Function File: F = primitive (f, t, F0)

Calculate the primitive of a function.

The function approximates the primitive (indefinite integral) of the univariate function handle f with constant of integration F0. The output is the primitive evaluated at the points t. The vector t must be ordered and ascending.

This function is a fancy way of calculating the cumulative sum,

F = cumsum (f(t).*diff (t)([1 1:end])).

Example: 

f = @(t) sin (2 * pi * 3 * t);
t = [0; sort(rand (100, 1))];
F = primitive (f, t, 0);
t_true = linspace (0, 1, 1e3).';
F_true = (1 - cos (2 * pi * 3 * t_true)) / (2 * pi * 3);
plot (t, F, 'o', t_true, F_true);

See also: quadgk, cumsum.

Demonstration 1

The following code

 f = @(t) sin (2*pi*3*t);
 t = [0; sort(rand (100, 1))];
 F = primitive (f, t, 0);
 t_true = linspace (0, 1, 1e3).';
 F_true = (1 - cos (2 * pi * 3 * t_true)) / (2 * pi * 3);
 h = plot (t, F, "o;Numerical primitive;", t_true, F_true, "-;True primitive;");
 set (h, "linewidth", 2);
 title ("Numerical primitive evaluated at random time points");

Produces the following figure

Figure 1

Package: signal