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Benchmarking of propagators. Notebook derived from https://qucontrol.github.io/krotov/v1.2.1/notebooks/06_example_3states.html
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<?xml version="1.0" standalone="no"?><!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"><svg version="1.1" width="1200" height="1146" onload="init(evt)" viewBox="0 0 1200 1146" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><!--Flame graph stack visualization. See https://github.com/brendangregg/FlameGraph for latest version, and http://www.brendangregg.com/flamegraphs.html for examples.--><!--NOTES: --><defs><linearGradient id="background" y1="0" y2="1" x1="0" x2="0"><stop stop-color="#eeeeee" offset="5%"/><stop stop-color="#eeeeb0" offset="95%"/></linearGradient></defs><style type="text/css">
text { font-family:"Verdana"; font-size:12px; fill:rgb(0,0,0); }
#title { text-anchor:middle; font-size:17px; }
#search { opacity:0.1; cursor:pointer; }
#search:hover, #search.show { opacity:1; }
#subtitle { text-anchor:middle; font-color:rgb(160,160,160); }
#unzoom { cursor:pointer; }
#frames > *:hover { stroke:black; stroke-width:0.5; cursor:pointer; }
.hide { display:none; }
.parent { opacity:0.5; }
</style><script type="text/ecmascript"><![CDATA[var nametype = 'Function:';
var fontsize = 12;
var fontwidth = 0.59;
var xpad = 10;
var inverted = true;
var searchcolor = 'rgb(230,0,230)';
var fluiddrawing = true;
var truncate_text_right = false;]]><![CDATA["use strict";
var details, searchbtn, unzoombtn, matchedtxt, svg, searching, frames;
function init(evt) {
details = document.getElementById("details").firstChild;
searchbtn = document.getElementById("search");
unzoombtn = document.getElementById("unzoom");
matchedtxt = document.getElementById("matched");
svg = document.getElementsByTagName("svg")[0];
frames = document.getElementById("frames");
searching = 0;
// Use GET parameters to restore a flamegraph's state.
var restore_state = function() {
var params = get_params();
if (params.x && params.y)
zoom(find_group(document.querySelector('[x="' + params.x + '"][y="' + params.y + '"]')));
if (params.s)
search(params.s);
};
if (fluiddrawing) {
// Make width dynamic so the SVG fits its parent's width.
svg.removeAttribute("width");
// Edge requires us to have a viewBox that gets updated with size changes.
var isEdge = /Edge\/\d./i.test(navigator.userAgent);
if (!isEdge) {
svg.removeAttribute("viewBox");
}
var update_for_width_change = function() {
if (isEdge) {
svg.attributes.viewBox.value = "0 0 " + svg.width.baseVal.value + " " + svg.height.baseVal.value;
}
// Keep consistent padding on left and right of frames container.
frames.attributes.width.value = svg.width.baseVal.value - xpad * 2;
// Text truncation needs to be adjusted for the current width.
var el = frames.children;
for(var i = 0; i < el.length; i++) {
update_text(el[i]);
}
// Keep search elements at a fixed distance from right edge.
var svgWidth = svg.width.baseVal.value;
searchbtn.attributes.x.value = svgWidth - xpad - 100;
matchedtxt.attributes.x.value = svgWidth - xpad - 100;
};
window.addEventListener('resize', function() {
update_for_width_change();
});
// This needs to be done asynchronously for Safari to work.
setTimeout(function() {
unzoom();
update_for_width_change();
restore_state();
}, 0);
} else {
restore_state();
}
}
// event listeners
window.addEventListener("click", function(e) {
var target = find_group(e.target);
if (target) {
if (target.nodeName == "a") {
if (e.ctrlKey === false) return;
e.preventDefault();
}
if (target.classList.contains("parent")) unzoom();
zoom(target);
// set parameters for zoom state
var el = target.querySelector("rect");
if (el && el.attributes && el.attributes.y && el.attributes._orig_x) {
var params = get_params()
params.x = el.attributes._orig_x.value;
params.y = el.attributes.y.value;
history.replaceState(null, null, parse_params(params));
}
}
else if (e.target.id == "unzoom") {
unzoom();
// remove zoom state
var params = get_params();
if (params.x) delete params.x;
if (params.y) delete params.y;
history.replaceState(null, null, parse_params(params));
}
else if (e.target.id == "search") search_prompt();
}, false)
// mouse-over for info
// show
window.addEventListener("mouseover", function(e) {
var target = find_group(e.target);
if (target) details.nodeValue = nametype + " " + g_to_text(target);
}, false)
// clear
window.addEventListener("mouseout", function(e) {
var target = find_group(e.target);
if (target) details.nodeValue = ' ';
}, false)
// ctrl-F for search
window.addEventListener("keydown",function (e) {
if (e.keyCode === 114 || (e.ctrlKey && e.keyCode === 70)) {
e.preventDefault();
search_prompt();
}
}, false)
// functions
function get_params() {
var params = {};
var paramsarr = window.location.search.substr(1).split('&');
for (var i = 0; i < paramsarr.length; ++i) {
var tmp = paramsarr[i].split("=");
if (!tmp[0] || !tmp[1]) continue;
params[tmp[0]] = decodeURIComponent(tmp[1]);
}
return params;
}
function parse_params(params) {
var uri = "?";
for (var key in params) {
uri += key + '=' + encodeURIComponent(params[key]) + '&';
}
if (uri.slice(-1) == "&")
uri = uri.substring(0, uri.length - 1);
if (uri == '?')
uri = window.location.href.split('?')[0];
return uri;
}
function find_child(node, selector) {
var children = node.querySelectorAll(selector);
if (children.length) return children[0];
return;
}
function find_group(node) {
var parent = node.parentElement;
if (!parent) return;
if (parent.id == "frames") return node;
return find_group(parent);
}
function orig_save(e, attr, val) {
if (e.attributes["_orig_" + attr] != undefined) return;
if (e.attributes[attr] == undefined) return;
if (val == undefined) val = e.attributes[attr].value;
e.setAttribute("_orig_" + attr, val);
}
function orig_load(e, attr) {
if (e.attributes["_orig_"+attr] == undefined) return;
e.attributes[attr].value = e.attributes["_orig_" + attr].value;
e.removeAttribute("_orig_" + attr);
}
function g_to_text(e) {
var text = find_child(e, "title").firstChild.nodeValue;
return (text)
}
function g_to_func(e) {
var func = g_to_text(e);
// if there's any manipulation we want to do to the function
// name before it's searched, do it here before returning.
return (func);
}
function update_text(e) {
var r = find_child(e, "rect");
var t = find_child(e, "text");
var w = parseFloat(r.attributes.width.value) * frames.attributes.width.value / 100 - 3;
var txt = find_child(e, "title").textContent.replace(/\([^(]*\)$/,"");
t.attributes.x.value = format_percent((parseFloat(r.attributes.x.value) + (100 * 3 / frames.attributes.width.value)));
// Smaller than this size won't fit anything
if (w < 2 * fontsize * fontwidth) {
t.textContent = "";
return;
}
t.textContent = txt;
// Fit in full text width
if (/^ *\$/.test(txt) || t.getComputedTextLength() < w)
return;
if (truncate_text_right) {
// Truncate the right side of the text.
for (var x = txt.length - 2; x > 0; x--) {
if (t.getSubStringLength(0, x + 2) <= w) {
t.textContent = txt.substring(0, x) + "..";
return;
}
}
} else {
// Truncate the left side of the text.
for (var x = 2; x < txt.length; x++) {
if (t.getSubStringLength(x - 2, txt.length) <= w) {
t.textContent = ".." + txt.substring(x, txt.length);
return;
}
}
}
t.textContent = "";
}
// zoom
function zoom_reset(e) {
if (e.attributes != undefined) {
orig_load(e, "x");
orig_load(e, "width");
}
if (e.childNodes == undefined) return;
for(var i = 0, c = e.childNodes; i < c.length; i++) {
zoom_reset(c[i]);
}
}
function zoom_child(e, x, ratio) {
if (e.attributes != undefined) {
if (e.attributes.x != undefined) {
orig_save(e, "x");
e.attributes.x.value = format_percent((parseFloat(e.attributes.x.value) - x) * ratio);
if (e.tagName == "text") {
e.attributes.x.value = format_percent(parseFloat(find_child(e.parentNode, "rect[x]").attributes.x.value) + (100 * 3 / frames.attributes.width.value));
}
}
if (e.attributes.width != undefined) {
orig_save(e, "width");
e.attributes.width.value = format_percent(parseFloat(e.attributes.width.value) * ratio);
}
}
if (e.childNodes == undefined) return;
for(var i = 0, c = e.childNodes; i < c.length; i++) {
zoom_child(c[i], x, ratio);
}
}
function zoom_parent(e) {
if (e.attributes) {
if (e.attributes.x != undefined) {
orig_save(e, "x");
e.attributes.x.value = "0.0%";
}
if (e.attributes.width != undefined) {
orig_save(e, "width");
e.attributes.width.value = "100.0%";
}
}
if (e.childNodes == undefined) return;
for(var i = 0, c = e.childNodes; i < c.length; i++) {
zoom_parent(c[i]);
}
}
function zoom(node) {
var attr = find_child(node, "rect").attributes;
var width = parseFloat(attr.width.value);
var xmin = parseFloat(attr.x.value);
var xmax = xmin + width;
var ymin = parseFloat(attr.y.value);
var ratio = 100 / width;
// XXX: Workaround for JavaScript float issues (fix me)
var fudge = 0.001;
unzoombtn.classList.remove("hide");
var el = frames.children;
for (var i = 0; i < el.length; i++) {
var e = el[i];
var a = find_child(e, "rect").attributes;
var ex = parseFloat(a.x.value);
var ew = parseFloat(a.width.value);
// Is it an ancestor
if (!inverted) {
var upstack = parseFloat(a.y.value) > ymin;
} else {
var upstack = parseFloat(a.y.value) < ymin;
}
if (upstack) {
// Direct ancestor
if (ex <= xmin && (ex+ew+fudge) >= xmax) {
e.classList.add("parent");
zoom_parent(e);
update_text(e);
}
// not in current path
else
e.classList.add("hide");
}
// Children maybe
else {
// no common path
if (ex < xmin || ex + fudge >= xmax) {
e.classList.add("hide");
}
else {
zoom_child(e, xmin, ratio);
update_text(e);
}
}
}
}
function unzoom() {
unzoombtn.classList.add("hide");
var el = frames.children;
for(var i = 0; i < el.length; i++) {
el[i].classList.remove("parent");
el[i].classList.remove("hide");
zoom_reset(el[i]);
update_text(el[i]);
}
}
// search
function reset_search() {
var el = document.querySelectorAll("#frames rect");
for (var i = 0; i < el.length; i++) {
orig_load(el[i], "fill")
}
var params = get_params();
delete params.s;
history.replaceState(null, null, parse_params(params));
}
function search_prompt() {
if (!searching) {
var term = prompt("Enter a search term (regexp " +
"allowed, eg: ^ext4_)", "");
if (term != null) {
search(term)
}
} else {
reset_search();
searching = 0;
searchbtn.classList.remove("show");
searchbtn.firstChild.nodeValue = "Search"
matchedtxt.classList.add("hide");
matchedtxt.firstChild.nodeValue = ""
}
}
function search(term) {
var re = new RegExp(term);
var el = frames.children;
var matches = new Object();
var maxwidth = 0;
for (var i = 0; i < el.length; i++) {
var e = el[i];
var func = g_to_func(e);
var rect = find_child(e, "rect");
if (func == null || rect == null)
continue;
// Save max width. Only works as we have a root frame
var w = parseFloat(rect.attributes.width.value);
if (w > maxwidth)
maxwidth = w;
if (func.match(re)) {
// highlight
var x = parseFloat(rect.attributes.x.value);
orig_save(rect, "fill");
rect.attributes.fill.value = searchcolor;
// remember matches
if (matches[x] == undefined) {
matches[x] = w;
} else {
if (w > matches[x]) {
// overwrite with parent
matches[x] = w;
}
}
searching = 1;
}
}
if (!searching)
return;
var params = get_params();
params.s = term;
history.replaceState(null, null, parse_params(params));
searchbtn.classList.add("show");
searchbtn.firstChild.nodeValue = "Reset Search";
// calculate percent matched, excluding vertical overlap
var count = 0;
var lastx = -1;
var lastw = 0;
var keys = Array();
for (k in matches) {
if (matches.hasOwnProperty(k))
keys.push(k);
}
// sort the matched frames by their x location
// ascending, then width descending
keys.sort(function(a, b){
return a - b;
});
// Step through frames saving only the biggest bottom-up frames
// thanks to the sort order. This relies on the tree property
// where children are always smaller than their parents.
var fudge = 0.0001; // JavaScript floating point
for (var k in keys) {
var x = parseFloat(keys[k]);
var w = matches[keys[k]];
if (x >= lastx + lastw - fudge) {
count += w;
lastx = x;
lastw = w;
}
}
// display matched percent
matchedtxt.classList.remove("hide");
var pct = 100 * count / maxwidth;
if (pct != 100) pct = pct.toFixed(1);
matchedtxt.firstChild.nodeValue = "Matched: " + pct + "%";
}
function format_percent(n) {
return n.toFixed(4) + "%";
}
]]></script><rect x="0" y="0" width="100%" height="1146" fill="url(#background)"/><text id="title" x="50.0000%" y="24.00">../../.tox/py38/bin/py-spy record -o profile.svg -- ../../.tox/py38/bin/python 06_example_3states.py</text><text id="details" x="10" y="40.00"> </text><text id="unzoom" class="hide" x="10" y="24.00">Reset Zoom</text><text id="search" x="1090" y="24.00">Search</text><text id="matched" x="1090" y="1135.00"> </text><svg id="frames" x="10" width="1180"><g><title>&lt;module&gt; (matplotlib/__init__.py:107) (16 samples, 0.18%)</title><rect x="0.0333%" y="260" width="0.1777%" height="15" fill="rgb(227,0,7)"/><text x="0.2833%" y="270.50"></text></g><g><title>_handle_fromlist (&lt;frozen importlib._bootstrap&gt;:1042) (16 samples, 0.18%)</title><rect x="0.0333%" y="276" width="0.1777%" height="15" fill="rgb(217,0,24)"/><text x="0.2833%" y="286.50"></text></g><g><title>_call_with_frames_removed (&lt;frozen importlib._bootstrap&gt;:219) (16 samples, 0.18%)</title><rect x="0.0333%" y="292" width="0.1777%" height="15" fill="rgb(221,193,54)"/><text x="0.2833%" y="302.50"></text></g><g><title>_find_and_load (&lt;frozen importlib._bootstrap&gt;:991) (16 samples, 0.18%)</title><rect x="0.0333%" y="308" width="0.1777%" height="15" fill="rgb(248,212,6)"/><text x="0.2833%" y="318.50"></text></g><g><title>_find_and_load_unlocked (&lt;frozen importlib._bootstrap&gt;:975) (16 samples, 0.18%)</title><rect x="0.0333%" y="324" width="0.1777%" height="15" fill="rgb(208,68,35)"/><text x="0.2833%" y="334.50"></text></g><g><title>_load_unlocked (&lt;frozen importlib._bootstrap&gt;:671) (16 samples, 0.18%)</title><rect x="0.0333%" y="340" width="0.1777%" height="15" fill="rgb(232,128,0)"/><text x="0.2833%" y="350.50"></text></g><g><title>exec_module (&lt;frozen importlib._bootstrap_external&gt;:783) (16 samples, 0.18%)</title><rect x="0.0333%" y="356" width="0.1777%" height="15" fill="rgb(207,160,47)"/><text x="0.2833%" y="366.50"></text></g><g><title>_call_with_frames_removed (&lt;frozen importlib._bootstrap&gt;:219) (16 samples, 0.18%)</title><rect x="0.0333%" y="372" width="0.1777%" height="15" fill="rgb(228,23,34)"/><text x="0.2833%" y="382.50"></text></g><g><title>&lt;module&gt; (qutip/__init__.py:137) (19 samples, 0.21%)</title><rect x="0.0333%" y="164" width="0.2111%" height="15" fill="rgb(218,30,26)"/><text x="0.2833%" y="174.50"></text></g><g><title>_find_and_load (&lt;frozen importlib._bootstrap&gt;:991) (19 samples, 0.21%)</title><rect x="0.0333%" y="180" width="0.2111%" height="15" fill="rgb(220,122,19)"/><text x="0.2833%" y="190.50"></text></g><g><title>_find_and_load_unlocked (&lt;frozen importlib._bootstrap&gt;:975) (19 samples, 0.21%)</title><rect x="0.0333%" y="196" width="0.2111%" height="15" fill="rgb(250,228,42)"/><text x="0.2833%" y="206.50"></text></g><g><title>_load_unlocked (&lt;frozen importlib._bootstrap&gt;:671) (19 samples, 0.21%)</title><rect x="0.0333%" y="212" width="0.2111%" height="15" fill="rgb(240,193,28)"/><text x="0.2833%" y="222.50"></text></g><g><title>exec_module (&lt;frozen importlib._bootstrap_external&gt;:783) (19 samples, 0.21%)</title><rect x="0.0333%" y="228" width="0.2111%" height="15" fill="rgb(216,20,37)"/><text x="0.2833%" y="238.50"></text></g><g><title>_call_with_frames_removed (&lt;frozen importlib._bootstrap&gt;:219) (19 samples, 0.21%)</title><rect x="0.0333%" y="244" width="0.2111%" height="15" fill="rgb(206,188,39)"/><text x="0.2833%" y="254.50"></text></g><g><title>&lt;module&gt; (qutip/__init__.py:149) (22 samples, 0.24%)</title><rect x="0.2444%" y="164" width="0.2444%" height="15" fill="rgb(217,207,13)"/><text x="0.4944%" y="174.50"></text></g><g><title>_find_and_load (&lt;frozen importlib._bootstrap&gt;:991) (22 samples, 0.24%)</title><rect x="0.2444%" y="180" width="0.2444%" height="15" fill="rgb(231,73,38)"/><text x="0.4944%" y="190.50"></text></g><g><title>_find_and_load_unlocked (&lt;frozen importlib._bootstrap&gt;:975) (22 samples, 0.24%)</title><rect x="0.2444%" y="196" width="0.2444%" height="15" fill="rgb(225,20,46)"/><text x="0.4944%" y="206.50"></text></g><g><title>_load_unlocked (&lt;frozen importlib._bootstrap&gt;:671) (22 samples, 0.24%)</title><rect x="0.2444%" y="212" width="0.2444%" height="15" fill="rgb(210,31,41)"/><text x="0.4944%" y="222.50"></text></g><g><title>exec_module (&lt;frozen importlib._bootstrap_external&gt;:783) (22 samples, 0.24%)</title><rect x="0.2444%" y="228" width="0.2444%" height="15" fill="rgb(221,200,47)"/><text x="0.4944%" y="238.50"></text></g><g><title>_call_with_frames_removed (&lt;frozen importlib._bootstrap&gt;:219) (22 samples, 0.24%)</title><rect x="0.2444%" y="244" width="0.2444%" height="15" fill="rgb(226,26,5)"/><text x="0.4944%" y="254.50"></text></g><g><title>&lt;module&gt; (qutip/bloch.py:46) (12 samples, 0.13%)</title><rect x="0.4888%" y="260" width="0.1333%" height="15" fill="rgb(249,33,26)"/><text x="0.7388%" 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fill="rgb(226,211,11)"/><text x="66.4020%" y="94.50">optimize_pulses (krotov/optimize.py:477)</text></g><g><title>serial_map (qutip/parallel.py:189) (3,041 samples, 33.78%)</title><rect x="66.1853%" y="100" width="33.7814%" height="15" fill="rgb(236,162,54)"/><text x="66.4353%" y="110.50">serial_map (qutip/parallel.py:189)</text></g><g><title>_forward_propagation_step (krotov/optimize.py:907) (3,031 samples, 33.67%)</title><rect x="66.2964%" y="116" width="33.6703%" height="15" fill="rgb(220,229,9)"/><text x="66.5464%" y="126.50">_forward_propagation_step (krotov/optimize.py:907)</text></g><g><title>&lt;module&gt; (06_example_3states.py:555) (8,833 samples, 98.12%)</title><rect x="1.8551%" y="68" width="98.1226%" height="15" fill="rgb(250,87,22)"/><text x="2.1051%" y="78.50">&lt;module&gt; (06_example_3states.py:555)</text></g><g><title>all (9,002 samples, 100%)</title><rect x="0.0000%" y="52" width="100.0000%" height="15" fill="rgb(239,43,17)"/><text x="0.2500%" y="62.50"></text></g></svg></svg>
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goerz commented Jun 13, 2021

The above profile.svg (click on the link to load the file in its own browser tab!) contains a profiling analysis of just the final optimization from In [35]

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