.__init__" title="Link to this definition"></a></dt>
 <dd></dd></dl>
 
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.ngrams.NGrams.load">
-<span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">super_collator.ngrams.NGrams</span></a></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.load" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">str</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">NGrams</span></a></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.load" title="Link to this definition"></a></dt>
 <dd><p>Split a string into N-Grams.</p>
 <dl class="field-list simple">
-<dt class="field-odd">Parameters</dt>
+<dt class="field-odd">Parameters<span class="colon">:</span></dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>s</strong> – the string to split into N-Grams</p></li>
 <li><p><strong>n</strong> – puts the N in N-Grams</p></li>
@@ -100,13 +145,13 @@
 
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.ngrams.NGrams.__str__">
-<span class="sig-name descname"><span class="pre">__str__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.__str__" title="Permalink to this definition"></a></dt>
+<span class="sig-name descname"><span class="pre">__str__</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">str</span></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.__str__" title="Link to this definition"></a></dt>
 <dd><p>Return str(self).</p>
 </dd></dl>
 
 <dl class="py method">
 <dt class="sig sig-object py" id="super_collator.ngrams.NGrams.similarity">
-<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">similarity</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">super_collator.ngrams.NGrams</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">super_collator.ngrams.NGrams</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.similarity" title="Permalink to this definition"></a></dt>
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">similarity</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">NGrams</span></a></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><a class="reference internal" href="#super_collator.ngrams.NGrams" title="super_collator.ngrams.NGrams"><span class="pre">NGrams</span></a></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">&#x2192;</span> <span class="sig-return-typehint"><span class="pre">float</span></span></span><a class="headerlink" href="#super_collator.ngrams.NGrams.similarity" title="Link to this definition"></a></dt>
 <dd><p>Return similarity between two NGrams objects.</p>
 <p>The similarity score is 2 times the count of common N-Grams divided by the total
 count of N-Grams.</p>
@@ -127,7 +172,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
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diff --git a/docs/_build/py-modindex.html b/docs/_build/py-modindex.html
index 977dc2a..b287ea7 100644
--- a/docs/_build/py-modindex.html
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@@ -3,7 +3,7 @@
 <head>
   <meta charset="utf-8" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Python Module Index &mdash; super-collator 0.0.2 documentation</title>
+  <title>Python Module Index &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -12,10 +12,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
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@@ -33,12 +34,16 @@
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       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -47,8 +52,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
@@ -65,8 +110,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>Python Module Index</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">Python Module Index</li>
       <li class="wy-breadcrumbs-aside">
       </li>
   </ul>
@@ -110,7 +155,7 @@ <h1>Python Module Index</h1>
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/_build/references.html b/docs/_build/references.html
index 625e5df..c2e9f57 100644
--- a/docs/_build/references.html
+++ b/docs/_build/references.html
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 <!DOCTYPE html>
 <html class="writer-html5" lang="en" >
 <head>
-  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+  <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
 
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>References &mdash; super-collator 0.0.2 documentation</title>
+  <title>References &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,10 +13,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
-        <script src="_static/doctools.js"></script>
+        <script src="_static/jquery.js?v=5d32c60e"></script>
+        <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script>
+        <script src="_static/documentation_options.js?v=47de8214"></script>
+        <script src="_static/doctools.js?v=888ff710"></script>
+        <script src="_static/sphinx_highlight.js?v=dc90522c"></script>
     <script src="_static/js/theme.js"></script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
@@ -28,12 +29,16 @@
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-scroll">
         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
     <input type="hidden" name="check_keywords" value="yes" />
     <input type="hidden" name="area" value="default" />
   </form>
@@ -42,8 +47,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul class="current">
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Overview of the Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.score"><code class="docutils literal notranslate"><span class="pre">Data.score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.m"><code class="docutils literal notranslate"><span class="pre">Data.m</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">References</a></li>
 </ul>
 
@@ -60,8 +105,8 @@
         <div class="rst-content">
           <div role="navigation" aria-label="Page navigation">
   <ul class="wy-breadcrumbs">
-      <li><a href="index.html" class="icon icon-home"></a> &raquo;</li>
-      <li>References</li>
+      <li><a href="index.html" class="icon icon-home" aria-label="Home"></a></li>
+      <li class="breadcrumb-item active">References</li>
       <li class="wy-breadcrumbs-aside">
             <a href="_sources/references.rst.txt" rel="nofollow"> View page source</a>
       </li>
@@ -72,18 +117,21 @@
            <div itemprop="articleBody">
              
   <section id="references">
-<h1>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h1>
-<dl class="citation">
-<dt class="label" id="gotoh1982"><span class="brackets">Gotoh1982</span></dt>
-<dd><p>Gotoh, O.  An Improved Algorithm for Matching Biological Sequences.
-1982.  J. Mol. Biol. 162, 705-708</p>
-</dd>
-<dt class="label" id="needlemanwunsch1970"><span class="brackets">NeedlemanWunsch1970</span></dt>
-<dd><p>Needleman, S.  Wunsch, C.  A General Method Applicable to the
+<h1>References<a class="headerlink" href="#references" title="Link to this heading"></a></h1>
+<div role="list" class="citation-list">
+<div class="citation" id="gotoh1982" role="doc-biblioentry">
+<span class="label"><span class="fn-bracket">[</span>Gotoh1982<span class="fn-bracket">]</span></span>
+<p>Gotoh, O. 1982.  <em>An Improved Algorithm for Matching Biological
+Sequences.</em>  J. Mol. Biol. 162, 705-708
+<a class="reference external" href="http://jaligner.sourceforge.net/references/gotoh1982.pdf">http://jaligner.sourceforge.net/references/gotoh1982.pdf</a></p>
+</div>
+<div class="citation" id="needlemanwunsch1970" role="doc-biblioentry">
+<span class="label"><span class="fn-bracket">[</span>NeedlemanWunsch1970<span class="fn-bracket">]</span></span>
+<p>Needleman, S.  Wunsch, C.  1970.  <em>A General Method Applicable to the
 Search for Similarities in the Amino Acid Sequence of Two
-Proteins.  1970.  J. Mol. Biol. 48, 443-453</p>
-</dd>
-</dl>
+Proteins.</em>  J. Mol. Biol. 48, 443-453</p>
+</div>
+</div>
 </section>
 
 
@@ -96,7 +144,7 @@ <h1>References<a class="headerlink" href="#references" title="Permalink to this
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
   </div>
 
   Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
diff --git a/docs/_build/search.html b/docs/_build/search.html
index e3f0bb0..480f38c 100644
--- a/docs/_build/search.html
+++ b/docs/_build/search.html
@@ -3,7 +3,7 @@
 <head>
   <meta charset="utf-8" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0" />
-  <title>Search &mdash; super-collator 0.0.2 documentation</title>
+  <title>Search &mdash; super-collator 0.0.3 documentation</title>
       <link rel="stylesheet" href="_static/pygments.css" type="text/css" />
       <link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
       <link rel="stylesheet" href="_static/custom.css" type="text/css" />
@@ -13,10 +13,11 @@
     <script src="_static/js/html5shiv.min.js"></script>
   <![endif]-->
   
-        <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
-        <script src="_static/jquery.js"></script>
-        <script src="_static/underscore.js"></script>
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@@ -29,12 +30,16 @@
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         <div class="wy-side-nav-search" >
-            <a href="index.html" class="icon icon-home"> super-collator
-            <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
+
+          
+          
+          <a href="index.html" class="icon icon-home">
+            super-collator
+              <img src="_static/logo-cceh-white.svg" class="logo" alt="Logo"/>
           </a>
 <div role="search">
   <form id="rtd-search-form" class="wy-form" action="#" method="get">
-    <input type="text" name="q" placeholder="Search docs" />
+    <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" />
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@@ -43,8 +48,48 @@
               <p class="caption" role="heading"><span class="caption-text">Contents:</span></p>
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="examples.html">Examples</a></li>
-<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a></li>
-<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a></li>
+<li class="toctree-l1"><a class="reference internal" href="algorithm.html">Collation Algorithm</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-1-build-table">Phase 1 - Build Table</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#phase-2-backtrack">Phase 2 - Backtrack</a></li>
+<li class="toctree-l2"><a class="reference internal" href="algorithm.html#parameters">Parameters</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="aligner.html">Aligner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Data"><code class="docutils literal notranslate"><span class="pre">Data</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__init__"><code class="docutils literal notranslate"><span class="pre">Data.__init__()</span></code></a></li>
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+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.p"><code class="docutils literal notranslate"><span class="pre">Data.p</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.q"><code class="docutils literal notranslate"><span class="pre">Data.q</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtrack"><code class="docutils literal notranslate"><span class="pre">Data.backtrack</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.prefilled"><code class="docutils literal notranslate"><span class="pre">Data.prefilled</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.backtracked"><code class="docutils literal notranslate"><span class="pre">Data.backtracked</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.arrow"><code class="docutils literal notranslate"><span class="pre">Data.arrow()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.__str__"><code class="docutils literal notranslate"><span class="pre">Data.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Data.str_size"><code class="docutils literal notranslate"><span class="pre">Data.str_size()</span></code></a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner"><code class="docutils literal notranslate"><span class="pre">Aligner</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.__init__"><code class="docutils literal notranslate"><span class="pre">Aligner.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.start_score"><code class="docutils literal notranslate"><span class="pre">Aligner.start_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.open_score"><code class="docutils literal notranslate"><span class="pre">Aligner.open_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.extend_score"><code class="docutils literal notranslate"><span class="pre">Aligner.extend_score</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align"><code class="docutils literal notranslate"><span class="pre">Aligner.align()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="aligner.html#super_collator.aligner.Aligner.align_debug"><code class="docutils literal notranslate"><span class="pre">Aligner.align_debug()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ngrams.html">NGrams</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams"><code class="docutils literal notranslate"><span class="pre">NGrams</span></code></a><ul>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__init__"><code class="docutils literal notranslate"><span class="pre">NGrams.__init__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.load"><code class="docutils literal notranslate"><span class="pre">NGrams.load()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.__str__"><code class="docutils literal notranslate"><span class="pre">NGrams.__str__()</span></code></a></li>
+<li class="toctree-l3"><a class="reference internal" href="ngrams.html#super_collator.ngrams.NGrams.similarity"><code class="docutils literal notranslate"><span class="pre">NGrams.similarity()</span></code></a></li>
+</ul>
+</li>
+</ul>
+</li>
 <li class="toctree-l1"><a class="reference internal" href="references.html">References</a></li>
 </ul>
 
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+      <li class="breadcrumb-item active">Search</li>
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@@ -91,7 +136,7 @@
   <hr/>
 
   <div role="contentinfo">
-    <p>&#169; Copyright 2022, Marcello Perathoner.</p>
+    <p>&#169; Copyright 2022-23, Marcello Perathoner.</p>
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new file mode 100644
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rename from docs/_images/tox-pypy38.svg
rename to docs/_images/tox-pypy39.svg
index 31b2618..c4205d9 100644
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+++ b/docs/_images/tox-pypy39.svg
@@ -1 +1 @@
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+<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="102" height="20" role="img" aria-label="pypy39: passing"><title>pypy39: passing</title><linearGradient id="s" x2="0" y2="100%"><stop offset="0" stop-color="#bbb" stop-opacity=".1"/><stop offset="1" stop-opacity=".1"/></linearGradient><clipPath id="r"><rect width="102" height="20" rx="3" fill="#fff"/></clipPath><g clip-path="url(#r)"><rect width="51" height="20" fill="#555"/><rect x="51" width="51" height="20" fill="#4c1"/><rect width="102" height="20" fill="url(#s)"/></g><g fill="#fff" text-anchor="middle" font-family="Verdana,Geneva,DejaVu Sans,sans-serif" text-rendering="geometricPrecision" font-size="110"><text aria-hidden="true" x="265" y="150" fill="#010101" fill-opacity=".3" transform="scale(.1)" textLength="410">pypy39</text><text x="265" y="140" transform="scale(.1)" fill="#fff" textLength="410">pypy39</text><text aria-hidden="true" x="755" y="150" fill="#010101" fill-opacity=".3" transform="scale(.1)" textLength="410">passing</text><text x="755" y="140" transform="scale(.1)" fill="#fff" textLength="410">passing</text></g></svg>
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diff --git a/docs/_static/custom.css b/docs/_static/custom.css
index 18ba401..1f3cb65 100644
--- a/docs/_static/custom.css
+++ b/docs/_static/custom.css
@@ -1 +1,49 @@
 .wy-side-nav-search a.icon.icon-home img.logo { width: 72px; }
+
+.rst-content img.sauml {
+    display: block;
+    margin-top: 12px;
+    margin-bottom: 12px;
+}
+
+.rst-content .std-term {
+    font-style: italic;
+}
+
+.rst-content .pic {
+    margin-bottom: 1em;
+}
+
+.rst-content .pic table {
+    min-width: 100%;
+}
+
+.rst-content .pic table th,
+.rst-content .pic table td {
+    border: 1px solid black;
+    padding: 0.2em;
+    text-align: left;
+}
+
+table.super-collator              { border-collapse: collapse }
+table.super-collator th,
+table.super-collator td.outer     { border: 1px solid black }
+table.super-collator td.inner     { width: 50%; padding: 0 0.5ex; text-align: right }
+table.super-collator td.prefilled { background-color: #eee }
+table.super-collator td.em        { font-weight: bold }
+table.super-collator th           { padding: 0 0.5ex; text-align: right }
+table.super-collator table        { width: 100% }
+table.super-collator-result td    { border: 1px solid black; padding: 0 1ex }
+
+table.super-collator {
+    margin-bottom: 1em;
+}
+
+#super-collator-phase2 td.outer.bt {
+    background-color: #fefece;
+    border: 1.5pt solid #a80136;
+}
+
+#super-collator-phase2 td.outer.bt .arrow {
+    color: #a80136;
+}
diff --git a/docs/_static/super-collator-phase1.html b/docs/_static/super-collator-phase1.html
new file mode 100644
index 0000000..546ed9c
--- /dev/null
+++ b/docs/_static/super-collator-phase1.html
@@ -0,0 +1,13 @@
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+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
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+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
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+</table>
+
diff --git a/docs/_static/super-collator-phase2.html b/docs/_static/super-collator-phase2.html
new file mode 100644
index 0000000..6ca182e
--- /dev/null
+++ b/docs/_static/super-collator-phase2.html
@@ -0,0 +1,13 @@
+<table class='super-collator super-collator-debug-matrix' id=super-collator-phase2><tr><th/><th class='top'></th><th class='top'>sick</th><th class='top'>fox</th><th class='top'>is</th><th class='top'>crazy</th></tr>
+<tr><th class='left'></th><td class='outer prefilled'><table><tr><td class='d inner'>0.00</td><td class='p inner'>0.00</td></tr><tr><td class='q inner'>0.00</td><td class='inner arrow'>⏹</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-1.10</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled bt'><table><tr><td class='d inner'>-0.50</td><td class='p inner em'>-0.50</td></tr><tr><td class='q inner'>-0.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-0.90</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.10</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner'>-1.30</td></tr><tr><td class='q inner em'>-0.90</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>quick</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.70</td></tr><tr><td class='q inner'>-0.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.70</td><td class='p inner'>-1.40</td></tr><tr><td class='q inner em'>-0.70</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>brown</th><td class='outer prefilled'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.90</td></tr><tr><td class='q inner'>-0.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.70</td><td class='p inner em'>-0.54</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner'>-1.04</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.50</td><td class='p inner'>-1.20</td></tr><tr><td class='q inner em'>-0.50</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>fox</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-1.10</td></tr><tr><td class='q inner'>-1.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.90</td><td class='p inner em'>-0.74</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.46</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-1.24</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>-0.04</td><td class='inner arrow'>←</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.00</td><td class='p inner'>-1.00</td></tr><tr><td class='q inner'>-0.24</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>jumps</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.30</td></tr><tr><td class='q inner'>-1.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.10</td><td class='p inner em'>-0.94</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.74</td><td class='p inner em'>-0.04</td></tr><tr><td class='q inner'>-1.44</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.54</td></tr><tr><td class='q inner'>-0.54</td><td class='inner arrow'>↖</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.04</td><td class='p inner'>-0.50</td></tr><tr><td class='q inner em'>0.14</td><td class='inner arrow'>←</td></tr></table></td></tr>
+<tr><th class='left'>over</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.50</td></tr><tr><td class='q inner'>-1.50</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.30</td><td class='p inner em'>-1.14</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.94</td><td class='p inner em'>-0.24</td></tr><tr><td class='q inner'>-1.64</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.04</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.74</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner em'>0.64</td><td class='p inner'>-0.36</td></tr><tr><td class='q inner'>-0.36</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>the</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.70</td></tr><tr><td class='q inner'>-1.70</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.50</td><td class='p inner em'>-1.34</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.14</td><td class='p inner em'>-0.44</td></tr><tr><td class='q inner'>-1.84</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.24</td><td class='p inner em'>-0.06</td></tr><tr><td class='q inner'>-0.94</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>0.14</td><td class='p inner em'>0.14</td></tr><tr><td class='q inner'>-0.56</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+<tr><th class='left'>lazy</th><td class='outer prefilled'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.90</td></tr><tr><td class='q inner'>-1.90</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.70</td><td class='p inner em'>-1.54</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.34</td><td class='p inner em'>-0.64</td></tr><tr><td class='q inner'>-2.04</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.44</td><td class='p inner em'>-0.26</td></tr><tr><td class='q inner'>-1.14</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner em'>0.40</td><td class='p inner'>-0.06</td></tr><tr><td class='q inner'>-0.76</td><td class='inner arrow'>↖</td></tr></table></td></tr>
+<tr><th class='left'>dog</th><td class='outer prefilled'><table><tr><td class='d inner'>-2.10</td><td class='p inner em'>-2.10</td></tr><tr><td class='q inner'>-2.10</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.90</td><td class='p inner em'>-1.74</td></tr><tr><td class='q inner'>-2.30</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-1.54</td><td class='p inner em'>-0.84</td></tr><tr><td class='q inner'>-2.24</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer'><table><tr><td class='d inner'>-0.64</td><td class='p inner em'>-0.46</td></tr><tr><td class='q inner'>-1.34</td><td class='inner arrow'>↑</td></tr></table></td><td class='outer bt'><table><tr><td class='d inner'>-0.26</td><td class='p inner em'>-0.10</td></tr><tr><td class='q inner'>-0.96</td><td class='inner arrow'>↑</td></tr></table></td></tr>
+</table>
+
diff --git a/docs/_static/super-collator-result.html b/docs/_static/super-collator-result.html
new file mode 100644
index 0000000..070559f
--- /dev/null
+++ b/docs/_static/super-collator-result.html
@@ -0,0 +1,4 @@
+<table class='super-collator super-collator-result' id=super-collator-result><tr><td>the</td><td>quick</td><td>brown</td><td>fox</td><td>jumps</td><td>over</td><td>the</td><td>lazy</td><td>dog</td></tr>
+<tr><td>-</td><td>sick</td><td>-</td><td>fox</td><td>is</td><td>-</td><td>-</td><td>crazy</td><td>-</td></tr>
+</table>
+
diff --git a/docs/algorithm.rst b/docs/algorithm.rst
new file mode 100644
index 0000000..6e527c4
--- /dev/null
+++ b/docs/algorithm.rst
@@ -0,0 +1,93 @@
+Collation Algorithm
+~~~~~~~~~~~~~~~~~~~
+
+The library uses an enhancement of the Needleman-Wunsch algorithm by Gotoh [Gotoh1982]_.
+This section provides a very high level overview of the algorithm.
+
+
+Phase 1 - Build Table
+---------------------
+
+In phase 1 the algorithm builds a table.  For example this is the table built for the
+two strings: *the quick brown fox jumps over the lazy dog* and *sick fox is crazy.*
+
+.. raw:: html
+   :file: _static/super-collator-phase1.html
+
+Every cell in the table contains three values: `D`, `P`, and `Q`, and an arrow, like this:
+
+.. raw:: html
+    :align: center
+
+   <table class='super-collator super-collator-debug-matrix' style="margin-left: auto; margin-right: auto">
+   <tr><td class='outer'>
+   <table>
+     <tr><td class='d inner'>D</td><td class='p inner'>P</td></tr>
+     <tr><td class='q inner'>Q</td><td class='inner arrow'>↖</td></tr>
+   </table>
+   </td>
+   </tr>
+   </table>
+
+We define the score `S` for each cell as:
+
+.. math::
+
+    S = \max(D, P, Q)
+
+The grayed cells in the first row and first column are initialized using the *gap start*
+and *gap extension* penalties.  The numbers for each remaining cell are calculated using
+only values from the three cells, to the top-left, the top, and the left, of the current
+cell:
+
+.. math::
+
+   D = S_↖ + \mbox{similarity}(word_←, word_↑)
+
+.. math::
+
+   P = \max(S_↑ + openingpenalty, P_↑ + extensionpenalty)
+
+.. math::
+
+   Q = \max(S_← + openingpenalty, Q_← + extensionpenalty)
+
+Finally the arrow in the current cell is set to point to that cell which yielded the
+highest of the current cell's `D`, `P`, and `Q` values.
+
+
+Phase 2 - Backtrack
+-------------------
+
+When the table is thus completed, two empty sequences are created.  Then the algorithm
+starts backtracking from the last (bottom-right) cell following the arrows until it
+reaches the first (top-left) cell.  If the arrow points:
+
+↑
+   the word in the row header is added to the first sequence, a hyphen is added to the
+   second sequence,
+↖
+   the word in the row header is added to the first sequence, the word in the column
+   header is added to the second sequence,
+←
+   a hyphen is added to the first sequence, the word in the column header is added to the
+   second sequence.
+
+.. raw:: html
+   :file: _static/super-collator-phase2.html
+
+Finally the two sequences are reversed and printed.
+
+.. raw:: html
+   :file: _static/super-collator-result.html
+
+
+Parameters
+----------
+
+The algorithm can be customized by setting:
+
+- a word comparison (similarity) function,
+- the starting gap penalty,
+- the gap opening penalty,
+- and the gap extension penalty.
diff --git a/docs/conf.py b/docs/conf.py
index c1d3b7a..b61c7b8 100755
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -18,11 +18,11 @@
 # -- Project information -----------------------------------------------------
 
 project = "super-collator"
-copyright = "2022, Marcello Perathoner"
+copyright = "2022-23, Marcello Perathoner"
 author = "Marcello Perathoner"
 
 # The full version, including alpha/beta/rc tags
-release = "0.0.2"
+release = "0.0.3"
 
 
 # -- General configuration ---------------------------------------------------
diff --git a/docs/index.rst b/docs/index.rst
index e0c3e2e..7b4883e 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -10,6 +10,7 @@ Needleman-Wunsch sequence alignment algorithm.
    :caption: Contents:
 
    examples
+   algorithm
    aligner
    ngrams
    references
diff --git a/docs/make_badges.py b/docs/make_badges.py
index 2ddb95c..3f9b58d 100755
--- a/docs/make_badges.py
+++ b/docs/make_badges.py
@@ -17,18 +17,17 @@
 badges = {}
 
 # one build=passing badge for each python version
-for filename in glob.glob(".tox/py*/log/2-commands*.log"):
+for filename in glob.glob(".tox/py*/log/*commands*.log"):
     with open(filename, "r") as fp:
         status = "passing"
         color = "success"
         for line in fp:
             if line.startswith("name: "):
                 name = line[6:].strip()
-            if line.startswith("==="):
-                if m := re.search(r"(\d+) failed", line):
-                    failed = int(m.group(1))
-                    status = "failed"
-                    color = "critical"
+            if m := re.search(r"===.*(\d+) failed", line):
+                failed = int(m.group(1))
+                status = "failed"
+                color = "critical"
     badge = requests.get(f"https://img.shields.io/badge/{name}-{status}-{color}").text
     filename = f"_images/tox-{name}.svg"
     with open(f"{DESTDIR}{filename}", "w") as dest:
diff --git a/docs/references.rst b/docs/references.rst
index f4cb5b2..2f5f9cc 100644
--- a/docs/references.rst
+++ b/docs/references.rst
@@ -1,9 +1,10 @@
 References
 ==========
 
-.. [Gotoh1982] Gotoh, O.  An Improved Algorithm for Matching Biological Sequences.
-               1982.  J. Mol. Biol. 162, 705-708
+.. [Gotoh1982] Gotoh, O. 1982.  *An Improved Algorithm for Matching Biological
+               Sequences.*  J. Mol. Biol. 162, 705-708
+               http://jaligner.sourceforge.net/references/gotoh1982.pdf
 
-.. [NeedlemanWunsch1970] Needleman, S.  Wunsch, C.  A General Method Applicable to the
+.. [NeedlemanWunsch1970] Needleman, S.  Wunsch, C.  1970.  *A General Method Applicable to the
                          Search for Similarities in the Amino Acid Sequence of Two
-                         Proteins.  1970.  J. Mol. Biol. 48, 443-453
+                         Proteins.*  J. Mol. Biol. 48, 443-453
diff --git a/pyproject.toml b/pyproject.toml
index 9071023..9058af1 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -78,7 +78,7 @@ legacy_tox_ini = """
 
 [tox]
 isolated_build = True
-envlist = pypy38,py39,py310,py311
+envlist = pypy39,py39,py310,py311,py312
 
 [testenv]
 allowlist_externals = make
diff --git a/requirements-dev.txt b/requirements-dev.txt
index d12a5cc..679795d 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -1,7 +1,9 @@
 black
 blackdoc
+build
 coverage[toml]
 hatchling
+lxml
 mypy
 pip
 pydocstyle
diff --git a/scripts/cli.py b/scripts/cli.py
index 04c7ff3..c656639 100755
--- a/scripts/cli.py
+++ b/scripts/cli.py
@@ -2,12 +2,19 @@
 """CLI script"""
 
 import argparse
+import logging
 import sys
 
+import super_collator.aligner
 from super_collator.aligner import Aligner
 from super_collator.ngrams import NGrams
-from super_collator.token import SingleToken
-from super_collator.super_collator import to_table
+from super_collator.super_collator import (
+    to_table,
+    to_table_html,
+    build_debug_matrix,
+    build_debug_matrix_html,
+    html_style,
+)
 
 
 def build_parser(description: str) -> argparse.ArgumentParser:
@@ -27,6 +34,51 @@ def build_parser(description: str) -> argparse.ArgumentParser:
         help="increase output verbosity",
         default=0,
     )
+    parser.add_argument(
+        "-d",
+        "--debug",
+        dest="debug",
+        action="store_true",
+        help="debug mode",
+        default=False,
+    )
+    parser.add_argument(
+        "--html",
+        action="store",
+        metavar="ID",
+        help="output a HTML table with this id",
+        default=None,
+    )
+    parser.add_argument(
+        "--style",
+        action="store_true",
+        help="output the HTML CSS stylesheet",
+        default=False,
+    )
+    parser.add_argument(
+        "--start",
+        type=float,
+        action="store",
+        metavar="N",
+        help="starting gap penalty",
+        default=0.5,
+    )
+    parser.add_argument(
+        "--open",
+        type=float,
+        action="store",
+        metavar="N",
+        help="gap opening penalty",
+        default=0.5,
+    )
+    parser.add_argument(
+        "--extend",
+        type=float,
+        action="store",
+        metavar="N",
+        help="gap extension penalty",
+        default=0.2,
+    )
     parser.add_argument(
         "inputs",
         metavar="TOKENS",
@@ -38,20 +90,75 @@ def build_parser(description: str) -> argparse.ArgumentParser:
     return parser
 
 
+def preprocess(seq):
+    return [[NGrams(t).load(t, 3)] for t in seq]
+
+
+def similarity(aa, bb):
+    sim = float("-inf")
+    for a in aa:
+        for b in bb:
+            score = NGrams.similarity(a, b)
+            if score > sim:
+                sim = score
+    return sim
+
+
+def merge(aa, bb):
+    return [a + b for a, b in zip(aa, bb)]
+
+
+def merge_strings(aa):
+    return [" ".join([b.user_data for b in a]) for a in aa]
+
+
+def gap(n: int = 1):
+    return [NGrams("-")] * n
+
+
+def extract(aligned, n):
+    """Extract the nth sequence."""
+    return [t[n].user_data for t in aligned]
+
+
+def to_string(aligned, n):
+    return " ".join(t[n].user_data for t in aligned)
+
+
 def main():
     parser = build_parser(__doc__)
     args = parser.parse_args()
-    aligner = Aligner()
+    if args.style:
+        print(html_style())
 
-    aa = [NGrams([s]).load(s, 2) for s in args.inputs[0].split()]
-    for n, inp in enumerate(args.inputs[1:]):
-        bb = [NGrams([s]).load(s, 2) for s in inp.split()]
-        aa, bb, score = aligner.align(
-            aa, bb, NGrams.similarity, lambda: NGrams(["-"] * n), lambda: NGrams(["-"])
+    aligner = Aligner(-args.start, -args.open, -args.extend)
+
+    a = args.inputs[0].split()
+    aa = preprocess(a)
+    for inp in args.inputs[1:]:
+        b = inp.split()
+        bb = preprocess(b)
+        aa, bb, _, matrix = aligner.align_debug(
+            aa, bb, similarity, lambda: gap(1), lambda: gap(1), args.debug
         )
-        aa = [NGrams.merge(a, b, list.__add__) for a, b in zip(aa, bb)]
+        if __debug__ and args.debug:
+            if args.html:
+                print(build_debug_matrix_html(matrix, a, b, args.html))
+            else:
+                print(build_debug_matrix(matrix, a, b))
+            a = merge_strings(aa)
+        aa = merge(aa, bb)
+
+    results = []
+    for n, inp in enumerate(args.inputs):
+        results.append(extract(aa, n))
+
+    if not args.debug:
+        if args.html:
+            print(to_table_html(args.html, *results))
+        else:
+            print(to_table(*results))
 
-    print(to_table(*zip(*[a.user_data for a in aa])).strip())
     return 0
 
 
diff --git a/src/super_collator/aligner.py b/src/super_collator/aligner.py
index 9597c83..cfcfba1 100644
--- a/src/super_collator/aligner.py
+++ b/src/super_collator/aligner.py
@@ -1,28 +1,87 @@
 """This module implements the aligner."""
 
 import collections
-import logging
 from typing import Tuple, List, Sequence, Optional, Callable
 
 
-DEBUG = False
-
 class Data:
     """Private data class for the Needleman-Wunsch+Gotoh sequence aligner."""
 
-    __slots__ = ("score", "p", "q", "pSize", "qSize")
+    __slots__ = ("score", "m", "p", "q", "prefilled", "backtrack", "backtracked")
 
     def __init__(self, score: float):
         self.score: float = score
-        """The current score."""
+        """The cumulative score up to this square."""
+        self.m: float = 0.0
+        """The score for this alignment as match."""
         self.p: float = 0.0
         """`P_{m,n}` in [Gotoh1982]_."""
         self.q: float = 0.0
         """`Q_{m,n}` in [Gotoh1982]_."""
-        self.pSize: int = 0
-        """The size of the p gap. `k` in [Gotoh1982]_."""
-        self.qSize: int = 0
-        """The size of the q gap. `k` in [Gotoh1982]_."""
+
+        self.backtrack: int | None = 0
+        """A copy of the backtracking matrix entry for debugging."""
+        self.prefilled: bool = False
+        """True if this cell was prefilled."""
+        self.backtracked: bool = False
+        """True if we actually backtracked through this entry."""
+
+    def arrow(self) -> str:
+        """Return the appropriate arrow form."""
+        if self.backtrack is None:
+            return "⏹"
+        if self.backtrack == 0:
+            return "↖"
+        if self.backtrack < 0:
+            return "↑"
+        return "←"
+
+    def __str__(self):
+        """Return the data as string useful for debugging."""
+
+        return "| {arrow} {self.q: 2.2f} {self.m: 2.2f} {self.p: 2.2f} ".format(
+            self=self,
+            arrow=self.arrow(),
+        )
+
+    def html(self) -> str:
+        """Return the data as HTML string useful for debugging."""
+
+        emph = [False, False, False]
+        if self.backtrack is not None:
+            if self.backtrack == 0:
+                emph[0] = True
+            elif self.backtrack < 0:
+                emph[1] = True
+            else:
+                emph[2] = True
+        klass: List
+        cells = []
+        for val, klass, em in zip((self.m, self.p, self.q), (["d"], ["p"], ["q"]), emph):  # type: ignore
+            klass.append("inner")
+            if em:
+                klass.append("em")
+            kl = " ".join(klass)
+            cells.append(f"<td class='{kl}'>{val:2.2f}</td>")
+        cells.append(f"<td class='inner arrow'>{self.arrow()}</td>")
+
+        klass = ["outer"]
+        if self.prefilled:
+            klass.append("prefilled")
+        if self.backtracked:
+            klass.append("bt")
+        kl = " ".join(klass)
+        a = [f"<td class='{kl}'><table><tr>"]
+        a.extend(cells[:2])
+        a.append("</tr><tr>")
+        a.extend(cells[2:])
+        a.append("</tr></table></td>")
+        return "".join(a)
+
+    @staticmethod
+    def str_size():
+        """Return the size of the string returned by __str__."""
+        return len("| ↖ -0.00 -0.00 -0.00 ")
 
 
 class Aligner:
@@ -81,90 +140,113 @@ def align(
     ) -> Tuple[Sequence[object], Sequence[object], float]:
         """Align two sequences.
 
-        :param similarity: a callable that returns the similarity of two objects
+        :param seq_a: the first sequence to align
+        :param seq_b: the second sequence to align
+        :param similarity: a callable that returns the similarity of two members of seq_a and seq_b
         :param gap_a: insert gap_a() for a gap in sequence a. None inserts None.
         :param gap_b: insert gap_b() for a gap in sequence b. None inserts gap_a().
         :return: the aligned sequences and the score
         """
+        return self.align_debug(seq_a, seq_b, similarity, gap_a, gap_b, False)[:3]
 
+    def align_debug(
+        self,
+        seq_a: Sequence[object],
+        seq_b: Sequence[object],
+        similarity: Callable[[object, object], float],
+        gap_a: Optional[Callable[[], object]] = None,
+        gap_b: Optional[Callable[[], object]] = None,
+        debug=False,
+    ) -> Tuple[Sequence[object], Sequence[object], float, List[List[Data]]]:
+        """Align two sequences and return debug information.
+
+        :param seq_a: the first sequence to align
+        :param seq_b: the second sequence to align
+        :param similarity: a callable that returns the similarity of two members of seq_a and seq_b
+        :param gap_a: insert gap_a() for a gap in sequence a. None inserts None.
+        :param gap_b: insert gap_b() for a gap in sequence b. None inserts gap_a().
+        :param debug: calculate debug information if True, debug info wastes memory
+        :return: the aligned sequences, the score, and the debug matrix
+        """
         gap_b = gap_b or gap_a
 
         len_a = len(seq_a)
         len_b = len(seq_b)
 
-        len_matrix: List[List[int]] = []  # list[len_a + 1]
-        """The backtracking matrix.  0 stands for a match.  Negative numbers represent a
-        DEL TOP operation.  Positive numbers represent an INS LEFT operation.  The abs()
-        of the number is the length of the gap.
+        back_matrix: List[List[int]] = []  # list[len_a + 1]
+        """The backtracking matrix.  0 stands for a match.  A negative integer
+        represents a DEL TOP operation.  A positive integer represent an INS LEFT
+        operation.  The abs() of the integer is the size of the gap.
         """
         matrix: List[List[Data]] = []
         """The scoring matrix. We need only the last row of the scoring matrix for our
-        calculations, so we build the full scoring matrix only when debugging.
+        calculations, so we build the full scoring matrix only while debugging.
         """
-        this_len_row: List[int] = []  # list[len_b + 1]
+        this_back_row: List[int] = []  # list[len_b + 1]
         """The current row of the backtracking matrix."""
         this_row: List[Data] = []  # list[len_b + 1]
         """The current row of the scoring matrix."""
 
-        # Initialize len_matrix and one row of the scoring matrix.
+        back_matrix.append(this_back_row)
 
-        len_matrix.append(this_len_row)
-        this_row.append(Data(0.0))
-        this_len_row.append(0)
+        # Initialize the first row of the matrix with start and extend scores
+        data = Data(0.0)
+        data.backtrack = None
+        data.prefilled = True
+        this_row.append(data)
+        this_back_row.append(0)
 
         for j in range(1, len_b + 1):
             data = Data(self.start_score + (j - 1) * self.extend_score)
-            data.p = data.score
-            # data.pSize = j;
+            data.p = data.m = data.q = data.score
+            data.backtrack = 1
+            data.prefilled = True
             this_row.append(data)
-            this_len_row.append(j)
+            this_back_row.append(j)  # INS LEFT
 
-        if __debug__ and DEBUG:
+        if __debug__ and debug:
             matrix = []
             matrix.append(this_row[:])
 
         # Score the matrix
         for i, a in enumerate(seq_a, start=1):
 
-            # add new len_row to matrix
-            this_len_row = []
-            len_matrix.append(this_len_row)
-            this_len_row.append(-i)
-            # DEL TOP
+            # add new back_row to back_matrix
+            this_back_row = []
+            back_matrix.append(this_back_row)
+            this_back_row.append(-i)  # DEL TOP
 
             diag = this_row[0]
             left = Data(self.start_score + (i - 1) * self.extend_score)
-            left.q = left.score
-            # left.qSize = i
-            j = 0
+            left.m = left.p = left.q = left.score
+            left.backtrack = -1
+            left.prefilled = True
+
             for j, b in enumerate(seq_b, start=1):
                 top = this_row[j]
                 curr = Data(0.0)
 
                 curr.p = top.score + self.open_score
-                curr.pSize = 1
                 if curr.p < top.p + self.extend_score:
                     curr.p = top.p + self.extend_score
-                    curr.pSize = top.pSize + 1
 
                 curr.q = left.score + self.open_score
-                curr.qSize = 1
                 if curr.q < left.q + self.extend_score:
                     curr.q = left.q + self.extend_score
-                    curr.qSize = left.qSize + 1
 
-                d: float = diag.score + similarity(a, b)
+                curr.m = diag.score + similarity(a, b)
 
                 # Decide which operation is optimal and perform it
-                if (d > curr.p) and (d > curr.q):
-                    curr.score = d
-                    this_len_row.append(0)
+                if (curr.m > curr.p) and (curr.m > curr.q):
+                    curr.score = curr.m
+                    curr.backtrack = 0  # SUBST
                 elif curr.q > curr.p:
                     curr.score = curr.q
-                    this_len_row.append(curr.qSize)  # INS LEFT
+                    curr.backtrack = 1  # INS LEFT
                 else:
                     curr.score = curr.p
-                    this_len_row.append(-curr.pSize)  # DEL TOP
+                    curr.backtrack = -1  # DEL TOP
+                this_back_row.append(curr.backtrack)
 
                 # Advance to next column
                 this_row[j - 1] = left
@@ -172,10 +254,10 @@ def align(
                 diag = top
                 left = curr
 
-            if __debug__ and DEBUG:
+            if __debug__ and debug:
                 matrix.append(this_row[:])
 
-        # Walk back and output alignments.
+        # Backtrack and output alignments.
 
         aligned_a: collections.deque[object] = collections.deque()
         aligned_b: collections.deque[object] = collections.deque()
@@ -183,82 +265,23 @@ def align(
         i = len_a
         j = len_b
         while (i > 0) or (j > 0):
-            len_m = len_matrix[i][j]
-            if len_m == 0:
+            if __debug__ and debug:
+                matrix[i][j].backtracked = True
+            back_m = back_matrix[i][j]
+            assert back_m is not None
+            if back_m == 0:
                 aligned_a.appendleft(seq_a[i - 1])
                 aligned_b.appendleft(seq_b[j - 1])
                 i -= 1
                 j -= 1
             else:
-                if len_m < 0:
-                    for _ in range(-len_m):
-                        aligned_a.appendleft(seq_a[i - 1])
-                        aligned_b.appendleft(gap_b() if gap_b else None)
-                        i -= 1
+                if back_m < 0:
+                    aligned_a.appendleft(seq_a[i - 1])
+                    aligned_b.appendleft(gap_b() if gap_b else None)
+                    i -= 1
                 else:
-                    for _ in range(len_m):
-                        aligned_a.appendleft(gap_a() if gap_a else None)
-                        aligned_b.appendleft(seq_b[j - 1])
-                        j -= 1
-
-        if __debug__ and DEBUG:
-            logging.debug(build_debug_matrix(matrix, len_matrix, seq_a, seq_b))
-
-        return aligned_a, aligned_b, this_row[-1].score
-
-
-def build_debug_matrix(
-    matrix: List[List[Data]],
-    len_matrix: List[List[int]],
-    ts_a: Sequence[object],
-    ts_b: Sequence[object],
-) -> str:
-    """Build a human-readable debug matrix.
-
-    :param matrix: the full scoring matrix
-    :param len_matrix: the backtracking matrix
-    :param ts_a: the first aligned string
-    :param ts_b: the second aligned string
-    :return str: the debug matrix as human readable string
-    """
-
-    s = []
-
-    s.append(str.format("{0:29s} | ", ""))
-    s.append(str.format("{0:29s} | ", ""))
-    for b in ts_b:
-        s.append(str.format("{0:29s} | ", str(b)))
-    s.append("\n")
-
-    for i, m in enumerate(matrix):
-        s.append(str.format("{0:>29s} | ", str(ts_a[i - 1]) if i > 0 else ""))
-        _debug_add(m, len_matrix[i], s)
-    s.append("\n")
-
-    return "".join(s)
+                    aligned_a.appendleft(gap_a() if gap_a else None)
+                    aligned_b.appendleft(seq_b[j - 1])
+                    j -= 1
 
-
-def _debug_add(data_row: List[Data], len_row: List[int], out: List[str]):
-    """
-    Private helper function.
-
-    :param data_row:
-    :param len_row:
-    :param out:
-    """
-
-    for i, data in enumerate(data_row):
-        l = len_row[i]
-        if l == 0:
-            out.append("↖ ")
-        else:
-            if l < 0:
-                out.append("↑ ")
-            else:
-                out.append("← ")
-        out.append(str.format("{0: 2.6f} ", data.score))
-        out.append(str.format("{0: 2.2f} ", data.p))
-        out.append(str.format("{0: 2d} ", data.pSize))
-        out.append(str.format("{0: 2.2f} ", data.q))
-        out.append(str.format("{0: 2d} | ", data.qSize))
-    out.append("\n")
+        return aligned_a, aligned_b, this_row[-1].score, matrix
diff --git a/src/super_collator/ngrams.py b/src/super_collator/ngrams.py
index 0d5b0d3..1fbca93 100644
--- a/src/super_collator/ngrams.py
+++ b/src/super_collator/ngrams.py
@@ -5,7 +5,7 @@ class NGrams:
     """A class that compares two strings using N-Grams."""
 
     def __init__(self, user_data=None):
-        self.ngrams = set()
+        self.ngrams = frozenset()
         self.user_data = user_data
 
     def load(self, s: str, n: int) -> "NGrams":
@@ -15,11 +15,11 @@ def load(self, s: str, n: int) -> "NGrams":
         :param n: puts the N in N-Grams
         """
         if n == 1:
-            self.ngrams.update(list(s))
+            self.ngrams = frozenset(list(s))
         else:
             pad = " " * (n - 1)
             sp = pad + s + pad
-            self.ngrams.update([sp[i : i + n] for i in range(len(s) + n - 1)])
+            self.ngrams = frozenset([sp[i : i + n] for i in range(len(s) + n - 1)])
         return self
 
     def __str__(self) -> str:
diff --git a/src/super_collator/super_collator.py b/src/super_collator/super_collator.py
index 896e51f..bced16b 100644
--- a/src/super_collator/super_collator.py
+++ b/src/super_collator/super_collator.py
@@ -1,6 +1,7 @@
 """Main module."""
 
-from typing import Sequence
+from typing import List, Sequence
+from super_collator.aligner import Data
 
 
 def to_string(seq: Sequence, f=str):
@@ -27,3 +28,113 @@ def to_table(*sequences: Sequence[str]):
             result.append(f"{str(s):<{length + 1}}")
         result.append("\n")
     return "".join(result)
+
+
+def to_table_html(id_: str, *sequences: Sequence[str]):
+    """Convert sequences of aligned strings into an HTML table."""
+
+    result = [f"<table class='super-collator super-collator-result' id={id_}>"]
+
+    for row in sequences:
+        result.append("<tr>")
+        for cell in row:
+            result.append(f"<td>{str(cell)}</td>")
+        result.append("</tr>\n")
+    result.append("</table>\n")
+    return "".join(result)
+
+
+def build_debug_matrix(
+    matrix: List[List[Data]],
+    ts_a: Sequence[object],
+    ts_b: Sequence[object],
+) -> str:
+    """Build a human-readable debug matrix as ASCII table.
+
+    :param matrix: the full scoring matrix
+    :param ts_a: the first input sequence
+    :param ts_b: the second input sequence
+    :return str: the debug matrix as human readable string
+    """
+
+    s = []
+    w = Data.str_size() - 2
+    w1 = max(len(str(a)) for a in ts_a)
+
+    # header row
+    headers = [""] + list(ts_b)
+    s.append(" " * w1)
+    s.append(" ")
+    for header in headers:
+        s.append(str.format("| {0:{w}s}", str(header), w=w))
+    s.append("\n")
+
+    # data rows
+    headers = [""] + list(ts_a)
+    for header, m in zip(headers, matrix):
+        # header column
+        s.append(str.format("{0:>{w}s} ", str(header), w=w1))
+        # data columns
+        for data in m:
+            s.append(str(data))
+        s.append("\n")
+    s.append("\n")
+
+    return "".join(s)
+
+
+def build_debug_matrix_html(
+    matrix: List[List[Data]],
+    ts_a: Sequence[object],
+    ts_b: Sequence[object],
+    id_: str,
+) -> str:
+    """Build a human-readable debug matrix as HTML table.
+
+    :param matrix: the full scoring matrix
+    :param ts_a: the first input sequence
+    :param ts_b: the second input sequence
+    :param id_: the HTML id for the table
+    :return str: the debug matrix as human readable string
+    """
+
+    s = [f"<table class='super-collator super-collator-debug-matrix' id={id_}>"]
+
+    # header row
+    headers = [""] + list(ts_b)
+    s.append("<tr><th/>")
+    for header in headers:
+        s.append(f"<th class='top'>{header}</th>")
+    s.append("</tr>\n")
+
+    # data rows
+    headers = [""] + list(ts_a)
+    for header, m in zip(headers, matrix):
+        # header column
+        s.append(f"<tr><th class='left'>{header}</th>")
+        # data columns
+        for data in m:
+            s.append(data.html())
+        s.append("</tr>\n")
+
+    s.append("</table>\n")
+    return "".join(s)
+
+
+def html_style():
+    """Output a style element for the debug matrix in HTML."""
+
+    return """
+    <style>
+    table.super-collator              { border-collapse: collapse }
+    table.super-collator th,
+    table.super-collator td.outer     { border: 1px solid black }
+    table.super-collator td.inner     { width: 50%; padding: 0 0.5ex; text-align: right }
+    table.super-collator td.prefilled { background-color: #eee }
+    table.super-collator td.bt        { background-color: #fdd }
+    table.super-collator td.em        { font-weight: bold }
+    table.super-collator th           { padding: 0 0.5ex; text-align: right }
+    table.super-collator table        { width: 100% }
+    table.super-collator-result td    { border: 1px solid black; padding: 0 1ex }
+    </style>
+    """
diff --git a/tests/unit/test_aligner.py b/tests/unit/test_aligner.py
index c36b455..edb1c5d 100644
--- a/tests/unit/test_aligner.py
+++ b/tests/unit/test_aligner.py
@@ -7,7 +7,13 @@
 import super_collator.aligner
 from super_collator.aligner import Aligner
 from super_collator.ngrams import NGrams
-from super_collator.super_collator import to_table
+from super_collator.super_collator import (
+    to_table,
+    to_table_html,
+    html_style,
+    build_debug_matrix,
+    build_debug_matrix_html,
+)
 
 
 @pytest.fixture
@@ -31,9 +37,6 @@ class TestAlignStrings:
     def to_string(aligned):
         return " ".join([str(t or "-") for t in aligned])
 
-    def similarity(a, b):
-        return 1.0 if a == b else 0.0
-
     def test_align_1(self, the_fox):
         aligner = Aligner()
         a = the_fox.split()
@@ -71,11 +74,19 @@ def test_align_2(self, n, the_fox):
         assert self.to_string(b) == "the - brown - - - - - dog"
 
     def test_align_3(self, n, the_fox):
-        super_collator.aligner.DEBUG = True
-        aligner = Aligner()
-        aligner.start_score = 0
+        aligner = Aligner(
+            0, 0, 0
+        )  # the gap penalties would overwhelm the small similarities
         a = self.preprocess(the_fox.split(), n)
-        b = self.preprocess("the sissy".split(), n)
-        a, b, score = aligner.align(a, b, NGrams.similarity, self.gap)
-        super_collator.aligner.DEBUG = False
-        assert self.to_string(b) == "- - - - - - the sissy -"
+        b = self.preprocess("that ox is crazy".split(), n)
+        a, b, score, matrix = aligner.align_debug(
+            a, b, NGrams.similarity, self.gap, self.gap, True
+        )
+        assert self.to_string(b) == "that - - ox is - - crazy -"
+
+        # go for full coverage
+        to_table((a, b))
+        to_table_html("FakeId", (a, b))
+        html_style()
+        build_debug_matrix_html(matrix, a, b, "FakeId")
+        build_debug_matrix(matrix, a, b)