Dosiero:Gradient ascent (contour).png
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[edit] Summary
The 'gradient ascent' method applied to a 2D function. This image shows the contour-line point of view. See also: image:gradient ascent (surface).png.
Created with Maple 10, using the following code:
> restart:with(VectorCalculus):with(plots):with(plottools):
> z:=(x,y)->sin(1/2*x^2-1/4*y^2+3)*cos(2*x+1-exp(y)):
> grad:=VectorCalculus[Gradient](z(x,y),[x,y]);
> plot3d(z(x,y),x=-1.2..1.2,y=-1.2..1.2,axes=normal,numpoints=1000);p3d:=%:
> contourplot(z(x,y),x=-1.2..1.2,y=-1.2..1.2,axes=normal,contours=30,numpoints=3000);cont:=%:
> start:=[-1/4,1/3];ptf[0]:=Vector(start):
> steps:=15;
> for i from 0 to steps do:
print(ptf[i]):
pt[i]:=Vector([convert(ptf[i],list)[],z(ptf[i][1],ptf[i][2])]):
dir[i]:=evalf(Normalize(evalVF(grad,ptf[i])));
par[i]:=ptf[i]+lambda*dir[i];
lambd[i]:=fsolve(diff(z(par[i][1],par[i][2]),lambda)=0,lambda=0);
ptf[i+1]:=eval(par[i],lambda=lambd[i]);
od:i:='i':
> display(cont,'point(convert(ptf[i],list),color=blue)'$'i'=0..steps,'plot([par[i][1],par[i][2],lambda=0..lambd[i]])'$'i'=0..steps);
> display(p3d,'point(convert(pt[i],list),color=blue,symbol=circle,symbolsize=4)'$'i'=0..steps,'spacecurve([par[i][1],par[i][2],z(par[i][1],par[i][2])],lambda=0
Made a screenshot, cropped with paint shop pro 4.12, saved with Irfanview.
[edit] Licensing
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I, the author of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: Afrikaans | Alemannisch | Aragonés | العربية | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Español | Esperanto | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Latina | Lietuvių | Magyar | Bahasa Melayu | Nederlands | Norsk (bokmål) | Norsk (nynorsk) | 日本語 | Polski | Português | Ripoarish | Română | Русский | Slovenčina | Slovenščina | Српски | Svenska | ไทย | Türkçe | Українська | Tiếng Việt | Walon | 简体中文 | 繁體中文 | 粵語 | +/- |
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