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| Keywords: Cauchy sequence illustration2.svg en Illustration of en Cauchy sequence Based on File Cauchy_sequence_illustration2 png by Oleg Alexandrov own 2011-02-11 Source Codes v draw an illustration of a sequence that is not Cauchy function main prepare the screen and define some parameters figure 1 ; clf; hold on; axis equal; axis off; fontsize 30; thick_line 3; thin_line 2; black 0 0 0; red 1 0 0; blue 0 0 1; arrowsize 0 5; arrow_type 1; arrow_angle 30; angle in degrees circrad 0 07; radius of ball showing up in places B 9; X 0 0 06 B; f inline ' X+2 / X+0 8 ' 'X' ; Y sin 5 X f X ; for i 1 length X ball X i Y i circrad blue ; end X 0 0 05 B+0 3 ; Z f X ; plot X Z 'r--' 'linewidth' thin_line plot X -Z 'r--' 'linewidth' thin_line draw the coordinate axes shift -3; Kx 1 1; Ky 1 3; L max Y ; arrow -1 shift Kx B shift thin_line arrowsize arrow_angle arrow_type black arrow -1 shift -1 Ky L thin_line arrowsize arrow_angle arrow_type black text Kx B+0 6 shift '\it n ' 'fontsize' fontsize 'HorizontalAlignment' 'c' text -1 Ky L+0 8 '\it x_n ' 'fontsize' fontsize 'HorizontalAlignment' 'c' save to disk saveas gcf 'Cauchy_sequence_illustration2 eps' 'psc2' export to eps 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' ; function arrow start stop th arrow_size sharpness arrow_type color Function arguments start stop start and end coordinates of arrow vectors of size 2 th 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' th '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' th 'Color' color ; plot real stop point1 imag stop point1 'LineWidth' th 'Color' color ; plot real stop point2 imag stop point2 'LineWidth' th 'Color' color ; end python from matplotlib pyplot import from mpl_toolkits axes_grid axislines import SubplotZero from numpy import arange sin x1 arange 0 9 1 05 x2 arange 0 9 6 1 z lambda x x+2 / x+ 8 y lambda x sin 5 x z x fig figure figsize 4 2 ax SubplotZero fig 111 fig add_subplot ax ax axis top set_visible False ax axis right set_visible False ax axis left set_axisline_style -> ax axis bottom set_axisline_style -> ax set_yticks ax set_xticks ax set_xlim -1 10 ax set_ylim -3 3 ax plot x1 y x1 'bo' ms 2 5 ax plot x2 z x2 'r--' lw 1 5 ax plot x2 -z x2 'r--' lw 1 5 ax text 10 -2 8 u' n ' ax text - 75 3 u' X_n ' fig savefig test svg bbox_inches tight pad_inches 15 convergence Images with Matlab source code Images with Python source code | ||||
