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Example 2: Arrays

Arrays of UncVal objects can be created and plotted.

Creating Arrays

Arrays of UncVal objects can be created by passing an array input to the constructor

x = UncVal(linspace(0, 1, 8), 0.02, "x");
a = UncVal(0, 0.04, "a");
y = x.^2 + a;
disp(y)
  1x8 UncVal array with properties:

        val: [0 0.0204 0.0816 0.1837 0.3265 0.5102 0.7347 1]
         id: "calc"
    uncType: "1-sigma"
    std_unc: [0.0400 0.0404 0.0416 0.0435 0.0461 0.0492 0.0527 0.0566]

Elements can be accessed like a normal array.

disp(x(2))
  UncVal with properties:

         val: 0.1429
          id: "x"
     uncType: "1-sigma"
     std_unc: 0.0200
    var_srcs: [1x6 table]

Arrays can be concatenated, transposed, and reshaped as expected.

xcat = [UncVal([0, 1], 0.1, "xc1"), UncVal([2, 3], 0.2, "xc2")]
xcat = 
        val: [0 1 2 3]
         id: "calc"
    uncType: "1-sigma"
    std_unc: [0.1000 0.1000 0.2000 0.2000]


xtranspose = xcat'
xtranspose = 
         val: [4x1 double]
          id: "calc"
     uncType: "1-sigma"
     std_unc: [4x1 double]
    var_srcs: [2x6 table]


xreshape = reshape(xcat, 2, [])
xreshape = 
        val: [2x2 double]
         id: "calc"
    uncType: "1-sigma"
    std_unc: [2x2 double]

Plotting Arrays

Arrays can be sent directly to the plot and errorbar commands. The plot command will only plot the nominal values. The errorbar command will plot uncertainty in x or y if an UncVal object is passed. If both x and y are UncVal objects, then the correlated uncertainty is plotted as the standard deviational ellipse. Error bars are drawn at at 95.54% confidence ( $2\sigma ;$ in the 1D case).

figure("defaultErrorBarLineWidth", 1.5, ...
    "Units", "in", "Position", [1,1,6,4]);
t = tiledlayout("flow");
title(t, "UncVal Plotting Options");
nexttile;hold on;xlabel("x");ylabel("y");
title("plot command", FontWeight="normal");
plot(x, y);

t.Title.Color = get(gca, "XColor"); % I have some funny defaults
t.Title.FontName = get(gca, "FontName");

ha = nexttile;hold on;xlabel("x");ylabel("y");
title("errorbar, x-only", FontWeight="normal")
errorbar(x, y.val, Marker="o");

nexttile;hold on;xlabel("x");ylabel("y");
title("errorbar, y-only", FontWeight="normal")
errorbar(x.val, y, Marker="d");

nexttile;hold on;xlabel("x");ylabel("y");
title("errorbar, x and y", FontWeight="normal")
errorbar(x, y);
figure_0

Functions that Reduce an Array

Many functions that normally reduce an array, do not reduce arrays of UncVal objects. These functions can be thought of as acting on the distribution in the UncVal object, and not on the array. For example, the mean and std functions, return the mean and standard deviation of the underlying distributions. The array returned is the same size as the UncVal array.

disp(x)
  1x8 UncVal array with properties:

        val: [0 0.1429 0.2857 0.4286 0.5714 0.7143 0.8571 1]
         id: "x"
    uncType: "1-sigma"
    std_unc: [0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200]

disp(mean(x))
         0    0.1429    0.2857    0.4286    0.5714    0.7143    0.8571    1.0000

disp(std(x))
    0.0200    0.0200    0.0200    0.0200    0.0200    0.0200    0.0200    0.0200

The sum function will reduce an array, but the statistical independence of the arguments must be considered. The average of multiple values have less uncertainty if they are statistically independent, this is not true if they are statistically dependent. Note that $1\sigma ;$ uncertainties are input to the constructors, but the $2\sigma ;$ value is displayed in the string.

xind = [UncVal(1, 0.1, "x1"), UncVal(2, 0.1, "x2")];
disp("average of xind = " + string(sum(xind)/length(xind)));
average of xind = UncVal (id=calc): 1.5 ± 0.141421 (2-sigma)

xdep = UncVal([1, 2], 0.1, "x");
disp("average of xdep = " + string(sum(xdep)/length(xdep)));
average of xdep = UncVal (id=calc): 1.5 ± 0.2 (2-sigma)