File:Lagrange very simple.svg
Original file (SVG file, nominally 512 × 452 pixels, file size: 1.83 MB)
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Summary
[edit]DescriptionLagrange very simple.svg |
Català: Fig. 2. Il·lustració del problema d'optimització restringida. English: Fig. 3. Illustration of the constrained optimization problem. Italiano: Figura 3. Illustrazione del problema di ottimizzazione vincolata. Nederlands: Afbeelding 3: eenvoudig voorbeeld. Polski: Wykresem funkcji jest płaszczyzna. W przestrzeni trójwymiarowej, równanie opisuje walec (u którego podstawy, na płaszczyźnie leży okrąg jednostkowy). Szukanie ekstremów warunkowych sprowadza się w tym wypadku do badania punktów ekstremalnych części wspólnej walca i płaszczyzny. |
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This file was derived from: Lagrange very simple.jpg: |
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This is a retouched picture, which means that it has been digitally altered from its original version. Modifications: Vectorization. The original can be viewed here: Lagrange very simple.jpg: . Modifications made by Zerodamage.
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Licensing
[edit]This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Source code
[edit]The graph was made in Matlab with the following source code. Corrected in Inkscape
% Function data [X,Y] = meshgrid(-1.2:0.1:1.2, -1.2:0.1:1.2); Z = X+Y; % Constraint data t = -pi:0.01:pi; xc = cos(t); yc = sin(t); zc = xc+yc; % Plot graph and 'constraint' figure(); surfc(X,Y,Z); hold on; plot3(xc, yc, zc, 'k', 'LineWidth', 2); plot3(xc, yc, -3*ones(1,length(t)), 'k', 'LineWidth', 1); set(1, 'Color', [1 1 1]); set(1, 'Position', [46 107 767 682]); % Axis labels text(0.2, -2.2, -3, 'x'); text(2.0, -.3, -3, 'y'); text(-1.8, -1.5, 0, 'z'); % Annotations of the max and min points % Point indicating max plot3(sqrt(2)/2, sqrt(2)/2, 1.45, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2)/2, sqrt(2)/2, -3, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex', 'String', '$$(\sqrt{2}/2, \sqrt{2}/2, \sqrt{2})$$',... 'Position', [.0 .3 1.9], 'FontSize', 20); % Point indicating min plot3(-sqrt(2)/2, -sqrt(2)/2, -sqrt(2), 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2)/2, -sqrt(2)/2, -3, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex', 'String', '$$(-\sqrt{2}/2, -\sqrt{2}/2, -\sqrt{2})$$',... 'Position', [-1.4 -1.0 -1.0], 'FontSize', 20); hold off view([34 24]); %interpolate for improved rendering shading interp; %plot2svg must be retrieved from http://www.zhinst.com/blogs/schwizer/ plot2svg;
Original upload log
[edit]This image is a derivative work of the following images:
- File:Lagrange_very_simple.jpg licensed with Cc-by-sa-3.0-migrated, GFDL
- 2007-09-20T13:31:36Z Loxley 685x597 (67879 Bytes) {{Information |Description= |Source=The graph was made in Matlab with the following source code % Function data [X,Y] = meshgrid(-1.2:0.01:1.2, -1.2:0.01:1.2); Z = XY; % Constraint data t = -pi:0.01:pi; xc = cos(t); yc = s
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:13, 7 August 2012 | 512 × 452 (1.83 MB) | Zerodamage (talk | contribs) | == {{int:filedesc}} == {{Information |Description={{ca|Fig. 2. Il·lustració del problema d'optimització restringida.}} {{en|Fig. 3. Illustration of the constrained optimization problem.}} {{it|Figura 3. Illustrazione del problema di ottimizzazione v... |
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Image title | Matlab Figure Converted by PLOT2SVG written by Juerg Schwizer |
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