Calculates the area of a series using the trapezoidal rule.
TRAPZ(series)
series |
- |
An interval or XY series, the input. |
TRAPZ(xseries, yseries)
xseries |
- |
A series, the X values. |
yseries |
- |
A series, the Y values. |
A scalar, the total area.
trapz(gsin(1000, 1/1000, 0.5))
returns 0.636618. For a sinusoid, the analytic computation is as follows:
With f = 0.5 and t = 1:
y1 = gnorm(1000, .001);
a1 = cumtrapz(y1);
a2 = trapz(y1);
Series a1 contains the cumulative area of y1 and scalar a2 contains the value of the total area of y1. Note that a1[end] == a2, the last point of the cumulative area equals the total area.
The trapezoidal rule fits a line between two data points and calculates the area under the resulting trapezoid such that:
where
See AREA to compute the total area using Simpson’s rule.
See CUMTRAPZ to compute the cumulative area using the trapezoidal rule.