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exp-IntrpRunge.lisp
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;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;; @file exp-IntrpRunge.lisp
;; @author Mitch Richling <https://www.mitchr.me>
;; @brief Demonstrate how adding more interpolation points may lead to worse fit.@EOL
;; @std Common Lisp
;; @copyright
;; @parblock
;; Copyright (c) 1997,1998,2004,2012,2015, Mitchell Jay Richling <https://www.mitchr.me> All rights reserved.
;;
;; Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
;;
;; 1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
;;
;; 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation
;; and/or other materials provided with the distribution.
;;
;; 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software
;; without specific prior written permission.
;;
;; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
;; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
;; LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
;; OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
;; LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
;; DAMAGE.
;; @endparblock
;; @filedetails
;;
;; Here we illustrate that adding points to an interpolation may not decrease the maximal deviation between the function being interpolated and the
;; interpolating polynomial.
;;
;; Reference:
;; Runge, Carl (1901); Uber empirische Funktionen und die Interpolation zwischen aquidistanten Ordinaten; Zeitschrift fur Mathematik und Physik; Vol 46; pp 224-243
;;
;; How to get a nice PNG of the output:
;;
;; 1) In the REPL:
;; (mjr_gnupl_send-command "set term pdfcairo")
;; (mjr_gnupl_send-command "set output \"foo.pdf\"")
;; (load "exp-IntrpRunge.lisp")
;; (mjr_gnupl_send-command "set output")
;; 2) In shell:
;; convert -density 300 -resize 1024x768 foo.pdf exIntrpRunge-ART.png
;; rm foo.pdf
;;
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(flet ((ifn (x) (/ (1+ (* x x)))))
(let* ((x11 (mjr_vec_make-seq :start -5 :end 5 :len 11))
(x15 (mjr_vec_make-seq :start -5 :end 5 :len 15))
(p11 (mjr_intrp::mjr_intrp_poly-newton x11 (map 'vector #'ifn x11)))
(p15 (mjr_intrp::mjr_intrp_poly-newton x15 (map 'vector #'ifn x15)))
(data (mjr_fsamp_dq-func-r123-r123 (list #'ifn
(lambda (x) (mjr_poly_eval p15 x))
(lambda (x) (mjr_poly_eval p11 x)))
:xdat '(:start -5.1 :end 5.1 :len 1000)
:func-lab '("1/(1+x^2)" "15 Uniformly Spaced Nodes" "11 Uniformly Spaced Nodes"))))
(mjr_gnupl_dquad data :ylim '(-1 7.5) :main "Higher Interpolating Polynomial Oscillation With Increased Node Count")))