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| Keywords: Nonquasiconvex function.png Made by myself with MATLAB graph Source code <pre> function main prepare the scrreen and define some parameters clf; hold on; axis equal; axis off; fontsize 25; thick_line 3; thin_line 2; black 0 0 0; red 1 0 0; arrowsize 0 1; arrow_type 1; arrow_angle 30; angle in degrees L 1 15; X -L 0 01 L ; f inline '2 X 4-X 2+1 -1 3' ; Y f X ; plot X Y 'linewidth' thick_line arrow X 1 0 X length X 0 thin_line arrowsize arrow_angle arrow_type black arrow 0 min Y -0 4 0 max Y +0 2 thin_line arrowsize arrow_angle arrow_type black a 0 5; Z X 0+a; plot X Z 'linewidth' thin_line 'linestyle' '--' 'color' 'r' ; x0 -10; for i 2 length X -1 x X i ; xp X i-1 ; if x < 0 f x < a f xp > a x0 x; elseif x < 0 f x > a f xp < a x1 x; elseif x > 0 f x < a f xp > a x2 x; elseif x > 0 f x > a f xp < a x3 x; end end plot x0 x1 0 0 'linewidth' 2 thick_line 'color' 'r' ; plot x2 x3 0 0 'linewidth' 2 thick_line 'color' 'r' ; saveas gcf 'Nonquasiconvex_function eps' 'psc2' export to eps 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 degrees 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 pi sharpness/180 ; 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 pi sharpness/180 /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 </pre> convexity functions Files by User Oleg Alexandrov from en wikipedia math | ||||
