I see that you intend to understand what the 3rd parameter (“b”) in “boundedline” function refers to.
As you know, the “boundedline” function is used to plot lines with shaded error or confidence bounds. The “b” parameter there specifies how far the shaded area (representing error or confidence bounds) extends from the main line you are plotting. It defines the "thickness" of the shaded region around the line.
Formally, the “b” parameter specifies the distance from the line to the boundary for each point along the line. It can account for the lower and upper bounds (or left and right, depending on orientation) and can vary for each line if multiple lines are plotted.
In essence, b controls how the shaded error/confidence region looks around your plotted line.
The “b” parameter is a multidimensional array with the following dimensions:
- Dimension 1 (npoint): Number of points along the line (should match the length of your x and y vectors).
- Dimension 2 (nside): Number of sides for the bounds (typically 2, for lower and upper bounds).
- Dimension 3 (nline): Number of lines being plotted (usually 1 for a single line)
Here are a few different scenarios showcasing the usage of “b”:
- Same Bounds for All Points: If size(b,1) == 1, the same bounds will apply to all points along the line. In this case, b could be a 1x2x1 array, where the two elements represent the symmetrical bounds.
% Setup
n = 500;
x = 1:n;
y = cumsum(randn(1, n));
% Definition of b
constant_bound = 3;
b = repmat(constant_bound, 1, 2);
% Plot
boundedline(x, y, b, '-r', 'alpha');
- Symmetrical Bounds: If size(b,2) == 1, the bounds are symmetrical on both sides of the line. This means you can provide a single value for both lower and upper bounds for each point.
% Setup
n = 500;
x = 1:n;
y = cumsum(randn(1, n));
% Definition of b
varying_bound = 1 + 1.5 * (1:n) / n;
b = varying_bound';
% Plot
boundedline(x, y, b, '-g', 'alpha');
- Asymmetrical Bounds: If size(b,2) != 1, the bounds are asymmetrical around the line. This means you can provide 2 different values for lower and upper bounds respectively for each point.
% Setup
n = 500;
x = 1:n;
y = cumsum(randn(1, n));
% Definition of b
lower_bound = 2 + 1 * (1:n) / n;
upper_bound = 1 + 2 * (n:-1:1) / n;
b = [lower_bound; upper_bound]';
% Plot
boundedline(x, y, b, '-b', 'alpha');
- Uniform Bounds Across Lines: If size(b,3) == 1, the same bounds apply to all lines described by the preceding x-y arrays.
% Setup
n = 500;
x = 1:n;
y1 = randn(1, n);
y2 = cumsum(y1);
% Definition of b
constant_bound = 3;
b = repmat(constant_bound, n, 2, 1);
% Plot
boundedline(x, [y1; y2]', b, '-m', 'alpha');
The “b” parameter is crucial for defining how the shaded error or confidence bounds are displayed around your plotted line. By adjusting the dimensions of “b”, you can control whether the bounds are constant, symmetrical, asymmetrical, or uniform across multiple lines.
Hope this clarifies the use of “b” parameter in “boundedline” function.
