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| Keywords: Gradient descent.png Gradient descent svg An illustration of the gradient descent method I graphed this with Matlab en wikipedia 2004-11-19 Olegalexandrov wikipedia en Created with MATLAB Moved from en Wikipedia converted to png and added the matlab source code Oleg Alexandrov 03 33 23 June 2007 UTC Source code MATLAB <source lang matlab > Illustration of gradient descent function main the ploting window figure 1 ; clf; hold on; set gcf 'color' 'white' ; set gcf 'InvertHardCopy' 'off' ; axis equal; axis off; the box Lx1 -2; Lx2 2; Ly1 -2; Ly2 2; the function whose contours will be plotted N 60; h 1/N; XX Lx1 h Lx2; YY Ly1 h Ly2; X Y meshgrid XX YY ; f inline '- y+1 4/25+ x-1 4/10+x 2+y 2-1 ' ; Z f X Y ; the contours h 0 3; l0 -1; l1 20; l0 h floor l0/h ; l1 h floor l1/h ; v l0 1 5 h 0 0 h l1 0 8 0 888; c h contour X Y Z v 'b' ; graphing settings small 0 08; small_rad 0 01; thickness 1; arrowsize 0 06; arrow_type 2; fontsize 13; red 1 0 0; white 0 99 1 1 1; initial guess for gradient descent x -0 6498; y -1 0212; run several iterations of gradient descent for i 0 4 H text x-1 5 small y+small/2 sprintf 'x_ d' i ; set H 'fontsize' fontsize 'color' 0 1 1 1 ; the derivatives in x and in y the step size u -2/5 x-1 3-2 x; v -4/25 y+1 3-2 y; alpha 0 11; if i< 4 plot x x+alpha u y y+alpha v ; arrow x y x y+alpha u v thickness arrowsize pi/8 arrow_type 1 0 0 x x+alpha u; y y+alpha v; end end some dummy text to expand the saving window a bit text -0 9721 -1 5101 ' ' 'color' white ; text 1 5235 1 1824 ' ' 'color' white ; save to eps saveas gcf 'Gradient_descent eps' 'psc2' function arrow start stop thickness arrow_size sharpness arrow_type color Function arguments start stop start and end coordinates of arrow vectors of size 2 thickness thickness of arrow stick arrow_size the size of the two sides of the angle in this picture -> sharpness angle between the arrow stick and arrow side in radians arrow_type 1 for filled arrow otherwise the arrow will be just two segments color arrow color a vector of length three with values in 0 1 convert to complex numbers i sqrt -1 ; start start 1 +i start 2 ; stop stop 1 +i stop 2 ; rotate_angle exp i sharpness ; points making up the arrow tip besides the stop point point1 stop - arrow_size rotate_angle stop-start /abs stop-start ; point2 stop - arrow_size/rotate_angle stop-start /abs stop-start ; if arrow_type 1 filled arrow plot the stick but not till the end looks bad t 0 5 arrow_size cos sharpness /abs stop-start ; stop1 t start+ 1-t stop; plot real start stop1 imag start stop1 'LineWidth' thickness 'Color' color ; fill the arrow H fill real stop point1 point2 imag stop point1 point2 color ; set H 'EdgeColor' 'none' else two-segment arrow plot real start stop imag start stop 'LineWidth' thickness 'Color' color ; plot real stop point1 imag stop point1 'LineWidth' thickness 'Color' color ; plot real stop point2 imag stop point2 'LineWidth' thickness 'Color' color ; end function ball x y r color Theta 0 0 1 2 pi; X r cos Theta +x; Y r sin Theta +y; H fill X Y color ; set H 'EdgeColor' 'none' ; </source> original upload log page en wikipedia Gradient_descent gif 2004-11-19 02 41 Olegalexandrov 471×492×8 27067 bytes <nowiki>An illustration of the gradient descent method I graphed this with Matlab PD </nowiki> Contour lines Optimization Files by User Oleg Alexandrov from en wikipedia Gradient descent Images with Matlab source code | ||||
