Xi-Language Reference: Integration and Differentiation
Parameters
derive ( x, y, value, tension = 0.0 )
Types: x double[]
y double[]
value double[]
tension double
Return
double[] (first derivative at desired coordinates)
Description
The function derive differentiates a curve at a given point
using a spline under tension. The curve is givin by x and
y. The desired abscissa values are determined by the vector
value. If tension is nearly zero the interpolation will be
approximately a cubic spline. For increasing tension the result comes
closer to a polygonal line. By default the function estimates internally
the slopes at the two ends of the curve.
Example
( 1)>x=dincarr(10)/3;
( 2)>y={2,4,3,2,5,4,7,5,4,7};
( 3)>value=x;
( 4)>print(derive(x,y,value));
<dblarr>
10.5 1.162708102 -6.150832408 5.440621532 2.388346282 3.005993341
3.587680355 -8.356714761 2.83917869 15
See also
derive
Parameters
integrate ( x, y, start, end, tension = 0.0, period = 0.0 )
Types: x double[]
y double[]
start double
end double
tension double
period double
Return
double (value of the integral)
Description
integrate integrates a function specified by a spline
under tension between two given limits. The curve is givin by x and
y. If tension is nearly zero the interpolation will be approximately
a cubic spline. For increasing tension the result comes closer to apolygonal
line. By default the function estimates internally the slopes at thetwo ends
of the curve. period is set integrate uses a periodic
interpolatory spline with this period.
Example
( 1)>x=interval(0,6.28,20);
Function interval defined
( 2)>y=sin(x);
( 3)>print(integrate(x,y,0,~pi));
<double> 2.00023
( 4)>print(integrate(x,y,0,~pi,\tension=10));
<double> 1.99132
( 5)>print(integrate(x,y,0,~pi,\period=2*~pi));
<double> 1.99997
See also
integrate
© 1995 by Bodo Junglas, Klaus Spanderen and Fabian Weis
- Last revised: Wed Jun 19 16:58:32 1996