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| View Original: | Level grad.svg (100x100) | |||
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| Keywords: Level grad.svg en Source code Lx1 -1 7; Lx2 2 3; Ly1 -2; Ly2 2; box dimensions N 60; split the box into N x N grid X Y meshgrid Lx1 1/N Lx2 Ly1 1/N Ly2 ; the grid f inline '- y+1 4/25+ x-1 4/10+x 2+y 2-1 ' ; draw the level sets of f fx inline '-2/5 x-1 3-2 x' ; fy inline '-4/25 y+1 3-2 y' ; partial deriv Z f X Y ; the function value figure 1 ; clf; hold on; axis equal; axis off; pop up a figure h 0 5; spacing between heights v -20 h 0 8 0 85; the heights c h contour X Y Z v 'b' ; the level sets at those heights x0 0 1333; y0 -0 0666; coordinates of the top of the hill delta 0 01; descend from the top of the hill with this step size Angles linspace 0 2 pi 20 ; will draw 19 descent curves with Angles i for i 1 length Angles x x0+0 1 cos Angles i ; y y0+0 1 sin Angles i ; starting point Curve_x x; Curve_y y; will hold a descent curve following the gradient descend from the hill for j 1 500 x x-delta fx x ; y y-delta fy y ; Curve_x Curve_x x; Curve_y Curve_y y; append the updated values if max abs x abs y > 5 stop when going beyond the picture frame break; end end plot Curve_x Curve_y 'r' plot the curve of steepest descent end axis Lx1 Lx2 Ly1 Ly2 ; the picture frame plot2svg 'level_grad svg' gcf ; Download plot2svg from Matlab central http //commons wikimedia org/wiki/File Level_grad png Oleg Alexandrov 2004-12-23 http //commons wikimedia org/wiki/File Level_grad png Source code modified by me to output SVG directly from Matlab Grids | ||||
