Spline(3pm)

💖 Spline — Math::Spline 💖

okay bestie, so this is Math::Spline, a User Contributed Perl Documentation page, and it's giving cubic spline interpolation of data. it's from Spline(3pm), and no cap, it's lowkey iconic for what it does. 🎀

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✨ NAME ✨

Math::Spline — Cubic Spline Interpolation of data 🦋

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✨ SYNOPSIS ✨

here's the whole vibe, fr fr:

use Math::Spline;
$spline = Math::Spline->new(\@x,\@y)
$y_interp=$spline->evaluate($x);

use Math::Spline qw(spline linsearch binsearch);
use Math::Derivative qw(Derivative2);
@y2=Derivative2(\@x,\@y);
$index=binsearch(\@x,$x);
$index=linsearch(\@x,$x,$index);
$y_interp=spline(\@x,\@y,\@y2,$index,$x);

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✨ DESCRIPTION ✨

so this package does cubic spline interpolation of numeric data, periodt. the data comes in as references to two arrays — one holding the x ordinates and one holding the y ordinates. you can use it as an exporter of the numerical functions, or, way more easily, as a class module. pick your fighter. 💅

the Math::Spline class constructor new takes references to the arrays of x and y ordinates of the data. then you do an interpolation with the evaluate method, which — when you hand it an x ordinate — gives you back the interpolated y ordinate at that value. slay. ✨

the spline function takes as arguments:

• references to the x and y ordinate array
• a reference to the 2nd derivatives (calculated using Derivative2)
• the low index of the interval in which to interpolate
• the x ordinate in that interval

and what does it return? the interpolated y ordinate, obviously. 💖

there are also two functions to look up the appropriate index in the array of x data:

• binsearch — for random calls, use this one. give it a reference to the x ordinates and the x lookup value, and it returns the low index of the interval in the data where that value lies.
• linsearch — where the lookups are strictly in ascending sequence (like when you're interpolating to produce a higher resolution data set to draw a curve), this one may be used more efficiently. it performs like binsearch, but it needs a third argument: the previous index value, which gets incremented if necessary.

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🌸 NOTE 🌸

requires Math::Derivative module 🫶

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✨ EXAMPLE ✨

require Math::Spline;
my @x=(1,3,8,10);
my @y=(1,2,3,4);
$spline = Math::Spline->new(\@x,\@y);
print $spline->evaluate(5)."\n";

produces the output

2.44

ate and left no crumbs, honestly. 🔥

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🦋 HISTORY 🦋

$Log: Spline.pm,v $ Revision 1.1 1995/12/26 17:28:17 willijar Initial revision

the initial revision, bestie. 1995. vintage. 👑

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💀 BUGS 💀

bug reports or constructive comments are welcome. (yes please, be nice about it 🙈)

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💜 AUTHOR 💜

John A.R. Williams <J.A.R.Williams@aston.ac.uk>

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🌈 SEE ALSO 🌈

"Numerical Recipies: The Art of Scientific Computing" W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Cambridge University Press. ISBN 0 521 30811 9.

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okay that's the whole page, you're basically a spline girlie now. this was written for perl v5.36.0, dated 2022-11-19, and it's the Spline(3pm) page. go interpolate something cute. 💅✨🎀🦋🌸