plotting - How can I draw ternary plot by these data?

I have these data and want to draw similar fifures in mathematica. any one can help me?

x1={0.7992,0.6902,0.6133,0.4953,0.3965,0.2934,0.1968,0.1044,0.692,0.5961,0.4954,0.3961,0.2899,0.1957,0.137,0.5944,0.496,0.399,0.2972,0.2005,0.1005,0.4967,0.394,0.2965,0.2029,0.0995,0.3986,0.2962,0.2176,0.0964,0.2944,0.2093,0.1193,0.2407,0.0967,0.0985};

x2={0.1002,0.2081,0.2891,0.4019,0.5025,0.6066,0.7016,0.7949,0.1072,0.1999,0.3028,0.4041,0.5141,0.5956,0.6713,0.1014,0.2015,0.3022,0.4052,0.5018,0.6007,0.1007,0.2025,0.3013,0.4002,0.5026,0.0999,0.2016,0.2953,0.4019,0.1022,0.2019,0.304,0.104,0.2035,0.1012};

z={0.0895,-0.1049,-0.2136,-0.3323,-0.3847,-0.3713,-0.3134,0.0492,0.211,0.017,-0.1612,-0.304,-0.3671,-0.3206,-0.2624,0.336,0.109,-0.0789,-0.2174,-0.2485,0.0555,0.3925,0.18,0.014,-0.093,0.0632,0.4262,0.2335,0.0845,0.012,0.3967,0.2321,0.1031,0.3684,0.1691,0.191};

I want to draw similar figures in mathematica by these data

Comments

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...

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...

plotting - Plot 4D data with color as 4th dimension

I have a list of 4D data (x position, y position, amplitude, wavelength). I want to plot x, y, and amplitude on a 3D plot and have the color of the points correspond to the wavelength. I have seen many examples using functions to define color but my wavelength cannot be expressed by an analytic function. Is there a simple way to do this? Answer Here a another possible way to visualize 4D data: data = Flatten[Table[{x, y, x^2 + y^2, Sin[x - y]}, {x, -Pi, Pi,Pi/10}, {y,-Pi,Pi, Pi/10}], 1]; You can use the function Point along with VertexColors . Now the points are places using the first three elements and the color is determined by the fourth. In this case I used Hue, but you can use whatever you prefer. Graphics3D[ Point[data[[All, 1 ;; 3]], VertexColors -> Hue /@ data[[All, 4]]], Axes -> True, BoxRatios -> {1, 1, 1/GoldenRatio}]

Blog

Search This Blog