From dd6929ccc521c307686957c0aaee7fb8d5e2cc5d Mon Sep 17 00:00:00 2001 From: Ichthyostega Date: Tue, 28 Nov 2023 22:46:59 +0100 Subject: [PATCH] Chain-Load: validate and improve statistics - present the weight centres relative to overall level count - detect sub-graphs and add statistics per subgraph - include an evaluation for ''all nodes'' - include number of levels and subgraphs --- tests/vault/gear/test-chain-load.hpp | 111 ++++++++++++++--- wiki/thinkPad.ichthyo.mm | 171 +++++++++++++-------------- 2 files changed, 179 insertions(+), 103 deletions(-) diff --git a/tests/vault/gear/test-chain-load.hpp b/tests/vault/gear/test-chain-load.hpp index 4197db620..ef0d96ad2 100644 --- a/tests/vault/gear/test-chain-load.hpp +++ b/tests/vault/gear/test-chain-load.hpp @@ -652,6 +652,7 @@ namespace test { /* ========= Graph Statistics Evaluation ========= */ + const string STAT_NODE{"node"}; ///< all nodes const string STAT_SEED{"seed"}; ///< seed node const string STAT_EXIT{"exit"}; ///< exit node const string STAT_INNR{"innr"}; ///< inner node @@ -660,8 +661,9 @@ namespace test { const string STAT_LINK{"link"}; ///< 1:1 linking node const string STAT_KNOT{"knot"}; ///< knot (joins and forks) - const std::array KEYS = {STAT_SEED,STAT_EXIT,STAT_INNR,STAT_FORK,STAT_JOIN,STAT_LINK,STAT_KNOT}; + const std::array KEYS = {STAT_NODE,STAT_SEED,STAT_EXIT,STAT_INNR,STAT_FORK,STAT_JOIN,STAT_LINK,STAT_KNOT}; const uint CAT = KEYS.size(); + const uint IDX_SEED = 1; // index of STAT_SEED namespace { template @@ -669,7 +671,8 @@ namespace test { prepareEvaluaions() { return std::array, CAT> - { [](NOD& n){ return isStart(n);} + { [](NOD& ){ return 1; } + , [](NOD& n){ return isStart(n);} , [](NOD& n){ return isExit(n); } , [](NOD& n){ return isInner(n);} , [](NOD& n){ return isFork(n); } @@ -697,9 +700,11 @@ namespace test { double pLW{0}; ///< average per level and level-width double cL {0}; ///< weight centre level for this indicator double cLW{0}; ///< weight centre level width-reduced + double sL {0}; ///< weight centre on subgraph + double sLW{0}; ///< weight centre on subgraph width-reduced void - addPoint (uint levelID, uint width, uint items) + addPoint (uint levelID, uint sublevelID, uint width, uint items) { REQUIRE (levelID == data.size()); // ID is zero based REQUIRE (width > 0); @@ -709,18 +714,32 @@ namespace test { pLW += items / double(width); cL += levelID * items; cLW += levelID * items/double(width); + sL += sublevelID * items; + sLW += sublevelID * items/double(width); } void - closeAverages (uint nodes) + closeAverages (uint nodes, uint levels, double avgheight) { - uint levels = data.size(); + REQUIRE (levels == data.size()); REQUIRE (levels > 0); frac = cnt / double(nodes); cL = pL? cL/pL :0; // weighted averages: normalise to weight sum cLW = pLW? cLW/pLW :0; + sL = pL? sL/pL :0; + sLW = pLW? sLW/pLW :0; pL /= levels; // simple averages : normalise to number of levels pLW /= levels; + cL /= levels-1; // weight centres : as fraction of maximum level-ID + cLW /= levels-1; + ASSERT (avgheight >= 1.0); + if (avgheight > 1.0) + { // likewise for weight centres relative to subgraph + sL /= avgheight-1; // height is 1-based, while the contribution was 0-based + sLW /= avgheight-1; + } + else + sL = sLW = 0.5; } }; @@ -731,7 +750,11 @@ namespace test { { uint nodes{0}; uint levels{0}; + uint segments{1}; + uint maxheight{0}; + double avgheight{0}; VecU width{}; + VecU sublevel{}; std::array indicators; @@ -744,23 +767,27 @@ namespace test { } void - addPoint (uint levelWidth, LevelSums& particulars) + addPoint (uint levelWidth, uint sublevelID, LevelSums& particulars) { levels += 1; nodes += levelWidth; width.push_back (levelWidth); + sublevel.push_back (sublevelID); ASSERT (levels == width.size()); ASSERT (0 < levels); ASSERT (0 < levelWidth); for (uint i=0; i< CAT; ++i) - indicators[i].addPoint (levels-1, levelWidth, particulars[i]); + indicators[i].addPoint (levels-1, sublevelID, levelWidth, particulars[i]); } void - closeAverages() + closeAverages (uint segs, uint maxSublevelID) { + segments = segs; + maxheight = maxSublevelID + 1; + avgheight = levels / double(segments); for (uint i=0; i< CAT; ++i) - indicators[i].closeAverages (nodes); + indicators[i].closeAverages (nodes,levels,avgheight); } private: @@ -768,6 +795,7 @@ namespace test { reserve (uint lvls) { width.reserve (lvls); + sublevel.reserve(lvls); for (uint i=0; i< CAT; ++i) { indicators[i] = Indicator{}; @@ -798,16 +826,31 @@ namespace test { auto classify = prepareEvaluaions(); Statistic stat(totalLevels); LevelSums particulars{0}; - size_t level{0}; + size_t level{0}, + sublevel{0}, + maxsublevel{0}; + size_t segs{0}; uint width{0}; + auto detectSubgraphs = [&]{ // to be called when a level is complete + if (width==1 and particulars[IDX_SEED]==1) + { // previous level actually started new subgraph + sublevel = 0; + ++segs; + } + else + maxsublevel = max (sublevel,maxsublevel); + }; for (Node& node : allNodes()) { if (level != node.level) - { // record statistics for previous level - stat.addPoint (width, particulars); + {// Level completed... + detectSubgraphs(); + // record statistics for previous level + stat.addPoint (width, sublevel, particulars); // switch to next time-level ++level; + ++sublevel; ENSURE (level == node.level); particulars = LevelSums{0}; width = 0; @@ -818,19 +861,48 @@ namespace test { particulars[i] += classify[i](node); } ENSURE (level = topLevel()); - stat.addPoint (width, particulars); - stat.closeAverages(); + detectSubgraphs(); + stat.addPoint (width, sublevel, particulars); + stat.closeAverages (segs, maxsublevel); return stat; } + /** + * Print a tabular summary of graph characteristics + * @remark explanation of indicators + * - »node« : accounting for all nodes + * - »seed« : seed nodes start a new subgraph or side chain + * - »exit« : exit nodes produce output and have no successor + * - »innr« : inner nodes have both predecessors and successors + * - »fork« : a node linked to more than one successor + * - »join« : a node consuming data from more than one predecessor + * - »link« : a node in a linear processing chain; one input, one output + * - »LEVL« : the overall number of distinct _time levels_ in the graph + * - »SEGS« : the number of completely disjoint partial subgraphs + * - »knot« : a node which both joins data and forks out to multiple successors + * - `frac` : the percentage of overall nodes falling into this category + * - `∅pL` : averaged per Level + * - `∅pLW` : count normalised to the width at that level and then averaged per Level + * - `γL◆` : weight centre of this kind of node, relative to the overall graph + * - `γLW◆` : the same, but using the level-width-normalised value + * - `γL⬙` : weight centre, but relative to the current subgraph or segment + * - `γLW⬙` : same but using level-width-normalised value + * Together, these values indicates how the simulated processing load + * is structured over time, assuming that the _»Levels« are processed consecutively_ + * in temporal order. The graph can unfold or contract over time, and thus nodes can + * be clustered irregularly, which can be seen from the weight centres; for that + * reason, the width-normalised variants of the indicators are also accounted for, + * since a wider graph also implies that there are more nodes of each kind per level, + * even while the actual density of this kind did not increase. + */ template inline TestChainLoad&& TestChainLoad::printTopologyStatistics() { - cout << "INDI cnt frac ∅pL ∅pLW γL γLW\n"; - _Fmt line{"%s %3d %3.0f%% %4.2f %4.2f %5.1f %5.1f\n"}; + cout << "INDI: cnt frac ∅pL ∅pLW γL◆ γLW◆ γL⬙ γLW⬙\n"; + _Fmt line{"%4s: %3d %3.0f%% %4.2f %4.2f %4.2f %4.2f %4.2f %4.2f\n"}; Statistic stat = computeGraphStatistics(); for (uint i=0; i< CAT; ++i) { @@ -842,8 +914,15 @@ namespace test { % indi.pLW % indi.cL % indi.cLW + % indi.sL + % indi.sLW ; } + cout << _Fmt{"LEVL: %3d\n"} % stat.levels; + cout << _Fmt{"SEGS: %3d h = ∅%3.1f / max.%2d\n"} + % stat.segments + % stat.avgheight + % stat.maxheight; cout << "───═══───═══───═══───═══───═══───═══───═══───═══───═══───═══───" << endl; return move(*this); diff --git a/wiki/thinkPad.ichthyo.mm b/wiki/thinkPad.ichthyo.mm index 48732a45a..bf59e7c8d 100644 --- a/wiki/thinkPad.ichthyo.mm +++ b/wiki/thinkPad.ichthyo.mm @@ -99280,8 +99280,8 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
 - - + + @@ -99410,8 +99410,8 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
 - - + + @@ -99423,126 +99423,99 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
 - - + + - - - +

Vector mit Zähldaten indiziert nach Level

- - + - - - +

Gesamt-Anzahl der Forks

- - + - - - +

Forks per Level ∅

- - + - - - +

Forks per Level-Width ∅

- - + - - - +

Forks Level-γ-Schwerpunkt (centre)

- - + - - - +

Forks Level-Width-γ -Schwerpunkt (centre)

- - + - - - +

lineare Regression der forks_pL über den Level

- - + - - - +

forks moving average über den Level

- - + - - - +

forks per width moving average (über den Level)

- - + @@ -99550,15 +99523,16 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
+ - + - - + + @@ -99605,12 +99579,29 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
- - - + + + + + + + + + + + + + + + + + + - + + + @@ -99632,21 +99623,39 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
 - - - - + + + + - - + + - - - + + + + + + + + + + +

+ ...grundsätzlich wären die wichtigsten Zeitreihen im Statistik-Report da, so daß man auch noch weitreichendere Auswertungen machen könnte — sofern das hier mal für mehr als für einige Lasttests verwendet wird... +

+ + + + + + + + @@ -99698,27 +99707,21 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
 - - - +

sollte vergleichsweise einfach zu implementieren sein

- - + - - - +

...will sagen, ich muß da nicht lang überlegen und kann es mehr oder weniger runterschreiben (auch wenn's ein paar Stunden braucht)

- - + @@ -99731,29 +99734,23 @@ Date:   Thu Apr 20 18:53:17 2023 +0200
- - - +

...es wäre zwar nicht notwendig, da in der Node-struct lauter pointer und einfache Werte gespeichert werden; aber eine Node-Kopie wäre ein hochgradig inkonsistentes Gebilde, da dann die Rück-Referenzen nicht mehr stimmen würden.

- - + - - - +

...das folgt aus dem Design von IterExplorer insgesamt. Es wäre hochgradig gefährlich, wenn man in der Gruppe Referenzen speichern würde. Wenn überhaupt, dann muß das explizit so angefordert werden, indem man in der Pipeline mit Pointern arbeitet.

- - +