| Syntax: |
vout = INTEGRAL(x,y)
|
The INTEGRAL function integrates the vector
y, the dependent variable, with respect to
vector x, the independent variable.
The output of this function is a vector with the same length as x. The last
element of the output vector is the integral over the full
range of x. Currently, integration using
interpolating splines, using no keyword or the keyword SMOOTH,
or the trapezoid rule, using keyword TRAPEZOID, are the only types available.
Interpolating splines
| Syntax: | vout = INTEGRAL(x,y)
|
This integration method utilizes an interpolating spline under tension. The spline tension
used is the current value of
TENSION, which may be
changed with the SET TENSION
command. The nature of the interpolating curve varies continuously from pure cubic
splines, for TENSION = 0, to a piecewise linear curve, that is,
points joined by straight line segments, for large TENSION.
x must be strictly monotonically increasing.
Example
The following code produces the picture below (except for the text which was added interactively).
clear
defaults
!
pi=acos(-1)
generate x 0,,2*pi 100
y = cos(x)^3+sin(x)^3
graph x y
!
set linecolor red
graph/overlay x integral(x,y)
set linecolor black
replot

Trapezoid rule
Syntax: vout = INTEGRAL(x,y,'TRAPEZOID')
This integration method uses the trapezoid rule.