Skip to main content

plotting - Mathematica: 3D plot based on combined 2D graphs


I have several sigmoidal fits to 3 different datasets, with mean fit predictions plus the 95% confidence limits (not symmetrical around the mean) and the actual data.


I would now like to show these different 2D plots projected in 3D as in enter image description here



but then using proper perspective.


In the link here they give some solutions to combine the plots using isometric perspective, but I would like to use proper 3 point perspective. Any thoughts? Also any way to show the mean points per time point for each series plus or minus the standard error on the mean would be cool too, either using points+vertical bars, or using spheres plus tubes.


Below are some test data and the fit function I am using. Note that I am working on a logit(proportion) scale and that the final vertical scale is Log10(percentage).


(* some test data *)
data = Table[Null, {i, 4}];
data[[1]] = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5,
4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5,
1.0}, {1, -6.8}, {2, -4.7}, {3, -1.0}, {4, 0.03}, {5,
2.8}}; (* data on logit(proportion) scale *)
data[[2]] = ((data[[1]] // Transpose))*{1, 0.8} // Transpose;

data[[3]] = ((data[[1]] // Transpose))*{1, 0.6} // Transpose;
data[[4]] = ((data[[1]] // Transpose))*{1, 0.4} //
Transpose; (* data points groups 1-4 on logit(proportion) scale *)
Logit[p_] = Log[p/(1 - p)];
Invlogit[x_] = Exp[x]/(1 + Exp[x]);
datalog = Table[Null, {i, 4}];
Do[datalog[[i]] =
Partition[
Riffle[(data[[i]] // Transpose)[[1]],
Log10[100*Invlogit[(data[[i]] // Transpose)[[2]]]]], 2], {i, 1,

4}];

(* fit function plus best fit & conf lims *)
fitfunc[t_, z_, Z_, p0_, s_] :=
z + (p0 (z - Z))/(-p0 + (-1 + p0) (1/(1 + s))^t);
predicted =
Table[NonlinearModelFit[
dat[[i]], {fitfunc[t, z, Z, p0, s]}, {{Z, 0.46}, {s, 20}, {p0,
0.0005}, {z, -6.4}}, t, MaxIterations -> 1000,
Method -> "LevenbergMarquardt"], {i, 4}];

pred[t_, i_] := Normal[predicted[[i]]];
conflims[t_, i_] := predicted[[i]]["MeanPredictionBands"];

Answer



You could make 2d plot and then convert 2d coord to 3d:


data1 = {{1, -5.8}, {2, -5.4}, {3, -0.8}, {4, -0.2}, {5, 
4.6}, {1, -6.4}, {2, -5.6}, {3, -0.7}, {4, 0.04}, {5,
1.0}, {1, -6.8}, {2, -4.7}, {3, -1.0}, {4, 0.03}, {5, 2.8}};

data = Table[{1, 1.2 - j*.2} i, {j, 4}, {i, data1}];


Logit[p_] = Log[p/(1 - p)];
Invlogit[x_] = Exp[x]/(1 + Exp[x]);
datalog = Table[Null, {i, 4}];

datalog =
Table[Transpose[{#1, Log10[100 Invlogit[#2]]} & @@
Transpose[data[[i]]]], {i, 1, 4}];

fitfunc[t_, z_, Z_, p0_, s_] :=
z + (p0 (z - Z))/(-p0 + (-1 + p0) (1/(1 + s))^t);


predicted =
Table[NonlinearModelFit[
data[[i]], {fitfunc[t, z, Z, p0, s],
Z > z && Z < 5 && s > 1 && s < 200 && p0 < 0.01 && p0 > 0 &&
z < -2 && z > -7}, {{Z, 0.3}, {s, 20}, {p0, 0.001}, {z, -6.5}},
t, MaxIterations -> 1000], {i, 4}];

pred[t_, i_] := Normal[predicted[[i]]];
conflims[t_, i_] := predicted[[i]]["MeanPredictionBands"];


cols = {Red, Darker[Green], Blue, Darker[Cyan]};

opac = 0.4;
colslight = {Directive[cols[[1]], Opacity[opac]],
Directive[cols[[2]], Opacity[opac]],
Directive[cols[[3]], Opacity[opac]],
Directive[cols[[4]], Opacity[opac]]};

Graphics3D[

Table[{Plot[{Log10[100*Invlogit[pred[t, i]]],
Evaluate[N@Log10[100*Invlogit[conflims[t, i]]]]}, {t, 1, 5},
Filling -> {2 -> {{1}, {colslight[[i]]}},
3 -> {{1}, {colslight[[i]]}}},
PlotStyle -> {cols[[i]], colslight[[i]],
colslight[[i]]}][[1]], {cols[[i]], PointSize[0.012],
Point[datalog[[i]]]}} /. {x_?NumericQ, y_?NumericQ} :> {x, i,
y}, {i, 1, 4}],
Axes -> {True, False, True},
Boxed -> {Right, Bottom, Back},

BoxRatios -> {1, 1, 0.5},
FaceGrids -> {{0, 0, -1}, {0, 1, 0}, {1, 0, 0}},
FaceGridsStyle ->
Directive[GrayLevel[0.3, 1], AbsoluteDashing[{1, 2}]],
ViewPoint -> {-2, -2.5, 1},
AxesLabel -> {"Day", "",
Rotate[Row[{Spacer[50], "Resistance (%)"}], 90 Degree]},
LabelStyle -> Directive[Black, Bold, 14],
ImageSize -> 500
]


enter image description here


Comments

Popular posts from this blog

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...