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exp-ODElorenzDEQ.lisp
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;; -*- Mode:Lisp; Syntax:ANSI-Common-LISP; Coding:us-ascii-unix; fill-column:158 -*-
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;
;; @file exp-ODElorenzDEQ.lisp
;; @author Mitch Richling <https://www.mitchr.me>
;; @brief Compute (with :MJR_ODE) and draw the Lorenz strange attracter.@EOL
;; @std Common Lisp
;; @copyright
;; @parblock
;; Copyright (c) 1997,1998,2004,2008,2010,2012,2015, 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
;; @todo Add code to generate povray data.@EOL@EOL
;; @filedetails
;;
;; Lorenz
;; $$\begin{array}{l}
;; \frac{\mathrm{d}x}{\mathrm{d}t} = a(y-x) \\
;; \frac{\mathrm{d}y}{\mathrm{d}t} = bx-y-xz \\
;; \frac{\mathrm{d}z}{\mathrm{d}t} = xy-cz \\
;; \end{array}$$
;; $$a=10, b=28, c=\frac{8}{3}$$
;; $$x(0)=\frac{1}{10}, y(0)=0, z(0)=0$$
;;
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(time (let* ((sol (mjr_ode_slv-ivp-erk-mesh (list (lambda (tim p)
(declare (ignore tim))
(let ((a 10)
(b 28)
(c 8/3)
(x (aref p 0))
(y (aref p 1))
(z (aref p 2)))
(vector (* a (- y x)) ;; dx/dt
(- (* b x) y (* x z)) ;; dy/dt
(- (* x y) (* c z)))))) ;; dz/dt
(list #(1 1 1))
'(:start 0 :step 0.009 :len 10000)
:algorithm #'mjr_ode_erk-step-euler-1)))
;; Add a single data element with the path points.
(mjr_dquad_add-data-from-map sol #'vector :data '("y_0" "y_1" "y_2") :ano-nam "path" :ano-typ :ano-typ-rvec)
(mjr_vtk_from-dsimp "exp-ODElorenzDEQ-OUT.vtk"
(mjr_dsimp_make-from-dquad sol 0 "path" :domain-data-names "time")
:simplices 1)))