Spline Toolbox | ![]() ![]() |
Minimum of a function in a given interval
Syntax
Description
fnmin(f)
returns the minimum value of the univariate spline in f
on its basic interval.
fnmin(f,interv)
returns the minimum value in the interval [
a
..b
] specified by
interv
.
[minval,minsite] = fnmin(f,...)
also returns a location, minsite
, at which the function in f
takes that minimum value, minval
.
Examples
Example 1. We construct and plot a spline with many local extrema, then compute its maximum as the negative of the minimum of
. We indicate this maximum value by adding a horizontal line to the plot at the height of the computed maximum.
rand('seed',21); f = spmak(1:21,rand(1,15)-.5); fnplt(f) maxval = -fnmin(fncmb(f,-1)); hold on, plot(fnbrk(f,'interv'),maxval([1 1])), hold off
Example 2. Since spmak(1:5,-1)
provides the negative of the cubic B-spline with knot sequence 1:5
, we expect the command
to return -2/3
for y
and 3
for x
.
Algorithm
fnmin
first changes the basic interval of the function to the given interval, if any. On the interval, fnmin
then finds all local extrema of the function as zeros of the function's first derivative. It then evaluates the function at these extrema and at the endpoints of the interval, and determines the minimum over all these values.
See Also
![]() | fnjmp | fnplt | ![]() |