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I have some data and I fitted it with a Gaussian fit. I now want to return some useful information from the plot: peak, base, $R^2$ (or the equivalent for a nonlinear fit), width at half-max, max y-value. The catch is that I want to show this information as a legend next to or on top of the graph, if possible. How do I do this after I've already plotted the data?

data = {{12.`, 178.`}, {13.`, 185.`}, {14.`, 198.`}, {15.`, 174.`}, {16.`, 204.`}, {17.`, 218.`}, {18.`, 227.`}, {19.`, 242.`}, {20.`, 215.`}, {21.`, 219.`}, {22.`, 216.`}, {23.`, 193.`}, {24.`, 198.`}, {25.`, 213.`}, {26.`, 232.`}, {27.`, 192.`}, {28.`, 220.`}, {29.`, 207.`}, {30.`, 202.`}, {31.`, 246.`}, {32.`, 249.`}, {33.`, 287.`}, {34.`, 354.`}, {35.`, 465.`}, {35.333`, 520.`}, {35.666`, 472.`}, {36.`, 582.`}, {36.333`, 530.`}, {36.666`, 598.`}, {37.`, 521.`}, {37.333`, 521.`}, {37.666`, 553.`}, {38.`, 548.`}, {38.333`, 504.`}, {38.666`, 526.`}, {39.`, 535.`}, {39.333`, 489.`}, {39.666`, 521.`}, {40.`, 510.`}, {40.333`, 497.`}, {40.666`, 410.`}, {41.`, 303.`}, {41.333`, 323.`}, {41.666`, 315.`}, {42.`, 335.`}, {42.333`, 348.`}, {42.666`, 377.`}, {43.`, 420.`}, {43.333`, 401.`}, {43.666`, 411.`}, {44.`, 475.`}, {44.166`, 628.`}, {44.333`, 749.`}, {44.333`, 727.01`}, {44.5`, 837.`}, {44.666`, 906.`}, {44.666`, 986.`}, {44.866`, 1014.`}, {45.`, 804.`}, {45.`, 881.`}, {45.166`, 581.`}, {45.333`, 275.`}, {45.333`, 329.`}, {45.5`, 279.`}, {45.666`, 236.`}, {45.666`, 256.`}, {46.`, 291.`}, {47.`, 278.`}, {48.`, 251.`}, {49.`, 278.`}, {50.`, 280.`}, {51.`, 285.`}, {52.`, 257.`}, {53.`, 269.`}, {54.`, 255.`}, {55.`, 279.`}, {56.`, 262.`}, {57.`, 261.`}, {58.`, 235.`}, {59.`, 263.`}, {60.`, 271.`}, {61.`, 270.`}, {62.`, 272.`}, {63.`, 246.`}, {64.`, 237.`}, {65.`, 261.`}, {66.`, 243.`}, {67.`, 255.`}, {68.`, 278.`}, {69.`, 294.`}, {70.`, 236.`}, {71.`, 263.`}, {72.`, 260.`}, {73.`, 281.`}, {74.`, 294.`}, {75.`, 264.`}, {76.`, 279.`}, {76.333`, 272.`}, {76.666`, 258.`}, {77.`, 282.`}, {77.333`, 262.`}, {77.666`, 279.`}, {78.`, 272.`}, {78.333`, 284.`}, {78.666`, 262.`}, {79.`, 265.`}, {79.333`, 284.`}, {79.666`, 277.`}, {80.`, 292.`}, {80.333`, 286.`}, {80.666`, 290.`}, {81.`, 266.`}, {82.`, 280.`}, {83.`, 274.`}, {84.`, 282.`}, {85.`, 294.`}, {86.`, 275.`}, {87.`, 332.`}, {87.333`, 291.`}, {87.666`, 295.`}, {88.`, 307.`}, {88.166`, 248.`}, {88.333`, 285.`}, {88.5`, 269.`}, {88.666`, 269.`}, {88.833`, 254.`}, {89.`, 298.`}, {89.166`, 286.`}, {89.5`, 275.`}, {89.666`, 280.`}, {89.833`, 295.`}, {90.`, 274.`}, {90.166`, 281.`}, {90.333`, 252.`}, {90.5`, 290.`}, {90.666`, 306.`}, {90.833`, 287.`}, {91.`, 293.`}, {91.333`, 304.`}, {91.666`, 329.`}, {92.`, 301.`}, {93.`, 301.`}, {94.`, 305.`}, {95.`, 285.`}, {96.`, 313.`}, {97.`, 297.`}, {98.`, 316.`}, {99.`, 348.`}, {99.333`, 394.`}, {99.666`, 374.`}, {100.`, 404.`}, {100.33`, 315.`}, {100.67`, 316.`}, {101.`, 280.`}, {102.`, 322.`}, {103.`, 285.`}, {104.`, 265.`}, {105.`, 295.`}, {106.`, 296.`}, {107.`, 259.`}, {108.`, 297.`}, {109.`, 297.`}, {110.`, 295.`}, {111.`, 304.`}, {112.`, 267.`}, {113.`, 275.`}, {114.`, 300.`}, {115.`, 321.`}, {116.`, 283.`}, {117.`, 283.`}, {118.`, 309.`}, {119.`, 310.`}, {120.`, 297.`}, {121.`, 300.`}, {122.`, 326.`}}; in1 = 43; fin1 = 47; data2 = Select[data, (in1 < #[[1]] < fin1) &]; ListPlot[data2] model[x_] = ampl Evaluate[PDF[NormalDistribution[x0, sigma], x]] + base; fit = FindFit[data2, model[x], {{ampl, 1000}, {x0, 44}, {sigma, 1}, {base, 200}}, x, MaxIterations -> 10000] Show[ListPlot[data1], Plot[model[x] /. fit, {x, in1, fin1}, PlotStyle -> Red]]

Output:

enter image description here

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  • $\begingroup$ See this for FWHM. $\endgroup$ Commented Sep 19, 2017 at 6:08

1 Answer 1

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This answer is going to assume that the parameters that are needed to be displayed on the plot, are already derived and stored in a variable eg 

params = {ampl -> 642.953, x0 -> 44.6798, sigma -> 0.360739, base -> 289.259}

The values of the parameters are retrieved by evaluating something like:

Part[params,All,1]/.params

We will assume that for displaying each distinct parameter value we might need potentially different Style and/or NumberForm options.

Clear[style, numberform] values = MapIndexed[ {First[#2], style[numberform[#1, n], opts]} &, Part[params,All,1]/.params ] /. { {1, style[numberform[x_, n_], opts]} :> Style[NumberForm[x, 5], Italic, Gray], {2, style[numberform[x_, n_], opts]} :> Style[NumberForm[x, 4], Italic, Gray], {3, style[numberform[x_, n_], opts]} :> Style[NumberForm[x, 3], Italic, Gray], {4, style[numberform[x_, n_], opts]} :> Style[NumberForm[x, 5], Italic, Gray] }

Similar considerations will apply for the headers of the parameters values:

Clear[style] headers = {Amplitude, Subscript[x, 0], σ, Base}; headers = MapIndexed[ {First[#2], style[#1, opts]} &, headers ] /. { {1, style[x_, opts]} :> Style[x, Bold], {2, style[x_, opts]} :> Style[x, Bold], {3, style[x_, opts]} :> Style[x, Bold, Italic], {4, style[x_, opts]} :> Style[x, Italic] };

In order to display the table of the parameters on the plot we'll use Legended; assuming plot1 is the ListPlot of the data and plot2 is the Plot of the fitted function then the following snippet

Legended[ Show[plot1, plot2], Placed[grid, Below] ]

produces

enter image description here

Alternatively, should we desire the legend to be placed inside the plot for some reason, evaluating

Show[ plot1, plot2, Graphics@Inset[grid, Scaled[{0.45, 0.2}]] ]

produces

enter image description here

Note how grid is composed by evaluating

grid = Grid[ {headers, values}, Frame -> True, Dividers -> All, Alignment -> Center ]
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