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| Keywords: Non-analytic smooth function.png Illustration of an non-analytic smooth function self-made with MATLAB 00 56 3 December 2007 UTC Oleg Alexandrov Image An infinitely differentiable function which is not analytic illustration png Source code MATLAB <source lang matlab > Illustration of an non-analytic smooth function function main thickness1 2 5; thickness2 1 5; arrowsize 0 15; arrow_type 1; ball_rad 0 03; arrow_angle 35; blue 0 129 205/256; black 0 0 0; fontsize floor 20 ; dist 0 01; a -1; b 5; h 0 01; X a h b; Y zeros length X 1 ; for i 1 length X x X i ; if x < 0 Y i 0; else Y i exp -1/x ; end end figure 1 ; clf; hold on; axis equal; axis off arrow a 0 b+0 2 0 thickness2 arrowsize arrow_angle arrow_type 0 0 0 arrow 0 -0 3 0 2 max Y thickness2 arrowsize arrow_angle arrow_type 0 0 0 plot X Y 'linewidth' thickness1 'color' blue ; plot X 0 Y+1 'linewidth' thickness2/1 5 'color' black 'linestyle' '--' ; arrow b+0 1 0 b+0 2 0 thickness2 arrowsize arrow_angle arrow_type 0 0 0 ball 0 0 ball_rad blue ; place_text_smartly 0 fontsize 5 dist '0' ; ball 0 1 ball_rad black ; place_text_smartly sqrt -1 fontsize 5 dist '1' ; saveas gcf 'Non-analytic_smooth_function eps' 'psc2' function place_text_smartly z fs pos d tx p cos pi/4 +sqrt -1 sin pi/4 ; z z + p pos d fs; shiftx 0 0003; shifty 0 002; x real z ; y imag z ; H text x+shiftx fs y+shifty fs tx ; set H 'fontsize' fs 'HorizontalAlignment' 'c' 'VerticalAlignment' 'c' 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' color ; 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 </source> differentiability functions Files by User Oleg Alexandrov from en wikipedia Images with Matlab source code math math | ||||
