DADiSP Worksheet Functions > Function Categories > Statistics and Calculus > TRAPZ

 

TRAPZ

Purpose:

Calculates the area of a series using the trapezoidal rule.

Syntax:

TRAPZ(series)

series

-

An interval or XY series, the input.

Alternate Syntax:

TRAPZ(xseries, yseries)

xseries

-

A series, the X values.

yseries

-

A series, the Y values.

Returns:

A scalar, the total area.

Example:

trapz(gsin(1000, 1/1000, 0.5))

 

returns 0.636618. For a sinusoid, the analytic computation is as follows:

 

image\area01.gif

 

With f = 0.5 and t = 1:

 

image\area02.gif

Example:

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.

Remarks:

The trapezoidal rule fits a line between two data points and calculates the area under the resulting trapezoid such that:

 

image\cumtrapz01.gif

 

where

 

image\cumtrapz02.gif

 

See AREA to compute the total area using Simpson’s rule.

 

See CUMTRAPZ to compute the cumulative area using the trapezoidal rule.

See Also:

AREA

CUMTRAPZ

DERIV

INTEG

LDERIV

RDERIV