Syntax: |
vout = DERIV(x,y)
|
The DERIV
function evaluates the first derivatives
of the vector y
, the dependent variable,
with respect to the vector x
, the independent variable,
at the x
locations. The vector
x
must be strictly monotonically increasing. The result
of this function is a vector with the same length as the vectors
x
and y
. Currently,
the derivatives are calculated using interpolating cubic splines, but more algorithms,
such as Lagrange interpolating polynomials, will be added in the future.
Interpolating splines
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
.
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 deriv(x,y)
set linecolor black
replot