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Licensing
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I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Source code (Matlab)
function main() % Subderivative illustration
% set up the plotting window, and some graphing paramenters
figure(1); clf; hold on; axis equal; axis off;
thick_line=2.5; thin_line=2; arrow_size=0.3; arrow_type=1; arrow_angle=20; %(angle in degrees)
font_size=30; ball_rad=0.04;
black=[0, 0, 0]; red=[1, 0, 0];
% define the function; plot the x and y axes and the function
a=-1.5; b=3; h=0.02;
X=[a 0 1 2 3]; Y=[0.3 0.2 0.5 1.5 3];
arrow([a 0], [b, 0], thin_line, arrow_size, arrow_angle, arrow_type, black)
arrow([0, min(Y)-1], [0, max(Y)], thin_line, arrow_size, arrow_angle, arrow_type, black);
plot(X, Y, 'linewidth', thick_line);
% the "tangent" lines
x0=X(3); y0=Y(3);
s=0.8; plot(X, s*(X-x0)+y0, 'linewidth', thick_line, 'color', [1, 0, 0])
s=0.5; plot(X, s*(X-x0)+y0, 'linewidth', thick_line, 'color', [1, 0, 0])
% auxiliary line
plot([x0 x0], [0, y0], 'linewidth', thin_line, 'color', [0, 0, 0], 'linestyle', '--')
% graph some suggestive balls
ball_full (x0, 0, ball_rad, [0 0 0 ]);
ball_full (x0, y0, ball_rad, [1 0 0 ]);
% text, sir
H=text(x0, -0.006*font_size, 'x_0');
set(H, 'fontsize', font_size, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')
axis(1.1*[a b min(Y)-1 max(Y)])
% save to postscript
saveas(gcf, 'Subderivative_illustration.eps', 'psc2')
function ball_full(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, 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
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with ((vector version available|new image name)).
It is recommended to name the SVG file “Subderivative illustration.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.
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La bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Licensing == ((PD-self)) ==Source code (Matlab)== <pre><nowiki> function main() % Subderivative illustration % set up the plotting window, and some graphing paramenters f
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
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