Maxima Function
linearinterpol (points)
linearinterpol(points,option)
Computes the polynomial interpolation by the linear method. Argument points must be either:
a two column matrix, p:matrix([2,4],[5,6],[9,3])
,
a list of pairs, p: [[2,4],[5,6],[9,3]]
,
a list of numbers, p: [4,6,3]
, in which case the abscissas will be assigned automatically to 1, 2, 3, etc.
In the first two cases the pairs are ordered with respect to the first coordinate before making computations.
With the option argument it is possible to select the name for the independent variable, which is 'x
by default; to define another one, write something like varname='z
.
Examples:
(%i1) load(interpol)$ (%i2) p: matrix([7,2],[8,3],[1,5],[3,2],[6,7])$ (%i3) linearinterpol(p); 13 3 x (%o3) (-- - ---) charfun2(x, minf, 3) 2 2 + (x - 5) charfun2(x, 7, inf) + (37 - 5 x) charfun2(x, 6, 7) 5 x + (--- - 3) charfun2(x, 3, 6) 3 (%i4) f(x):=''%; 13 3 x (%o4) f(x) := (-- - ---) charfun2(x, minf, 3) 2 2 + (x - 5) charfun2(x, 7, inf) + (37 - 5 x) charfun2(x, 6, 7) 5 x + (--- - 3) charfun2(x, 3, 6) 3 (%i5) /* Evaluate the polynomial at some points */ map(f,[7.3,25/7,%pi]); 62 5 %pi (%o5) [2.3, --, ----- - 3] 21 3 (%i6) %,numer; (%o6) [2.3, 2.952380952380953, 2.235987755982989] (%i7) load(draw)$ /* load draw package */ (%i8) /* Plot the polynomial together with points */ draw2d( color = red, key = "Linear interpolator", explicit(f(x),x,-5,20), point_size = 3, color = blue, key = "Sample points", points(args(p)))$ (%i9) /* Change variable name */ linearinterpol(p, varname='s); 13 3 s (%o9) (-- - ---) charfun2(s, minf, 3) 2 2 + (s - 5) charfun2(s, 7, inf) + (37 - 5 s) charfun2(s, 6, 7) 5 s + (--- - 3) charfun2(s, 3, 6) 3