add example to documentation

docs/build/html/.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: bf5d7a5092cc0a3570505fe93d3c95c2
+config: 582d0f8e2f1710734c73a1e8e7af2ead
 tags: 645f666f9bcd5a90fca523b33c5a78b7

docs/build/html/_sources/example.rst

@@ -0,0 +1,58 @@
+Example
+=======================
+
+An example of use is given in ``./examples/one-dimensional_channel.ipynb``. 
+
+There is also a time-complexity study in ``./examples/time_complexity.ipynb``.
+
+1. Construct a linear-chain tight-binding Hamiltonian
+--------------------------------------------------------
+
+.. code-block:: python
+
+   from fuNEGF.models import LinearChain
+
+   chain = LinearChain(N=100, eps_0=0.0, t=1.0, a=1.0, H_impurity=None, plot_dispersion=True)
+
+.. image::
+   ./_images/linear_chain_dispersion_analytic_vs_diagonalized.png
+   :width: 550px
+   :align: center
+
+2. Impurity - *quantum resistors in series*
+--------------------------------------------------------
+.. code-block:: python
+
+   H_impurity = np.zeros((N, N), dtype=complex)
+
+   # (1) add a single impurity in the middle
+   H_impurity[N // 2, N // 2] += -2 * t
+
+   chain.add_H_impurity(H_impurity, plot_dispersion=False)
+   chain.plot_onsite_energy()
+
+.. image::
+   ./_images/impurity_single_middle.png
+   :width: 450px
+   :align: center
+
+
+3. Transmission function
+--------------------------------------------------------
+
+.. math::
+   \bar{T}(E)=\operatorname{Trace}\left[\boldsymbol{\Gamma}_1 \mathbf{G}^R \boldsymbol{\Gamma}_2 \mathbf{G}^A\right]
+
+Cases:
+   1. without impurities it is constant :math:`T(E) = 1.0` 
+   2. with a single impurity of :math:`U=-2 t`, it reaches maximum of :math:`T(E) = 0.5`
+   3. with two impurities of :math:`U=-t` each, the function looks almost the same, but with strong oscillations
+
+.. code-block:: python
+
+    chain.plot_transmission()
+
+.. image::
+   ./_images/transmission_single_imp_middle.png
+   :width: 250px
+   :align: center

docs/build/html/_sources/index.rst

@@ -39,6 +39,7 @@ Navigation
    :maxdepth: 3
 
    theory
+   example
    modules
    classes
 

docs/build/html/_static/_sphinx_javascript_frameworks_compat.js

@@ -0,0 +1,134 @@
+/*
+ * _sphinx_javascript_frameworks_compat.js
+ * ~~~~~~~~~~
+ *
+ * Compatability shim for jQuery and underscores.js.
+ *
+ * WILL BE REMOVED IN Sphinx 6.0
+ * xref RemovedInSphinx60Warning
+ *
+ */
+
+/**
+ * select a different prefix for underscore
+ */
+$u = _.noConflict();
+
+
+/**
+ * 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;
+}

docs/build/html/_static/basic.css

@@ -4,7 +4,7 @@
  *
  * Sphinx stylesheet -- basic theme.
  *
- * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
@@ -236,11 +236,17 @@ div.body p, div.body dd, div.body li, div.body blockquote {
 a.headerlink {
     visibility: hidden;
 }
+a.brackets:before,
+span.brackets > a:before{
+    content: "[";
+}
 
-a:visited {
-    color: #551A8B;
+a.brackets:after,
+span.brackets > a:after {
+    content: "]";
 }
 
+
 h1:hover > a.headerlink,
 h2:hover > a.headerlink,
 h3:hover > a.headerlink,
@@ -328,17 +334,11 @@ aside.sidebar {
 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;
@@ -377,17 +377,13 @@ div.body p.centered {
 
 div.sidebar > :last-child,
 aside.sidebar > :last-child,
-nav.contents > :last-child,
-aside.topic > :last-child,
 div.topic > :last-child,
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     margin-bottom: 0;
 }
 
 div.sidebar::after,
 aside.sidebar::after,
-nav.contents::after,
-aside.topic::after,
 div.topic::after,
 div.admonition::after,
 blockquote::after {
@@ -612,27 +608,19 @@ ol.simple p,
 ul.simple p {
     margin-bottom: 0;
 }
-
-aside.footnote > span,
-div.citation > span {
+dl.footnote > dt,
+dl.citation > dt {
     float: left;
+    margin-right: 0.5em;
 }
-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 {
+
+dl.footnote > dd,
+dl.citation > dd {
     margin-bottom: 0em;
 }
-aside.footnote > p:last-of-type:after,
-div.citation > p:last-of-type:after {
+
+dl.footnote > dd:after,
+dl.citation > dd:after {
     content: "";
     clear: both;
 }
@@ -648,6 +636,10 @@ dl.field-list > dt {
     padding-left: 0.5em;
     padding-right: 5px;
 }
+dl.field-list > dt:after {
+    content: ":";
+}
+
 
 dl.field-list > dd {
     padding-left: 0.5em;
@@ -674,16 +666,6 @@ 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;
@@ -752,14 +734,6 @@ 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 {

docs/build/html/_static/doctools.js

@@ -4,7 +4,7 @@
  *
  * Base JavaScript utilities for all Sphinx HTML documentation.
  *
- * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */

docs/build/html/_static/documentation_options.js

@@ -1,4 +1,5 @@
-const DOCUMENTATION_OPTIONS = {
+var DOCUMENTATION_OPTIONS = {
+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
     VERSION: '0.1.11',
     LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
@@ -7,7 +8,7 @@ const DOCUMENTATION_OPTIONS = {
     LINK_SUFFIX: '.html',
     HAS_SOURCE: true,
     SOURCELINK_SUFFIX: '',
-    NAVIGATION_WITH_KEYS: false,
+    NAVIGATION_WITH_KEYS: true,
     SHOW_SEARCH_SUMMARY: true,
     ENABLE_SEARCH_SHORTCUTS: true,
 };