# Plotting scaled coefficients for each example

## Mathematica program

 ```(* Plotting scaled coefficients for each example *) sect = "cplots"; entity = "figure"; savefile = "\\temp\\saveabc.dat"; Get[savefile]; c = asave[name]; b = bsave[name]; mean = csave[name]; If[!NumberQ[c] || !NumberQ[b] || !NumberQ[mean] || newabc == True, goodness[bx_, cx_] := (ensc = Table[Abs[func[[n]]/cx^n/n^bx], {n, 3, nm}]; men = Length[ensc]; mean = (Plus @@ ensc)/men; scal = Max[ensc]; mean/scal); mtrial = 30; cmax = 5; bmax = 20; goodtab = Table[c = cmax^(m/mtrial); b = bmax n/mtrial; {{b, c}, goodness[b, c]}, {m, -mtrial, mtrial}, {n, -mtrial, mtrial}]; goodtab = Flatten[goodtab, 1]; {b0, c0} = Sort[goodtab, #1[[2]] > #2[[2]] &][[1, 1]]; Print[{b0, c0} // N]; b1 = b0 + bmax(1/mtrial); c1 = c0 cmax^(1/mtrial); s = FindMinimum[-goodness[bx, cx], {bx, {b0, b1}}, {cx, {c0, c1}}, MaxIterations -> 111]; Print[s]; {b0, c0} = {bx, cx} /. s[[2]]; Print[{b0, c0} // N]; (*Refining step*) goodtab = Table[c = c0 cmax^(1/mtrial^(3/2)); b = b0 + bmax(n/mtrial^(3/2)); {{b, c}, goodness[b, c]}, {m, -mtrial, mtrial}, {n, -mtrial, mtrial}]; goodtab = Flatten[goodtab, 1]; {b0, c0} = Sort[goodtab, #1[[2]] > #2[[2]] &][[1, 1]]; Print[{b0, c0} // N]; b1 = b0 + bmax(1/mtrial^(3/2)); c1 = c0 cmax^(1/mtrial^(3/2)); s = FindMinimum[-goodness[bx, cx], {bx, {b0, b1}}, {cx, {c0, c1}}, MaxIterations -> 111]; Print[s]; {b, c} = {bx, cx} /. s[[2]]; mean = Sum[Abs[func[[n]]/n^b/c^n], {n, 2, nm}]/(nm-1); Clear[asave, bsave, csave]; asave[name] = c; bsave[name] = b; csave[name] = mean; Save[savefile, {asave, bsave, csave}] ]; If[newfigure == True, enplus = enminus = enall = {}; Do[ener = func[[n]]/n^b/c^n/mean; enall = Append[enall, {n, ener}]; If[ener >= 0, enplus = Append[enplus, {n, ener}]]; If[ener < 0, enminus = Append[enminus, {n, ener}]], {n, 2, nm}]; rat = 1/GoldenRatio // N; pntsz = 0.015 30/(15 + nm); pltplus = If[Length[enplus] == 0, {}, ListPlot[enplus, PlotStyle -> {RGBColor[1, 0, 0], PointSize[pntsz]}, AxesOrigin -> {0, 0}, DisplayFunction -> Identity]]; pltminus = If[Length[enminus] == 0, {}, ListPlot[enminus, PlotStyle -> {RGBColor[0, 0, 1], PointSize[pntsz]}, AxesOrigin -> {0, 0}, DisplayFunction -> Identity]]; pltall = ListPlot[enall, PlotStyle -> {Thickness[pntsz/4], RGBColor[0.5, 0.5, 0.5]}, PlotJoined -> True, DisplayFunction -> Identity]; plt = Show[pltall, plt0, pltplus, pltminus, AxesLabel -> {"\!\(\* StyleBox[\"n\",\nFontFamily->\"Times\",\nFontSlant->\"Italic\"]\)", "\!\(\* StyleBox[ FractionBox[ StyleBox[\(E\_n\),\nFontFamily->\"Times\"], \ StyleBox[\(c\\ n\^\(\(\\ \)\(b\)\)\\ a\^\(\(\\ \)\(n\)\)\),\n\ FontFamily->\"Times\"]],\nFontSlant->\"Italic\"]\)"}, AspectRatio -> rat, PlotRange -> {{0, nm + 0.3}, All}, AxesOrigin -> {0, 0}, DisplayFunction -> Identity]; outfile = ToFileName[dir, sect <> ".gif"]; Export[outfile, plt, "GIF", ImageSize -> 320 {1, rat}, ImageResolution -> 150]; outfile1 = StringReplace[outfile, ".gif" -> ".pdf"]; plt1 = Show[plt, PlotRegion -> {{0.05, 0.95}, {0.05, 0.95}}, DisplayFunction -> Identity]; Export[outfile1, plt1, "PDF", ImageSize -> Automatic, ImageOffset -> Automatic, ImageRotated -> True]; ]; " sect <> "\">
" // p; "" // p; "" // p; "" <> "
" <> "Scaled coefficients of Moller-Plesset perturbation theory." <> "
Parameters a = "<>printF[c,6,4]<>", b = "<>printF[b,6,4]<>" and c = "<>printF[mean,6,4]<> "
are chosen so that scaled coefficients remain of order of one in magnitude for all n."<> "
Coefficient E1 = "<>printF[func[[1]],4,2]<>" is not shown because it is too small and out of scale"<> "
" <> " sect <> ".gif?"<>rndm<>"\" WIDTH=666 HEIGHT=412 ALT=\"Plot of MP coefficients\">
" // p; printprogr[sect]; printnav;```

 All Mathematica programs used to study M. - P. series Work in UMassD Unpublished reports

Designed by A. Sergeev.