Ian Jauslin
summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
Diffstat (limited to 'figs/energy.fig')
-rw-r--r--figs/energy.fig/2020-10-15+energy.dat15
-rw-r--r--figs/energy.fig/Makefile37
-rw-r--r--figs/energy.fig/bigeq.dat100
-rw-r--r--figs/energy.fig/energy.gnuplot41
-rw-r--r--figs/energy.fig/medeq.dat100
-rw-r--r--figs/energy.fig/simpleq.dat100
6 files changed, 393 insertions, 0 deletions
diff --git a/figs/energy.fig/2020-10-15+energy.dat b/figs/energy.fig/2020-10-15+energy.dat
new file mode 100644
index 0000000..358e2dc
--- /dev/null
+++ b/figs/energy.fig/2020-10-15+energy.dat
@@ -0,0 +1,15 @@
+# Potential: e^{-|x|}
+# rho E E+dE eta eta+deta Jastrow E Jastrow E+dE Jastrow eta Jastrow eta+deta
+1e-6 7.90e-6 7.91e-6
+1e-4 8.344e-4 8.345e-4 0.017 0.018 8.355e-4 8.356e-4 0.015 0.016
+1e-3 9.1338e-3 9.1339e-3 0.048 0.049 9.142e-3 9.143e-3 0.045 0.046
+5e-3 5.0613e-2 5.0614e-2 0.080 0.081 5.0648e-2 5.0649e-2 0.070 0.071
+1e-2 1.06107e-1 1.06108e-1 0.087 0.088 1.0627e-1 1.0628e-1 0.073 0.074
+1.5e-2 1.6337e-1 1.6338e-1 0.090 0.091 1.6342e-1 1.6343e-1 0.088 0.089
+2e-2 2.2162e-1 2.2163e-1 0.093 0.094 2.2169e-1 2.2170e-1 0.090 0.091
+5e-2 5.8044e-1 5.8045e-1 0.091 0.092 5.8046e-1 5.8047e-1 0.091 0.092
+1e-1 1.1918e+0 1.1919e+0 0.088 0.089 1.1919e+0 1.1920e+0 0.085 0.086
+1e-0 1.2430e+1 1.2431e+1 0.058 0.059 1.245e+1 1.246e+1 0.05 0.06
+1e+1 1.2544e+2 1.2545e+2 0.031 0.032
+5e+1 6.2803e+2 6.2804e+2 0.02 0.03
+
diff --git a/figs/energy.fig/Makefile b/figs/energy.fig/Makefile
new file mode 100644
index 0000000..139aecd
--- /dev/null
+++ b/figs/energy.fig/Makefile
@@ -0,0 +1,37 @@
+PROJECTNAME=energy
+
+SIMPLESOLV=~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src
+
+DATS=simpleq.dat medeq.dat bigeq.dat
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(DATS)
+ gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
+ pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+simpleq.dat:
+ julia $(SIMPLESOLV)/main.jl -p "eq=simpleq;tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp energy_rho > $@
+medeq.dat:
+ julia $(SIMPLESOLV)/main.jl -p "eq=medeq;tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M easyeq -U exp energy_rho > $@
+bigeq.dat:
+ julia -p 8 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;tolerance=1e-11;maxiter=21;v_a=1;minlrho=-6;nlrho=100;maxlrho=2" -M anyeq -U exp energy_rho > $@
+
+
+install: $(PDFS)
+ cp $^ $(INSTALLDIR)/
+
+clean-aux:
+ rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-dat:
+ rm -f $(DATS)
+
+clean-tex:
+ rm -f $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/energy.fig/bigeq.dat b/figs/energy.fig/bigeq.dat
new file mode 100644
index 0000000..0b867a1
--- /dev/null
+++ b/figs/energy.fig/bigeq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06 7.933345669932108e-06 1.704968357654747e-12
+ 1.204503540258781e-06 9.561695772478549e-06 3.479042916950106e-13
+ 1.450828778495940e-06 1.152494614052415e-05 1.105615828881523e-13
+ 1.747528400007683e-06 1.389218915189634e-05 6.516057629638973e-13
+ 2.104904144512022e-06 1.674683575161553e-05 2.538927058524327e-13
+ 2.535364493970111e-06 2.018960215367572e-05 1.880964786680250e-14
+ 3.053855508833412e-06 2.434212593011697e-05 2.973660811899432e-14
+ 3.678379771828634e-06 2.935134616878758e-05 2.601027107910687e-14
+ 4.430621457583877e-06 3.539481155461295e-05 2.963343053481389e-13
+ 5.336699231206313e-06 4.268711577772934e-05 8.111082866158586e-13
+ 6.428073117284319e-06 5.148770312835425e-05 1.258065696556162e-12
+ 7.742636826811277e-06 6.211034042585299e-05 1.460046719339352e-12
+ 9.326033468832200e-06 7.493461690987080e-05 1.403493327361502e-12
+ 1.123324032978027e-05 9.041991424013260e-05 1.190931394710978e-12
+ 1.353047774579808e-05 1.091223876997595e-04 9.122943906836504e-13
+ 1.629750834620643e-05 1.317156211714737e-04 6.270289167996145e-13
+ 1.963040650040272e-05 1.590157675195849e-04 3.932273380946167e-13
+ 2.364489412645407e-05 1.920121690316943e-04 2.176631964805619e-13
+ 2.848035868435805e-05 2.319046775947738e-04 1.026358506480137e-13
+ 3.430469286314919e-05 2.801491713026256e-04 4.446534105626415e-14
+ 4.132012400115334e-05 3.385131054920545e-04 4.144974620326791e-14
+ 4.977023564332114e-05 4.091433566527190e-04 2.207980896760987e-14
+ 5.994842503189409e-05 4.946491352779899e-04 4.572485754229845e-14
+ 7.220809018385471e-05 5.982033804561970e-04 6.770202411898077e-14
+ 8.697490026177834e-05 7.236668315738020e-04 8.932369095090413e-14
+ 1.047615752789665e-04 8.757399333684964e-04 1.182248084569074e-13
+ 1.261856883066021e-04 1.060148908761868e-03 1.344231243816312e-13
+ 1.519911082952935e-04 1.283873775901215e-03 1.493216888971958e-13
+ 1.830738280295370e-04 1.555427846566146e-03 1.699458131695914e-13
+ 2.205130739903046e-04 1.885200386765900e-03 2.059019619099669e-13
+ 2.656087782946686e-04 2.285876721564974e-03 2.649891700928507e-13
+ 3.199267137797384e-04 2.772953210497389e-03 3.620701665273268e-13
+ 3.853528593710532e-04 3.365368304619666e-03 4.982472417338292e-13
+ 4.641588833612782e-04 4.086275430706575e-03 6.801465168364811e-13
+ 5.590810182512228e-04 4.963988854528130e-03 9.137218648090623e-13
+ 6.734150657750828e-04 6.033140090007556e-03 1.205112818608528e-12
+ 8.111308307896872e-04 7.336089997726976e-03 1.568949512234829e-12
+ 9.770099572992256e-04 8.924650630547374e-03 2.015537944839303e-12
+ 1.176811952434999e-03 1.086218134368278e-02 2.551669271262342e-12
+ 1.417474162926806e-03 1.322613594632949e-02 3.175541504984204e-12
+ 1.707352647470692e-03 1.611115205690737e-02 3.882570582394582e-12
+ 2.056512308348653e-03 1.963279076107542e-02 4.659084950581694e-12
+ 2.477076355991711e-03 2.393205473004278e-02 5.480860359934871e-12
+ 2.983647240283340e-03 2.918083689398976e-02 6.316773798635380e-12
+ 3.593813663804629e-03 3.558848057549190e-02 7.128689280361588e-12
+ 4.328761281083062e-03 4.340966694307487e-02 7.877742721930180e-12
+ 5.214008287999690e-03 5.295388832723841e-02 8.538097040660639e-12
+ 6.280291441834260e-03 6.459681825795255e-02 9.099882246799092e-12
+ 7.564633275546291e-03 7.879395326961169e-02 9.571289375001028e-12
+ 9.111627561154896e-03 9.609698014020246e-02 9.973223641678962e-12
+ 1.097498765493057e-02 1.171734181893564e-01 5.721422548997492e-15
+ 1.321941148466031e-02 1.428302028457424e-01 2.220152020103125e-15
+ 1.592282793341094e-02 1.740420176882147e-01 3.826728826701929e-15
+ 1.917910261672489e-02 2.119853520055517e-01 2.868300139436348e-15
+ 2.310129700083163e-02 2.580794649360160e-01 7.610004429207492e-15
+ 2.782559402207126e-02 3.140356819487004e-01 6.059675090044115e-15
+ 3.351602650938848e-02 3.819167428256006e-01 3.079883529777644e-15
+ 4.037017258596558e-02 4.642082722623484e-01 5.845027410285226e-15
+ 4.862601580065354e-02 5.639048668198076e-01 3.816993895235883e-15
+ 5.857020818056673e-02 6.846137999573778e-01 3.474232903786021e-15
+ 7.054802310718646e-02 8.306799580954581e-01 4.088512836639771e-15
+ 8.497534359086456e-02 1.007336356586333e+00 3.416440773537374e-15
+ 1.023531021899027e-01 1.220885470968219e+00 3.150210853153027e-15
+ 1.232846739442068e-01 1.478917686986172e+00 2.371648956613387e-15
+ 1.484968262254467e-01 1.790574459885084e+00 2.131970502004566e-15
+ 1.788649529057435e-01 2.166865324247355e+00 1.071205796436568e-15
+ 2.154434690031887e-01 2.621049764085537e+00 9.990417291453287e-12
+ 2.595024211399737e-01 3.169097203910113e+00 9.249109275328039e-12
+ 3.125715849688241e-01 3.830241093220283e+00 8.462348103996382e-12
+ 3.764935806792471e-01 4.627646323429371e+00 7.654951972758785e-12
+ 4.534878508128591e-01 5.589213151008605e+00 6.847954951876310e-12
+ 5.462277217684348e-01 6.748545540181854e+00 6.060205450067071e-12
+ 6.579332246575682e-01 8.146117547346687e+00 5.306471340562747e-12
+ 7.924828983539185e-01 9.830678245708585e+00 4.598704413056710e-12
+ 9.545484566618347e-01 1.186094397111715e+01 3.945605710986110e-12
+ 1.149756995397738e+00 1.430763664633719e+01 3.351869307817862e-12
+ 1.384886371393875e+00 1.725593895734062e+01 2.820957127030768e-12
+ 1.668100537200059e+00 2.080845162887957e+01 2.352147114974057e-12
+ 2.009233002565050e+00 2.508875548012610e+01 1.943437328683651e-12
+ 2.420128264794383e+00 3.024570193985361e+01 1.592153241178217e-12
+ 2.915053062825182e+00 3.645858099358198e+01 1.293588310581549e-12
+ 3.511191734215135e+00 4.394334600051280e+01 1.042306124720846e-12
+ 4.229242874389508e+00 5.296011151374482e+01 8.333799477286008e-13
+ 5.094138014816386e+00 6.382218443728761e+01 6.605722153418092e-13
+ 6.135907273413176e+00 7.690694209247896e+01 5.199590335170479e-13
+ 7.390722033525790e+00 9.266893489306236e+01 4.063068137082775e-13
+ 8.902150854450392e+00 1.116556685689670e+02 3.149814651697356e-13
+ 1.072267222010325e+01 1.345266139156320e+02 2.426172104464820e-13
+ 1.291549665014885e+01 1.620761041088648e+02 1.855737958789898e-13
+ 1.555676143930475e+01 1.952609146057077e+02 1.407488425834523e-13
+ 1.873817422860387e+01 2.352334832362353e+02 1.059912258811251e-13
+ 2.257019719633922e+01 2.833819239247995e+02 7.975496994680734e-14
+ 2.718588242732946e+01 3.413782233614627e+02 5.927022309304956e-14
+ 3.274549162877732e+01 4.112362940653811e+02 4.383487153196387e-14
+ 3.944206059437664e+01 4.953818995066683e+02 3.264119493319829e-14
+ 4.750810162102803e+01 5.967368791641958e+02 2.438476380986774e-14
+ 5.722367659350220e+01 7.188205979063790e+02 1.780368664039960e-14
+ 6.892612104349709e+01 8.658721421294766e+02 1.399123723605710e-14
+ 8.302175681319753e+01 1.042997505438325e+03 1.067384124266308e-14
+ 1.000000000000000e+02 1.256346874319010e+03 8.538692087201394e-15
diff --git a/figs/energy.fig/energy.gnuplot b/figs/energy.fig/energy.gnuplot
new file mode 100644
index 0000000..0214040
--- /dev/null
+++ b/figs/energy.fig/energy.gnuplot
@@ -0,0 +1,41 @@
+set title ""
+set ylabel "$\\displaystyle\\frac{\\tilde e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+set xrange [0.000001:100]
+
+set ytics 8, 1, 13
+set mytics 2
+set yrange [7.5:13]
+
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key bottom right box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "."
+set style line 2 linetype rgbcolor "#DC143C" linewidth 2
+set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
+set style line 4 linetype rgbcolor "#4B0082" linewidth 2
+set style line 5 linetype rgbcolor "#DAA520" linewidth 2
+set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
+
+set pointsize 1
+
+set logscale x
+
+a=1.2543564105910647
+
+plot \
+ "simpleq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 title "simple" ,\
+ "medeq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 3 title "med",\
+ "bigeq.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 5 title "big",\
+ "2020-10-15+energy.dat" using 1:($2/$1) with points ls 2 title "QMC" ,\
+ 2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY"
+
diff --git a/figs/energy.fig/medeq.dat b/figs/energy.fig/medeq.dat
new file mode 100644
index 0000000..59df07e
--- /dev/null
+++ b/figs/energy.fig/medeq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06 7.934286257047021e-06 3.350843411796514e-14
+ 1.204503540258781e-06 9.563044082528665e-06 2.273624432538743e-14
+ 1.450828778495940e-06 1.152686262633478e-05 1.298430519766377e-14
+ 1.747528400007683e-06 1.389489317614862e-05 1.894777566363843e-14
+ 2.104904144512022e-06 1.675062919238505e-05 1.653650872454784e-14
+ 2.535364493970111e-06 2.019490280396468e-05 2.336983658291679e-14
+ 3.053855508833412e-06 2.434951404943966e-05 2.214775068136617e-14
+ 3.678379771828634e-06 2.936162846930739e-05 3.805584891901638e-14
+ 4.430621457583877e-06 3.540910828910534e-05 1.427802345533630e-14
+ 5.336699231206313e-06 4.270697869633961e-05 2.003273138190368e-14
+ 6.428073117284319e-06 5.151527512777095e-05 2.551774430173645e-14
+ 7.742636826811277e-06 6.214857192276333e-05 3.705994224138530e-14
+ 9.326033468832200e-06 7.498755947811933e-05 7.265095211681475e-14
+ 1.123324032978027e-05 9.049311901844221e-05 1.264190454286157e-14
+ 1.353047774579808e-05 1.092234447947087e-04 1.053352694614131e-14
+ 1.629750834620643e-05 1.318548872942263e-04 2.368465480922291e-14
+ 1.963040650040272e-05 1.592073432336066e-04 1.660337987885090e-14
+ 2.364489412645407e-05 1.922752053054458e-04 8.646141141307886e-15
+ 2.848035868435805e-05 2.322651149462809e-04 2.442896517713713e-14
+ 3.430469286314919e-05 2.806420446977329e-04 9.776919033399443e-15
+ 4.132012400115334e-05 3.391855851696971e-04 1.271987985520055e-14
+ 4.977023564332114e-05 4.100587399374810e-04 2.239769985922260e-14
+ 5.994842503189409e-05 4.958920578361200e-04 2.600603141419754e-14
+ 7.220809018385471e-05 5.998865777048775e-04 3.305695605996821e-14
+ 8.697490026177834e-05 7.259398517100161e-04 1.348707825208008e-14
+ 1.047615752789665e-04 8.788002810614415e-04 2.107644168610072e-14
+ 1.261856883066021e-04 1.064256179216188e-03 3.010939452255121e-14
+ 1.519911082952935e-04 1.289367416181562e-03 4.528098249733624e-14
+ 1.830738280295370e-04 1.562749244492149e-03 7.011583917825588e-14
+ 2.205130739903046e-04 1.894920022439264e-03 1.127696093174950e-13
+ 2.656087782946686e-04 2.298727102221577e-03 1.467479187573012e-13
+ 3.199267137797384e-04 2.789868219377111e-03 2.329360329563977e-13
+ 3.853528593710532e-04 3.387529396559262e-03 2.906251121896537e-13
+ 4.641588833612782e-04 4.115164764506077e-03 3.999178759473060e-13
+ 5.590810182512228e-04 5.001448927349123e-03 5.543444903233915e-13
+ 6.734150657750828e-04 6.081438699757301e-03 7.247686124008659e-13
+ 8.111308307896872e-04 7.397988387264389e-03 9.394231632434480e-13
+ 9.770099572992256e-04 9.003471469917696e-03 1.188210506033121e-12
+ 1.176811952434999e-03 1.096187182983169e-02 1.453939404386284e-12
+ 1.417474162926806e-03 1.335131984243035e-02 1.748927540773990e-12
+ 1.707352647470692e-03 1.626716311543043e-02 2.048075825913765e-12
+ 2.056512308348653e-03 1.982567889735244e-02 2.340515412122970e-12
+ 2.477076355991711e-03 2.416855580506204e-02 2.605854351607331e-12
+ 2.983647240283340e-03 2.946829731035233e-02 2.824445163694187e-12
+ 3.593813663804629e-03 3.593472933729397e-02 2.981866401807997e-12
+ 4.328761281083062e-03 4.382283052883180e-02 3.067362472205469e-12
+ 5.214008287999690e-03 5.344214766200744e-02 3.073513956716823e-12
+ 6.280291441834260e-03 6.516811202317233e-02 3.006095534695811e-12
+ 7.564633275546291e-03 7.945563730982247e-02 2.868424849163193e-12
+ 9.111627561154896e-03 9.685545817966755e-02 2.674678867537749e-12
+ 1.097498765493057e-02 1.180337637230369e-01 2.440734483972164e-12
+ 1.321941148466031e-02 1.437957952077961e-01 2.184363028675561e-12
+ 1.592282793341094e-02 1.751142163796972e-01 1.917824774341397e-12
+ 1.917910261672489e-02 2.131632321105708e-01 1.656059900213277e-12
+ 2.310129700083163e-02 2.593596329389756e-01 1.410306668963206e-12
+ 2.782559402207126e-02 3.154121858791141e-01 1.195131021990613e-12
+ 3.351602650938848e-02 3.833810840481612e-01 9.871852649538251e-13
+ 4.037017258596558e-02 4.657495191763944e-01 8.136332883253271e-13
+ 4.862601580065354e-02 5.655098640080871e-01 6.823741984126656e-13
+ 5.857020818056673e-02 6.862674605812320e-01 5.705185315457055e-13
+ 7.054802310718646e-02 8.323656230237174e-01 4.590853816780889e-13
+ 8.497534359086456e-02 1.009036201088274e+00 3.723504950962481e-13
+ 1.023531021899027e-01 1.222580938798058e+00 3.740344313966540e-13
+ 1.232846739442068e-01 1.480589932164776e+00 2.590030624091089e-13
+ 1.484968262254467e-01 1.792204778156467e+00 4.308044222824868e-13
+ 1.788649529057435e-01 2.168435558712142e+00 1.711857922602610e-13
+ 2.154434690031887e-01 2.622542672548128e+00 2.630630812010949e-13
+ 2.595024211399737e-01 3.170496778713019e+00 4.862348792954930e-13
+ 3.125715849688241e-01 3.831532827526695e+00 3.222631437243052e-13
+ 3.764935806792471e-01 4.628817420866958e+00 9.063217628519465e-14
+ 4.534878508128591e-01 5.590252678180098e+00 3.126299632971088e-13
+ 5.462277217684348e-01 6.749444523712865e+00 5.271767714437587e-13
+ 6.579332246575682e-01 8.146869018854765e+00 7.067258691723872e-13
+ 7.924828983539185e-01 9.831277239349690e+00 1.976481716430481e-13
+ 9.545484566618347e-01 1.186138747922958e+01 1.213984608946686e-13
+ 1.149756995397738e+00 1.430792353920593e+01 1.001843165310050e-13
+ 1.384886371393875e+00 1.725606987330165e+01 7.356460075303617e-14
+ 1.668100537200059e+00 2.080842884092954e+01 1.207511033175393e-13
+ 2.009233002565050e+00 2.508858274495347e+01 1.420167716375784e-13
+ 2.420128264794383e+00 3.024538433481086e+01 2.404214126545545e-13
+ 2.915053062825182e+00 3.645812474662149e+01 8.020433476813964e-14
+ 3.511191734215135e+00 4.394275831754763e+01 7.725490959360697e-14
+ 4.229242874389508e+00 5.295940040730246e+01 9.193832425125519e-14
+ 5.094138014816386e+00 6.382135855972534e+01 5.965887874370161e-14
+ 6.135907273413176e+00 7.690601057644308e+01 7.369357116862908e-14
+ 7.390722033525790e+00 9.266790720131583e+01 6.733622484011242e-14
+ 8.902150854450392e+00 1.116545543551900e+02 7.236758339264480e-14
+ 1.072267222010325e+01 1.345254228973254e+02 7.214733858698264e-14
+ 1.291549665014885e+01 1.620748459530638e+02 4.566762659089573e-14
+ 1.555676143930475e+01 1.952595988278435e+02 4.016462557967500e-14
+ 1.873817422860387e+01 2.352321191121707e+02 4.222275907971552e-14
+ 2.257019719633922e+01 2.833805204158014e+02 4.452644207417061e-14
+ 2.718588242732946e+01 3.413767890516622e+02 9.381962021977345e-14
+ 3.274549162877732e+01 4.112348371110992e+02 2.985855401371043e-14
+ 3.944206059437664e+01 4.953804275968574e+02 4.510651797992799e-14
+ 4.750810162102803e+01 5.967353994911545e+02 2.755681866935816e-14
+ 5.722367659350220e+01 7.188191171458401e+02 2.159989114361577e-14
+ 6.892612104349709e+01 8.658706664291410e+02 2.997352502706469e-14
+ 8.302175681319753e+01 1.042996040413900e+03 4.590753851046225e-14
+ 1.000000000000000e+02 1.256345425056825e+03 2.310603796838004e-14
diff --git a/figs/energy.fig/simpleq.dat b/figs/energy.fig/simpleq.dat
new file mode 100644
index 0000000..62fa048
--- /dev/null
+++ b/figs/energy.fig/simpleq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06 7.934458317554770e-06 1.253408725811047e-14
+ 1.204503540258781e-06 9.563293402409969e-06 1.640998151881320e-14
+ 1.450828778495940e-06 1.152722385213290e-05 3.251262837839683e-14
+ 1.747528400007683e-06 1.389541646472593e-05 3.019030546809478e-14
+ 2.104904144512022e-06 1.675138713852244e-05 2.275714260526642e-14
+ 2.535364493970111e-06 2.019600045252957e-05 3.271639597766372e-14
+ 3.053855508833412e-06 2.435110335988150e-05 2.142094245826877e-14
+ 3.678379771828634e-06 2.936392920320935e-05 1.339250507659264e-14
+ 4.430621457583877e-06 3.541243815820425e-05 3.893851454934391e-14
+ 5.336699231206313e-06 4.271179685321251e-05 3.095940660023124e-14
+ 6.428073117284319e-06 5.152224486652221e-05 5.125396859042871e-14
+ 7.742636826811277e-06 6.215865101443218e-05 2.890206750836624e-14
+ 9.326033468832200e-06 7.500213022394945e-05 2.241466297924041e-14
+ 1.123324032978027e-05 9.051417532865902e-05 2.370776274109386e-14
+ 1.353047774579808e-05 1.092538610497785e-04 4.796262972662893e-14
+ 1.629750834620643e-05 1.318988043420983e-04 4.229814231373338e-14
+ 1.963040650040272e-05 1.592707219208866e-04 3.808954617986591e-14
+ 2.364489412645407e-05 1.923666192393963e-04 2.141860559824167e-14
+ 2.848035868435805e-05 2.323968842530530e-04 4.584119591708702e-14
+ 3.430469286314919e-05 2.808318548521666e-04 2.138418227061501e-14
+ 4.132012400115334e-05 3.394587942820992e-04 1.918556578598127e-14
+ 4.977023564332114e-05 4.104516606676139e-04 1.694104962972332e-14
+ 5.994842503189409e-05 4.964566151029166e-04 3.002291274309623e-14
+ 7.220809018385471e-05 6.006969022092982e-04 4.294873137027481e-14
+ 8.697490026177834e-05 7.271015873319120e-04 2.062540444418305e-14
+ 1.047615752789665e-04 8.804636812878449e-04 3.334031557301778e-14
+ 1.261856883066021e-04 1.066634469195621e-03 7.194072311053829e-14
+ 1.519911082952935e-04 1.292762434131901e-03 8.278169514315650e-14
+ 1.830738280295370e-04 1.567587086789660e-03 1.161190654702787e-13
+ 2.205130739903046e-04 1.901800344392313e-03 1.797096379984733e-13
+ 2.656087782946686e-04 2.308490918746631e-03 2.637598652434219e-13
+ 3.199267137797384e-04 2.803690553578959e-03 3.722231676096834e-13
+ 3.853528593710532e-04 3.407044978502708e-03 5.427762733833543e-13
+ 4.641588833612782e-04 4.142637205871173e-03 7.734027562664818e-13
+ 5.590810182512228e-04 5.039996370506877e-03 1.084741759773931e-12
+ 6.734150657750828e-04 6.135331779936552e-03 1.475538242058165e-12
+ 8.111308307896872e-04 7.473039279209971e-03 1.968813103343645e-12
+ 9.770099572992256e-04 9.107535515599206e-03 2.559305054777023e-12
+ 1.176811952434999e-03 1.110548530561432e-02 3.246800230285997e-12
+ 1.417474162926806e-03 1.354849819420097e-02 3.999740063734383e-12
+ 1.707352647470692e-03 1.653638267729146e-02 4.785597934980074e-12
+ 2.056512308348653e-03 2.019106081393928e-02 5.541961698394948e-12
+ 2.477076355991711e-03 2.466126270506543e-02 6.209989300668736e-12
+ 2.983647240283340e-03 3.012814052292188e-02 6.719913925774575e-12
+ 3.593813663804629e-03 3.681196682685592e-02 7.010516326080206e-12
+ 4.328761281083062e-03 4.498011366911493e-02 7.042737419751455e-12
+ 5.214008287999690e-03 5.495654983134250e-02 6.803473563255481e-12
+ 6.280291441834260e-03 6.713314618359296e-02 6.316173694015080e-12
+ 7.564633275546291e-03 8.198314659254460e-02 5.630438859203436e-12
+ 9.111627561154896e-03 1.000772469953260e-01 4.814460500479356e-12
+ 1.097498765493057e-02 1.221028309649795e-01 3.948371699573414e-12
+ 1.321941148466031e-02 1.488870387812890e-01 3.104931054226393e-12
+ 1.592282793341094e-02 1.814245009403908e-01 2.339516913805968e-12
+ 1.917910261672489e-02 2.209107486051246e-01 1.688210571908239e-12
+ 2.310129700083163e-02 2.687825259198435e-01 1.167659413279469e-12
+ 2.782559402207126e-02 3.267664771683836e-01 7.775556337126751e-13
+ 3.351602650938848e-02 3.969379725867567e-01 4.949300609691499e-13
+ 4.037017258596558e-02 4.817921803787671e-01 3.047835972157860e-13
+ 4.862601580065354e-02 5.843299025667947e-01 1.744034034347572e-13
+ 5.857020818056673e-02 7.081611855740870e-01 2.145108372619088e-13
+ 7.054802310718646e-02 8.576303130499369e-01 1.004811457230378e-13
+ 8.497534359086456e-02 1.037966511958588e+00 4.718419633908083e-14
+ 1.023531021899027e-01 1.255465580586508e+00 2.639823583877913e-14
+ 1.232846739442068e-01 1.517708710502109e+00 1.889177952517916e-13
+ 1.484968262254467e-01 1.833826060755470e+00 1.262402568827356e-13
+ 1.788649529057435e-01 2.214814195859386e+00 2.307786324072868e-13
+ 2.154434690031887e-01 2.673918372281924e+00 3.831494558709393e-14
+ 2.595024211399737e-01 3.227092915163674e+00 6.546666422710970e-14
+ 3.125715849688241e-01 3.893555644968086e+00 8.786410093299553e-14
+ 3.764935806792471e-01 4.696455586182800e+00 3.094041097523017e-14
+ 4.534878508128591e-01 5.663677129915349e+00 1.346721396138190e-14
+ 5.462277217684348e-01 6.828808565598630e+00 2.348290345391161e-14
+ 6.579332246575682e-01 8.232308608511897e+00 6.075413859670748e-14
+ 7.924828983539185e-01 9.922911427699711e+00 3.551771518542288e-14
+ 9.545484566618347e-01 1.195931896203401e+01 8.585404990085891e-14
+ 1.149756995397738e+00 1.441223928837902e+01 4.176255867225544e-14
+ 1.384886371393875e+00 1.736684182166722e+01 1.114486677072019e-13
+ 1.668100537200059e+00 2.092571459958015e+01 5.653897977104765e-14
+ 2.009233002565050e+00 2.521242633713612e+01 1.048273767790111e-14
+ 2.420128264794383e+00 3.037581693424489e+01 8.488597666410238e-15
+ 2.915053062825182e+00 3.659516541136894e+01 5.400259352206385e-14
+ 3.511191734215135e+00 4.408641471307532e+01 5.485916680303097e-14
+ 4.229242874389508e+00 5.310966951429405e+01 5.278885434248808e-14
+ 5.094138014816386e+00 6.397822736362556e+01 2.945680129079298e-15
+ 6.135907273413176e+00 7.706945673674652e+01 1.960764876087084e-15
+ 7.390722033525790e+00 9.283789969933954e+01 3.647567907334253e-15
+ 8.902150854450392e+00 1.118310541195708e+02 1.199399938192319e-15
+ 1.072267222010325e+01 1.347083834068206e+02 5.355510579254647e-14
+ 1.291549665014885e+01 1.622642138164582e+02 9.997141006638315e-15
+ 1.555676143930475e+01 1.954553143409147e+02 1.109395412861689e-14
+ 1.873817422860387e+01 2.354341167917606e+02 1.106759345282809e-15
+ 2.257019719633922e+01 2.835887295111127e+02 2.010906753044690e-14
+ 2.718588242732946e+01 3.415911340329474e+02 1.043218765631230e-14
+ 3.274549162877732e+01 4.114552381359539e+02 1.315017988355486e-14
+ 3.944206059437664e+01 4.956068009543682e+02 1.004394652722235e-14
+ 4.750810162102803e+01 5.969676580241880e+02 5.364915392605858e-14
+ 5.722367659350220e+01 7.190571706518009e+02 5.378285825138610e-14
+ 6.892612104349709e+01 8.661144220395618e+02 5.426311368936924e-14
+ 8.302175681319753e+01 1.043245402953268e+03 9.067219514460403e-12
+ 1.000000000000000e+02 1.256600297381089e+03 6.252162647544124e-12