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exp-IntrpMitch.lisp
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exp-IntrpMitch.lisp
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;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;; @file exp-IntrpMitch.lisp
;; @author Mitch Richling <https://www.mitchr.me>
;; @brief Error Interpolating Runge's Function with Mitch Nodes of the First Kind vs Chebyshev Nodes.@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
;;
;; 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-IntrpMitch.lisp")
;; (mjr_gnupl_send-command "set output")
;; 2) In shell:
;; convert -density 300 -resize 1024x768 foo.pdf exIntrpMitch-ART.png
;; rm foo.pdf
;;
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(flet ((ifn (x) (/ (1+ (* x x)))))
(let* ((n 7)
(xm (mjr_vvec_to-vec (list :vvec-type :vvt-mitch1 :start -5 :end 5 :len n)))
(xc (mjr_vvec_to-vec (list :vvec-type :vvt-cheb :start -5 :end 5 :len n)))
(xu (mjr_vvec_to-vec (list :start -5 :end 5 :len n)))
(pm (mjr_intrp::mjr_intrp_poly-newton xm (map 'vector #'ifn xm)))
(pu (mjr_intrp::mjr_intrp_poly-newton xu (map 'vector #'ifn xu)))
(pc (mjr_intrp::mjr_intrp_poly-newton xc (map 'vector #'ifn xc)))
(dat (mjr_dquad_make-from-axis "x" '(:start -5.0 :end 5.0 :len 1000))))
(mjr_dquad_add-data-from-map dat #'ifn :axes 't :ano-nam "Function" :ano-typ :ano-typ-real)
(mjr_dquad_add-data-from-map dat (lambda (x) (mjr_poly_eval pm x)) :axes 't :ano-nam "Mitch Nodes" :ano-typ :ano-typ-real)
(mjr_dquad_add-data-from-map dat (lambda (x) (mjr_poly_eval pu x)) :axes 't :ano-nam "Uniform Nodes" :ano-typ :ano-typ-real)
(mjr_dquad_add-data-from-map dat (lambda (x) (mjr_poly_eval pc x)) :axes 't :ano-nam "Chebyshev Nodes" :ano-typ :ano-typ-real)
(mjr_gnupl_dquad dat :main "Error Interpolating Runge's Function (Uniform, Mitch vs Chebyshev)")))